<?page no="0"?> Götz Rohwer | Andreas Behr Financial Capital. Data and Models <?page no="1"?> utb 5552 Eine Arbeitsgemeinschaft der Verlage Böhlau Verlag · Wien · Köln · Weimar Verlag Barbara Budrich · Opladen · Toronto facultas · Wien Wilhelm Fink · Paderborn Narr Francke Attempto Verlag / expert verlag · Tübingen Haupt Verlag · Bern Verlag Julius Klinkhardt · Bad Heilbrunn Mohr Siebeck · Tübingen Ernst Reinhardt Verlag · München Ferdinand Schöningh · Paderborn transcript Verlag · Bielefeld Eugen Ulmer Verlag · Stuttgart UVK Verlag · München Vandenhoeck & Ruprecht · Göttingen Waxmann · Münster · New York wbv Publikation · Bielefeld Wochenschau Verlag · Frankfurt am Main <?page no="2"?> Dr. Götz Rohwer ist Professor (em.) für Statistik an der Ruhr-Universität Bochum. Dr. Andreas Behr ist Professor für Statistik an der Universität Duisburg-Essen. <?page no="3"?> Götz Rohwer, Andreas Behr Financial Capital. Data and Models UVK Verlag · München <?page no="4"?> Umschlagabbildung: © AM-C · iStock Bibliografische Information der Deutschen Nationalbibliothek Die Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über http: / / dnb.dnb.de abrufbar. 1. Auflage 2021 © UVK Verlag 2021 - ein Unternehmen der Narr Francke Attempto Verlag GmbH + Co. KG Dischingerweg 5 · D-72070 Tübingen Das Werk einschließlich aller seiner Teile ist urheberrechtlich geschützt. Jede Verwertung außerhalb der engen Grenzen des Urheberrechtsgesetzes ist ohne Zustimmung des Verlags unzulässig und strafbar. Das gilt insbesondere für Vervielfältigungen, Übersetzungen, Mikroverfilmungen und die Einspeicherung und Verarbeitung in elektronischen Systemen. Internet: www.narr.de eMail: info@narr.de Einbandgestaltung: Atelier Reichert, Stuttgart CPI books GmbH, Leck utb-Nr. 5552 ISBN 978-3-8252-5552-7 (Print) ISBN 978-3-8385-5552-2 (ePDF) <?page no="5"?> Preface This book has two goals. One is to provide a basic understanding of financial capital defined as consisting of contracts which, with some probability, provide a monetary profit. The definition is consistent with a distinction made between money and financial capital. We consider debt and saving contracts, stock and investment fund shares, and some forms of derivatives. The most basic and important form of financial capital consists of debt contracts purchased by banks and paid with self-generated money. This insight contradicts the still widespread belief in the loanable funds theory, which assumes that banks lend out previously received deposits. It also requires to distinguish between two money circuits: one originating from the central bank, and another one originating from private banks. In order to illustrate the discussion of different forms of financial capital, we mostly use data from the euro area. This allows us to refer to a largely consistent body of data. To support the discussion, we use simple models consisting of symbolic references to economic units and formally defined relationships. In contrast to econometric models aiming to establish empirical regularities, these models are intended to serve the discussion of mechanisms, which contribute to the working of financial capital. They also help show that most of these mechanisms can be described as zero-sum games. Understanding these models does not require specific mathematical or statistical knowledge. A second goal of the book is to contribute to the discussion of the financialization of capitalist economies. We focus on one particularly significant aspect, namely, the growth of financial wealth—both money and financial capital—that greatly exceeds increases in the production of goods and services. Banks play a decisive role in this aspect of financialization because they are the creators of almost the entire money supply except for a small part of cash money. Furthermore, in the institutional framework that we consider, banks mediate government expenditures, allowing them—indirectly—to purchase government bonds with their own deposit money. This con- <?page no="6"?> 6 tributes significantly to making government expenditures exceeding receipts from taxes a driving force of financialization. In order to discuss sources of the expansion of financial wealth, we use a model that basically consists in a macroeconomic accounting framework. Definitions of macroeconomic aggregates are, however, derived from references to individual economic units. This allows us to use the same framework also for a discussion of mechanisms which contribute to the huge inequality in the distribution of financial wealth. We thank Christoph Schiwy for help with finding data; we also thank Wanda Vrasti and Paul Meyers for proofreading parts of the text. <?page no="7"?> Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.1 Markets, money, financial capital . . . . . . . . . . . . 9 1.2 Notations for models . . . . . . . . . . . . . . . . . . . 11 2 Beginning with banks . . . . . . . . . . . . . . . . . . . . . 15 2.1 Two money circuits . . . . . . . . . . . . . . . . . . . 15 2.2 Banks’ deposit money . . . . . . . . . . . . . . . . . . 18 2.3 Usages of reserves . . . . . . . . . . . . . . . . . . . . 28 2.4 Zero-sum games and debts . . . . . . . . . . . . . . . 32 3 Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.1 Some data . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.2 Orientation to returns . . . . . . . . . . . . . . . . . . 40 3.3 Government bond spreads . . . . . . . . . . . . . . . . 46 3.4 Financing of government debt . . . . . . . . . . . . . . 49 3.5 Appendix: Modern Money Theory . . . . . . . . . . . 59 4 Tradable shares . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.1 Some data . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.2 Speculative pricing . . . . . . . . . . . . . . . . . . . . 65 4.3 Dividends . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.4 Real and virtual gains . . . . . . . . . . . . . . . . . . 76 5 Investment funds . . . . . . . . . . . . . . . . . . . . . . . . 83 5.1 Some data . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.2 Speculation with fund shares . . . . . . . . . . . . . . 85 5.3 Exchange-traded funds . . . . . . . . . . . . . . . . . . 89 6 Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 6.1 Forwards and futures . . . . . . . . . . . . . . . . . . . 95 6.2 Options . . . . . . . . . . . . . . . . . . . . . . . . . . 101 6.3 Credit default swaps . . . . . . . . . . . . . . . . . . . 108 7 Financialization . . . . . . . . . . . . . . . . . . . . . . . . 115 7.1 Expansion of financial wealth . . . . . . . . . . . . . . 115 7.2 Inequality of financial wealth . . . . . . . . . . . . . . 139 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 <?page no="9"?> 1 Introduction This chapter explains our understanding of some core concepts and then introduces notations, which are used in subsequent chapters to formulate models. 1.1 Markets, money, financial capital Markets. We think of markets as institutions, meaning, organized environments in which actors (representing economic units) communicate and decide about transactions. Markets exist in many different forms. Most often, they are organized by enterprises as environments in which they can sell products or, more generally, offer transactions serving their profits. We distinguish between: markets for goods and services, including financial services, and financial markets where actors can sell and buy financial products which we define as contracts entailing, with some probability, a future monetary gain and thereby can be considered as capital. In both cases there is a basic asymmetry: only enterprises can create and extend markets, whereas customers can only visit already existing markets. Money. Common understandings of money highlight three functions: 1) Money serves as a “means of payment” for the settlement of transactions. 2) Money serves as a “measure of value” that can be used to specify prices at which things might be or have been bought/ sold for. The phrase “measure of value” is, however, easily misleading because it suggests an analogy with scales used for measurements. Yet money cannot be used to measure something and there is no measurement procedure that allows one to determine prices. 3) Money serves as a “storage medium of value”, which means that a person who owns money can wait for some time before spending the money. The idea that something is “stored” relates to purchasing power, which is not a property of money but depends on prices and what a person wants to buy. <?page no="10"?> 10 1 INTRODUCTION The lack of clarity in thinking of money as a “storage medium” is evident in definitions of a money supply. Relying on the idea that money is a means of payment, the public money supply only consists of peoples’ cash and their deposit money in bank accounts. Instead, following the idea that a “value of money” can be stored, leads to a much broader definition, e.g., that: “Money is the stock of assets that can be readily used to make transactions.” (Mankiw 2017, p. 80) The idea that anything that can be exchanged into money within a short period represents money obscures a basic difference between money and capital. Money and capital. In this text, we systematically distinguish between money and capital. Before it is spent, the usage of money is undetermined. So it does not “have a value” but only purchasing power in regard to possible uses. Some of these uses consist in spending money on buying capital or something that can be transformed into capital. As a general definition we state: something is capital if, and insofar as, it is intended to serve generating a monetary profit. 1 Financial capital. We define financial capital as capital, which exists in the form of contracts providing, with some probability, a monetary profit. Different from Hilferding’s notion of Finanzkapital (1910), we do not presuppose a specific constellation of economic institutions. We distinguish between the following forms: saving contracts (including term deposits). A unit (most often a household) buys a saving contract from a bank or insurance company and thereby acquires financial capital. bank loans. A unit sells to a bank a debt contract and by buying this contract the bank acquires financial capital. bonds emitted by firms or state institutions become financial capital owned by units buying the bonds. stocks which can be bought and sold on stock markets (both inside 1 In order to illustrate this view, Karl Marx (1990, p. 126) cited the then famous bishop Butler: “The value of a thing is just as much as it will bring.” <?page no="11"?> 1.2 NOTATIONS FOR MODELS 11 and outside of a stock exchange). Stocks represent financial capital in the form of company shares. shares of investment funds. derivatives. An important similarity between the different forms of financial capital is that they can be bought and (not always but very often) also sold on markets. The development of financial capital, therefore, makes possible a specific kind of investment, which consists in buying something that already is capital (and need not be transformed into capital by entrepreneurial activities). 1.2 Notations for models To support our discussion we are using, in several places, simple models consisting of symbolic references to economic units and formally defined relationships. They mainly serve the purpose of representing economic mechanisms which are not immediately conceivable and to make the assumptions of our arguments explicit. The present section explains some basic notations; additional notations will be introduced when needed. Economic units. We distinguish between three kinds of units: 1) households. In the present text this always means private households and non-for-profit organizations. 2) firms, which: employ wage labor in order to receive revenues by selling goods, services or financial products; use financial capital in order to receive gains; organize investment funds accumulating financial capital for share holders. 3) state institutions serving politically defined purposes. In contrast to firms, which by definition intend to make profits, the activities of state institutions depend on political decisions. 2 They also depend on political decisions regarding public tasks organized by 2 Of course, these decisions can also serve, partly or even primarily, the interest of firms. See, e.g., R¨ ugemer (2008), H¨aring (2010: Chap. 6). <?page no="12"?> 12 1 INTRODUCTION U i refers to a unit indexed by i U index set of all units F index set of firms H index set of households S index set of state institutions B index set of banks N index set of nonbanks (households, firms without banks) F \B index set of firms without banks τ refers to a point in time t refers to a period of time t ij,τ payment from U i to U j at time τ t ij,t sum of payments from U i to U j in period t state institutions or private enterprises. However, in order to get a clear distinction, we also consider enterprises owned partly or completely by state institutions as belonging to the category of firms. We use the symbol U i to refer to units, where the index i identifies the unit. Index sets serve to distinguish between groups of units. U denotes the set of indices of all units, and consists of three subsets: H (households), F (firms) and S (state institutions). We also use B for banks (considered as a subset of F) and N for households and firms other than banks, briefly referred to as “nonbanks”. The time framework. We assume a sequence of periods denoted by t = 0, 1, 2, 3, . . . Durations are, e.g., days or months, and depend on the purpose of a model. A large number of transactions, occurring at specific points in time, can take place during a period. For referring to points in time we use the symbol τ . The beginning and the end of a period will be considered as points in time. <?page no="13"?> 1.2 NOTATIONS FOR MODELS 13 Transactions and money. Transactions take place at specific points in time. As a generic notation we use: t ij,τ meaning the amount of payment given by unit U i to unit U j at the point in time τ . The set of transactions, which have taken place during a period, can be described as a flow. As a generic notation we use: t ij,t = ∑ τ ∈ t t ij,τ The notation “τ ∈ t” means that the summation covers all points in time within the period t at which transactions have taken place. Plots of time series. Throughout the text we use numerous plots of time series, where the time axis (abscissa) is a sequence of years. For example: 2000 2005 2010 2015 2020 Labels indicate the beginning of a year. Monthly data is therefore placed at y + m/ 12, whereas yearly data (both flows and stocks at the end of a year) at y + 1. <?page no="15"?> 2 Beginning with banks This chapter considers institutions that can create money, namely, banks. There are two kinds. Central banks can create money that is legal tender in a currency area, e.g. the ECB in the euro area. Private banks (subsequently banks) can create money held by clients with the bank. This chapter is structured as follows. The first section introduces a basic framework to understand money circuits: one which starts from a central bank and another starting from private banks. They are illustrated with data from the euro area. The second section uses a simple model to explain banks’ creation of deposit money and the implied clearing and settlement problem among banks. It turns out that banks only need a relatively small amount of central bank money (reserves) for dealing with liabilities due to the circulation of their deposit money. The third section considers the question of how banks use the huge amounts of money they receive from central banks or via state expenditures. We argue that the money is used primarily for speculative transactions in the interbank market and, in particular, for speculation with derivatives in OTC (over the counter) environments. As an example, we consider interest rate swaps. The fourth section uses a simple model to discuss how banks’ zero-sum games increase their indebtedness and thereby contribute to their need for reserves. 2.1 Two money circuits We consider a single currency area with a single central bank and a single government, 1 and presuppose an institutional setting characterized by four conditions. accounts of the government are located with the central bank. This implies that transactions involving the government require central bank money. 1 The role played by financial capital in the exploitation of transactions between different currencies is therefore outside of the scope of the present text. <?page no="16"?> 16 2 BEGINNING WITH BANKS Fig. 2.1 Two money circuits Government Central bank Banks Nonbanks ✲ ✛ M ∗ ❄ M ∗ ❄ M ∗ ✲ M ✻ M ∗ ✻ M ∗ ✛ M private units consist of banks, which also have accounts with the central bank, as well as nonbanks (households and firms other than banks) having accounts with banks. payments between banks use central bank money (reserves). payments between the government and nonbanks, and analogously between the central bank and nonbanks, are mediated by banks. The framework requires us to distinguish between two different types of money circuits, as shown in Fig. 2.1. One circuit starts from the central bank and uses central bank money (denoted by M ∗ , which consists of both cash and deposits with the central bank); the other one starts from banks and uses deposit money (denoted by M ) which can be created by banks. To simplify, we have omitted the circulation of cash between banks and nonbanks from the figure. In each circuit there is a single stock of money, which can grow and shrink as follows from the creation and destruction of money. M ∗ denotes the stock of central bank money. It is created by the central bank increasing the balances in the accounts of governments and banks, and it is destroyed when these balances are decreased. Cash must be purchased from the central bank and, therefore, does not change banks’ reserves. Since the central bank can create its own money, it does not have an account holding this money. Backflows of money, in the figure indicated by dashed lines, do not provide funds but allow the central bank to extinguish liabilities. <?page no="17"?> 2.1 TWO MONEY CIRCUITS 17 2000 2005 2010 2015 2020 0 1000 2000 3000 4000 5000 billion Euro Loans Securities Total assets Fig. 2.2 Asset side of the consolidated Eurosystem balance sheet. Source: https: / / sdw.ecb.europa.eu/ browse.do? node=bbn24. Correspondingly, M denotes banks’ deposit money held by nonbanks. It is created, and destroyed, by increasing and decreasing the balances of the bank accounts of nonbank units. As the central bank does not hold central bank money, banks do not have accounts holding their own deposit money. Again, backflows of money do not provide funds but allow banks to extinguish liabilities. 2 Banks’ central bank money. To illustrate the provision of central bank money, we refer to the Eurosystem, which consists of the ECB and the national central banks in the euro area. Note that the central banks in this system are not permitted to directly credit governments. The arrows in Fig. 2.1, which directly connect the central bank and the government, can therefore be ignored. 2 They nevertheless play an important role in a bank’s profit and loss account. Since banks can use their own deposit money also for payments to managers and shareholders (except other banks and the government), justifications of such payments critically depend on legal rules for the profit and loss accounts. For example, in contrast to repayments of loans, the interest received contributes to profits. <?page no="18"?> 18 2 BEGINNING WITH BANKS 2000 2005 2010 2015 2020 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 Cash M1 billion Euro Fig. 2.3 Development of the money supply M1 in the euro area (changing composition). https: / / sdw.ecb.europa.eu/ browse.do? node=9691572. Fig. 2.2 provides data about the asset side of the consolidated Eurosystem’s balance sheet. There are mainly two kinds of assets: loans and debt securities. The loans are almost completely granted to banks. Debt securities are mainly government bonds but recently also other kinds have been used in QE (quantitative easing) programs. The money supply. The money supply is defined as the sum of deposit money and cash held by nonbank units. Fig. 2.3 shows the development in the euro area. Only a small part consists of cash. As shown in Fig. 2.4, the money supply has grown much faster than the gross domestic product (GDP) in market prices. This is one sign of the financialization of the economy that will be discussed later in this text. 2.2 Banks’ deposit money This section considers banks’ deposit money. In principle, its creation can be easily understood. 3 Assume, for example, that a bank grants a 10,000 Euro loan to a person or organization having an account with 3 For extended discussions we refer to: McLeay, Radia and Thomas (2014), Werner (2014a, 2014b), Jakab and Kumhof (2019), Deutsche Bundesbank (2017). <?page no="19"?> 2.2 BANKS’ DEPOSIT MONEY 19 2000 2005 2010 2015 2020 0 100 200 300 400 500 GDP M1 Fig. 2.4 Development of the money supply M1 and the GDP in market prices. Index 2000 (Dec.) = 100. Data refer to the euro area in changing composition. Source of GDP data: https: / / sdw.ecb.europa.eu/ browse.do? node=9691186. that bank. Having set up a contract, providing the money simply consists of a bookkeeping operation whereby the account is increased by the loan amount. This operation creates new deposit money, which the owner of the account can then exchange for cash or use for cashless payments. The conditions, which banks must observe when creating new deposit money, have very few restrictions. For short term liabilities, which include deposits, banks need to hold a minimum reserve at the central bank. The reserve ratio is, however, mostly very low (e.g., 1 % in the euro area), and does not entail any significant restrictions to banks’ possibilities to create deposit money. More important is the fact that banks must be able to balance their mutual liabilities resulting from the flow of deposit money between banks. As will be seen below, this requirement also does not entail significant restrictions for the banking sector as a whole. Creation of deposit money takes place whenever a bank either buys something from a nonbank unit and pays by increasing the balance in the unit’s account, or it increases the accounts of nonbank shareholders, the bank’s management or external supporters. Quan- <?page no="20"?> 20 2 BEGINNING WITH BANKS 2000 2005 2010 2015 2020 0 5000 10000 Loans to nonbanks (without governments) Loans to governments billion Euro Fig. 2.5 Loans of banks (without the central bank) to nonbanks and governments in the euro area (historical composition); stocks at the end of the month. Source: https: / / sdw.ecb.europa.eu/ browse.do? node=bbn28. titatively speaking, most important is the creation of deposit money through the provision of credit: the bank buys a debt contract (financial capital) and pays with deposit money. We distinguish between three forms: bilateral debt contracts (loans) between a bank and a nonbank unit. Fig. 2.5 shows the expansion of such contracts in the euro area. (Since loans between banks, and between banks and the government, are using central bank money, they do not contribute to the expansion of deposit money.) the purchase of bonds, emitted by nonbank firms, on primary markets, that is, where the bonds are sold for the first time. the purchase of government bonds. Since banks must pay with central bank money, these purchases do not immediately increase the money supply. However, since subsequent government expenditures are mediated by banks, they increase the deposit money of the final recipients. (This will be further discussed in Section 3.4.) Money creation with loans. In order to better understand the creation of deposit money, we use a simple model and consider the <?page no="21"?> 2.2 BANKS’ DEPOSIT MONEY 21 M ij,τ U j ’s deposit money in an account with the bank U i at τ M ij,t U j ’s deposit money with the bank U i at the end of t d ij,τ,τ ′ loan by which the bank U i increased U j ’s bank account at τ τ ′ denotes the point in time when the loan must be repaid i ij,τ,τ ′ total interest for the loan given at τ which must be paid at τ ′ d ij,t sum of loans, which the bank U i credited to U j during t t b ii ′ ,τ amount of deposit money, which flows at time τ from U i to U i ′ T b ii ′ ,t balance of payments between bank U i and U i ′ in period t T b i,t change in bank U i ’s central bank money in period t provision of loans. As a time framework, we presuppose a sequence of periods indexed by t = 1, 2, 3, . . .; points in time will be denoted by τ . In order to distinguish between banks and nonbanks, we use index sets B and N , respectively. It is assumed that all units have at least one bank account. M ij,τ denotes the deposit money, which unit U j (j ∈ N ) holds at time τ in its bank account with the bank U i (i ∈ B). Having agreed on a contract, a bank granting a loan to a unit U j simply consists of a bookkeeping operation by which the bank increases the unit’s deposit money. 4 We use the following notation: d ij,τ,τ ′ is the loan amount by which the bank U i has increased U j ’s bank account at time τ , where τ ′ denotes the point in time when the loan must be repaid. The increase in U j ’s account can be referred to as 5 M ij,τ += d ij,τ,τ ′ (2.1) i ij,τ,τ ′ denotes the interest, which must be paid for the loan. In order to simplify notations, we assume that the whole interest must be paid at the repayment time τ ′ . 4 How it practically works was discussed by Werner (2014a) based on a real example. 5 We use += and − = to mean, respectively, “increased by” and “decreased by”. <?page no="22"?> 22 2 BEGINNING WITH BANKS The following flows can be derived: d ij,t = ∑ τ ∈ t d ij,τ,τ ′ (2.2) represents the sum of loan amounts, which the bank U i credited to U j ’s bank account during the period t. ∑ τ ′ ∈ t d ij,τ,τ ′ (2.3) represents the sum of money, which must be repaid by U j during the period t; and ∑ τ ′ ∈ t i ij,τ,τ ′ (2.4) is the total interest, which U j has to pay during the period t. We note that the expression “repayment” is possibly misleading because it suggests that a unit receives back money previously given away. However, a bank granting a loan does not “give away” previously owned money but creates new money through a bookkeeping operation. 6 Therefore, by the repayment of a loan previously granted to a nonbank, the bank does not receive money that could be put into an account of its own. The idea of an account where a bank holds deposit money is senseless because a bank can simply create deposit money by bookkeeping operations. The repayment of a loan is, nonetheless, important because the bank can delete a liability in its balance sheet, and it can also get rid of certain costs connected with the loan. These consist of obligations 6 In the literature, one often finds a misleading view, for example: “Let us assume that nonbanks deposit cash and coins in the amount of US $ 100 with the banking sector and that the banking sector issues liabilities in the form of sight deposits in the same amount. Assuming a minimum reserve rate of 2 %, the banking sector is required to keep US $ 2 as minimum reserves. Excess reserves amount to US $ 98. With the latter, the banking sector as a whole can extend loans to the private sector until the excess reserves are fully absorbed by minimum reserves.” (Belke and Polleit, 2009, p. 31) For a critique of such “loanable funds theories” see, e.g., Lindner (2015) and Bofinger and Ries (2017). <?page no="23"?> 2.2 BANKS’ DEPOSIT MONEY 23 to hold reserves at the central bank and, more importantly, costs incurred by the circulation of deposit money between banks. Flows of deposit money between banks. When a bank grants a loan, the newly created deposit money firstly exists in an account controlled by the bank. However, the money is then used for payments and thereby often flows into accounts held with different banks, and this changes the bank’s liabilities. To illustrate, we assume that a bank U i grants a loan amount of 1,000 to a nonbank U j . Initially, this creates a liability of the bank against the debtor U j . If, then, the money flows into an account of a unit U j ′ , located at a bank U i ′ , the liability against U j changes into a liability against U i ′ . In order to record flows of deposit money between banks, we use the following notation (as already mentioned we ignore flows of cash): t b ii ′ ,τ denotes the amount of deposit money, which at time τ flows from an account with the bank U i to an account with the bank U i ′ . So one can define, for each pair of banks, a balance: T b ii ′ ,t = ∑ τ ∈ t (t b ii ′ ,τ − t b i ′ i,τ ) (2.5) Depending on whether this balance is greater or less than zero, there is a liability of U i against U i ′ or vice versa. Note that these are flows. In contrast, M ij,t records the stock of money held by U j in an account with the bank U i at the end of the period t. In order to compensate for imbalances of liabilities, a clearing and settlement process takes place at the end of each business day. We therefore now think of the periods t as days. There are two methods. 1) One method employs bilateral credits between banks: if T b ii ′ ,t > 0, U i is granted a credit in the value of this amount by U i ′ . The increase in liabilities on the passive side of U i ′ ’s balance sheet (through the inflow of deposit money) then equals the increase in credit claims on the active side. This method requires securities and sufficient trust among banks. <?page no="24"?> 24 2 BEGINNING WITH BANKS 2) Another method (which can follow if the first one is not completed) consists in a clearing process organized by the central bank. At the end of t, if T b ii ′ ,t > 0, this amount is transferred from U i ’s to U i ′ ’s account with the central bank. If this is done for all pairs of banks, their balance sheets are again balanced. When all payments involving a bank U i have been settled, the bank’s reserves have changed by the amount T b i,t = ∑ i ′ ∈B T b ii ′ ,t (2.6) If thereby the bank’s balance becomes negative, the bank must borrow additional reserves from the central bank. This entails that, although ∑ i ∈B T b i,t = 0, the settlement can lead to an increase in the total amount of central bank money. Numerical illustration. We consider a system consisting of 10 banks (U 1 , . . . , U 10 ) and 10,000 nonbank units; each 1,000 of the nonbanks have an account with the bank U i . At the beginning of day t = 1, the money in each account is M ij, 0 = 100. In this illustration, we consider loans to nonbanks. It is assumed that, on each day, 300 randomly selected units receive loans, all having the amount d ij,τ,τ ′ = 50 and an identical duration of τ ′ − τ = 100 days. By the end of day t, the sum of granted loans is: 7 ∑ i ∈B ∑ j ∈N ∑ τ ≤ t d ij,τ,τ ′ (2.7) Subtracting the repayments, that is, ∑ i ∈B ∑ j ∈N ∑ τ ′ ≤ t d ij,τ,τ ′ (2.8) one obtains the sum of outstanding loans. In our example, this sum increases until the end of day 100, and then remains at the level of 1,500,000. Beginning with day 101, the total money supply is 2,500,000. 7 The notation “τ ≤ t” is intended to mean that the summation covers all points in time until the end of period t. <?page no="25"?> 2.2 BANKS’ DEPOSIT MONEY 25 0 500 1000 1500 2000 20000 30000 40000 50000 t Fig. 2.6 Development of the amount of reserves required for clearing, as defined in (2.9). The mean value (t > 100) is 36,700. We now assume that, on each day, about 90 % of this money supply flows between randomly selected nonbank accounts. 8 This entails changes in the distribution of each bank’s deposit money across the set of other banks. If the clearing and settlement is executed through bilateral credits, the total amount of redistribution is 1 2 ∑ i ∈B ∑ i ′ ∈B | T b ii ′ ,t | (2.9) which equals the sum of all positive T b ii ′ ,t terms. Fig. 2.6 shows the development in our example. The mean amount of reserves required for clearing on each day is 36,700, that is, about 1.5 % of the money supply. We note that, if the central bank operates as a clearing house, instead of the quantity defined in (2.9), the smaller amount 1 2 ∑ i ∈B | T b i,t | (2.10) would suffice. In our example, the mean amount of required reserves would be 7,484, only about 0.3 % of the money supply. 8 Firstly, two units are randomly selected, and 10 % of one account is transferred to the other one. This is repeated until about 90 % of the money supply has been transferred. <?page no="26"?> 26 2 BEGINNING WITH BANKS 0 500 1000 1500 2000 -2000 -1000 0 1000 2000 3000 4000 5000 t Fig. 2.7 Development of the cumulated amount of reserves required for clearing, as defined in (2.11), for the bank U 2 . The mean value (t > 100) is 1,525. A further considerations applies to individual banks because their need for reserves can increase and decrease over sequences of days. For bank U i the cumulated need of reserves is t ∑ l = t 0 T b i,l (2.11) Fig. 2.7 shows the development for bank U 2 , beginning on day t 0 = 101. In our simplistic model, except for random fluctuations, significant differences between banks only concern mean values. The extent of banks’ reserves. So far, our discussion examined the clearing and settlement of liabilities due to the circulation of deposit money. The settlement does not immediately determine the development of the extent of reserves. Let M ∗ i,t − denote the balance of reserves in the account of bank U i with the central bank at the end of day t, but before the settlement takes place. Then after the settlement: M ∗ i,t = M ∗ i,t − − T b i,t (2.12) If T b i,t is positive due to a positive balance of liabilities, the bank’s <?page no="27"?> 2.2 BANKS’ DEPOSIT MONEY 27 reserves decrease; otherwise they increase. The development then depends on how the banks react to these changes. There is, however, an asymmetry. While banks must try to avoid negative balances, they are free to keep positive balances of any size. Of course, banks with an excess of reserves might lend to other banks having a need for additional reserves, and to the extent that this takes place, a growth of reserves could be avoided. However, as will be discussed in the next section, banks also use reserves for other kinds of investments. Money circulation and defaults. The money supply expands primarily due to bank loans granted to nonbanks. We note that defaults of such loans do not change the money supply. Given that a debtor has spent the money received from a loan, in the case of a default, it simply remains “forever” in the money supply. We also note that defaults do not have a direct impact on the amount of reserves required for the daily clearing and settlement. Of course, a default entails that the creditor cannot get rid of the corresponding liability. However, ceteris paribus , the creditor’s liabilities simply remain at their previous level. One can imagine that the loan, beginning with its default, is converted into a new one with unlimited duration and without interest. These new conditions do not change the liabilities of the creditor against other banks. Coping with credit defaults. Defaults can occur with all kinds of credit and between all kinds of units (banks, nonbanks, governments). There are mainly two strategies for coping with risks of default. One strategy consists in supplementing a debt contract with an agreement about collateral which belongs to the creditor in the case of a default. For example, loans serving to finance real estate include agreements about mortgages. When banks grant loans for financial investments, mostly securities serve as collateral. Frequently used are repurchase agreements (repos). These are debt contracts with a collateral whose value is continuously adapted to changing market conditions. 9 9 A survey of the European repo market, performed in December 2019 by the International Capital Market Association (ICMA, 2020), provides an estimate of 8,310 billion Euro. <?page no="28"?> 28 2 BEGINNING WITH BANKS Another strategy aims to get rid of the default risk by transferring it to other parties. Two often used methods are credit default swaps and securitization, that is, the transformation of bilateral debt contracts into tradable securities. Both methods are variants of a general strategy for coping with risks resulting from financial investments: the transformation of risks into new investment opportunities. Credit default swaps will be considerd in Section 6.3. 2.3 Usages of reserves In the example discussed in the previous section, banks need only a very small amount of reserves for the daily clearing and settlement of liabilities resulting from the circulation of deposit money. One therefore wonders why banks actually receive very large amounts of reserves from central banks. 10 We note that also banks financing loans to governments and purchases of government bonds cannot explain these huge amounts because, as soon as governments spend the borrowed money, it flows back to banks, and the final recipients can be paid with banks’ deposit money. Also, in these cases an additional demand for reserves eventually only results from the clearing and settlement of the circulation of deposit money. 11 One therefore has to focus on transactions among banks. As shown in Fig. 2.8 for the euro area, these transactions mainly consist in mutual lending and borrowing. Our question concerns what drives these transactions insofar as they do not originate from the circulation of deposit money. In the remainder of this section, and in the following one, we consider banks’ speculation with derivatives in OTC (over the counter) environments. We argue that, with these investments, banks are engaging in zero-sum games, which generate 10 The formulation is intended to be neutral with respect to the driving forces of the expansion of central bank money. It has been argued that: “[t]he total level of reserves in the banking system is determined almost entirely by the actions of the central bank and is not affected by private banks’ lending decisions” (Keister and McAndrews 2009, p. 2). However, without banks’ willingness to receive reserves (by selling assets), the central bank cannot increase the extent of reserves. For further discussion, see Rule (2011). 11 The argument will be elaborated in Section 3.4. <?page no="29"?> 2.3 USAGES OF RESERVES 29 2000 2005 2010 2015 2020 0 2000 4000 6000 8000 Loans to MFIs Debt securities from nonbanks from MFIs billion Euro Fig. 2.8 Data from the aggregated balance sheets of MFIs (banks and money market funds) in the euro area. Loans and debt securities (emitted by other MFIs or by nonbanks, including governments) held at the end of months. Source: https: / / sdw.ecb.europa.eu/ browse.do? node=bbn28. debts, and thereby contribute to borrowing both in the interbank market and from the central bank. Speculation with derivatives. Speculation with derivatives consists in bets on possible future changes of the price of anything that has or can be given a price. There are two environments for participating in such bets. One is organized by stock exchanges and offers highly standardized betting contracts. Two kinds of such contracts (futures and options) will be discussed in Chapter 6. Another one is the OTC environment in which banks and other financial institutions invest in bilateral bets. One can get an impression of these bets from master agreements, which provide a starting point for the formulation of contracts. For example, a master agreement for financial derivatives transactions distributed by the Association of German Banks (Deutscher Bankenverband), 12 begins as follows: 12 Internationally, master agreements, which have significantly contributed to the development of OTC markets for derivatives, are distributed by the International Swap Dealer Association (ISDA) (www.isda.org). <?page no="30"?> 30 2 BEGINNING WITH BANKS Purpose and Scope of Agreement In order to manage interest and exchange rate risks and other price risks arising within the scope of their business operations, the parties hereto intend to enter into financial derivatives transactions the object of which is: a) the exchange of amounts of money denominated in various currencies or amounts of money calculated by reference to floating or fixed interest rates, exchange rates, prices or any other calculation basis, including average values (indices) relating thereto, or b) the delivery or transfer of securities, other financial instruments or precious metals, or the performance of similar obligations. Financial derivatives transactions also include options, interest rate protection and similar transactions that require a party to render performance in advance, or a performance that is subject to a condition. 13 Interest rate swaps. As an example, we consider interest rate swaps. These are contracts between a bank and another party which, of course, can also be a bank, concerning the exchange of payments, which are calculated as interest on a fictive capital. A basic form has the following specifications: 1) A sequence of periods t = 1, . . . , T , which typically have a duration of 3, 6 or 12 months. Normally, the first period begins when the contract is made. 2) A nominal amount N serving as the basis for the calculation of interest. 3) A fixed interest rate r f , also called swap rate, which can be used to calculate an interest r f N for each period. 4) A variable interest rate r v t , which depends on the future economic development and is only known at the beginning of each period. Only r v 1 is known at the time that the contract is made. Libor or Euribor interest rates are most commonly used in correspondence with the duration of periods in the contract. 13 This master agreement, and several more specific forms of agreement, can be found at www.bankenverband.de/ service/ . <?page no="31"?> 2.3 USAGES OF RESERVES 31 5) Finally, one party is determined as a payer and the other one as a receiver. If ∆ t = N (r f − r v t ) is positive in the period t, the payer pays this amount to the receiver, otherwise the payer receives −∆ t from the receiver. Obviously, this is a speculative bet where, in each period, one party gains what the other party loses, that is, a zero-sum game. 14 To illustrate, we assume that a five-year contract is made at the beginning of 2014. The bank is the receiver. The nominal value is N = 100 million Euro, the variable interest rate is the EURIBOR for periods of 12 months (mean values from the previous December), and the parties have agreed on a swap rate of 0.3 %. Table 2.1 shows the development of payments. In the first two periods, the bank must pay out the payer; after that the decreasing interest rates generate gains for the bank. The example also illustrates that the amount of money that actually changes between the payer and the receiver is substantially less than the nominal value of a contract: ∑ T t =1 ∆ t = 840, 000 = 0.84 % of the nominal value. 14 We only briefly consider the question of how the swap rate is determined. A common guiding notion is that the swap rate be fixed in such a way that the expected gains for both parties are equal. A frequently used approach considers the swap to be a combination of two bonds whose market value can be derived from discounting. The condition, which must be met, can then be written as: T ∑ t =1 N r f (1 + r t ) t + N (1 + r T ) T = T ∑ t =1 N r v t (1 + r t ) t + N (1 + r T ) T where r t denotes the discount rate (see Section 3.2). An equivalent formulation is T ∑ t =1 r f − r v t (1 + r t ) t = 0 (2.13) To determine a swap rate r f one needs assumptions about the variable interest rates and the discount rates. The literature provides several considerations (see e.g., Hull (2009), B¨osch (2014, p. 231)). What is important is the fact that the condition (2.13) is compatible with different assumptions about the development of future interest (and discount) rates. This not only involves that a swap rate always result from a bargaining process, it also means that the parties can believe that the condition (2.13) holds and the contract thereby formulates a “fair bet”. <?page no="32"?> 32 2 BEGINNING WITH BANKS Table 2.1 Development of an interest rate swap with a nominal value of N = 100 million Euro based on using the EURIBOR for periods of 12 months. t Year r v t (%) r f (%) ∆ t (in 1000) 1 2014 0.54 0.3 −240 2 2015 0.33 0.3 −30 3 2016 0.06 0.3 240 4 2017 −0.08 0.3 380 5 2018 −0.19 0.3 490 BIS data on interest rate derivatives. Data on OTC transactions of banks with derivatives are provided by the Bank for International Settlements (BIS). The data originates from surveys based on reports from 74 big international banks conducted biannually since 1998. 15 As shown in Fig. 2.9, transactions with derivatives have massively grown since 2000. The figure also shows that interest rate derivatives contribute the largest part (about 80 %). Of course, only a small fraction of the nominal values shown actually circulates between the participating players. But even assuming a small fraction of about 1 %, the gains and losses generated are extremely high. And it is noteworthy that these gains and losses are generated by only the small number of 74 big banks. As shown in Fig. 2.10, almost all OTC bets with derivatives take place among banks and other financial corporations. 2.4 Zero-sum games and debts All types of speculation with derivatives are basically bets where one party gains what another one loses. We use a simple model to discuss how such zero-sum games can contribute to banks’ demand for reserves. The model. The time framework consists of a sequence of periods (days), t = 0, 1, 2, . . . There are N banks, U i , i ∈ B = {1, . . . , N }. The box on the next page shows notations (stocks at the end of the 15 We use copies of the data available on the website of the Deutsche Bundesbank. <?page no="33"?> 2.4 ZERO-SUM GAMES AND DEBTS 33 2000 2005 2010 2015 2020 0 100 200 300 400 500 600 trillion Euro Total Interest rate derivatives Fig. 2.9 Nominal values of contracts with derivatives reported by 74 international banks in biannual surveys of the Bank for International Settlements. Deutsche Bundesbank time series portal: BBK01.QUY208, BBK01.QUY213. 2000 2005 2010 2015 2020 0 100 200 300 400 500 trillion Euro Total Contracts with financial firms Contracts with nonfinancial firms Fig. 2.10 Nominal values of interest rate derivatives reported by 74 international banks in biannual surveys of the Bank for International Settlement. Deutsche Bundesbank time series portal: BBK01.QUY213, BBK01.QUY214, BBK01.QUY215, BBK01.QUY216. period t). If during t, the central bank grants a credit c to U i , then M ∗ i,t += c and D ∗ cb i,t += c. Conversely, if U i pays back an amount c, <?page no="34"?> 34 2 BEGINNING WITH BANKS M ∗ i,t records U i ’s reserves D ∗ cb i,t records U i ’s debts with the central bank C ∗ b i,t records U i ’s loans granted to other banks D ∗ b i,t records U i ’s debts due to loans from other banks M ∗ m i,t defines the minimum reserves, which U i needs for the daily clearing and settlement then M ∗ i,t −= c and D ∗ cb i,t −= c. With D ∗ b i,t instead of D ∗ cb i,t the notations can also be used for debt relations between banks. We assume that a payment from U i to another bank or to the central bank only takes place if by that payment M ∗ i,t does not fall below M ∗ m i,t . In each period, m bets take place. Each bet proceeds as follows: two banks, U i and U j , are randomly selected, with probability 0.5, either M ∗ i,t += b and M ∗ j,t −= b or M ∗ i,t −= b and M ∗ j,t += b. To simplify notations we assume that bets are settled until the end of the period when they started. A bank U i can finance its participation in a bet in period t out of available reserves if M ∗ i,t − 1 ≥ M ∗ m i,t + b. Otherwise, the bank borrows an amount of money that suffices for M ∗ i,t not to fall below the required minimum. In any case, the sum of banks’ reserves equals their debts: ∑ i ∈B M ∗ i,t = ∑ i ∈B D ∗ cb i,t (2.14) Illustrations. In the following, we begin by assuming that banks borrow money from the central bank, and then consider borrowing among banks. In all settings, at the end of each period, gains from betting are first used for the repayment of debts that exceed the minimum M ∗ m i,t . <?page no="35"?> 2.4 ZERO-SUM GAMES AND DEBTS 35 0 10 20 30 40 50 60 70 80 90 100 0 10000 20000 30000 40000 t Fig. 2.11 Amounts of money borrowed from the central bank for betting in one run of the model (setting 1). (1) We consider 100 banks. In each period m = 5 bets take place, b = 300. The minimum reserves are M ∗ m i,t = 200 for all banks. At the beginning M ∗ i, 0 = D ∗ cb i, 0 = 200, and banks must borrow money from the central bank in order to finance their bets. Afterwards winners can repay debts, and finance new bets out of gains, while losers and newcomers must again borrow money. Fig. 2.11 shows the development of the sum of reserves borrowed from the central bank for financing the bets: ∑ i D ∗ cb i,t − M ∗ m i,t . Participating in a bet is a financial investment. The bank invests an amount b and either receives 2 b or nothing. In the current setting, until the end of period t the bank U i has invested D ∗ cb i,t − M ∗ m i,t and received M ∗ i,t − M ∗ m i,t ; so its gain, or loss, is Y ∗ i,t = M ∗ i,t − D ∗ cb i,t (2.15) Fig. 2.12 shows a frequency distribution of these quantities at t = 100. The sum of positive gains is 35,400 and equals the sum of money borrowed from the central bank for investments in betting. The process can simply be described as a continuous redistribution, through bets, of money borrowed from the central bank. <?page no="36"?> 36 2 BEGINNING WITH BANKS -3000 -2000 -1000 0 1000 2000 3000 0 5 10 15 % Fig. 2.12 Distribution of Y ∗ i,t , defined in (2.15), at t = 100 in one run of the model (setting 1). (2) We now assume that banks lend their betting gains to other banks for financing bets. As long as there are banks with M ∗ i,t − 1 > M ∗ m i,t + b, other banks can borrow from a randomly selected member of these banks. Borrowing from the central bank only takes place if borrowing from other banks is not possible. Extending (2.15), we consider the quantities Y ∗ i,t = M ∗ i,t + C ∗ b i,t − D ∗ b i,t − D ∗ cb i,t (2.16) as representing U i ’s gains or losses from betting (in the sense of changes in assets which can be attributed to betting and reinvestment of gains). For a comparison with the previous setting, we refer again to t = 100. The distribution of Y ∗ i, 100 is similar to the distribution shown in Fig. 2.12. The relevant difference concerns the sources of the gains. While in the previous setting the gains from betting were reserves borrowed from the central bank, they now almost completely do exist only as liabilities among banks. The process quickly reaches an autopoietic state in which the bets can be almost completely financed through the lending of their gains. Eventually, most banks are simultaneously both creditors and debtors. The extent of the mutual indebtedness of the banks at the <?page no="37"?> 2.4 ZERO-SUM GAMES AND DEBTS 37 Table 2.2 Setting 2 n ∑ i Y ∗ i, 100 ∑ i ˜ M ∗ i, 100 ∑ i ˜ D ∗ cb i, 100 ∑ i C ∗ b i, 100 ∑ i D ∗ b i, 100 G1 45 36900 600 0 69900 33600 G2 55 −36900 2100 2700 48300 84600 100 0 2700 2700 118200 118200 Setting 3 n ∑ i Y ∗ i, 100 ∑ i ˜ M ∗ i, 100 ∑ i ˜ D ∗ cb i, 100 ∑ i C ∗ b i, 100 ∑ i D ∗ b i, 100 G1 45 36900 25500 0 11100 0 G2 55 −36900 300 25800 300 11400 100 0 25800 25800 11400 11400 end of period t can be described by the quantity 1 2 ∑ i ∈B ∑ j ∈B | D ∗ b ij,t − D ∗ b ji,t | (2.17) where D ∗ b ij,t is the debt of U i with U j . In one run of the model, shown in the upper panel in Table 2.2, 16 the value of this quantity at the end of period t = 100 is 118,200. Almost all claims are purely fictitious, that is, not backed by available reserves. (3) The two settings can be combined. To illustrate, we assume that banks require loans to be repayed after maximal 10 periods. As shown in Fig. 2.13, bets are now financed both by borrowing reserves and bank loans. Correspondingly, gains consist both of actually received reserves and claims against other banks. The lower panel in Table 2.2 shows the situation at t = 100. Conclusion. The discussion suggests the following conclusion: by increasing banks’ reserves above the amount needed for the daily 16 The two groups consist of banks having made gains and losses, respectively. Reserves are shown net of the required minimum: ˜ M ∗ i,t = M ∗ i,t − M ∗ m i,t and ˜ D ∗ cb i,t = D ∗ cb i,t − M ∗ m i,t . <?page no="38"?> 38 2 BEGINNING WITH BANKS 0 10 20 30 40 50 60 70 80 90 100 0 10000 20000 30000 40000 t Fig. 2.13 One run of setting 3. Dashed line: money borrowed from the central bank for betting. Grayed: money borrowed among banks. clearing and settlement of liabilities that results from the circulation of deposit money, banks are enabled to use reserves for mutual betting with derivatives. This leads to rising imbalances between banks and, in particular, to a rising demand for reserves by banks having incurred losses. A central bank aiming to care for a functioning banking system then probably provides the required reserves and, thereby, contributes to financing the continuation of the betting games. We note that also bets on derivatives between banks and nonbanks can contribute to increasing the demand for reserves. Assume, for example, that a bank U 1 lends money to a hedge fund which uses the money for betting with a bank U 2 . If the hedge fund loses the money, a liability of U 1 against U 2 results. Otherwise, it depends on how the hedge fund spends the gain. So this example also confirms that a demand for reserves due to direct or indirect bets between banks differs from a demand resulting from the circulation of deposit money. <?page no="39"?> 3 Bonds The previous chapter has argued that banks contribute to the expansion of the money supply mainly by granting loans and purchasing bonds from nonbank units and governments. In this chapter we focus on bonds. We begin with providing data from the euro area on outstanding bonds, which shows that bonds are mainly used for financing financial investments (of banks and other financial corporations) and government debts. In order to better understand bonds, we discuss definitions of yields and illustrate their development. We then briefly consider differences in yields (spreads) of government bonds. Finally, we discuss the financing of government bonds and show that banks, due to their mediation of government expenditures, play a decisive role, and are able to finance their purchases of such bonds with their deposit money. An appendix to the section critically discusses views of the financing of government expenditures proposed by the Modern Money Theory (MMT). 3.1 Some data Primary and secondary markets. The primary market is the market where bonds find an initial buyer and, thereby, come into existence. The purchases can take place at a stock exchange or in nonformally organized networks connecting banks and corporations (OTC [over the counter] transactions). Banks occupy a special position because not only can they mediate the emission of bonds, they can also organize a primary market for selling bonds of their own. When a bond has found buyers on a primary market, it can also be traded on a secondary market. The statistics, therefore, distinguish between newly emitted bonds and stocks of outstanding bonds. Fig. 3.1 shows the growth of outstanding bonds in the euro area. There are two main groups of emitters. On the one hand, these are banks and other firms employing financial capital and, on the other hand, these are governments. Obviously, in the euro area, bonds play only a minor role in financing nonfinancial corporations. <?page no="40"?> 40 3 BONDS 1990 1995 2000 2005 2010 2015 2020 0 5000 10000 15000 billion Euro Total Governments Nonfinancial corporations Banks Financial corporations Fig. 3.1 Outstanding bonds in the euro area (historical composition) emitted by different kinds of units. Values refer to stocks at the end of a month. Source: https: / / sdw.ecb.europa.eu/ browse.do? node=9691436. Issuers and owners of bonds. Table 3.1 provides information about Germany. Based on a distinction made between several sectors, the table shows the amounts of outstanding bonds emitted and owned by units of these sectors. The “rest of the world” sector indicates the extent of international linkages: for instance, 36.5 % of bonds emitted in Germany were owned by foreign units; conversely, 37.4 % of the bonds owned in Germany originated from foreign units. 3.2 Orientation to returns We refer to bonds consisting of a fixed number of pieces. All pieces have the same nominal value (emission volume divided by the number of pieces), the same duration and the same coupon rate defined in <?page no="41"?> 3.2 ORIENTATION TO RETURNS 41 Table 3.1 Credits and bonds in Germany at the end of 2019 in billion Euro. Source: Deutsche Bundesbank, Statistical Series Financial Accounts June 2020. Credits Bonds granted borrowed owned emitted Banks and central bank 3673.6 − 1752.1 1220.7 Financial services 356.7 744.9 16.0 166.0 Investment funds 38.3 66.3 1066.5 − Insurance companies 294.1 27.2 530.5 26.6 Nonfinancial firms 319.1 1561.7 45.1 208.8 State institutions 150.3 534.3 132.1 1733.4 Households − 1857.3 121.3 − Nonprofit organizations − 18.2 31.9 − Rest of the world 1146.0 1168.3 1841.2 2181.4 Total 5978.2 5978.2 5536.8 5536.8 percent of the nominal value (e.g., 5 %). Also bond prices will be recorded in percent, so there is no need to explicitly refer to nominal values. It is assumed that there is a fixed repayment price (mostly 100 %). The initial price refers to the point in time when the bond finds a buyer, for the first time. Yields of bonds. We consider a bond having at time τ the price P τ and at time τ + ∆ the price P τ +∆ . The yield for the period ∆ is defined by r τ, ∆ = P τ +∆ − P τ + A ∆ P τ (3.1) A ∆ denotes the accrued interest for the period ∆, and P τ +∆ − P τ is the gain or loss due to changing prices. Of course, the yield is only known at the end of the period ∆, up to that point in time one can only think in terms of expectations. An alternative definition relates to the period up until the bond’s maturity, say T (in the following always measured in years). The price P τ + T is then known in advance. The common definition of a yield to maturity is based on discounting the expected yields. To explain the definition, we consider a bond having the remaining duration T (being <?page no="42"?> 42 3 BONDS P τ price at time τ T maturity in years A ∆ accrued interest for the period ∆ A t coupon in period t K(r) discounted value of the bond r discount rate r τ, ∆ yield for the period ∆ an integral number of years) and yearly coupons A t (t = 1, . . . , T ). The discounted value of the bond at time τ (the beginning of period 1) is defined by K(r) = T ∑ t =1 A t (1 + r) t + P τ + T (1 + r) T (3.2) where r denotes the discount rate. Then, if P τ is the price at time τ , the yield to maturity is defined as the solution r to the equation P τ = K(r). This yield can be interpreted as a mean annual interest rate resulting from a capital amounting to P τ invested at time τ . To illustrate the definition, we consider a bond, which has at time τ a remaining duration of three years. The maturity price is 100 %, and the coupons are A 1 = A 2 = A 3 = 5 %. Formula (3.2) then becomes K(r) = 5 (1 + r) + 5 (1 + r) 2 + 5 + 100 (1 + r) 3 (3.3) As illustrated in Fig. 3.2, there is an inverse relationship: decreasing prices lead to increasing yields, and vice versa. If P τ = P τ + T , the yield equals the mean interest: 5/ 100 = 5 %. Example. As an example, we use a German government bond that was emitted in January 2002 with a volume of about 10 billion Euro (ISIN: DE0001135192). The duration was 10 years, the annual coupon rate 5 %, and the repayment price 100 %. <?page no="43"?> 3.2 ORIENTATION TO RETURNS 43 0 1 2 3 4 5 6 7 8 9 10 80 90 100 110 120 r K(r) Fig. 3.2 Relationship between the price and the yield of a bond calculated with formula (3.3). The upper part of Fig 3.3 shows the development of the bond’s price. 1 The initial price was 100.52 %, followed by substantial up and downs until, eventually, the price approached the repayment price. The lower part of the figure illustrates the inverse relationship between prices and yields with smoothed curves. Are changing prices relevant? Of primary relevance for the emitters of bonds are: the initial price which influences the amount of money received from the emission and the coupon rate which determines the payment of interest. Changing prices of outstanding bonds are only indirectly relevant if they influence the conditions for subsequent emissions. With respect to buyers, one needs to distinguish between them. On the one hand, there are buyers intending to receive yields up until the bond’s maturity. For these investors, price changes occurring after they have bought the bonds are irrelevant. Price changes are, however, relevant for investors intending to profit from betting on rising prices. In fact, since bond prices can be used as a basis for 1 From the time series with daily values we selected the prices registered on the first trading day of each month. <?page no="44"?> 44 3 BONDS 2002 2004 2006 2008 2010 2012 95 100 105 110 115 2002 2004 2006 2008 2010 2012 0 1 2 3 4 5 6 2002 2004 2006 2008 2010 2012 95 100 105 110 115 0 1 2 3 4 5 6 % % Prices Yields Prices Yields Fig. 3.3 Development of prices and yields to maturity of a German government bond (ISIN DE0001135192). Source: Time series portal of the Deutsche Bundesbank: BBK01.WT4012 and BBK01.WT4013. <?page no="45"?> 3.2 ORIENTATION TO RETURNS 45 1990 1995 2000 2005 2010 2015 2020 0 5 10 % Fig. 3.4 Dashed: Monthly means (weighted with outstanding volumes) of daily yields of German government bonds with a remaining duration of more than four years. Source: Time series portal of the Deutsche Bundesbank: BBK01.WU0017. The solid line shows a smoothed trend derived from the monthly data. derivatives, investors can bet on both rising and falling bond prices without the need to actually buy and sell bonds (this will be further discussed in Chapter 6). For example, one can think of an investor who buys the Government bond illustrated in Fig. 3.3 at the beginning of January 2004 at a price of 106.3 %. If he sells at the end of 2005 at a price of 110.1 %, he receives an annualized yield of about 6.5 %; but if he waits until maturity, the annualized yield is only about 4 %. Long-term development of yields. As shown in Fig. 3.1, the extent of bonds very much increased during the last decades. Paralleling this development, the yields decreased. This is illustrated in Fig. 3.4 based on German government bonds. The values shown are monthly means (weighted with outstanding volumes) of daily yields of bonds with a remaining duration of more than four years. The solid line shows the decreasing trend. Since bonds have fixed repayment prices (normally 100 %), the falling trend cannot result from rising prices. Instead, the main reason <?page no="46"?> 46 3 BONDS 1990 1995 2000 2005 2010 2015 2020 0 1 2 3 4 5 6 7 % Fig. 3.5 Development of coupon rates of government bonds in Germany. Source: Time series portal of the Deutsche Bundesbank: Money and capital markets > Interest rates and yields > Prices and yields of listed Federal securities (per ISIN) > Yields. has been a decrease in coupon rates. Fig. 3.5 illustrates this with coupon rates of German government bonds. Each point in the figure represents the coupon rate of a bond emitted in the corresponding month. 3.3 Government bond spreads This section discusses differences in the yields of government bonds. As an illustration, Fig. 3.6 compares the yields of 10-year bonds emitted by the German and the Italian government, respectively. Obviously, significant differences developed since about 2009. How can we understand the processes generating spreads? Since objective conditions (as, e.g., the indebtedness of a government) cannot directly influence bond prices, one has to start from the actors involved: firstly, the emittents of bonds who determine durations, coupon rates and repayment prices; then the buyers of bonds on the primary market whose purchases determine the emission price and thereby the initial yield; and finally, buyers and sellers on the secondary market whose activities lead to subsequent changes of prices. <?page no="47"?> 3.3 GOVERNMENT BOND SPREADS 47 2000 2005 2010 2015 2020 0 2 4 6 8 DE IT % Fig. 3.6 Yields of 10-year bonds emitted by the German government (DE) and by the Italian government (IT). Values relate to the last trading day of each month. Source: Historical data portal of de.investing.com. Fig. 3.7 compares a German and an Italian government bond. 2 The German bond, which has a duration of 10 years, was emitted on January 29, 2014, the Italian bond, which has a duration of 10.5 years, was emitted on March 1, 2014. While the repayment price is 100 % in both cases, the coupon rates are significantly different: the German bond provides 1.75 %, the Italian bond 3.75 %. The initial yield also depends on the emission price, which was 99.74 % for the German bond and 103.11 % for the Italian bond entailing initial yields of 1.78 and 3.44 %, respectively. So there is a simple answer to the question of why the initial yield is significantly higher in the Italian case: mainly because of the higher coupon rate. As shown in Fig. 3.7, the development of subsequent prices does not contribute much to differences in yields. Also, the differences in yields shown in Fig. 3.6 are mainly a result of different coupon rates. Fig. 3.8 shows that the coupon rates of the Italian bonds are continuously higher than the German coupon rates. This also entails much higher payments of interest by the Italian gov- 2 DE0001102333 (time series portal of the German bundesbank: BBK01.WT4177) and IT0005001547 (borse.quifinanza.it/ borsa-italiana/ titoli-stato). <?page no="48"?> 48 3 BONDS 2014 2015 2016 2017 2018 2019 100 105 110 115 120 125 IT DE % Fig. 3.7 Prices (at the beginning of each month) of a German and an Italian government bond, which have been emitted in 2014. 2008 2010 2012 2014 2016 2018 2020 0 1 2 3 4 5 6 DE IT % Fig. 3.8 Coupon rates of 10-year government bonds in Germany and Italy. Coupon rates of the German bonds have been taken from Fig. 3.5; coupon rates of the Italian bonds have been downloaded from www.bonboard.de. ernment. The total emission volume of the 20 Italian bonds referred to in Fig. 3.8 is 415.3 billion Euro and requires a mean interest of 3.5 %. The emission volume of the German bonds amounts to 799 billion Euro and requires a mean interest of 2.5 %. <?page no="49"?> 3.4 FINANCING OF GOVERNMENT DEBT 49 2008 2010 2012 2014 2016 2018 2020 0 1 2 3 4 5 6 7 % Fig. 3.9 Yields of Italian government bonds (10 - 10.5 years) taken from Fig. 3.6, and coupon rates of newly emitted bonds taken from Fig. 3.8. What determines coupon rates? We do not have information about the decision processes by which governments decide about acceptable coupon rates. It is plausible, however, that actual yields of bonds with a similar duration are used to provide an orientation. The data for Italy (as well as for Germany) supports this assumption. The dashed line in Fig. 3.9 shows yields of Italian government bonds (already shown in Fig. 3.6). The crosses, taken from Fig. 3.8, show the coupon rates of newly emitted bonds. Obviously, there is a close relationship. So one can also conclude that the development of bond prices on secondary markets can contribute, mediated by decisions about coupon rates, to the development of spreads. 3.4 Financing of government debt As shown in Fig. 3.1, the indebtedness of governments in the euro area has massively grown. In this section we argue that an important reason for this development is the ability of banks to finance state expenditures with their own deposit money. Mediation of expenditures and taxes. We begin by considering how banks mediate transactions involving the government. We <?page no="50"?> 50 3 BONDS presuppose the institutional setting described at the beginning of Section 2.1, and in addition assume that the central bank is not permitted to directly buy bonds from the government, as is the case for example in the euro area. There are then two money circuits, as depicted in Fig. 2.1, without arrows directly connecting the central bank and the government. For the first money circuit, which starts from the central bank, we use the notation M ∗ = M ∗ g + M ∗ b (3.4) where the two summands denote, respectively, the money in the accounts of the government and the banks. For the second money circuit it suffices to use the notation M to denote the stock of deposit money held by nonbanks. Note that there is no stock of money for the central bank and the private banks. Instead, M ∗ and M contribute, respectively, to their liabilities. We now consider transactions between the government and nonbank units. We begin with government expenditures and then consider taxes. (1) We assume that the government intends to pay an amount X to a nonbank unit U . The transaction is mediated by a bank where U has an M -account. So, eventually, the bank must increase the account by X, which entails: 3 M += X. The bank can do this with selfgenerated deposit money but will require an equal amount from the government. So the government must ask the central bank to organize an exchange: M ∗ g −= X and M ∗ b += X (3.5) There are, of course, a huge number of similar transactions on any given day. If, at the end of a day, the government’s M ∗ g -account or the consolidated M ∗ b -account of the banks is negative, the final settlement requires that the institution with a negative account must borrow money from other institutions including the central bank. In any case, the bank that organized the transaction eventually has a 3 We use += and − = to mean, respectively, “increased by” and “decreased by”. <?page no="51"?> 3.4 FINANCING OF GOVERNMENT DEBT 51 claim against the government, which equals its liability created by increasing U ’s account. (2) We now consider the payment of taxes by a nonbank unit U . The process starts with U ’s asking the bank, where U has an M -account, to pay an amount X to the government: M −= X. In addition, an exchange M ∗ b −= X and M ∗ g += X (3.6) must take place. We note that this is possible even if the bank does not have sufficient reserves at the point in time when the exchange takes place. It is only by the end of the day that the clearing and settlement process described above must be completed. Eventually, there is a reduction in the bank’s balance sheet: both its liability against U and its M ∗ -account reduce by X. Further questions arise concerning the financing of the settlement process. Yet, the above discussion already allows three conclusions: a) Government expenditures do not require previous receipts of taxes. b) Payments of taxes do not require previous government expenditures. c) Payments of taxes increase the government’s M ∗ -account and, in this sense, provide funds for expenditures. Debt-based government expenditures. There are two financing problems for the government. A short-term problem concerns the daily settlement. This problem occurs when, at the end of a day, M ∗ g is negative and the government must borrow money for the settlement. We will assume that this problem can be solved with short-term loans, which—depending on the institutional setting—are available from the central bank and/ or private banks. Another problem concerns the financing over a longer period of time. We refer to years indexed by t. X t denotes the expenditures made by the government in the year t. Financing requires an inflow to M ∗ g which suffices for these expenditures. There are two sources. <?page no="52"?> 52 3 BONDS First the taxes the government receives in the year t, which will be denoted by Y tx t . The second source is debt. So we may write: X t = Y tx t + Y debt t (3.7) where Y debt t denotes the required money for debt-based expenditures. In order to discuss the financing of Y debt t , we presuppose an institutional setting characterized by two conditions: (1) Y debt t is financed by the emission of bonds; and (2) on the primary market, only banks—not the central bank—are permitted to purchase government bonds. These conditions characterize, for example, the situation in the euro area. Of course, after being initially purchased by banks, government bonds can be sold to other institutions. Fig. 3.10 provides information about the euro area. We assume that the quantity of the emitted bonds is calculated in a way that it can finance net expenditures Y nexp t . Then, if bonds have a duration of m periods, one can use the formula Y debt t = Y nexp t + r m ∑ l =1 Y debt t − l + Y debt t − m (3.8) where r is the rate of interest (which, for simplicity, is assumed constant) and Y debt t − m is the repayment of previously emitted bonds. The net borrowing (new debt) is Y debt t − Y debt t − m = Y nexp t + X int t (3.9) where the second summand on the right-hand side, X int t , denotes the interest which must be paid. Banks’ financing of government bonds. We now show that banks can finance the government bonds, which they eventually own, with their own deposit money. For developing the argument we assume that the financing begins with banks borrowing the required money from the central bank: M ∗ b += Y debt t . This money is then used to buy the bonds from the government: M ∗ b −= Y debt t and M ∗ g += Y debt t (3.10) <?page no="53"?> 3.4 FINANCING OF GOVERNMENT DEBT 53 2014 2015 2016 2017 2018 2019 2020 0 1000 2000 3000 4000 5000 6000 7000 8000 billion Euro Remainder Banks (MFI) Insurance companies, pension funds Other financial corporations Central bank Fig. 3.10 Amounts of outstanding government bonds in the euro area held by the specified institutions. The remainder at the bottom includes: non-financial firms, private households, not-for-profit organizations, state institutions and a very small number of not sectorized institutions. Source: https: / / sdw.ecb.europa.eu/ browse.do? node=9691130. The banks now own the bonds, and we assume that fractions α and β are sold, respectively, to the central bank and to nonbank units. This entails: Debts of the banks = (1 − α) Y debt t and M −= β Y debt t (3.11) The government then spends the money it has received from selling the bonds. For simplicity, we assume that the complete amount is <?page no="54"?> 54 3 BONDS 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 10 20 30 40 50 60 Increase of banks’ bonds Banks’ reserves Banks’ liabilities β Fig. 3.11 Illustration based on (3.17) with α = 0.2. spent in the current period t, and the fractions α and β remain constant across time. So the central bank receives α (Y debt t − m + X int t ). The remainder is mediated by banks: M ∗ b += Y debt t − α (Y debt t − m + X int t ) = (1 − α) Y debt t + α Y nexp t (3.12) After the repayment of the remaining debts, the increase in banks’ reserves is ∆M ∗ b = α Y nexp t . Since payments of the government include repayments of bonds, the assets of the banks have increased by: Bonds = (1 − α − β) (Y debt t − Y debt t − m ) (3.13) Reserves = α Y nexp t (3.14) On the other hand, banks must create deposits that equal the receipts of nonbanks: M += Y nexp t + β (Y debt t − m + X int t ) (3.15) Taking into account the previous reduction of M (see (3.11)), the final increase in banks’ liabilities against nonbanks is ∆M = (1 − β) Y nexp t (3.16) <?page no="55"?> 3.4 FINANCING OF GOVERNMENT DEBT 55 which is less than the increase on the banks’ asset side. The difference equals (1 − α − β) X int t , that is, the interest received by the banks. Example. To illustrate, we use a numerical example: Y debt t (100) = Y nexp t (60) + Y debt t − m (30) + X int t (10) (3.17) If α = 0.2 and β = 0.5, the asset side of the banks has increased by 21 (bonds) + 12 (reserves). On the other hand, their liabilities have increased by 0.5 · 60 = 30. The difference equals the interest received by the banks. The following table depicts the outcome as a balance sheet: Assets α Y nexp t = 0.2 · 60 = 12 (1 − α − β) Y debt t = (1 − 0.2 − 0.5) 100 = 30 −(1 − α − β) Y debt t − m = −(1 − 0.2 − 0.5) 30 = −9 Liabilities (1 − β) Y nexp t = (1 − 0.5) 60 = 30 (1 − α − β) X int t = (1 − 0.2 − 0.5) 10 = 3 Fig. 3.11 illustrates how the outcome depends on β. Conclusion. Using “financing” to mean “providing money”, in the presupposed framework only banks finance government debts. Neither the central bank nor the nonbank units contribute through purchasing bonds on secondary markets. One may say that the central bank finances banks’ purchases of government bonds. At the end of the period, however, the borrowed money has been paid back; and there is no longer an increase in M ∗ that can be attributed to financing government debts. A lasting increase in M ∗ only results from the central bank’s purchasing of bonds from private banks, and serves to supply banks with reserves. 4 If α = 0, debt-based government expenditures simply have two effects: an increase in government bonds 4 This statement assumes that the interest, which the central bank receives, does not flow back to the government. If it does, the backflow formally increases M ∗ . <?page no="56"?> 56 3 BONDS 1990 2000 2010 2020 2030 2040 2050 Fig. 3.12 Temporal placement of 55 German government bonds. owned by banks and nonbanks, and an increase of the M -circuit according to (1 − β) Y nexp t . However, instead of viewing this backflow as contributing to financing the government, it seems preferable to think of a waiving of interest that allows the government to use a modified formula instead of Eq. (3.8): Y debt t = Y nexp t + r m ∑ l =1 (1 − λ t − l ) Y debt t − l + Y debt t − m (3.18) where λ t − l denotes the fraction of bonds, emitted in the period t − l, which are currently owned by the central bank. The financing of receipts from the actually emitted bonds is not affected by using this modified formula. <?page no="57"?> 3.4 FINANCING OF GOVERNMENT DEBT 57 2000 2005 2010 2015 2020 0 100 200 300 400 500 600 700 800 billion Euro Fig. 3.13 Development of the level of indebtedness. Illustration with German data. To illustrate some aspects of this discussion, we refer to 55 bonds emitted by the German government since the beginning of 1992 and for which there is information on the time series portal of the Deutsche Bundesbank. 5 In addition, we have used information from the Deutsche Finanzagentur which organizes the emissions. The bonds have durations of 10 or 30 years, the total emission volume amounts to about 1,029 billion Euro. Fig. 3.12 shows the temporal placement of the bonds. To describe our calculations, we use the following notations. V i denotes the emission volume, A i the coupon rate, τ i the starting, and τ ′ i the ending time (day) of the ith bond (i = 1, . . . , 55). For each point in time τ , the level of indebtedness can be calculated by ∑ τ i ≤ τ ≤ τ ′ i V i (3.19) where the summation covers all bonds which did not start later or ended earlier than τ . Fig. 3.13 shows this development. The first repayment took place in December 2012. Subsequently, we use years. 5 Retrieved at the end of November, 2018 from: Deutsche Bundesbank Time series portal: Money and capital markets > Interest rates and yields > Prices and yields of listed Federal securities (per ISIN) > Yields. <?page no="58"?> 58 3 BONDS Table 3.2 German government bonds: interest and repayments in the period 2012-2018 (in billion Euro). Net Increase Interest Year Emission Repayment borrowing of debt actual 5 %-coupon 2012 68.5 39.0 29.5 29.5 24.5 31.0 2013 54.0 38.0 16.0 45.5 24.0 32.5 2014 79.5 48.0 31.5 77.0 23.4 33.3 2015 46.0 44.0 2.0 79.0 22.9 34.9 2016 51.0 47.5 3.5 82.5 21.7 35.0 2017 63.0 39.0 24.0 106.5 19.9 35.1 2018 42.0 21.0 21.0 127.5 18.6 36.3 Total 404.0 276.5 127.5 127.5 155.0 238.1 In the year t, the emission volume is ∑ τ i ∈ t V i , and the sum of repayments is ∑ τ ′ i ∈ t V i . The difference is the net borrowing that year. In order to calculate the interest, we assume that coupons are paid at annual intervals and use, for the year t, the formula: ∑ τ i ≤ t − 1 ≤ τ ′ i V i A i / 100 (3.20) where t − 1 denotes the last day in the year t − 1. Table 3.2 shows these quantities for the years 2012-2018. The column “Increase of debt” contains the cumulated net borrowing. The last column shows hypothetical payments of interest based on the assumption of a constant 5 % coupon rate. Summing up these figures, the table shows: during a seven-year period the government has emitted a volume of 404 billion Euro. In the same period, repayments and interest amounted to 276.5 + 155 = 431.4 billion Euro. This is 27.5 billion larger than the emission volume. <?page no="59"?> 3.5 MODERN MONEY THEORY 59 3.5 Appendix: Modern Money Theory In this appendix to the previous section we refer to views proposed by the Modern Money Theory (MMT) to further clarify some distinctions between debtand tax-based state expenditures. (1) We begin by considering the MMT view on taxes. As explained for example by Tymoigne and Wray (2013), there is a simple framework: State M ∗ ←−−−→ Private sector (3.21) The state includes both a government and a central bank, and the private sector includes both banks and nonbanks. Transactions between the two sectors use central bank money. This means that when receiving taxes from the private sector, the government receives central bank money. However, using this simplistic scheme, MMT makes a further assumption: that the government and the central bank can be viewed as a single institution with a single balance sheet. This then leads to the following conclusion: Taxes cannot be a source of revenue in the consolidated balance sheet [of the government and the central bank]. They do not add monetary assets, they reduce liabilities. (Tymoigne and Wray 2013, p. 15) The presupposition of a consolidated balance sheet is, of course, counterfactual and can, therefore, be criticized (e.g., Fiebiger, 2012). As was shown in the previous section, given two separate balance sheets, taxes contribute to financing government expenditures. We also note that this remains true even if the government can autonomously decide about the extent of central bank money to be used for its expenditures. 6 (2) In response to critics of the consolidation of the government and 6 In Section 7.1 we consider a model that allows comparing financing government expenditures with bonds and with autonomously created central bank money. <?page no="60"?> 60 3 BONDS the central bank into a single unit, Tymoigne and Wray (2013, p. 30) considered a setting in which both institutions are separate units: The question [then] becomes how the Treasury acquired the deposits it has in its account at the central bank. In the current institutional framework, the apparent answer is through taxation and bond offerings. While usually economists stop here, MMT goes one step further and wonders where the receipts of taxation and bond purchases came from; the answer is from the central bank. This must be the case because taxes and bond offerings drain CB currency so the central bank had to provide the funds (as it is the only source). The logical conclusion is then that CB currency injection has to come before taxes and bond offerings. We find the argumentation misleading and think that the mistake is due, now, to a simplistic conception of the private sector, which ignores the distinction between banks and nonbanks, and the role played by banks’ capability to create deposit money. This leads the authors to consider only the money circuit starting from the central bank and to ignore the second one starting from private banks (see Fig. 2.1). 7 Consider this example: A bank provides a loan to a firm, which uses it to pay wages. Out of these wages must be paid taxes. Corresponding to the payment of these taxes there is no prior injection of central bank money into the private sector. So one cannot conclude that an injection of central bank money is required before private units can pay taxes. Obviously, wage earners can pay taxes out of their wages, that is, with money created by banks. Central bank money is only needed subsequently when the taxes are to be transferred to the government. However, as was discussed in the previous section, since also government expenditures are mediated by banks, there will always be sufficient reserves for making the transfer possible. 7 This disregard can well be seen, for example, in a paper by Fullwiler, Kelton, and Wray (2012), which explicitly refers to the French-Italian circuit approach but only considers the circulation of central bank money. <?page no="61"?> 3.5 MODERN MONEY THEORY 61 The example shows that separating the two money circuits is important. Contrary to what the above quotation suggests, the tax payments of nonbanks do not originate in the M ∗ -circuit but in another one organized by banks. This means that the payment of taxes by nonbanks does not depend on a previous injection of central bank money into the private sector. 8 Moreover, the transfer of nonbanks’ taxes to the government account in the M ∗ -circuit does not “simply destroy them” (Tcherneva 2006, p. 80). The money received would only be destroyed if it flows to the central bank. However, much more likely is its use for new expenditures entailing that it flows back to banks. (3) We now consider debt-based government expenditures that exceed the receipts from taxes. Referring to the simple framework (3.21), Tymoigne and Wray (2013, p. 17) offer two statements: Usually the domestic private sector desires to net save (i.e. to accumulate net worth beyond the accumulation of real assets) so the government must be in deficit. MMT argues the fiscal position of the government sector is ultimately driven by the desired net financial accumulation of the non-government sectors. Both statements are misleading in our view. (a) Due to simple accounting, positive net savings of the private sector imply negative net savings by the state. However, only individual units, not the private sector, can have the desire for accumulating financial wealth. In fact, it is easily possible that a subset of private units accumulate financial wealth without requiring a state deficit. Think, for example, of a public company offering new shares, which are then bought by other private units. (b) Also the second statement is misleading. Government debt comes 8 This critique also applies to Parguez (2002) who, like MMT, does not distinguish between the two circuits and (therefore) believes that the state must first, via expenditures, “provide households with enough money to meet their tax commitments” (p. 89). <?page no="62"?> 62 3 BONDS into being when governments decide to offer bonds and other institutions decide to buy them. So one has to distinguish between the two settings, which we have considered previously. - If government bonds are initially bought by the central bank, government debt obviously does not originate from the desire of private units to accumulate financial wealth. - If initially bought by private banks, one might say that these banks, which belong to the private sector, contribute to generating government debt. Of course, there could be good reasons for debt-based government expenditures, but that is not the content of the cited statement. If Tymoigne and Wray had said that the government should rule debts to support private units’ accumulation of financial wealth, that would be a debatable normative statement. However, in its actual formulation, the statement makes a causal claim, and it is this claim that we dispute. In fact, if there is a causal relationship, it is the other way around: government’s debt-based expenditures increase nonbanks’ holding of money created by banks and thereby motivate its use for financial investments. This will be further discussed in Section 7.1, where we argue that debt-based government expenditures are an important driving force of financialization. <?page no="63"?> 4 Tradable shares This chapter considers a second basic form of financial capital: tradable shares (stock) of public companies. We begin with data illustrating the growth of stock. We then argue that stock yields have an essentially speculative nature, and we use a simple model to illustrate the argument. Then we extend the model to take into account expectations about dividends. Finally, we continue to discuss the distinction between real yields, resulting from dividends and realized price gains, and virtual yields which can only be realized by selling shares. 4.1 Some data Like bonds, most shares of stock come into being on a primary market where they find, for the first time, a buyer. 1 Afterwards, they can be traded on secondary markets. One has to distinguish between the nominal and the market value. The nominal value is determined by the emitting company, for example, 2 Euro per share. If then the company sells 1 million shares of stock, the registered capital (or its increase) amounts to 2 million Euro. The market value is the actual price at which the stock is purchased and afterwards traded. The number of shares, multiplied by its price, is the market capitalization (shareholder value) of a company. The upper curve in Fig. 4.1 shows the development of the market value of stocks in the euro area. The ups and downs result primarily from changes in price. As shown by the lower curve in the figure, changes of the number and nominal value of stocks do not contribute significantly to the up and downs. This is also confirmed by data from the Deutsche Bundesbank. For example, the market value of outstanding shares in Germany was 1,614.4 billion Euro at the end of 2015, and 1,676.4 billion Euro at the end of 2016. While this is an increase of 62 billion, the market value of the stock newly emitted 1 We note they also can be distributed directly by a company to shareholders and the management. <?page no="64"?> 64 4 TRADABLE SHARES 1990 1995 2000 2005 2010 2015 2020 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 billion Euro A B Fig. 4.1 (A) Market value of stocks in the euro area (historical composition) at the end of each month. (B) Since January 1990 cumulated market value of net change (newly emitted stock minus redemptions). Source: https: / / sdw.ecb.europa.eu/ browse.do? node=bbn46. in 2016 amounts to only 4.41 billion. The difference results from the change in price of outstanding stock. Who owns shares? Paralleling Table 3.1 in Section 3.1, Table 4.1 provides information about Germany. Only registered shares of companies and investment fund shares belong to our definition of financial capital. However, also not registered shares can become a source of financial capital gains. <?page no="65"?> 4.2 SPECULATIVE PRICING 65 Table 4.1 Shares of German companies and investment funds at the end of 2019 (billion Euro). Source: Deutsche Bundesbank, Statistical Series Financial Accounts June 2020. Company shares Investment fund registered not registered shares owned emitted owned emitted owned emitted Banks, central bank 25.5 29.5 161.4 475.4 188.7 2.1 Financial services 109.2 62.7 102.3 47.1 37.8 − Investment funds 497.9 − 84.6 − 521.3 2443.7 Insurance companies 28.1 165.5 271.6 172.8 1238.4 − Nonfinancial firms 397.3 1692.6 1730.7 1415.5 189.9 − State institutions 72.9 − 555.3 − 42.7 − Households 359.2 − 343.6 − 680.3 − Nonprofit organ. 15.0 − − − 88.6 − Rest of the world 1106.8 661.6 573.4 1712.2 194.2 735.9 Total 2611.9 2611.9 3823.0 3823.0 3181.8 3181.8 4.2 Speculative pricing For defining yields of tradable shares, one can use the same formula (3.1) that was used in Section 3.2 for bond yields: r τ, ∆ = P τ +∆ − P τ + A ∆ P τ (4.1) P τ and P τ +∆ now record the share’s market price at points in time τ and τ + ∆, respectively, while A ∆ records dividends whose payment depends on the circumstances and cannot safely be anticipated. A more important difference consists in the fact that there is no definite time-line, which results from a fixed duration and repayment price as there is with bonds. Consequently, with shares there is also no inverse relationship between market price and yield. Instead, the formula suggests that rising stock prices can easily lead to rising yields. This is important to understand the processes that generate stock prices: these prices result solely from the expectations of the actors buying and selling stock. If these actors believe that an increase in stock prices (subsequently called “price gains”) is valuable in the same <?page no="66"?> 66 4 TRADABLE SHARES r τ, ∆ yield for the period ∆ A i,t dividend paid by U i in period t P i,t stock price on the day when the dividend was paid r i,t annual yield in the year t r p i,t the part due to price changes r d i,t the part due to dividends V(x) variance of x Cov(x, y) covariance of x and y way as dividends, 2 speculative pricing can also seem like a source of value creation. Illustration. To illustrate the yield formula (4.1), we use data on dividends and stock prices from 289 public companies in Germany during the years from 2005 to 2019. 3 For each company U i , we know the following for some of these years: - A i,t : the dividend paid in year t. - P i,t : the stock price on the day when the dividend was paid. 4 We consider yields r i,t = r p i,t + r d i,t . The first part is due to price gains and losses: r p i,t = (P i,t − P i,t − 1 )/ P i,t − 1 (4.2) The second part is due to dividends: r d i,t = A i,t / P i,t − 1 (4.3) 2 A formulation endorsing this view can be found in an often cited paper by Miller and Modigliani: “ ‘Rational behavior’ means that investors always prefer more wealth to less and are indifferent as to whether a given increment to their wealth takes the form of cash payments or an increase in the market value of their holdings of shares” (1961, p. 412). 3 The data was retrieved from Yahoo Finance on July 9, 2019. 4 If dividends were paid on two or more days, we use the latest day for the sum of payments. <?page no="67"?> 4.2 SPECULATIVE PRICING 67 0 5 10 0 5 10 15 20 25 -100 -50 0 50 100 150 0 5 10 15 20 25 30 % % % % Fig. 4.2 Frequency distribution of r p i,t (lower part) and of r d ı ,t (upper part). For each of the two parts, the number of observations is n = 2291. 5 Fig. 4.2 shows a frequency distribution of r p i,t in the lower part and of r d i,t in the upper part (both in %). Mean values are 12.4 and 3.2 %, respectively. Obviously, most of the dispersion in the yields is due to price gains and losses. Only a very small part results from dividends. This can 5 An observation is available if the stock price is known for two consecutive years. <?page no="68"?> 68 4 TRADABLE SHARES 2005 2010 2015 2020 -40 -30 -20 -10 0 10 20 30 40 50 % ¯ r p t ¯ r d t t Fig. 4.3 Development of the mean values defined in (4.5). also be shown by decomposing the variance: V(r i,t ) ︸ ︷︷ ︸ 1761 . 7 = V(r p i,t ) ︸ ︷︷ ︸ 1718 . 7 + V(r d i,t ) ︸ ︷︷ ︸ 9 . 7 + 2 Cov(r p i,t , r d i,t ) ︸ ︷︷ ︸ 16 . 6 (4.4) This finding supports the view that yields of tradable shares mainly result from speculative transactions. Correspondingly, one should expect that the speculative part of the yield exhibits large temporal fluctuations. This is confirmed by Fig. 4.3, which shows the development of the mean values: ¯ r p t = ∑ i r p i,t / n t and ¯ r d t = ∑ i r d i,t / n t (4.5) where n t records the number of observations in year t. A simple model of speculative pricing. To demonstrate how speculation can lead to rising stock prices, we use a simple model. There are 10 different stocks (k = 1, . . . , 10), each consisting of 100,000 shares, and there are 1, 000 actors (i = 1, . . . , 1000) starting with identical portfolios consisting of 100 shares of every individual stock. The market develops in a sequence of periods (e.g., days) indexed by t = 0, 1, 2, 3, . . .; P k,t is the price of stock k at the end of the period t. The initial price of all shares is P k, 0 = 20 Euro. <?page no="69"?> 4.2 SPECULATIVE PRICING 69 P k,t price of stock k at the end of the period t N o k,t total offer of stock k in the period t N d k,t total demand of stock k in the period t M i,t balance of i’s account at the end of t DA t measure of inequality defined in (4.8) There are two kinds of actors. 100 actors do not change their portfolio, whereas 900 speculators aim to increase the market value of their portfolio by selling and purchasing shares. In the present version of the model, we assume that the speculators, over each period, aim to buy 10 shares of one stock and to sell 10 shares of another stock. The shares are selected randomly (with equal probability) from the actual portfolios. So there is, within period t, for each stock k a total offer N o k,t and total demand N d k,t . Finally, there is a simple pricing rule. Actors who want to sell a share of stock k decide on a minimum price, and they decide on a maximum price if they want to buy a share of stock k. We assume that all actors use the actual price P k,t − 1 as the minimum selling price and a price P k,t − 1 α as a maximum purchasing price. So the pricing rule simply is P k,t = { P k,t − 1 α if N d k,t > N o k,t P k,t − 1 otherwise (4.6) We also assume α > 1. The rule entails that stock prices cannot decrease. To illustrate, we use α = 1.02. One then gets the following example of a randomly generated process. The mean stock price increased from initially 20 to a mean value of 22.04 Euro at the end of the 10th period. Correspondingly, the mean market value of the portfolios increased by about 10 % to a mean value of 22,044 Euro. This is equally true for speculators and for actors who do not change their portfolios. Virtual and real (monetary) gains. In contrast to dividends, a price gain is a virtual gain, which only exists as an increased valuation <?page no="70"?> 70 4 TRADABLE SHARES of a share. 6 In order to realize a price gain, the share must be sold and thereby gets a new owner. In fact, the source of the realized price gain is the money paid by the buyer of the share. Although our model does not take into account dividends, there also is a source of real gains and losses resulting from selling and buying shares. To make this explicitly visible, we set up, for each actor i, an account recording the balance of gains and losses of the transactions. M i,t denotes the balance at the end of period t; at the beginning M i, 0 = 0. Since transactions only take place among speculators, the equation N ∑ i =1 M i,t = 0 (4.7) holds, showing that gains are paid by losses. In our example, at the end of the 10th period, a part of the speculators are indebted for the amount of 76,007 Euro to the rest of speculators. However, the mean debt is only 84 Euro, which is only a small fraction of the mean price gain of 2,044 Euro. The maximum debt is 641 Euro and occurred to an actor with a price gain of 2,737 Euro. The financing of transactions seems easily possible for a bank that accepts portfolios as securities for loans. Rising inequality. We assume that only speculators buy and sell shares. As shown by Eq. (4.7), the sum of their gains equals the sum of their losses. This conceals, however, the rising inequality resulting from the iteration of the zero-sum game. A suitable measure of the degree of this inequality starts from the absolute differences between M i,t and M i ′ ,t for each selection of two actors i and i ′ , and then takes the mean: DA t = ∑ n − 1 i =1 ∑ n i ′ = i +1 | M i,t − M i ′ ,t | n (n − 1)/ 2 (4.8) where n = 900 within the present application. Fig. 4.4 shows the development of this measure over 30 periods. 6 Analogously, one can think about ‘virtual losses’ resulting from decreasing stock prices. <?page no="71"?> 4.3 DIVIDENDS 71 0 10 20 30 0 100 200 300 400 500 DA t (Euro) t Fig. 4.4 Development of the measure of inequality defined in (4.8). 4.3 Dividends In the previous section, we used a model where offered and demanded shares are randomly selected. Investors mostly follow strategies and use a variety of information which, in their view, seems relevant. The strategies depend mainly on whether investors are primarily interested in price gains or in dividends. The present section considers an extension of the previous model in which there is also a group of actors primarily interested in future dividends. Discounted expectations. Notations are as before: periods are indexed by t, stocks by k, and actors by i; P k,t is the price of a share of stock k at the end of period t. We assume that actors can form expectations about future dividends. Dividends are only paid in larger time intervals (most often years). If, for example, the periods of the model are days, a stock k will not provide a dividend in most of the periods. We therefore use the following notation: A ∗ ik,t,j denotes the dividend of a share of stock k, which the actor i expects for the jth year (j = 1, 2, . . .) following the period t. How can these expectations be used for the evaluation of shares? A widespread approach is based on discounting expectations. A first <?page no="72"?> 72 4 TRADABLE SHARES part concerns expected gains from dividends. For a number of ∆ years, using a discount rate r i,t , the current value of expected dividends is A ∗∗ ik,t, ∆ = ∆ ∑ j =1 A ∗ ik,t,j (1 + r i,t ) − j (4.9) A second part results from the discounted expected market value of the share at the end of ∆ years: P ∗ ik,t, ∆ (1 + r i,t ) − ∆ (4.10) The sum of both components can be interpreted as an evaluation of the current value of a share of stock k by the actor i. Referring to a group of actors (i = 1, . . . , n 1 ), it would be possible to think of a mean evaluation: 1 n 1 n 1 ∑ i =1 (A ∗∗ ik,t, ∆ + P ∗ ik,t, ∆ (1 + r i,t ) − ∆ ) (4.11) There is, however, no immediate relationship with stock prices. The subjective evaluations of individual actors can only influence stock prices when used in their decisions to offer and demand shares. How stock prices change then depends on the resulting order books. Decisions about a time horizon. In the previously described approach, evaluations significantly depend on the time horizon ∆. To illustrate, we consider an actor i who aims to compare stocks k and k ′ . The time horizon is ∆ = 10 years, the discount rate is 2 %, and the actor expects the following dividends: t : 1 2 3 4 5 6 7 8 9 10 k : 10 10 0 0 0 0 0 0 0 0 k ′ : 0 0 0 0 5 5 5 5 5 5 Assuming that the actor expects identical stock prices at the end of the time horizon, it suffices to consider the expected dividends. <?page no="73"?> 4.3 DIVIDENDS 73 Discounted values are A ∗∗ ik,t, ∆ = 19.4 and A ∗∗ ik ′ ,t, ∆ = 25.4. It does not follow, however, that the actor should prefer k ′ to k. A rational decision requires that one first decides about a time horizon. In our example, the comparison would obviously be different if the actor had used a time horizon of two years. Since shares can be sold at any time, it seems sensible even to take into account only expectations about dividends and prices in the immediately following period. Moreover, the longer the time horizon the more uncertain the expectations until they eventually become meaningless. We, therefore, assume for our model that actors only take into account expectations about the next payment of dividends. These expectations will be denoted by A ∗ ik,t . How can expectations be formed? Due to their large fluctuation, information about past dividends is not very helpful for forming expectations about next dividends of individual stocks. More important is actual information about the economic situation of a corporation. The following picture provides an orientation. ✲ t t + I k,t I k,t +1 I k,t +2 · · · payment of dividend t + denotes the period in which the next dividend is paid. (To simplify, we assume that all payments take place in the same period.) In each period t, until t + , new information can arrive which we record by variables I k,t . As a very simple example, we assume that there only are three values: I k,t =  1 a hint on a rising dividend −1 a hint on a falling dividend 0 no hint on a change (4.12) The notation implies that this information is available for all actors. One should assume, however, that actors use the information differ- <?page no="74"?> 74 4 TRADABLE SHARES ently. In our numerical illustration, we use the following scheme: A ∗ ik,t = A ∗ ik,t − 1 / (1 − δ i ) if I k,t = 1 A ∗ ik,t = A ∗ ik,t − 1 (1 − δ i ) if I k,t = −1 (4.13) where δ i is a parameter depending on the actor i. This sequential approach seems sensible also because the amount of dividends is not determined in periods before t + . Nevertheless, one can assume that mean expectations of actors eventually come close to the realized dividend: 1 n 1 n 1 ∑ i =1 A ∗ ik,t −→ A k,t + (t → t + ) (4.14) This assumption also simplifies the construction of a model because assumptions about realized dividends can be introduced indirectly by assumptions held about the information variables I k,t . Extension of the previous model. We start from the model described in the previous section. As before, there are 10 different stocks (k = 1, . . . , 10) each consisting of 100,000 shares, and there are N = 1000 actors (i = 1, . . . , 1000) starting with identical portfolios consisting of 100 shares of stock each. The market develops in a sequence of periods (e.g., days) indexed by t = 0, 1, 2, 3, . . . P k,t is the price of stock k at the end of the period t. The initial price of all shares is P k, 0 = 20 Euro. The difference is that there are now three groups of actors: G1 n 1 = 600 actors who are primarily interested in dividends, G2 n 2 = 300 actors who are primarily interested in price gains, G3 n 3 = 100 actors who do not change their portfolios. It is assumed that, in each period, actors in G1 and G2 aim to buy 10 shares of one stock and aim to sell 10 shares of another stock. As before, actors in G2 randomly decide about the offered and demanded shares. For actors in G1 we assume that their decisions are based on expectations about dividends, which will be paid in period t + = 20. <?page no="75"?> 4.3 DIVIDENDS 75 Initially, all actors have an identical expectation A ∗ ik, 0 = 2. In subsequent periods, the actors use values of the information variables I k,t for modifying their expectations according to the scheme (4.13). The individual parameters δ i are uniformly distributed random numbers in the interval from 0 to 0.1. Assumptions about the information variables are as follows: k 1 2 3 4 5 6 7 8 9 10 Pr(I k,t = 1) 0.28 0.26 0.24 0.22 0.20 0.18 0.16 0.14 0.12 0.10 Pr(I k,t = − 1) 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 To simplify the model we also assume that all actors use the same discount rate (zero), and they do not expect a significant change in stock prices until the payment of dividends. They, therefore, base their decisions simply on the size of β ik,t = A ∗ ik,t / P k,t − 1 (4.15) In each period, actor i demands shares with the highest β ik,t and offers shares with the lowest β ik,t . For generating price changes, we use the rule (4.6) with α = 1.02, which entails that also in the present version of the model (subsequently Version 2) stock prices cannot decrease. A random realization of the model for periods t = 1, . . . , 20 leads, for example, to a mean increase in stock prices from 20 to 24.5 Euro. However, because actors in G1 use information, which is different for the 10 stocks, their prices now develop differently. This is illustrated in Fig. 4.5. Since the generation of prices depends on expectations about future dividends, the prices do not causally depend on the eventually paid dividends. Assumptions about actually paid dividends are, however, needed for allowing comparisons between the three groups of actors. According to (4.14), we assume that the dividends paid in period t = 20 equal the mean expectations of the actors in G1 within this period. In our example, the mean payment per actor is 1,949 Euro in G1, 1,903 Euro in G2, and 1,934 Euro in G3. Given our assumptions about the predictability of dividends, the differences appear quite small. Considering the results of random repetitions of the <?page no="76"?> 76 4 TRADABLE SHARES 0 1 2 3 4 5 6 7 8 9 10 20 25 30 Euro k Fig. 4.5 Prices of stock k = 1, . . . , 10 at the end of period 20 in a random realization of model Version 2. model shows that the variability of these figures is much larger than their differences. 4.4 Real and virtual gains We now continue with a discussion on the differences between real and virtual gains already begun in Section 4.2. To support the argument, we use a model in which actors aim to realize monetary gains, as large as possible, both from dividends and from price gains. Description of the model. The time framework is a sequence of days t = 1, . . . , 250 representing one year on the stock market. F pu is an index set for corporations whose shares are tradable on the stock market. In order to simplify notations, it is assumed that, on each day t, there is a single price P k,t for shares of the corporation U k (k ∈ F pu ). The index set of the units that can hold a portfolio is U . The number of shares of a corporation U k owned by a unit U i at the end of t is a i,k,t ≥ 0. The market value of U i ’s portfolio is V i,t = ∑ k ∈F pu a i,k,t P k,t <?page no="77"?> 4.4 REAL AND VIRTUAL GAINS 77 F pu index set of public companies a i,k,t number of shares of U k hold by U i at the end of t P k,t price of U k ’s shares at the end of t A k,t dividend paid on day t for a share of stock k V i,t market value of U i ’s portfolio at the end of t e i,t money which U i receives or pays on day t M i,t U i ’s account used for buying new shares Y i,t U i ’s account recording gains It is assumed that, on each day t, a unit only buys or sells shares of a single corporation. The number of shares is ∆ ∗ i,k,t { > 0 if U i aims to buy the shares < 0 if U i aims to sell the shares Decisions about these quantities take place at the beginning of each day and are recorded randomly in an order book. The realized quantities ∆ i,k,t are then determined to maximize sales. This entails the following changes in the portfolios: a i,k,t = a i,k,t − 1 + ∆ i,k,t The total amount of money which U i receives or pays on day t is e i,t = ∑ k ∈F pu a i,k,t A k,t − ∆ i,k,t P k,t where A k,t denotes the dividend paid on that day for a share of the company U k . In order to keep track of these flows, we use two kinds of accounts. M i,t stores money that can be used the next day for buying new shares. The initial value is M i, 0 = 1000. Y i,t stores the sum of net gains the unit has received until the end of day t from dividends and from selling shares. The initial value is Y i, 0 = 0. <?page no="78"?> 78 4 TRADABLE SHARES A net gain is considered that part of the inflow of money which exceeds a minimum value M i, min . In other words: if M i,t − 1 + e i,t > M i, min , the net gain is M i,t − 1 + e i,t − M i, min . Consequently, Y i,t = Y i,t − 1 + max{M i,t − 1 + e i,t − M i, min , 0} M i,t = min{M i,t − 1 + e i,t , M i, min } In contrast to the Y -account, the amount of money in the M -account can decrease, also below the minimum value, but cannot become negative. Illustration. To illustrate the model, we consider a simulation with 10 corporations and N = 1000 units. In the beginning, the units hold identical portfolios a i,k, 1 = 100 (k = 1, . . . , 10) and have identical M -accounts M i, 0 = 1000; the minimum value is M i, min = M i, 0 . The units randomly decide whether to buy shares (∆ ∗ i,k,t = 10) 7 or to sell shares (∆ ∗ i,k,t = −10). Also k is selected randomly from the set F pu . Initial stock prices are P k, 0 = 20 so that each portfolio has the market value V i, 0 = 20000. Beginning with day 1, prices are randomly changed: P k,t = P k,t − 1 (1 + ǫ k,t ) (4.16) where ǫ k,t is a random number normally distributed with µ = 0 and σ = 0.05. Finally, we assume that each share receives a dividend of 1 on the last day t = 250. Fig. 4.6 shows the relationship between net gains and market values of the portfolios at the end of the year (t = 250). As a comparison, one can think of a process without trading and stock prices that do not change. Then, at the end of the year, each unit still has the portfolio V i, 250 = 20000 and a gain from dividends amounting to Y i, 250 = 1000. The trading of shares, however, leads to substantial differences between the units. Some receive higher, others receive lower net gains. As shown by the figure, there is a negative correlation between net gains and the portfolio values. 7 If M i,t does not suffice to buy 10 stocks, ∆ ∗ i,k,t is determined as the maximum number that can be financed with M i,t . <?page no="79"?> 4.4 REAL AND VIRTUAL GAINS 79 18000 20000 22000 24000 26000 28000 30000 32000 0 1000 2000 3000 4000 V i, 250 Y i, 250 + M i, 250 − M i, 0 Fig. 4.6 Realized net gains and market values of portfolios at the end of the year (t = 250). Real and virtual yields. A unit’s yield until the end of the year can be expressed in the following way: r i = Y i, 250 + M i, 250 − M i, 0 V i, 0 + M i, 0 + V i, 250 − V i, 0 V i, 0 + M i, 0 (4.17) The denominator is the capital invested at the beginning of the year. The first summand represents a real yield because its numerator is the amount the unit has actually received from the investment. The second summand represents a virtual yield because its numerator is only a price gain resulting from a modified evaluation of the portfolio. The upper part of Fig. 4.7 shows a frequency distribution of the real yields varying between 0 and 18 %. In the lower part, the virtual yields vary between 0 and 50 %. Again, there is a strong negative correlation. In order to demonstrate that virtual yields are fictitious, in a sense, we now modify the model and assume that there is a rising trend of stock prices: P k,t = P k,t − 1 (1 + ǫ k,t ) + 0.04 (4.18) <?page no="80"?> 80 4 TRADABLE SHARES -2 0 2 4 6 8 10 12 14 16 18 0 5 10 15 -5 0 5 10 15 20 25 30 35 40 45 50 0 5 10 % % Fig. 4.7 Frequency distributions of real yields (upper part) and virtual yields (lower part). where, as before, ǫ k,t is a random number normally distributed with µ = 0 and σ = 0.05. Fig. 4.8 again shows distributions of the yields. While the distribution of real yields remains almost unchanged, the distribution of the virtual yields has dramatically changed. 8 However, these very high virtual yields are fictitious because they do not represent real gains (cash). 8 If instead of (4.18) one assumes a falling trend of stock prices, one gets an analogous result: while the distribution of real yields remains almost unchanged, the virtual yields become negative. <?page no="81"?> 4.4 REAL AND VIRTUAL GAINS 81 -2 0 2 4 6 8 10 12 14 16 18 0 5 10 15 40 45 50 55 60 65 70 75 80 85 90 95 100 105 0 5 10 % % Fig. 4.8 Frequency distributions of real yields (upper part) and virtual yields (lower part) resulting from a rising trend of stock prices. Inequality of gains. The gains at the end of the year consist of dividends and of realized price gains. The realized price gains are Y ∗ i, 250 = Y i, 250 + M i, 250 − M i, 0 − Dividend i, 250 (4.19) The mean value is zero. This shows that aiming to realize price gains is a zero-sum game. As already discussed in Section 4.2, this entails a substantial redistribution among the players. Fig. 4.9 shows the distribution of the realized price gains and losses as defined in (4.19). Again, the measure DA t defined in (4.8)—now with Y ∗ i,t instead of <?page no="82"?> 82 4 TRADABLE SHARES -1000 0 1000 2000 3000 0 5 10 15 % Y ∗ i, 250 Fig. 4.9 Frequency distribution of the realized price gains and losses defined in (4.19) generated with a model based on (4.16). M i,t —can be used to describe the rising inequality. The measure increases from zero at the beginning to the value of 778 by the end of the year. <?page no="83"?> 5 Investment funds Shares of investment funds can be bought on markets and, in many cases, redeemed when a shareholder wants. There are also funds whose shares can be traded on a stock exchange. In any case, such shares are a further basic form of financial capital. In many respects they are similar to shares of public companies. There is, however, one important difference: selling and buying shares of an investment fund always takes place on a primary market. In other words, whenever a fund sells a share, new financial capital is created. Investment funds, therefore, play an important role in the expansion of financial capital. In this chapter, we begin with providing some data on investment funds. We then use a simple model for showing that speculative gains can only result from a fund selling new shares or part of its assets. Finally we discuss exchange-traded funds (ETF) using an accumulating index fund as an example. 5.1 Some data There are open-end and closed-end funds. In both cases, the fund is organized by a firm that defines the investment rules and finances the fund by selling shares. Shares of open-end funds can normally be purchased and redeemed (possibly with some restrictions) at any time; shares of closed-end funds are sold during an initial offering and then are fixed for the fund’s lifetime. Legally, the assets of a fund are owned by the shareholders. However, as is the case with public companies, all relevant investment decisions are made by the managers of the firm that created and organize the fund. Assets can consist of financial capital (e.g., bonds and stock) or non-financial capital (e.g., real estate or firms owned by the fund). In any case, shares are to be considered financial capital, and an essential function of funds consists in their ability to transform any kind of capital into financial capital for shareholders. It was estimated that the market value of the assets of all investment funds worldwide amounted to about 37.1 trillion US-$ at the end of the first half of 2018 (Deutsche Bundesbank 2018, p. 84). <?page no="84"?> 84 5 INVESTMENT FUNDS 2010 2015 2020 0 5000 10000 15000 billion Euro Fig. 5.1 Development of the market value of the assets of open-end investment funds in the euro area (historical composition), values at the end of months. https: / / sdw.ecb.europa.eu/ browse.do? node=9691348. 2000 2005 2010 2015 2020 0 500 1000 1500 2000 Public funds Special funds Total billion Euro Fig. 5.2 Development of the market value of the assets of open-end funds in Germany. Source: Time series portal of the Deutsche Bundesbank Investment companies > open-ended investment companies > assets of mutual funds. Fig. 5.1 shows the growth in the market value of open-end investment funds across the euro area between 2008-2017. The mean increase was about 12 % per year. <?page no="85"?> 5.2 SPECULATION WITH FUND SHARES 85 Table 5.1 Information about open-end funds in Germany, November 2019. Source: Deutsche Bundesbank, Capital Market Statistics, Statistical Supplement 2 to the Monthly Report, November 2019. Public funds Special funds Number of funds 2731 4124 Total assets (billion Euro) 542.8 1825.8 thereof: Bank deposits 28.4 60.2 Bonds 118.0 954.4 Stock 231.1 258.7 Shares of investment funds 79.7 425.8 Liabilities 21.4 62.0 More detailed data is available from the Deutsche Bundesbank. The data distinguishes between two kinds of open-end funds. Socalled public funds (Publikumsfonds) whose shares can be purchased by anyone, and special funds whose shares can only be purchased by banks and nonbank institutional investors. Fig. 5.2 shows how the assets of these funds developed. Table 5.1 provides additional information about the number of funds and the composition of assets at the end of 2019. Note that liabilities are subtracted from the assets. 5.2 Speculation with fund shares There are two ways in which shareholders of an investment fund can achieve profits. Profits can result from payments made by the fund. Fig. 5.3 uses data from Germany for an illustration. One has to keep in mind, however, that not all funds make such payments. There are many accumulating funds which reinvest the gains received from their assets and from selling shares. Independent of whether a fund is accumulating or not, profits (and losses) can also result from speculation, which means that an investor buys shares in the hope that the shares, after some time, can be redeemed at a higher price. In the following, we use a simple model to show that speculative gains can only result from a fund selling new shares or part of its assets. This is true for both accumulating and not accumulating funds. <?page no="86"?> 86 5 INVESTMENT FUNDS 2000 2005 2010 2015 2020 0 1 2 3 4 5 Public funds Special funds % Fig. 5.3 Annual payments to shareholders divided by the annual average of the market value of assets belonging to open-end funds in Germany. Source: Time series portal of the Deutsche Bundesbank (Investment companies > open-ended investment companies); own calculations. In our model, we assume a fund which uses gains from its assets for payments to shareholders. This entails that speculative profits can only result from changes in the value of the fund’s assets. A simple model. The time framework is a sequence of periods t = 0, 1, 2, . . . (e.g., days). To allow simple notations, we assume an openend fund, which invests the money of shareholders in a single type of stock. 1) a t denotes the number of stocks that the fund owns at the end of the period t and p t denotes the stock price at that point in time. The market value of the fund’s asset is v t = a t p t . 2) n t records the number of investors holding shares of the fund at the end of the period t. It is assumed that each investor holds a single share for a fixed number of δ periods. The value of a share at the end of t is w t = v t / n t . 3) During t shares can be redeemed and new shares bought at the price w t − 1 . The number of investors buying a share in the period t will be denoted by d t (d t = 0 if t ≤ 0). It follows that the number <?page no="87"?> 5.2 SPECULATION WITH FUND SHARES 87 of redeemed shares is d t − δ and the total number of shares develops according to n t = max{ n t − 1 + d t − d t − δ , 0 }. 4) The amount of money, which the fund receives, or loses, in period t is ∆ t = w t − 1 (d t − d t − δ ). If ∆ t ≥ 0, redeemed shares can be paid from the money, which the fund has received from new shares, otherwise the fund must sell part of its assets. 5) It is assumed that, in period t, the fund can buy and sell stocks at the price p t − 1 . Assuming that ∆ t / p t − 1 is integral, the number of stocks held by the fund develops according to a t = a t − 1 + ∆ t / p t − 1 and the value of the fund’s assets develops according to: v t = a t p t = (v t − 1 + ∆ t ) p t p t − 1 Finally, we get: w t = w t − 1 p t p t − 1 (5.1) for the value of the fund shares. 6) An investor who has bought a share in the period t − δ leaves the fund in the period t with a gain or loss w t − 1 − w t − 1 − δ . Applying (5.1) recursively, one finds a simple result: w t − 1 − w t − 1 − δ = w t − 1 − δ ( p t − 1 p t − 1 − δ − 1 ) (5.2) If stock prices increased during the investor’s participation in the fund, he receives a gain, otherwise a loss. This result does not mean, however, that speculative gains result from increasing stock prices. Rising stock prices do not lead to an inflow of money. As far as possible, therefore, gains are paid with the money which the fund receives from selling new shares. Changing stock prices should be considered as a medium for a temporal redistribution between investors who enter and exit the fund in different periods. <?page no="88"?> 88 5 INVESTMENT FUNDS Table 5.2 w t −1 · w t −1 − t d t d t −1− δ n t a t p t v t w t w t −1 d t d t −1− δ w t −1− δ 0 0 0 0 0 10.0 0 5.0 1 10 0 10 5 10.2 51 5.1 50 0 0.0 2 10 0 20 10 10.4 104 5.2 51 0 0.0 3 10 0 30 15 10.6 159 5.3 52 0 0.0 4 10 0 40 20 10.8 216 5.4 53 0 0.0 5 10 0 50 25 11.0 275 5.5 54 0 0.0 6 10 10 50 25 11.2 280 5.6 55 55 0.5 7 10 10 50 25 11.4 285 5.7 56 56 0.5 8 10 10 50 25 11.6 290 5.8 57 57 0.5 9 10 10 50 25 11.8 295 5.9 58 58 0.5 10 10 10 50 25 12.0 300 6.0 59 59 0.5 11 0 10 40 20 10.0 200 5.0 0 60 0.5 12 0 10 30 15 10.0 150 5.0 0 50 −0.6 13 0 10 20 10 10.0 100 5.0 0 50 −0.7 14 0 10 10 5 10.0 50 5.0 0 50 −0.8 15 0 10 0 0 10.0 0 − 0 50 −0.9 545 545 0.0 Illustration. Table 5.2 shows a numerical illustration of the model. In each period, until t = 10, there are d t = 10 new shareholders, afterwards d t = 0. The length of stay is δ = 5 periods. The stock price increases from initially 10 to a value of 12 and afterwards falls back to the initial value. In the first period, shares can be bought at the price w 0 = 5. The total amount of money, which the fund receives from selling shares is 545, and the same amount is paid out. So, in this example, there is a zero-sum game. But this hides a temporal redistribution: investors who bought shares until period six achieved a gain, whereas investors who bought shares after that made a loss. If the inflow of money from selling shares does not suffice for paying redeemed shares, the fund must sell part of his assets. The money received from these sales depends on the actual stock prices, and so it is possible that the outflow of money exceeds the inflow. As an illustration, Table 5.3 shows a modification of the previous example in which the stock price, beginning in period 10, stays at <?page no="89"?> 5.3 EXCHANGE-TRADED FUNDS 89 Table 5.3 w t −1 · w t −1 − t d t d t −1− δ n t a t p t v t w t w t −1 d t d t −1− δ w t −1− δ 0 0 0 0 0 10.0 0 5.0 1 10 0 10 5 10.2 51 5.1 50 0 0.0 2 10 0 20 10 10.4 104 5.2 51 0 0.0 3 10 0 30 15 10.6 159 5.3 52 0 0.0 4 10 0 40 20 10.8 216 5.4 53 0 0.0 5 10 0 50 25 11.0 275 5.5 54 0 0.0 6 10 10 50 25 11.2 280 5.6 55 55 0.5 7 10 10 50 25 11.4 285 5.7 56 56 0.5 8 10 10 50 25 11.6 290 5.8 57 57 0.5 9 10 10 50 25 11.8 295 5.9 58 58 0.5 10 10 10 50 25 12.0 300 6.0 59 59 0.5 11 0 10 40 20 12.0 240 6.0 0 60 0.5 12 0 10 30 15 12.0 180 6.0 0 60 0.4 13 0 10 20 10 12.0 120 6.0 0 60 0.3 14 0 10 10 5 12.0 60 6.0 0 60 0.2 15 0 10 0 0 12.0 0 − 0 60 0.1 545 585 4.0 the constant price 12. The fund can then pay out a sum total of 585 and every participant achieves a gain. As the table shows, there is still a temporal redistribution. The example shows that an investment fund does not always work like a temporally extended zero-sum game. However, the model does not provide a complete answer to the question where the gains originate from. It simply assumes that there are sufficient buyers for the stock the fund aims to sell. 5.3 Exchange-traded funds Exchange-traded funds are open-end funds whose shares are tradable on a stock exchange. Fig. 5.4 (adapted from Deutsche Bundesbank, 2018) shows the construction. The emitter of the fund exchanges shares with authorized participants who serve as market makers for trading the fund shares on a stock exchange. According to the actual situation, they can redeem shares or buy additional shares from the <?page no="90"?> 90 5 INVESTMENT FUNDS Fig. 5.4 ✲ ✛ ✲ ✛ stock exchange authorized participants emitter of ETF ❄ ✻ buyer and seller emitter. Resulting from this construction, shares of the fund have a market value that can continuously change. Most ETF are index funds. As an example, we consider the iShares Core DAX UCITS ETF (DE) , which was emitted by the investment company BlackRock in December 2000 (ISIN: DE0005933931). 1 This fund intends to replicate the DAX performance index by holding a portfolio of stock corresponding to the DAX. The fund is accumulating, meaning, gains from dividends are not paid out to shareholders but reinvested. At the end of February 2018, the market value of the fund was 6.875 billion Euro. The price of a share was 98.26 Euro, and the number of shares was about 70 million. Fig. 5.5 shows how the price of shares developed since the beginning of 2005. Gains and losses. If an ETF is accumulating, shareholders can only achieve gains through redeeming shares. To illustrate, we use the development of prices shown in Fig. 5.5. n t denotes the number of new shares purchased on the day t. For simulating a process we assume: 2 n t = rnd (100 (1 + ǫ)) where ǫ is a random number uniformly distributed across the interval 1 Information about BlackRock can be found in Jakobs (2016) and R¨ ugemer (2018). 2 The operator rnd() means: rounded to the next integer. <?page no="91"?> 5.3 EXCHANGE-TRADED FUNDS 91 2005 2010 2015 2020 0 50 100 Euro Fig. 5.5 Price of the iShares Core DAX ETF in the period from January 2005 until December 2018 (initial prices on the first trading day of each month). Source: www.finanzen.net. from 0 to 1. This means that the number of new shares randomly varies between 100 and 200 per day. Also, the number of days a share remains in the fund is determined randomly: δ = rnd (100 + 300 ǫ) This number varies between 100 and 400 days; the mean value is 250 corresponding with the number of stock exchange trading days in one year. Using these assumptions, an example of a randomly generated process for the period from 2005 to 2018 consists of 530,311 new shares for which one knows the starting day t and the number of days, δ, until the share is sold again. 3 One also knows, from the data shown in Fig. 5.5, the price P t paid when buying the share and the selling price P t + δ (if sold before the end of 2018). 4 The gain or loss is P t + δ − P t . 3 For each new share, a separate value of δ was generated. 4 Note that due to using the data from Fig. 5.5, P t refers to the beginning of the period t. This is different from the notation used in Section 5.2. <?page no="92"?> 92 5 INVESTMENT FUNDS -40 -30 -20 -10 0 10 20 30 40 0 5 10 15 20 % Euro Fig. 5.6 Frequency distribution of gains and losses achieved by 492,986 shares sold and purchased between the beginning of 2005 and the end of 2018. Fig. 5.6 shows a frequency distribution of the gains and losses of 492,986 shares sold and purchased between the beginning of 2005 and the end of 2018. The mean value is 4.52 Euro. Where do these gains originate from? The money for redeemed shares can come from inflows which the fund achieves from dividends and by selling new shares and parts of its assets. Actually, in our example, all receipts of shareholders completely result from the fund selling new shares. To illustrate, we refer to our simulation. For each day t, let Y t and X t denote, respectively, the fund’s receipts from selling and payouts for redeeming shares. The upper part of Fig. 5.7 shows the development of the balance Y t − X t in one run of the simulation. Obviously, there are several days on those the required payouts exceed the inflows. However, with respect to our question it is important to consider the development of the cumulated balances: ∑ t l =0 Y l − X l . As shown in the lower part of Fig. 5.7, this cumulated balance is always positive, and we may conclude that the cumulated payouts, and thereby all gains which shareholders receive, can be financed with the inflow of money from selling new shares. Of course, <?page no="93"?> 5.3 EXCHANGE-TRADED FUNDS 93 2005 2010 2015 2020 -6000 -4000 -2000 0 2000 4000 6000 2005 2010 2015 2020 550 600 650 700 Euro × 1000 Euro Fig. 5.7 Development of the balance Y t − X t (upper) and the cumulated balance ∑ t l =0 Y l − X l (lower). the fund also receives dividends from its ownership of stocks. However, these inflows only serve to accumulate the fund’s assets and cannot, until the fund’s liquidation, contribute to gains of shareholders. <?page no="95"?> 6 Derivatives Compared with loans and bonds, shares of public companies and investment funds provide new and extended forms of speculation. A further extension of speculation was made possible by the development of derivatives. With these forms of financial capital the contracts concern possible future changes of prices of anything which could be given a price. One example, interest rate swaps, has already been discussed in Section 2.3. In the first two sections of this chapter we consider two other kinds of derivatives: futures and options. Betting with these derivatives takes place both in OTC (over the counter) environments and on stock exchanges. Here we focus on standardized betting games organized by stock exchanges. We show that these are zero-sum games where profits of one party result from losses of one or more other parties. In the third section we discuss credit default swaps. 6.1 Forwards and futures Forwards. A forward is a contract between two parties, A and B, which is made at time τ 0 and concerns the price, say P ∗ 1 , at which B can buy from or sell to A, at a later time τ 1 , a specified amount of the underlying (e.g., commodities, securities or currency). Conversely, A is committed to deliver, or to accept, the agreed amount at the price P ∗ 1 . For B the contract eliminates the uncertainty about the future price P 1 , and for A there is a possible future gain or loss which depends on P 1 − P ∗ 1 . This variant of a forward assumes that B is interested in hedging a future transaction and thereby differs from A who is interested in a possible speculative gain. In other variants also B acts as a speculator who is interested in the possible profit P ∗ 1 − P 1 . Futures. These are standardized forwards offered by a stock exchange. Subsequently, we explain the basic features of the standardization with an example, which uses the DAX Performance Index as <?page no="96"?> 96 6 DERIVATIVES 0 50 100 150 200 11500 12000 12500 13000 13500 14000 Points Fig. 6.1 Daily opening prices of a DAX future offered by EUREX in the period between January 1 and September 28, 2018. the underlying. 1 For a numerical illustration we use a DAX future offered by the stock exchange EUREX (www.eurexchange.com). 1) The stock exchange firstly defines a period of time during which speculators can buy a contract. In our example, we use the sequence of trading days, t = 1, . . . , T = 190, beginning on January 1 and ending on September 28, 2018. 2) On each day t, the stock exchange determines a future price P t that is derived from the DAX and, like the DAX, expressed in points. For our time axis, Fig. 6.1 shows prices determined by the EUREX. 2 3) The stock exchange defines the value of contracts. In our example, the value amounts to 25 Euro for each point of the future price. If, for example, the price is 12,000 points, contracts have a value of 300,000 Euro. 1 For further information about futures we refer to Steiner and Bruns (2000), Geyer and Uttner (2007), Hull (2009), B¨osch (2014). 2 ISIN: DE0008469008. The data was retrieved on January 2, 2019, from the time series wkn 846959 historic at www.ariva.de. <?page no="97"?> 6.1 FORWARDS AND FUTURES 97 T trading days t = 1, . . . , T P t future price on day t I t index set of participants on day t i refers to participants t i begin of i’s participation m i number of contracts bought δ i purchase or sale contract G i,t i’s gain or loss on day t K i,t i’s cumulated gains and losses on day t 4) On each day (until T − 1) speculators can buy contracts. Let I t denote the index set of speculators who participate on day t with at least one contract. For each participant i ∈ I t , let m i denote the number of contracts, t i the day on which they were bought, and δ i = { 1 if purchase contracts −1 if sale contracts 5) A speculator i, who buys m i contracts on the day t i , must deposit a safety margin amounting to α m i 25 P t Euro. For our example we assume α = 0.1. 6) Gains and losses result from changing future prices in the following way (for t > t i ): G i,t = δ i m i 25 (P t − P t − 1 ) If P t > P t − 1 , owners of purchase contracts achieve a gain amounting to 25 (P t −P t − 1 ) for each contract, and owners of sale contracts make a corresponding loss. The outcome is reversed if the future price falls. 7) When selling contracts, the stock exchange ensures that the num- <?page no="98"?> 98 6 DERIVATIVES ber of purchase contracts equals the number of sale contracts: ∑ i ∈I t δ i m i = 0 (6.1) This entails a zero-sum game: ∑ i ∈I t G i,t = 0. 8) The settlement of gains and losses takes place through the accounts containing the safety margins. To record the cumulated gains and losses we use accounts K i,t . Ignoring the safety margins, K i,t = 0 at the beginning, and afterwards K i,t = K i,t − 1 + G i,t . Since it is a zero-sum game, the equation ∑ i ∈I t K i,t = 0 (6.2) holds on each day t. 9) Participants can leave the game by purchasing opposite contracts. For example, if a speculator has bought m i purchase contracts on day t, he can leave on a day t ′ > t by purchasing m i sale contracts. Since the total value is zero, both contracts can be eliminated from the system by the stock exchange. Numerical illustration. To illustrate the zero-sum game, we use the future prices shown in Fig. 6.1. We assume that, on each trading day t = 1, . . . , 190, n t speculators (randomly selected from a set of N potential participants) want to buy m ∗ i contracts. We randomly determine whether these are purchase or sale contracts, and then find the maximum number of contracts satisfying the condition (6.1). The realized number of contracts is m i . In the first variant, we assume N = 2000, n t = 10 and m ∗ i = 1 , and also assume that all participants hold their contracts until the final day T . Consequently, there is for each participant a balance K i,T that records the cumulated gains and losses. Fig. 6.2 shows a frequency distribution of these balances as they result from a randomly generated process. The distribution is symmetric with a mean value zero. <?page no="99"?> 6.1 FORWARDS AND FUTURES 99 -30000 -20000 -10000 0 10000 20000 30000 0 5 10 15 20 % Fig. 6.2 Frequency distribution of the cumulated gains and losses K i,T if all participants stay until T (variant 1) In this realization of the game, the number of participants is 1,462 (731 contracts of each type). At the end, the yield achieved by a speculator i who bought contracts on the day t i is m i 25 (P T − P t i ) α m i 25 P t i = 1 α P T − P t i P t i (6.3) Due to the leverage, which is 1/ α = 10 in our example, these yields can take large positive and negative values as shown by the frequency distribution in Fig. 6.3. Early leaving the betting game. We now consider a variant in which speculators leave the game when their losses exceed a certain limit. To illustrate this variant, we assume that a participant i leaves when K i,t < −10000 Euro. We also assume that there is a sufficient number of new contracts for compensating the withdrawn contracts. In a random realization of the game, starting from N = 3000 potential participants, there are now 2,412 participants of which 1,012 drop out before T . Fig. 6.4 shows the frequency distribution of the cumulated gains and losses. For participants who dropped out on the day t < T , the balance K i,t is always less than -10,000 Euro, the mean <?page no="100"?> 100 6 DERIVATIVES -100 -50 0 50 100 0 5 10 15 % Fig. 6.3 Frequency distribution of the yields defined in Eq. (6.3), with leverage 1/ α = 10 at time T . -30000 -20000 -10000 0 10000 20000 30000 0 5 10 15 20 25 30 35 40 % Fig. 6.4 Frequency distribution of the cumulated gains and losses if players leave the game when their losses exceed 10,000 Euro (variant 2). loss is -12,048. For those who participate until T , the mean value of their balances K i,T is 8,709 Euro. One might think that participants can achieve an advantage by not leaving early. But that is not necessarily the case. In fact, most <?page no="101"?> 6.2 OPTIONS 101 Table 6.1 Variant 3 with three groups. Participants Drop out Gain/ loss G0 748 0 −354 participating until T G1 743 393 −2902 leaving if K i,t < −10000 G2 742 398 3263 leaving if K i,t > +10000 2233 791 0 total participants speculating with futures leave early for different reasons. As an illustration, we use a further variant (variant 3) in which there is also a group of speculators who leave the game when their gain exceeds 10,000 Euro. Table 6.1 shows the result of a random realization. Of course, these results cannot be generalized. EUREX data on futures. The EUREX Monthly Statistics of November 2018 reports that in this month 34.5 million future contracts, with a value of about 1,631.6 billion euro, have been sold; of these are 2.3 million FDAX futures having a value of 660.178 billion Euro. No information is given about the amount of the realized gains and losses, and it seems not possible to estimate this amount. One can, however, safely assume that the amount of gains and losses is substantially less than the total value of contracts. This can be illustrated with the first variant of our example. There are 1,462 contracts having a value of 459.8 million Euro. The sum of gains (or losses) amounts to 5.9 million which is about 1.3 % of the value of the contracts. 6.2 Options An option is a contract that defines for one party, called the buyer, an option which he can exercise at a later point in time. Correspondingly, there is another party, called the writer, who guarantees this right to the buyer. Like forwards and futures, options relate to an underlying (e.g., commodities, stock, price indices, currency). There are two kinds of options. A call (option) gives the buyer the right <?page no="102"?> 102 6 DERIVATIVES to purchase, a put (option) provides the right to sell the underlying (whose amount and price is fixed in the contract) at a later point in time. For this right, the buyer has to pay an option price (premium) to the writer. Options not only differ by underlyings but also by institutional arrangements. There are mainly three forms: - OTC (over the counter) contracts that, like forwards, are agreed to by two parties. - Options that, like futures, are offered by a stock exchange. There are two different forms: so-called European options that can be exercised only at the point in time when the option ends, and American options that can be exercised at any point in time until the ending time. 3 - Securitized options which can be traded. 4 In the following, we use a simple model for discussing some basic aspects of the betting with options offered by stock exchanges. A simple model. The model refers to American options. We begin with describing the formal framework. 1) The stock exchange defines a period of time, t = 1, . . . , T , during which participants can become buyers or writers of options; T is the last day for exercising the option. 2) The stock exchange defines the value of call and put contracts. In our example, the value relates to one piece of a specified stock. 5 Therefore, the value of a contract bought or sold on the day t equals the stock price on that day, subsequently denoted by P b t . 3) The stock exchange defines strike prices at which the option can be exercised until T . In our model, there are only two such prices: 3 Note that there is no relationship with the geographical place where the contract is made. 4 See, e.g., Steiner and Bruns (2000, p. 399), B¨osch (2014, p. 126). 5 Stock options offered by EUREX normally relate to 100 shares. <?page no="103"?> 6.2 OPTIONS 103 T trading days 1, . . . , T P b t value of a contract on day t P a c strike price for calls P a p strike price for puts I c t,t a index set of participants who bought or offered a call on day t a and still participate on day t I p t,t a index set of participants who bought or offered a put on day t a and still participate on day t i refers to participants t i begin of i’s participation m i number of contracts bought δ i i is buyer or writer Q c t option price for call contracts on day t Q p t option price for put contracts on day t ˜ G c i,t i’s gain or loss if exercising a call on day t G c i,t i’s gain or loss if selling a call on day t ˜ G p i,t i’s gain or loss if exercising a put on day t G p i,t i’s gain or loss if selling a put on day t P a c for calls and P a p for puts. 4) Speculators can buy contracts on each day. We use the following index sets: I c t,t a identifies participants who, on the day t a , bought a call, or offered to write a call, and who still participate on day t. I p t,t a identifies participants who, on the day t a , bought a put, or offered to write a put, and who still participate on day t. In any case, m i denotes the number of call or put contracts which <?page no="104"?> 104 6 DERIVATIVES a participant i has signed on day t a , and δ i = { 1 if i is the buyer of a call or put −1 if i is the writer of a call or put 5) When selling contracts, the stock exchange ensures that for each option there is a corresponding write contract. This entails the conditions ∑ i ∈I c t,ta δ i m i = ∑ i ∈I p t,ta δ i m i = 0 (6.4) 6) For each contract that a participant buys on a day t must be paid an option price: Q c t if it is a call, Q p t if it is a put. 6 These prices are determined by the stock exchange on the basis of the current order book in such a way that the sales are maximal. 7) Let i ∈ I c t,t a refer to a participant who, on the day t a , has bought m i calls. The gain or loss which i would achieve if exercising the call on day t is defined by ˜ G c i,t = δ i m i ( max{P b t − P a c , 0} − Q c t a ) (6.5) max{P b t − P a c , 0} is called the intrinsic value of the call. Since the same formula, with δ i = −1, can be used for a writer i ∈ I c t,t a , exercising is a zero-sum game: ∑ i ∈I c t,ta ˜ G c i,t = 0 (6.6) There is, however, an important asymmetry. For the buyer, the maximum gain has no upper limit while the maximum loss is given by the initially paid option price. For the writer, it is the other way around: the maximum gain is given by the initially received option price while the maximum loss has no upper limit. 6 In addition, a writer i who, on a day t a , sells m i contracts must deposit a safety margin whose amount is determined by the stock exchange and can vary from day to day. No safety margin is needed for buyers because, after having paid the option price, no further losses can occur. <?page no="105"?> 6.2 OPTIONS 105 8) Normally, if t < T , the option price Q c t is greater than the intrinsic value on that day. Therefore, the gain (or loss) from selling the option will be greater (or lesser) than from exercising: G c i,t = δ i m i ( Q c t − Q c t a ) > ˜ G c i,t (6.7) This entails that, normally, call options will be sold instead of exercised; but this does not change the zero-sum character of the game. If i sells a call contract on day t, this contract is replaced by another one bought at the price Q c t , and the formula (6.6) still holds. 9) Let now i ∈ I p t,t a refer to a participant who, on the day t a , has bought m i puts. Analogous to Eq. (6.5), if exercising on day t, the gain or loss would be ˜ G p i,t = δ i m i ( max{P a p − P b t , 0} − Q p t a ) (6.8) where now max{P a p − P b t , 0} denotes the intrinsic value. Also in this case, the option price is normally greater than the intrinsic value, which entails that it is normally preferable to sell the contract instead of exercising: G p i,t = δ i m i ( Q p t − Q p t a ) > ˜ G p i,t (6.9) As in the case of call contracts, speculation with put contracts is a zero-sum game as shown by the equation ∑ i ∈I p t,ta G p i,t = 0 (6.10) Illustration. In order to illustrate the model, we use options based on stocks of the Deutsche Bank. The period of possible contracts begins on April 17, 2019 (t = 1) and ends on December 19, 2019 (t = 172, trading days). The upper part of Fig. 6.5 shows stock prices, the mid and lower parts of the figure show the development of option prices and intrinsic values for call and put contracts, respectively <?page no="106"?> 106 6 DERIVATIVES 0 20 40 60 80 100 120 140 160 180 6 7 8 0 20 40 60 80 100 120 140 160 180 0 0.5 1 1.5 2 0 20 40 60 80 100 120 140 160 180 0 0.5 1 1.5 Euro P b t Q c t Q p t max{P b t −P a c , 0} max{P a p −P b t , 0} t Stock price Call option Put option Fig. 6.5 Upper part: Deutsche Bank stock price in Euro from t = 1 (April 17, 2019) to t = 172 (Dec. 19, 2019). Lower parts: prices and intrinsic values of call and put contracts, respectively, in Euro. <?page no="107"?> 6.2 OPTIONS 107 0 20 40 60 80 100 120 140 160 180 -1 -0.5 0 0.5 0 20 40 60 80 100 120 140 160 180 -1 -0.5 0 0.5 G c i,t ˜ G c i,t Call option t G p i,t ˜ G p i,t Put option t Fig. 6.6 Gains and losses of a call and of a put contract, beginning on t = 20, calculated on the basis of the data shown in Fig. 6.5. (strike prices are P a c = 6.4 and P a p = 7.0). It is seen that option prices always exceed the intrinsic value. The difference becomes smaller and eventually becomes zero when the process terminates. The upper part of Fig. 6.6 shows possible gains and losses, as defined in Eqs. (6.5) and (6.7), of a call contract bought on May 17 (t = 20). The lower part of the figure provides the same information for a put contract bought on the same day. In both cases, as we have argued above, selling contracts is preferable to exercising. However, whether the betting game ends with selling or with exercising, it is always a zero-sum game. <?page no="108"?> 108 6 DERIVATIVES 6.3 Credit default swaps In this section we consider credit default swaps (CDS). They are similar to the interest rate swaps discussed in Section 2.3. Instead of interest rates, the underlying of CDS contracts consists of possible defaults of a specified amount of financial capital, most often loans or bonds. The contract is a bilateral agreement between two parties, valid for a sequence of periods t = 1, . . . , T . At the beginning of each period, as long as no default has occurred, the buyer of the contract has to pay a premium to the seller. If a default occurs, the buyer receives from the seller a payment that equals the loss (as defined in the contract). In cases where the buyer owns the underlying, this mechanism provides a kind of insurance against the risk of default. The market for CDS contracts is dominated by a small number of large banks. Fig. 6.7 shows data from surveys organized by the Bank for International Settlement. 7 Both the extremely fast growth until 2008 and the decrease which took place afterwards indicate that CDS are highly speculative. To a large extent, this is also due to the possibility that investors can buy CDS contracts without owning the underlying, which then serve purely speculative purposes. In the following, we consider CDS contracts having as underlying bonds of a reference unit (a company or government). We refer to bonds with nominal value N for a sequence of periods t = 1, . . . , T . Interest is paid at the end of each period, the interest rate is r f . Probabilities of default. Probabilities of default are used to take into account a possible default. Since these probabilities cannot be estimated reliably, they must be considered as hypothetical quantities. For allowing simple notations, we assume that a default can only take place at the end of a period. This allows us to use a single random variable ˜ D, and a notation Pr( ˜ D = t) meaning the probability that a default occurs at the end of the period t. To formulate assumptions about default probabilities, it is helpful 7 Aldasoro and Ehlers (2018) provide detailed information about the development of the CDS market. <?page no="109"?> 6.3 CREDIT DEFAULT SWAPS 109 2005 2010 2015 2020 0 10 20 30 40 trillion Euro Fig. 6.7 Nominal values of credit derivatives reported by 74 international banks in biannual surveys of the Bank for International Settlement. Source: Deutsche Bundesbank time series portal: BBK01.QUY217. to refer to hazard rates: γ t = Pr( ˜ D = t | ˜ D ≥ t) = Pr( ˜ D = t) Pr( ˜ D ≥ t) (6.11) This is the probability that a default takes place at the end of the period t, given that a default did not occur earlier. The probability of the condition is 8 Pr( ˜ D ≥ t) = t − 1 ∏ k =1 (1 − γ k ) (6.12) and the unconditional (marginal) probability of a default at the end of t is Pr( ˜ D = t) = γ t Pr( ˜ D ≥ t) (6.13) 8 Since 1 − γ k = Pr( ˜ D ≥ t + 1)/ Pr( ˜ D ≥ t), we may write: t −1 ∏ k =1 (1 − γ k ) = Pr( ˜ D ≥ 2) Pr( ˜ D ≥ 1) Pr( ˜ D ≥ 3) Pr( ˜ D ≥ 2) · · · Pr( ˜ D ≥ t) Pr( ˜ D ≥ t − 1) = Pr( ˜ D ≥ t) Pr( ˜ D ≥ 1) Since Pr( ˜ D ≥ 1) = 1, this is equal to Pr( ˜ D ≥ t). <?page no="110"?> 110 6 DERIVATIVES Finally, the probability of no default until and including T is Pr( ˜ D > T ) = T ∏ t =1 (1 − γ t ) (6.14) Expected yields. The following equation defines the yield r 0 if no default takes place: N = T ∑ t =1 r f N (1 + r 0 ) t + N (1 + r 0 ) T (6.15) The left-hand side records the invested capital, the right-hand side records the sum of payments discounted with the yield r 0 (see Section 3.2). Since the nominal value N is not used in the calculation, we subsequently assume N = 1. To determine an expected yield, say ˜ r, one firstly has to consider yields for each possible situation of default. Without a default, the yield is r 0 = r f . If a default takes place at the end of the first period, the yield is ˜ r 1 = −1. If the default takes place at the end of the second period, the yield ˜ r 2 is defined by the equation r f 1 + ˜ r 2 = 1 entailing ˜ r 2 = r f − 1. In general, in order to find ˜ r t , one can use the equation t − 1 ∑ k =1 r f (1 + ˜ r t ) k = 1 Finally, one can calculate the expected yield as the expectation ˜ r = T ∑ t =1 ˜ r t Pr( ˜ D = t) + r f Pr( ˜ D > T ) (6.16) As an example, we consider a bond with duration T = 5 periods and an interest rate r f = 0.05. Also the yield calculated with Eq. (6.15) <?page no="111"?> 6.3 CREDIT DEFAULT SWAPS 111 is r 0 = 0.05. Assuming a constant hazard rate γ = 0.01, one obtains from Eq. (6.16) the value ˜ r γ = 0.011. Fig. 6.8 shows how the expected yield depends on γ. A simple CDS contract. We consider a CDS contract having as its underlying the bond described above. If a default occurs at the end of the period t, the CDS buyer receives a payment amounting to 1 − α + r f , multiplied by N , where α denotes the proportion of N that can be recovered in the case of a default. 9 Using a discount rate ρ, the expectation of the present value of these payments is T ∑ t =1 Pr( ˜ D = t) (1 − α + r f ) (1 + ρ) − t (6.17) On the other hand, at the beginning of each period, as long as no default has occurred, the buyer must pay a premium, say π, multiplied by N , to the seller of the contract. The expectation of the present value of these payments is T ∑ t =1 Pr( ˜ D ≥ t) π (1 + ρ) 1 − t (6.18) A possible approach to defining the CDS premium is based on equating the two expectations: π = (1 − α + r f ) ∑ T t =1 Pr( ˜ D = t) (1 + ρ) − t ∑ T t =1 Pr( ˜ D ≥ t) (1 + ρ) 1 − t (6.19) With a constant hazard rate γ, one simply obtains π γ = (1 − α + r f ) γ 1 + ρ (6.20) We note that these formulas serve the construction of models. Since 9 We assume that the recovery rate α is fixed by the CDS contract. Alternatively, if the CDS buyer owns the underlying, the contract could specify α = 0 and the CDS seller becomes the owner of the defaulted bonds. <?page no="112"?> 112 6 DERIVATIVES 0 0.01 0.02 0.03 0.04 0.05 0.06 -5 0 5 % γ ˜ r γ π γ ˜ r ∗ γ Fig. 6.8 Dependence of the premium π γ , and the yields ˜ r γ and ˜ r ∗ γ , on the constant hazard rate γ, based on the example with T = 5, r f = 0.05 and α = ρ = 0. default probabilities cannot be objectively determined, CDS premiums cannot be determined with these formulas. References to supposed default probabilities and recovery rates should be viewed as possible arguments in the bilateral bargaining processes in which the details of a CDS contract are fixed. Gains and losses. We first consider a covered, then an uncovered CDS contract. (1) We refer to an investor who has bought the underlying bonds. Without a CDS contract, he has invested N = 1 and bears the risk of default. If he buys a CDS contract, the initial investment is N = 1 plus the payment of the initial premium π. - Without default: the CDS buyer receives, at the end of each period t < T , the interest r f from which must be paid π at the beginning of the next period. In the last period, t = T , he receives 1 + r f from which 1 + π is used for repayment of the initial investment. In each period, therefore, the net receipt of interest is r f − π. <?page no="113"?> 6.3 CREDIT DEFAULT SWAPS 113 Table 6.2 t Pr( ˜ D = t) Pr( ˜ D ≥ t) receipt payment net receipt 1 0.0100 1.0000 0.65 0.0065 0.6435 2 0.0099 0.9900 0.65 0.0130 0.6370 3 0.0098 0.9801 0.65 0.0195 0.6305 4 0.0097 0.9703 0.65 0.0260 0.6240 5 0.0096 0.9606 0.65 0.0325 0.6176 6 0.9510 0 0.0325 −0.0325 - If there is a default at the end of period t, the buyer receives 1 − α + r f from the seller. Since it is assumed that α (if positive) can be recovered, the expected receipt is 1+r f = (r f −π)+(1+π). Analogous to formula (6.15), in order to calculate the expected yield ˜ r ∗ until the end of a period t, one can use the equation 1 + π = t ∑ k =1 r f − π (1 + ˜ r ∗ ) k + 1 + π (1 + ˜ r ∗ ) t (6.21) where the left-hand side records the invested capital. Independent of t, the solution is ˜ r ∗ = r f − π 1 + π (6.22) To illustrate, we use our example and assume α = 0, a constant hazard rate γ, and a discount rate ρ = 0. The dashed curve in Fig. 6.8 shows the yield ˜ r ∗ γ = (r f − π γ )/ (1 + π γ ). Obviously, it exceeds the expected yield without a CDS contract and allows the creditor to accept a significantly higher default risk. Note that this is true although the expectation of the net receipts from the contract is zero. (2) We now consider an uncovered CDS contract. We continue with our example and assume a recovery rate α = 0.4. We also assume that the premium is calculated with a hazard rate γ = 0.01 and a discount rate ρ = 0: π γ = 0.0065. Using this premium, Table 6.2 shows what the CDS buyer must pay to and receives from the seller. <?page no="114"?> 114 6 DERIVATIVES Values in the first five rows are conditional on a default event in the period t; in the last row it is assumed that no default occurs. Since the definition of the premium is based on equating the expected receipts and payments, the expectation of the net receipts in the last column is zero. However, the expectation also depends on assumptions about the development of the hazard rate until the end of the contract. If the default risk increases, the CDS buyer can expect a gain. To illustrate, we assume the following development: t 1 2 3 4 5 6 γ t 0.01 0.01 0.02 0.02 0.02 Pr( ˜ D ≥ t) 1.0000 0.9900 0.9801 0.9605 0.9413 0.9225 Pr( ˜ D = t) 0.0100 0.0099 0.0196 0.0192 0.0188 Using these values, the CDS buyer’s expectation of net receipts is 0.0187 instead of zero. One can conclude that buying uncovered CDS contracts is mainly driven by beliefs in rising probabilities of default. Of course, for the CDS seller the situation is reversed. However, independent of their expectations, buying and selling CDS contracts is always a zero-sum game. <?page no="115"?> 7 Financialization A broad definition was proposed by G. A. Epstein: Financialization means the increasing role of financial motives, financial markets, financial actors and financial institutions in the operation of the domestic and international economies. (2005, p. 3) The definition suggests that financialization is a complex phenomenon with many aspects, which cannot be reduced to a single mechanism. 1 In this chapter, we focus on one particularly significant aspect: a massive expansion of financial wealth—both money and financial capital—which greatly exceeds increases in the production of goods and services. The first section uses a simple formal framework for describing the expansion, 2 the second section discusses mechanisms which contribute to the huge inequality in the distribution of financial wealth. 7.1 Expansion of financial wealth We define the financial wealth of a nonbank unit (household or firm) as consisting of both the money and the financial capital that the unit owns at a point in time. 3 This is gross financial wealth without subtraction of debts and other kinds of liabilities. To understand the expansion of financial wealth, we distinguish between changes due to new money and financial capital and changing evaluations of already existing financial capital. We begin with considering the expansion 1 We also refer to Palley (2013), Krippner (2005), Hudson (2006), Orhangazi (2008), van Treeck (2009), Wray (2009), van der Zwan (2014), Davis (2016), D¨ unnhaupt (2016), Bezemer and Hudson (2016). 2 This framework is similar to what Bezemer (2016) has called “an ‘accounting view’ of money, banking and the macroeconomy”. 3 Note that, when we speak of ‘firms’ (the index set is F ), this includes investment funds, which we consider as separate units, different from the corporations which founded and organize these units (see the remarks on p. 146). <?page no="116"?> 116 7 FINANCIALIZATION 2000 2005 2010 2015 2020 0 5000 10000 15000 billion Euro GDP M1 Fig. 7.1 Development of the money supply (M1) and the GDP (yearly values in market prices) in the euro area since the end of 2000. Source: see Fig. 2.4. of the money supply and then use a simple model for discussing the accumulation of financial wealth. Expansion of the money supply. As already shown in Section 2.1, and again in Fig. 7.1, the money supply in the euro area has grown much faster than the GDP in market prices. In the period shown in the figure, the mean annual growth rates of the money supply and the GDP in market prices were 8 % and 3 % respectively. This is a significant aspect of financialization not only because the money supply, according to our definition, already counts as financial wealth. A further reason is due to the implication that a rising part of the money supply is not required for transactions involving goods and services and therefore can, and will, be used for financial investments. To discuss the sources of the expansion of the money supply, we use a few formal notations. The time framework is a sequence of periods t = 0, 1, 2, . . . (e.g., days or weeks). The elementary events are transactions which take place at points in time: t ij,τ records a payment from a unit U i to a unit U j at time τ . It is assumed that all transactions are made by units having indices in a set U . The <?page no="117"?> 7.1 EXPANSION OF FINANCIAL WEALTH 117 transactions taking place in a period can be aggregated: t ij,t = ∑ τ ∈ t t ij,τ (7.1) We assume that all payments are made with banks’ deposit money. This implies that payments between banks, and between banks and state institutions, are not represented. We can assume, however, that transactions between state units and nonbanks, since they are mediated by banks, use deposit money. The stock of money held by a nonbank U i (i ∈ N ) at the end of period t will be denoted by M i,t . Note that neither banks nor state institutions hold stocks of deposit money (their accounts are located with the central bank). When a bank receives money from nonbanks it is destroyed (by diminishing liabilities in its balance sheet), and this is also true when the bank mediates payments from nonbanks to state institutions (see Section 2.1). The money supply at the end of period t is M t = ∑ i ∈N M i,t (7.2) The change in the stock of money of a nonbank U i is ∆M i,t = M i,t − M i,t − 1 = ∑ j ∈N (t ji,t − t ij,t ) + ∑ j ∈S (t ji,t − t ij,t ) + ∑ j ∈B (t ji,t − t ij,t ) (7.3) On the right-hand side, the first summand records the part resulting from transactions with other nonbank units, then follow net receipts (inflows minus outflows) from state institutions and banks, respectively. All components can be negative. The total change in the money supply is ∆M t = ∑ i ∈N ∆M i,t = ∑ j ∈S ∑ i ∈N (t ji,t − t ij,t ) + ∑ j ∈B ∑ i ∈N (t ji,t − t ij,t ) (7.4) <?page no="118"?> 118 7 FINANCIALIZATION The right-hand side records the parts which, respectively, state institutions and banks contribute to the expansion of the money supply. Since banks mediate payments of state institutions, in both cases the new money is created by banks. Beginning with a simple model. We now discuss how the expansion of the money supply, followed by financial investments, contributes to the expansion of financial wealth. We begin with a simple model, which later will be gradually extended. 4 The initial version is based on the following assumptions: a) Firms (other than banks) only engage in making profits through selling goods and services, based on nonfinancial investments financed with bank loans, which are repayed in the current period and do not contribute to an increase in the money supply. These bank loans are the only form of financial capital entailing that all firms are privately owned. b) All profits of firms (including banks) are paid out and eventually received by households. c) Households do not make financial investments, which entails that their financial wealth only consists in money. d) Government expenditures are mediated by banks. This entails that government expenditures that exceed the receipt of taxes contribute to an increase in the money supply. The term “taxes” will be used for all kinds of payments of households and firms which are due to public regulations. Initially, we also assume that governments can finance these expenditures with autonomously generated central bank money and therefore do not need to pay interest. 4 Two basic notions will be used in the following way: All units can purchase labor, goods, services and financial capital. If these purchases serve to receive revenues (which in the case of financial capital can always be assumed), they will be called investments, otherwise it will be said that they are used for consumption. For this distinction it is not relevant whether the purchased things are durable or not but only their intended use. It will be assumed that only households and state institutions spend money on consumption. <?page no="119"?> 7.1 EXPANSION OF FINANCIAL WEALTH 119 U i refers to a unit indexed by i U index set of all units H index set of households S index set of state institutions B index set of banks F index set of firms (including investment funds) F \ B index set of firms without banks N index set of nonbanks (H + F \ B) t ij,τ payment from U i to U j at time τ t ij,t sum of payments from U i to U j during the period t M i,t U i ’s stock of money at the end of period t ∆M i,t change in U i ’s stock of money during the period t M t money supply at the end of period t ∆M t change in the money supply during the period t Y i,t income of U i in the period t Y w i,t U i ’s income from wages Y s i,t U i ’s income from shares Y tr i,t U i ’s income from state institutions (transfers, wages) Y tx i,t U i ’s payment of taxes Y rp i,t retained profits of a firm U i Y int i,t balance of U i ’s received and paid interest Y nbb i,t U i ’s net borrowing from banks C i,t consumption of a household U i in the period t σ i,t saving rate in the period t ∆F w i,t change in U i ’s financial wealth in period t ∆F dep i,t change in U i ’s nonmonetary deposits ∆F bnk i,t change in U i ’s nonbasic financial wealth F w t total stock of financial wealth at the end of t. Notations for sums: If a symbol omits the reference to a unit, as for example ∆M t , it is meant to denote the sum over all units. If the reference to a unit is replaced by an index set, the sum over all units in the index set is meant, e.g., C H ,t = ∑ i ∈H C i,t . <?page no="120"?> 120 7 FINANCIALIZATION The income that a household U i (i ∈ H) receives in a period t is Y i,t = Y w i,t + Y s i,t + Y tr i,t − Y tx i,t (7.5) The first two components record, respectively, wages and receipts from shares, which households receive from firms: Y w i,t + Y s i,t = ∑ j ∈F t ji,t (7.6) Then follow transfers (including wages) received from state institutions: Y tr i,t = ∑ j ∈S t ji,t (7.7) Finally, payments of taxes are subtracted: Y tx i,t = ∑ j ∈S t ij,t (7.8) Households spend a part of their income on consumption, that is, for buying goods and services from firms: C i,t = (1 − σ i,t ) Y i,t = ∑ j ∈F t ij,t (7.9) where σ i,t denotes the saving rate in period t. The remainder is hoarded as an increase in the household’s stock of money: ∆M i,t = Y i,t − C i,t = σ i,t Y i,t (7.10) Aggregation over all households leads to ∆M H ,t = Y H ,t − C H ,t = Y w H ,t + Y s H ,t + Y tr H ,t − Y tx H ,t − C H ,t (7.11) which, in the present version of our model, equals the increase in households’ financial wealth. Note that saving rates can be negative if consumption is (partly) financed out of previously accumulated financial wealth. This will be discussed in Section 7.2. <?page no="121"?> 7.1 EXPANSION OF FINANCIAL WEALTH 121 Fig. 7.2 Governments Firms Households ✛ ✲ C H ,t = 1200 Y w H ,t + Y s H ,t = 1500 ✲ ❄ ❄ ✛ Y tx F ,t = 100 C S ,t = 400 Y tr H ,t = 600 Y tx H ,t = 400 In addition to transfers to households, state institutions also use expenditures for directly buying goods and services from firms. The corresponding receipts of firms are C S ,t = ∑ i ∈S ∑ j ∈F t ij,t (7.12) Taxes paid by firms are Y tx F ,t = ∑ i ∈F ∑ j ∈S t ij,t (7.13) Fig. 7.2 depicts the flow of money between the three consolidated sectors. Government expenditures minus receipts of taxes will subsequently be called excess government expenditures = C S ,t + Y tr H ,t − Y tx H + F (7.14) Since we have assumed that firms finance the production of goods and services with bank loans that do not contribute to an increase in the money supply, and do not retain profits, excess government expenditures are the only source of the increase in the money supply: ∆M t = C S ,t + Y tr H ,t − Y tx H + F ,t (7.15) We therefore may equate ∆M H ,t and ∆M t , 5 and from Eqs. (7.11) and (7.15) one can derive C t = C H ,t + C S ,t = Y w H ,t + Y s H ,t + Y tx F ,t (7.16) 5 We note that this is an ex post equation. See Bibow (2001) for a discussion of dynamic relationships. <?page no="122"?> 122 7 FINANCIALIZATION as already depicted in Fig. 7.2 with a numerical illustration. 6 We stress that the increase in households’ financial wealth, ∆M H ,t , is not, in any causal sense, a result of households’ saving decisions. It is a result of the increase in the money supply that was used for financing the excess government expenditures. Given the assumption that firms do not retain profits, the increase in the money supply necessarily shows up as an increase in the bank accounts of households. As will be discussed in Section 7.2, the individual saving decisions of households are nevertheless important because they mediate the distribution of the increase in financial wealth. Basic financial wealth. So far we have assumed that the change in a unit’s financial wealth only consists in the change in its holding of money: ∆M i,t . We now take into account that units can use money for buying financial capital from banks. We consider three forms: Term deposits, other kinds of saving contracts, and bank bonds. For referring to these financial investments, we speak of nonmonetary deposits and use the notation ∆F dep i,t . 7 This notation will be understood as recording a change in U i ’s ownership of the three categories of financial capital. For example, buying a saving contract will increase, and redeeming the contract will decrease ∆F dep i,t . Ownership 6 The equation relates to a consolidated sector of firms. Let t firm ij,t denote the payment from a firm U i to another firm U j for purchases of investment goods and/ or for interest and dividends, and let t con ij,t denote the payment of a household or state institution U i to a firm U j for purchases of consumption goods. The net revenues of a firm U i , which can be used for paying wages and payouts to households, paying taxes, or held as retained profits, are Y net i,t = ∑ j ∈F (t firm ji,t − t firm ij,t ) + ∑ j ∈H+S t con ji,t (7.17) Summation leads to Y net F ,t = ∑ i ∈F Y net i,t = =0 ︷ ︸︸ ︷ ∑ i ∈F ∑ j ∈F (t firm ji,t − t firm ij,t ) + ∑ i ∈F ∑ j ∈H+S t con ji,t = C t (7.18) A formal framework that explicitly represents ownership relations among units was considered by Rohwer and Behr (2020). 7 The designation is chosen to remind of the difference between money (demand deposits) and financial capital (nonmonetary deposits). <?page no="123"?> 7.1 EXPANSION OF FINANCIAL WEALTH 123 of bank bonds can also change through transactions on secondary markets. However, for the moment we assume that all transactions use the initial purchase price. The assumption entails that buying and selling (redeeming) nonmonetary deposits only change the composition, not the size, of a unit’s financial wealth. For referring to both of its components, we use the term “basic financial wealth”; for i ∈ N the notation will be: Change in U i ’s basic financial wealth = ∆M i,t + ∆F dep i,t (7.19) It follows from Eq. (7.15) that the total change in the basic financial wealth in a period equals the excess government expenditures: ∆M t + ∆F dep t = C S ,t + Y tr H ,t − Y tx H + F ,t (7.20) Note that nonmonetary deposits hide a part of the increase in the money supply that was initially used to finance the excess government expenditures. In the present version of our model, this increase must have become a part of the income of households before it could be used for purchasing nonmonetary deposits, which reduce the previously increased money supply. Accumulation. For understanding the expansion of financial wealth, it is important to recognize that Eq. (7.20) records changes which accumulate over a sequence of periods. Let F w t denote the total financial wealth at the end of period t. 8 Since so far financial wealth only consists of money and nonmonetary deposits, we may write: F w t = F w 0 + t ∑ l =1 ∆M l + ∆F dep l (7.21) The contribution of excess government expenditures to the growth of financial wealth is described by F w t = F w 0 + t ∑ l =1 C S ,l + Y tr H ,l − Y tx H + F ,t (7.22) 8 Recall that, according to our definition, only nonbank units hold financial wealth. To ease notations, we define the financial wealth of banks as being zero. <?page no="124"?> 124 7 FINANCIALIZATION 0 5 10 15 20 0 10 20 30 t C S ,t + Y tr H ,t − Y tx H+F ,t F w t Fig. 7.3 Illustration of the fast growth of basic financial wealth as defined in Eq. (7.22). Fig. 7.3 provides an illustration. It is assumed that total consumption, C t , grows with 3 % per period, beginning with C 0 = 100. We also assume that excess government expenditures contribute in each period 1 % of the consumption (∆M t + ∆F dep t = 0.01 C t ) and, therefore, grow with the same rate. Beginning with F w 0 = 0, the figure illustrates the development of F w t . Households’ debt-based consumption. A further source of the accumulation of financial wealth is debt-based consumption of households. Extending Eq. (7.5), the revenues of a household are now recorded as Y i,t = Y w i,t + Y s i,t + Y tr i,t − Y tx i,t + Y nbb i,t + Y int i,t (7.23) where Y nbb i,t denotes the household’s net borrowing from banks in the period t (which might be negative), and Y int i,t denotes its balance of received and paid interest. We assume that households borrow from banks, which entails that the sum of net borrowing, Y nbb H ,t , contributes to the increase in the money supply. We also assume that the interest which banks receive is paid out to shareholders and thereby eventually flows back to households; this entails Y int H ,t = 0. Given these <?page no="125"?> 7.1 EXPANSION OF FINANCIAL WEALTH 125 assumptions, Eq. (7.20) can immediately be extended into ∆M t + ∆F dep t = C S ,t + Y tr H ,t + Y nbb H ,t − Y tx H + F ,t (7.24) showing that the total increase in the basic financial wealth is the result of both the excess government expenditures and the households’ net borrowing. Retained profits of firms. So far we have assumed that firms completely pay out their profits. Actually, firms retain some part of their profits. 9 We therefore extend our model and use Y rp i,t to denote the retained profits of a firm U i (i ∈ F). 10 To ease notations, we maintain the assumption that banks do not retain profits (Y rp i,t = 0 if i ∈ B). The sum of retained profits is Y rp F ,t , and the total sum of profits is Y s H ,t + Y rp F ,t . Instead of Eq. (7.16), we may then write: 11 C t = C H ,t + C S ,t = Y w H ,t + Y s H ,t + Y rp F ,t + Y tx F ,t (7.25) As long as we assume that financial investments only consist in nonmonetary deposits, the retained profits equal firms’ basic financial wealth: Y rp F ,t = ∆M F ,t + ∆F dep F ,t . Since retained profits do not alter the total financial wealth, Eq. (7.24) is still valid, and the total change in basic financial wealth is ∆M t + ∆F dep t = (∆M H ,t + ∆F dep H ,t ) + (∆M F ,t + ∆F dep F ,t ) (7.26) Fig. 7.4 illustrates the rise of this basic financial wealth by taking into account the term deposits and saving contracts of households and firms. 12 9 Several authors have observed that financialization has been accompanied by significant increases in retained profits. See, e.g., Chen, Karabarbounis and Neiman (2017), Dao and Maggi (2018), Gruber and Kamin (2015). 10 We only include profits actually realized in a period, not claims to possible future profits (e.g, due to supplier credits). 11 Like Eq. (7.16), this equation relates to a consolidated sector of firms, see footnote 6. 12 According to our definition, ∆F dep t also includes bank bonds held by nonbank units. The consolidated balance sheet of euro area MFIs reports that, at the end of 2019, outstanding bonds amounted to 2,188.7 billion Euro. <?page no="126"?> 126 7 FINANCIALIZATION 2000 2005 2010 2015 2020 0 5000 10000 15000 2000 2005 2010 2015 2020 billion Euro M1 + saving contracts M1 GDP Fig. 7.4 Development of the GDP (yearly values in market prices), the money supply M1, and saving contracts (including all kinds of term deposits) in the euro area (changing composition). Source: Fig. 2.4 and https: / / sdw.ecb.europa.eu/ browse.do? node=bbn28. Debt-based expenditures of firms. So far we have assumed that only excess government expenditures and household debts contribute to the increase in the money supply and, thereby, to the expansion of financial wealth. We now take into account that also nonbank firms finance investments with debts that increase the money supply. The net borrowing of a firm U i from banks in the period t will be denoted by Y nbb i,t . 13 The sum of firms’ net borrowing is Y nbb F ,t . This equals the contribution of nonbank firms to the increase in the money supply. Accordingly, Eq. (7.24) must be extended into ∆M t + ∆F dep t = C S ,t + Y tr H ,t + Y nbb H ,t + Y nbb F ,t − Y tx H + F ,t (7.27) Again, we assume that the interest which banks receive is paid out to shareholders and thereby eventually flows back to households or nonbank firms. Consequently, like the interest paid by households, also the interest paid by nonbank firms does not contribute to the expansion of financial wealth. Note that Eq. (7.27) holds irrespective 13 Y nbb i,t = 0 if i ∈ B . <?page no="127"?> 7.1 EXPANSION OF FINANCIAL WEALTH 127 Fig. 7.5 Governments Firms Households ✛ ✲ C H ,t = 1200 Y w H ,t + Y s H ,t = 1500 ✲ ❄ ❄ ✛ Y tx F ,t = 100 C S ,t = 400 Y tr H ,t = 600 Y tx H ,t = 400 ✻ Y nbb F ,t = 300 ✻ Y nbb H ,t = 100 of whether the borrowed money is used for nonfinancial or financial investments, or even for payouts and interest. Fig. 7.5 shows how Y nbb F ,t parallels households’ net borrowing from banks. The numerical entries in the figure provide an illustration of Eq. (7.26), which still holds: ∆M H ,t + ∆F dep H ,t ︸ ︷︷ ︸ 600 + ∆M F ,t + ∆F dep F ,t ︸ ︷︷ ︸ 300 = 900 (7.28) The figure also illustrates that Eq. (7.25) must be extended in order to include the additional source of new money: C t + Y nbb F ,t = Y w H ,t + Y s H ,t + Y rp F ,t + Y tx F ,t (7.29) The equation underlines that the contribution of Y nbb F ,t to the increase in financial wealth does not originate from firms’ sales of goods and services but from an increase in the money supply. Fig. 7.6 illustrates the expansion of loans, both to firms and households, in the euro area. Debt-based government expenditures. So far we have assumed that excess government expenditures are financed with an increase in the money supply that is autonomously created by governments. Actually, in the euro area almost all excess government expenditures have been financed with government bonds, which entails that governments have to pay interest to units holding the bonds. However, as was argued in Section 3.4, we can assume that the payment of <?page no="128"?> 128 7 FINANCIALIZATION 2000 2005 2010 2015 2020 4000 7000 10000 13000 billion Euro GDP Bank loans Fig. 7.6 Expansion of banks’ loans granted to nonbanks and governments, compared with the GDP in market prices. Data refer to the euro area in changing composition. Source: Fig. 2.4 and https: / / sdw.ecb.europa.eu/ browse.do? node=bbn28. interest forms a part of the excess government expenditures. Equations recording the contribution of these expenditures to the increase in the money supply can, therefore, simply be extended. For example, Eq. (7.15), which records the contribution of excess government expenditures in the initial model, can be extended into ∆M t = C S ,t + Y tr H ,t − Y int S ,t (7.30) where Y int S ,t denotes governments’ balance of received and paid interest in period t. The interest paid by governments simply increases the contribution of excess government expenditures to the expansion of financial wealth. Fig. 7.7 illustrates how debt-based expenditures of governments in the euro area have contributed to the expansion of financial wealth. Debt-based government expenditures require a further extension of the formal framework because nonbanks can also hold government bonds, which then form a part of their financial wealth. For a nonbank unit U i , we use ∆F gov i,t to denote its change in holding government bonds in the period t. However, when buying or selling government <?page no="129"?> 7.1 EXPANSION OF FINANCIAL WEALTH 129 2000 2005 2010 2015 2020 0 2000 4000 6000 8000 billion Euro Fig. 7.7 Outstanding bonds emitted by governments in the euro area (changing composition). Source: Fig. 3.1. bonds, the unit only changes the composition of its financial wealth. 14 We, therefore, consider government bonds held by nonbanks as a part of their basic financial wealth, and extend the previous definition (7.19) into: Change in U i ’s basic financial wealth = ∆M i,t + ∆F dep i,t + ∆F gov i,t (7.31) In previous equations involving basic financial wealth, as e.g. (7.27), one can simply change ∆F dep i,t into ∆F dep i,t + ∆F gov i,t . This again elucidates that the contribution of excess government expenditures to increasing financial wealth does not depend on whether they are financed autonomously or with bonds. This difference only concerns the additional contribution through the payment of interest. Financial capital purchased from nonbanks. Except for holding money, financial wealth consists in financial capital that comes into being through financial investments. So far we have considered 14 For the moment, as for bank bonds, we assume that transactions involving government bonds use the initial emission prices. <?page no="130"?> 130 7 FINANCIALIZATION 1990 2000 2010 2020 0 500 1000 1500 2000 billion Euro Public funds Special funds Fig. 7.8 Assets managed by open-end investment funds in Germany. Source: BVI Investmentstatistik [www.bvi.de]. nonmonetary deposits and government bonds. We now consider purchases of new financial capital from nonbanks. There are four kinds: a) Saving contracts purchased from nonbanks (e.g., insurance companies). While the unit that buys the contract only changes the composition of its financial wealth, the financial wealth of the company that sells the contract increases by the received money. 15 b) Public companies and investment funds can increase their financial wealth through selling new shares, whereas the units which buy the shares only change the composition of their financial wealth. We note that, in particular, investment funds have contributed to the expansion of financial capital. For example, from the end of 2008 to the end of 2019 the assets of open-end funds in the euro area increased from 4,385 to 13,577 billion Euro, that is a mean yearly increase of 10.8 %. 16 A longer time series that is available for Germany shows how the expansion began in the 1990s, see Fig. 7.8. 15 Recall that we always refer to gross financial wealth without subtraction of debts and other kinds of liabilities. 16 https: / / sdw.ecb.europa.eu/ browse.do? node=9691362. <?page no="131"?> 7.1 EXPANSION OF FINANCIAL WEALTH 131 c) Units can also increase their financial wealth by borrowing money from other nonbank units. Again, the unit that lends out money only changes the composition of its financial wealth, whereas the debtor, by selling a debt contract and thereby receiving money, increases its financial wealth. d) Also, purchases of contracts for bets with derivatives create new financial capital. However, these contracts cease to exist as soon as the betting game is settled, and the financial wealth of nonbank players can only increase through losses of banks paid with new money. Bets between nonbanks only redistribute the existing financial wealth without contributing to its size. In all cases, the new financial capital consists of contracts sold by nonbank firms and households. These contracts form a part of the financial wealth of their owners, subsequently referred to as nonbasic financial wealth. In parallel to ∆F dep i,t and ∆F gov i,t , we use the notation ∆F nbk i,t = change in U i ’s nonbasic financial wealth (7.32) The label ‘nbk’ shall remind of the fact that these kinds of financial wealth are created by nonbanks. Since several kinds are tradable, ∆F nbk i,t can also change through transactions on secondary markets. Again, for the moment we assume that these transactions use the initial purchase prices. This assumption allows us to record the total change in the financial wealth of a unit by ∆F w i,t = ∆M i,t + ∆F dep i,t + ∆F gov i,t ︸ ︷︷ ︸ basic financial wealth + ∆F nbk i,t ︸ ︷︷ ︸ nonbasic f. wealth (7.33) Expansion of nonbasic financial wealth. We first consider financial investments of households, then of firms. (1) We refer to households’ purchases of financial capital from nonbank firms recorded by ∆F nbk H ,t . 17 To illustrate, we extend Fig. 7.5 17 We ignore borrowing money from other households. We also do not consider consumer credits which do not provide money. In these cases, households receive consumption goods and pay with debt contracts. We consider the repayment, and the payment of interest, if it occurs in a period t, as being a part of C H ,t . <?page no="132"?> 132 7 FINANCIALIZATION Fig. 7.9 Governments Firms Households ✛ ✲ C H ,t = 1200 Y w H ,t + Y s H ,t = 1500 ✲ ❄ ❄ ✛ Y tx F ,t = 100 C S ,t = 400 Y tr H ,t = 600 Y tx H ,t = 400 ✻ Y nbb F ,t = 300 ✻ Y nbb H ,t = 100 ❅ ❅■ ∆F nbk H ,t = 300 by assuming financial investments of households amounting to 300. Fig. 7.9 shows the new situation. The basic financial wealth does not change (to ease notations, we do not record government bonds): ∆M H ,t + ∆F dep H ,t ︸ ︷︷ ︸ 300 + ∆M F ,t + ∆F dep F ,t ︸ ︷︷ ︸ 600 = 900 (7.34) There is, however, an increase in nonbasic financial wealth consisting in the financial capital bought by households: ∆M H ,t + ∆F dep H ,t + ∆F nbk H ,t ︸ ︷︷ ︸ 600 + ∆M F ,t + ∆F dep F ,t ︸ ︷︷ ︸ 600 = 1200 (7.35) Comparing this equation with Eq. (7.28) shows that households only changed the composition of their financial wealth, while firms have received additional basic financial wealth. (2) Firms can use money received from financial investments of households and other firms, as well as retained profits, for nonfinancial and financial investments. Nonfinancial investments require the belief that the goods and services produced with them can successfully be sold. These investments are eventually limited by consumption expenditures of households and state institutions. In contrast, there are no such limits to financial investments. The sum of nonbank firms’ purchases of financial capital from other nonbank firms is ∆F nbk F\B ,t . Correspondingly, the sellers receive money that can immediately be used for new financial investments, which <?page no="133"?> 7.1 EXPANSION OF FINANCIAL WEALTH 133 again create nonbasic financial wealth. Referring to Fig. 7.9, if for example firms use the money received from households’ purchases of financial capital for buying shares of investment funds, their financial wealth would increase to ∆M F ,t + ∆F dep F ,t + ∆F nbk F\B ,t = 900 (7.36) and the total increase in financial wealth would be 1,500 instead of 1,200. The increase would consist in nonbasic financial wealth, while the basic financial wealth would still amount to only 900: 300 ︷ ︸︸ ︷ ∆M H ,t + ∆F dep H ,t + 300 ︷ ︸︸ ︷ ∆F nbk H ,t ︸ ︷︷ ︸ 600 + 600 ︷ ︸︸ ︷ ∆M F ,t + ∆F dep F ,t + 300 ︷ ︸︸ ︷ ∆F nbk F\B ︸ ︷︷ ︸ 900 (7.37) The sources of the expansion of basic and nonbasic financial wealth are different. Buying financial capital from a bank, or buying bonds directly from the government, only changes the composition of financial wealth but does not contribute to its expansion; an increase can only result from an increase in the money supply. In contrast, money used for buying new financial capital from nonbanks remains in circulation, and the newly created contracts increase the financial wealth. One can assume that units buy such contracts in order to receive gains, which increase their financial wealth. So it is important to note that payments of interest and dividends made by nonbank units only redistribute the money supply. 18 This entails that these payments do not contribute to increasing the total financial wealth. The same is true for transactions on secondary markets, which only redistribute money between buyers and sellers. These transactions, however, lead to changes in market prices of tradable financial capital. A further question, therefore, concerns whether changes in these prices can also contribute to the expansion of financial wealth. 18 Recall that, if governments finance expenditures with bonds, we assume that they also finance the payment of interest out of debts and thereby increase the money supply. <?page no="134"?> 134 7 FINANCIALIZATION Market prices on secondary markets. So far we have used initial purchase prices for quantifying financial capital. This is certainly sensible for nontradable financial capital. With respect to tradable contracts, there are two possibilities. Quantification can be based on the initial purchase price that was paid when the contract was created on a primary market, or one can refer to constantly changing market prices resulting from trading contracts on secondary markets. The definitions of ∆F dep i,t , ∆F gov i,t , and ∆F bnk i,t are based on assuming that transactions on secondary markets also use the initial purchase prices. This theoretical fiction is intended to provide a sensible valuation of financial capital. The argument is that only the initial purchase prices allow to assess the liabilities which result from the generation of new financial capital. These liabilities do not change by transactions on secondary markets and are not, therefore, affected by the development of market prices. There remains the question of whether changing market prices of tradable financial capital should be viewed as contributing to changes in financial wealth. For discussing this question, we use three additional notations: ∆ ˜ F dep i,t records ∆F dep i,t evaluated in market prices ∆ ˜ F gov i,t records ∆F gov i,t evaluated in market prices ∆ ˜ F bnk i,t records ∆F bnk i,t evaluated in market prices (7.38) The change in U i ’s financial wealth evaluated in market prices can then be defined as ∆ ˜ F w i,t = ∆M i,t + ∆ ˜ F dep i,t + ∆ ˜ F gov i,t + ∆ ˜ F bnk i,t (7.39) The numerical example in Table 7.1 provides an illustration. There are four units. Initially, each unit owns the same amount of money, and U 2 and U 3 also own a piece of stock of the same kind having the market price 10 (which equals the initial emission price). Then U 1 buys U 2 ’s piece of stock and pays the amount 20 so that there is a rise in the market price from 10 to 20. In addition, U 1 buys from U 4 a different kind of stock on a primary market, the initial price is 10. <?page no="135"?> 7.1 EXPANSION OF FINANCIAL WEALTH 135 Table 7.1 Initial situation Subsequent situation Money Stock f. Wealth Money Stock f. Wealth U 1 50 0 50 20 30 50 U 2 50 10 60 70 0 70 U 3 50 10 60 50 20 70 U 4 50 0 50 60 0 60 200 20 220 200 50 250 Table 7.2 ∆M i ∆ ˜ F bnk i ∆ ˜ F w i ∆M i ∆F bnk i ∆F w i U 1 −30 30 0 −20 20 0 U 2 20 −10 10 10 −10 0 U 3 0 10 10 0 0 0 U 4 10 0 10 10 0 10 0 30 30 0 10 10 The left-hand side of Table 7.2 shows the evaluation with market prices. Although there is only one new piece of financial capital having the initial price 10, the financial wealth increased by 30; the difference is due to changing market prices. The right-hand side of the table shows the evaluation with emission prices. The financial wealth then changes only by 10, reflecting the increase in U 4 ’s liabilities. Representative data that would allow to assess the contribution of changing market prices to the expansion of financial wealth are not easily available. For a limited illustration, we refer to the development of stock prices in the euro area shown in Fig. 4.1. The upper graph (A) can be interpreted as showing the development of ˜ F t = ˜ F 0 + t ∑ l =1 ∆ ˜ F l (7.40) restricted to stock in the euro area, where t = 1, 2, 3, . . . is a sequence of months beginning in January 1990. A corresponding reference to the development on primary markets would be F t = F 0 + ∑ t l =1 ∆F l . Unfortunately, the graph (B) provides information <?page no="136"?> 136 7 FINANCIALIZATION 1990 1995 2000 2005 2010 2015 2020 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 billion Euro A B ∗ Fig. 7.10 (A) Market value of stocks in the euro area (historical composition) at the end of each month. (B ∗ ) 2000 plus since January 1990 cumulated market value of net change (newly emitted stock minus redemptions). Source: Fig. 4.1. only about monthly changes, 19 the initial value of F 0 is not known. In Fig. 7.10 we have arbitrarily assumed a value of 2,000 billion Euro. The grayed area then indicates the excess of market prices over the initial purchase prices that results from transactions on secondary markets. Belief in virtual financial wealth. How to think of the contribution of changing market prices to financial wealth depends on the 19 Newly emitted stock evaluated in emission prices minus redemptions evaluated in current prices. <?page no="137"?> 7.1 EXPANSION OF FINANCIAL WEALTH 137 interest in holding, or trading with, financial capital. One possibility is that investors are interested in revenues (interest and dividends) which they receive, with some probability, from owning financial capital. These revenues depend on the number and kind of contracts contained in a portfolio, and this characteristic of a portfolio is not affected by changing market prices. Another possibility is that investors are interested in gains which might be realized by selling financial capital (virtual gains 20 ). Since the actual market price is the result of transactions that already have taken place, it cannot be equated with the selling price in a future transaction. Nevertheless, the belief is widespread that the market price of a piece of financial capital provides a sensible indicator of its sale value, and this belief then suggests to use ∆ ˜ F w i,t , instead of ∆F w i,t , for recording changes in financial wealth. Economists support this belief and make it a part of economic rationality; for example: “Rational behavior” means that investors always prefer more wealth to less and are indifferent as to whether a given increment to their wealth takes the form of cash payments or an increase in the market value of their holdings of shares. (Miller and Modigliani, 1961, p. 412) Whether striving for virtual wealth (∆ ˜ F w i,t − ∆F w i,t ) is “rational” can well be disputed. However, whether sensible or not, the belief in virtual wealth certainly contributes to the ideological foundations of financialization. Due to this belief, transactions on secondary markets, which actually perform a zero-sum game, can appear as creating, or destroying, wealth. The ideology, moreover, conceals that financial wealth can only originate from an increase in the money supply or an expansion of contracts representing liabilities. Conclusion. The discussion has led us to distinguish between four sources of the expansion of financial wealth: 1) Government expenditures which exceed taxes and therefore increase the money supply. 20 See the discussion in Section 4.4. <?page no="138"?> 138 7 FINANCIALIZATION 2000 2005 2010 2015 2020 0 10000 20000 30000 40000 50000 billion Euro GDP M1 + term deposits Bonds Stock Investment fund shares Fig. 7.11 Financial wealth of households and nonbank firms compared with the GDP in market prices. Values refer to the euro area (historical composition). Source: Fig. 7.4, 3.1, 4.1, 5.1. 2) Net borrowing of households and firms from banks which also increases the money supply. 3) Purchases of financial capital from households and firms made by other nonbank units on primary markets. 4) Increasing market prices of financial capital resulting from transactions on secondary markets. In the first two cases, the expansion of financial wealth results from an increase in the money supply. In the third case, the money supply does not change. Financial investments are financed out of the existing money supply, and the money received by the sellers of new financial <?page no="139"?> 7.2 INEQUALITY OF FINANCIAL WEALTH 139 capital can be used for further financial investments. This mechanism therefore makes possible an expansion of financial wealth that exceeds basic financial wealth. Also nonbanks’ purchases of financial capital on secondary markets do not lead to changes in the money supply. Since these purchases, also if made by banks, do not change the number and kinds of contracts which form the basis of financial capital, they also do not change the liabilities from which, possibly, can result revenues. In this sense, transactions on secondary markets only affect the distribution of money and virtual gains. Based on previously presented data, Fig. 7.11 summarizes components which have contributed to the expansion of financial wealth in the euro area. 21 The figure suggests that there is a lot of duplication. For example, substantial amounts of stock are held by investment funds and, according to the legal fiction, owned by shareholders of the funds. However, stocks of a public company and shares of an investment fund are different kinds of financial capital, which exist simultaneously and represent separate liabilities. The example shows that the duplication is, in fact, an essential characteristic of the expansion of financial wealth. 7.2 Inequality of financial wealth In this section, we consider the distribution of financial wealth focusing on households. The leading question concerns mechanisms which contribute to the huge inequality of financial wealth. Unequal saving rates. We begin with considering saving rates that transform a part of household income into an increase in financial wealth. The most important mechanism that contributes to the inequality of financial wealth results from a positive correlation between household income and saving rates. This correlation entails that the inequality of savings greatly exceeds the inequality of incomes. To illustrate the mechanism, we use data from the German part of 21 Further components include shares of pension and money market funds, life insurances, and derivatives. <?page no="140"?> 140 7 FINANCIALIZATION 0 50 100 150 200 250 0 5 10 15 0 0.5 1 0 50 100 150 200 250 0 0.1 0.2 0.3 0.4 % σ(Y ) Y (×1000 Euro) Fig. 7.12 Upper part: Frequency distribution and cumulated distribution function of annual gross income of households in Germany (2016), up to 240000 Euro. Source: HFCS. Lower part: Assumed saving rates. the Household Finance and Consumption Survey (HFCS) that took place in the year 2017 (Deutsche Bundesbank, 2019). The sample contains 4,942 households representing an estimated totality of 40.35 million households. Since very high incomes are not properly represented, we restrict our subsample to 4,816 households with a gross annual income (in the year 2016) of up to 240,000 Euro representing about 98.6 % of the estimated totality of households. Fig. 7.12 shows the distribution of these incomes. 22 22 We note that the HFCS replaces missing values by imputed estimates and provides five versions of each data set, which randomly differ. In Fig. 7.12 we have used the variable DI2000 from the first version, which suffices for an illustration. <?page no="141"?> 7.2 INEQUALITY OF FINANCIAL WEALTH 141 Now we remind that referring to an income distribution presupposes an implicit reference to a process that has generated the incomes, and that process crucially depends on consumption expenditures (both of households and state institutions, see Eq. (7.25)). Since suitable data are not easily available, we are content with a hypothetical consideration. 23 We start from the sum of income values in the distribution in Fig. 7.12, which is 1,948 billion Euro, and assume that debt-based consumption of households and expenditures of state institutions have generated a sum of savings that equals 128 billion, resulting in a mean saving rate of 6.6 % (see Eq. (7.24) describing the relationship). We then consider a saving function, σ(Y ), which leads to the same mean saving rate. Of course, there is no unique solution; the lower part of Fig. 7.12 shows just one example. In any case, however, if saving rates rise with rising incomes, the inequality of savings will exceed that of the incomes. Using the example from Fig. 7.12, this can be seen from the Lorenz curves in Fig. 7.13. The Gini coefficients are, respectively, 0.40 and 0.74. 24 Negative saving rates. So far we have assumed that saving rates are nonnegative. A negative saving rate of a household U i occurs if the consumption exceeds its income: X i,t = C i,t − Y i,t > 0 (7.41) X i,t could be financed by debt or out of of previously accumulated financial wealth. Here we focus on the second possibility. The household redeems, or sells, some part of its financial capital (e.g., redeems term deposits). In any case, U i ’s financial wealth will decrease by X i,t . However, the same amount will be received by the firms from which U i buys the consumption goods. It follows that consumption out of financial wealth does not change the sum of financial wealth in the Below, we compare Gini coefficients calculated with the different versions. 23 For information about saving rates in Germany based on another survey (Einkommens- und Verbrauchsstichprobe) see Sp¨ ath and Schmid (2016). 24 The Gini coefficient of the income distribution is 0.40 in all five versions of the data, Gini coefficients of the saving distributions vary between 0.73 and 0.74. <?page no="142"?> 142 7 FINANCIALIZATION 0 0.5 1 0 0.5 1 Y i σ(Y i ) Y i Fig. 7.13 Lorenz curves of the distribution of gross annual household incomes, Y i , shown in Fig. 7.12 and the derived savings, σ(Y i ) Y i . X-axis: cumulated shares of households, y-axis: cumulated shares of income/ savings. economy. We note that possible implications for the overall distribution of financial wealth cannot sensibly be defined. The reason is that the money that firms receive from U i ’s expenditures forms, in most cases, an unidentifiable part of their total receipts. The question of how “this part” further circulates is, therefore, not sensible. Even if one could identify a group of households comprising all those who in a period reduce their financial wealth for financing consumption, the only definite conclusion would be that the sum of financial wealth received by all other units, both households and firms, would have increased. <?page no="143"?> 7.2 INEQUALITY OF FINANCIAL WEALTH 143 0 50 100 150 200 250 0 500 1000 Y i, 0 Y i, 10 F w i, 10 Fig. 7.14 Illustration of the accumulation of financial wealth according to Eqs. (7.42) and (7.43). Accumulation of households’ financial wealth. We now consider that households’ savings accumulate over a sequence of periods. To focus on the mechanism, we assume that incomes only increase through gains from previously accumulated financial wealth: Y i,t = Y i,t − 1 + r i,t F w i,t − 1 (7.42) where r i,t denotes the profit rate from financial wealth. The stock of financial wealth increases through saving out of current income: F w i,t = F w i,t − 1 + σ(Y i,t ) Y i,t (7.43) To illustrate, we assume that both the distribution of Y i, 0 and the saving function are given as shown in Fig. 7.12, and r i,t = 3 %. Fig. 7.14 shows the result after 10 periods. The accumulation of savings affects the distributions of incomes and financial wealth differently. This can be seen by comparing households in the lowest and the highest decile of Y i, 0 (values in Euro): Lowest decile Highest decile Mean of Y i, 10 − Y i, 0 43 31, 060 Mean of F w i, 10 − F w i, 0 318 267, 785 <?page no="144"?> 144 7 FINANCIALIZATION 0 50 100 150 200 250 0 5 10 15 0 10 20 30 40 50 60 70 % % Fig. 7.15 Proportion of households owning stock of public corporations (solid line) and shares of investment funds (dotted line), calculated in income classes 0 (50) 240. Also shown: the frequency distribution of incomes taken from Fig. 7.12. Source: HFCS. Different portfolios. We now take into account that households’ financial wealth consists of different kinds, which differently contribute to income and thereby to the accumulation of financial wealth. We roughly distinguish between three kinds: Money generates no profits; term deposits and saving contracts generate profits according to a fixed, but low, interest rate; tradable financial capital generates randomly fluctuating profits with a relatively high expectation. Fig. 7.15 illustrates that the proportion of the last category is positively correlated with household income. In order to investigate how the accumulation of financial wealth depends on its composition, we use a simple model. We assume that the income of a household in period t only depends on an initial value, Y i, 0 , and the accumulation of gains from previous financial wealth: Y i,t = Y i, 0 + r a F a i,t − 1 + r b F b i,t − 1 (7.44) where F a i,t and F b i,t denote, respectively, U i ’s stocks of saving contracts and tradable financial wealth. The accumulation in period t takes <?page no="145"?> 7.2 INEQUALITY OF FINANCIAL WEALTH 145 0 50 100 150 200 250 0 500 1000 G1 G2 Y i, 0 (×1000) F a i, 10 + F b i, 10 (×1000) Fig. 7.16 Comparison of the distribution of accumulated financial wealth between two groups, based on the model described in the text. place through saving, S i,t = σ(Y i, 0 ) (Y i, 0 + r a F a i,t − 1 + r b F b i,t − 1 ) (7.45) as follows: F a i,t = F a i,t − 1 + α i S i,t F b i,t = F b i,t − 1 + (1 − α i ) S i,t (7.46) where α i denotes the proportion of savings used for increasing saving contracts. The process begins in period 1 with F a i, 0 = F b i, 0 = 0. To illustrate, we compare two groups. Households in group G1 have a fixed value α i = 80 %. For households in group G2 we assume that α i is a decreasing function of their income: α i = 1 − Y i,t 0.9/ 250. The initial distribution of incomes, Y i, 0 , and the saving rates are identical in both groups; we use the values from Fig. 7.12. Finally, we assume a fixed rate r a = 0.02 and a randomly varying rate r b which is uniformly distributed in the interval [ 0, 0.2 ]. Fig. 7.16 describes the result after 10 periods. In both groups, the accumulated financial wealth strongly increases with the initial income; this is mainly an effect of the saving rates which are identical <?page no="146"?> 146 7 FINANCIALIZATION in both groups. The difference between the two wealth distributions is due to the assumption that in group G2 the investments in tradable financial capital rise with income. Share buybacks. The term refers to the phenomenon that public companies use profits for purchasing part of their own stock. Fig. 7.17 illustrates this phenomenon with data from the U.S. In a sense, stock buybacks supplement the payment of dividends. In both cases, profits are paid to shareholders. However, share buybacks also contribute to the inequality of financial wealth in more specific ways because they lead to an increase in the market price of a company’s stock. 25 This then allows not only shareholders, but also the company itself, to participate in speculating with the company’s shares, for example, by selling back repurchased stock. Moreover, the management can profit from rising values of shares through additional remuneration and stock options. 26 Demarcation of financial wealth. Since firms and investment funds also hold financial wealth, there is the question of whether a part of it should be viewed as also belonging to households. (1) A simple relationship exists if a household, say U 1 , holds a portfolio that is managed by an asset management company, say U 2 . In this case it is obvious that U 1 is the owner of the portfolio, and U 2 provides services and receives commissions. (2) Now let U 2 refer to an investment fund organized by a company U 3 . Relationships can be depicted as follows. U 1 s 12 −−−→ U 2 ⇐= U 3 (7.47) s 12 denotes the percentage of shares held by U 1 at some point in time. These shares are part of U 1 ’s financial wealth. It would be misleading to think of these shares as representing ownership of a 25 For empirical evidence of this effect, see ECB (2007). 26 For further discussion we refer to Lazonick (2010, 2014, 2016), Kotnik, Sakinc, and Guduras (2018). <?page no="147"?> 7.2 INEQUALITY OF FINANCIAL WEALTH 147 1990 2000 2010 2020 0 250 500 750 1000 billion USD Dividends Share buybacks Fig. 7.17 Yearly dividends and share buybacks of firms listed in the S&P Composite Index. Source: Zeng and Luk (2020, p. 6). part of the fund’s assets. In fact, they represent a (possibly restricted) right to redeem the shares, and, if the fund is not accumulating, the right to receive payouts. Who then owns the fund’s assets? The legal fiction is that the assets are the property of the fund, not of the company U 3 that has founded and organizes the fund. Actually, however, it is U 3 which determines the fund’s investment strategies and its commissions, and normally also has the right to liquidate the fund. (3) We now consider a situation where U 1 holds shares in a public company U 2 , and U 2 holds shares in a firm or investment fund U 3 : U 1 s 12 −−−→ U 2 s 23 −−−→ U 3 (7.48) The shares s 12 form a part of the financial wealth of U 1 ; and the shares s 23 form part of the assets of U 2 and, if tradable, also form a part of its financial wealth. In any case, U 1 only owns the shares in U 2 and, thereby, only has the right to receive payouts, sell the shares, and participate in some of U 2 ’s decision processes. <?page no="148"?> 148 7 FINANCIALIZATION 0 50 100 150 200 250 0 5 10 15 0 10 20 30 40 50 % % Fig. 7.18 Proportion of households owning and actively participating in a business, calculated in income classes 0 (50) 240. Also shown: the frequency distribution of incomes taken from Fig. 7.12. Source: HFCS. (4) Referring again to the diagram (7.48), we finally consider a situation where U 2 is privately owned by U 1 , and the shares s 23 are tradable and therefore represent financial wealth. It now seems sensible to consider the financial wealth owned by U 2 as also forming a part of the financial wealth of U 1 . The unequal distribution of private ownership in firms is then a further source contributing to the inequality of households’ financial wealth. To illustrate, we again use data from the HFCS for Germany. Fig. 7.18 shows how the proportion of households owning and actively participating in a business is highly correlated with their annual income. One can also assume that the firms’ financial wealth due to the accumulation of retained profits is positively correlated with the annual income of their owners. Limitations of data. Households with high income and financial assets are always severely underrepresented in surveys. The HFCS is no exception. To illustrate we compare information from the HFCS with data provided by the Deutsche Bundesbank. We use a measure of financial wealth, say f i , that includes: cash, demand and term deposits, bonds, tradable shares, and managed accounts. We consider <?page no="149"?> 7.2 INEQUALITY OF FINANCIAL WEALTH 149 0 250 500 750 1000 0 1000 2000 3000 3471 billion Euro y (×1000 Euro) cumf(y) Fig. 7.19 Cumulated values of financial wealth as defined in (7.49). Source: HFCS. the cumulated values: cumf(y) = ∑ y i ≤ y f i w i (7.49) The calculation is based on all i = 1, . . . , 4, 942 households which participated in the survey; y i records the annual household income, w i denotes the weight. The highest reported income is 2.56 million Euro. The weighted sum of the assets is 4942 ∑ i =1 f i w i = 1, 587 billion Euro (7.50) The corresponding value reported by the Deutsche Bundesbank for the year 2016 is 3,471 billion Euro. 27 Fig. 7.19 not only illustrates the large gap, but also suggests that it is due to underreporting of households with very high incomes. 27 Deutsche Bundesbank, Financial accounts for Germany 2011 to 2016, Special Statistical Publication 4, May 2017. <?page no="150"?> References Aldasoro, I., Ehlers, T. 2018. The credit default swap market: what a difference a decade makes. BIS Quarterly Review , June 2018. Belke, A., Polleit, T. 2009. Monetary economics in globalised financial markets. Springer. Bezemer, D. J. 2016. Towards an ‘accounting view’ of money, banking and the macroeconomy: history, empirics, theory. Cambridge Journal of Economics, 40, 1275-1295. Bezemer, D., Hudson, M. 2016. Finance is not the economy: Reviving the conceptual distinction. Journal of Economic Issues, 50, 745-768. Bibow, J. 2001. The loanable funds fallacy: Exercises in the analysis of disequilibrium. Cambridge Journal of Economics, 25, 591-616. Bofinger, P., Ries, M. 2017. Excess saving and low interest rates: Theory and empirical evidence. Discussion Paper DP12111. Centre for Economic Policy Research. B¨osch, M. 2014. Derivate. Verstehen, anwenden und bewerten. M¨ unchen: Verlag Franz Vahlen. Chen, P., Karabarbounis, L., Neiman, B. 2017. The global rise of corporate saving. Federal Reserve Bank of Minneapolis: Working Paper , No. 736. Dao, M. C., Maggi, Chiara 2018. The rise in corporate saving and cash holding in advanced economies: aggregate and firm level trends. IMF Working Paper , WPI/ 8/ 262. Davis, L. E. 2016. Identifying the ‘financialization’ of the nonfinancial corporation in the U.S. economy: A decomposition of firm-level balance sheets. Journal of Post Keynesian Economics, 39, 115-141. Deutsche Bundesbank 2013. The financial system in transition: the new importance of repo markets. Monthly Report, December 2013 . Deutsche Bundesbank 2017. The role of banks, non-banks and the central bank in the money creation process. Monthly Report, April 2017. Deutsche Bundesbank 2018. The growing importance of exchange-traded funds in the financial markets. Monthly Report, October 2018. Deutsche Bundesbank 2019. Household wealth and finances in Germany: results of the 2017 survey. Monthly Report, April 2019 . D¨ unnhaupt, P. 2016. Financialization and the crises of capitalism. Working Paper No. 67/ 2016. Hochschule f¨ ur Wirtschaft und Recht Berlin. <?page no="151"?> 151 ECB 2007. Share buybacks in the euro area. ECB Monthly Bulletin, May 2007, 103-111. Epstein, G. (ed.) 2005. Financialization and the world economy. Cheltenham: Edward Elgar. Fiebiger, B. 2012. Modern Money Theory and the ‘real-world’ accounting of 1-1¡0: The U.S. treasury does not spend as per a bank. Political Economy Research Institute Working Paper No. 279, 1-16. Fullwiler, S., Kelton, S., Wray, L. R. 2012. Modern Monetary Theory: A response to critics. Political Economy Research Institute Working Paper No. 279, 17-26. Geyer, C., Uttner, V. 2007. Praxishandbuch B¨orsentermingesch¨ afte. Verlag Gabler. Gruber, J.W., Kamin, S.B. 2015. The corporate saving glut in the aftermath of the global financial crisis. International Finance Discussion Papers 1150 . H¨ aring, N. 2010. Markt und Macht. Stuttgart: Sch¨ affer-Poeschel Verlag. Hilferding, R. 1910. Das Finanzkapital. Eine Studie ¨ uber die j¨ ungste Entwicklung des Kapitalismus. Wien. Hudson, M. 2006. Saving, asset-price inflation, and debt-induced deflation. In: L. R. Wray, M. Forstater (eds.), Money, Financial Instability and Stabilization Policy, 104-124. Edgar Elger. Hull, J. C. 2009. Optionen, Futures und andere Derivate, 7. Aufl. M¨ unchen: Pearson Studium. ICMA 2020. European repo market survey no. 38 (conducted in December 2019 by the International Capital Market Association). April 2020. Jakab, Z., Kumhof, M. 2019. Banks are not intermediaries of loanable funds - facts, theory and evidence. Bank of England, Staff Working Paper No. 761. Jakobs, H.-J. 2016. Wem geh¨ort die Welt? Die Machtverh¨ altnisse im globalen Kapitalismus. M¨ unchen: Knaus. Keister, T., McAndrews, J. 2009. Why are banks holding so many excess reserves? Federal Reserve Bank of New York Staff Report No. 380. Kotnik, P., Sakinc, M. E., Guduras, D. 2018. Executive compensation in Europe: Realized gains from stock-based pay. Institute for New Economic Thinking, Working Paper No. 78 . Krippner, G. R. 2005. The financialization of the american economy. Socio- Economic Review, 3, 173-208. <?page no="152"?> 152 Lazonick, W. 2010. The explosion of executive pay and the erosion of American prosperity. Entreprises et Histoire, 57, 141-164. Lazonick, W. 2014. Profits without prosperity: how stock buybacks manipulate the Market and leave most americans worse off. Available at: https: / / www.ineteconomics.org/ uploads/ papers/ . Lazonick, W. 2016. The value-extracting CEO: How executive stock-based pay undermines investment in productive capabilities. Institue for New Economic Thinking, Working Paper No. 54 . Lindner, F. 2015. Does saving increase the supply of credit? A critique of loanable funds theory. World Economic Review, 4, 1-26. Mankiw, N. G. 2017. Macroeconomics, 7th ed. New York: Worth Publishers. Marx, K. 1990 [1867]. Capital, Vol. I. Penguin Classics. McLeay, M., Radia, A., Thomas, R. 2014. Money creation in the modern economy. Bank of England Quarterly Bulletin, 54 (Q1), 14-27. Miller, M. H., Modigliani, F. 1961. Dividend policy, growth, and the valuation of shares. Journal of Business, 34, 411-433. Orhangazi, ¨ O. 2008. Financialisation and capital accumulation in the nonfinancial corporate sector: A theoretical and empirical investigation on the US economy: 1973 - 2003. Cambridge Journal of Economics, 32, 863-886. Palley, T. I. 2013. Financialization. The economics of finance capital domination. Palmgrave Macmillan. Parguez, A. 2002. A Monetary Theory of Public Finance. International Journal of Political Economy 32, 80-97. Rohwer, G., Behr, A. 2020. Revenues from financial capital. A formal framework. MPRA Paper No. 99306 . R¨ ugemer, W. 2008. Privatisierung in Deutschland. Eine Bilanz. M¨ unster: Westf¨ alisches Dampfboot. R¨ ugemer, W. 2018. Die Kapitalisten des 21. Jahrhunderts. K¨oln: Papy- Rossa Verlag. Rule, G. 2011. Issuing central bank securities. Available at: www. bankofengland.co.uk/ education/ ccbs/ handbooks lectures.htm. Sp¨ ath, J., Schmid, K. D. 2016. The Distribution of Household Savings in Germany. Hans B¨ockler Stiftung: IMK Studly, Nr. 50/ 2016. Steiner, M., Bruns, C. 2000. Wertpapiermanagement, 7. Aufl. Stuttgart: Sch¨ affler-Poeschel. <?page no="153"?> 153 Tcherneva, P. R. 2006. Chartalism and the tax-driven approach to money. In: P. Arestis, M. Sawyer (eds.), A Handbook of Alternative Monetary Economics, 69-86. Cheltenham: Edward Elgar. Tymoigne, ´ E., Wray, L. R. 2013. Modern Money Theory 101: A reply to critics. Levy Economics Institute Working Paper No. 778. van der Zwan, N. 2014. Making sense of financialization. Socio-Economic Review 12, 99-129. van Treeck, T.2009. The political economy debate on ‘financialization’ - A macroeconomic perspective. Review of International Political Economy, 16, 907-944. Werner, R. A. 2014a. Can banks individually create money out of nothing? - The theories and the empirical evidence. International Review of Financial Analysis, 36, 1-19. Werner, R. A. 2014b. How do banks create money, and why can other firms not do the same? An explanation for the coexistence of lending and deposit-taking. International Review of Financial Analysis, 36, 71-77. Wray, L. R. 2009. The rise and fall of money manager capitalism: A Minskian approach. Cambridge Journal of Economics, 33, 807-828. Zeng, L., Luk, P. 2020. Examining share repurchasing and the S&P buyback indices in the U.S. market. S&P Dow Jones Indices , March 2020. <?page no="154"?> Index Bonds, 39 Capital, 10 Central bank money, 17 Clearing and settlement, 23 Consumer credits, 131 Consumption, 118 Credit default swaps, 108 Credit defaults, 27 Debt contracts, 20 Deposit money, 18, 21 Derivatives, 29, 95 Economic units, 11 Eurosystem, 17 Excess government expenditures, 61, 121 Exchange-traded funds, 89 Financial capital, 10 Financial investments, 11, 129 Financial products, 9 Financial wealth, 61, 115, 123, 134 basic, 123, 129 nonbasic, 131 virtual, 137 Financialization, 18, 115 Forwards, 95 Futures, 95 Government bonds, 46 coupons, 49 spreads, 46 Hazard rate, 109 HFCS, 140 Index funds, 90 Index sets, 12 Interest rate swaps, 30 Investment, 118 Investment funds, 83, 146 accumulating, 85, 90 Leverage, 99 Modern Money Theory, 59 Money, 9 and capital, 10 Money circuits, 15 Money supply, 10, 18 Nonmonetary deposits, 122 Notations flows, 13 transactions, 13 Options, 101 OTC (over the counter), 28 Primary market, 20, 39, 83 Repurchase agreements, 27 Reserves, 28 Retained profits, 125 Saving rate, 120 Secondary market, 39 Share buybacks, 146 Stock, 63 dividends, 71 market prices, 65 price gains, 65 yields, 65 Swap rate, 30 Taxes, 118 Transactions, 13 Virtual gains, 69, 76, 137 Yields, 42 expected, 110 of bonds, 41 to maturity, 41 Zero-sum game, 31, 32, 70, 81, 88, 95, 98, 104, 114, 137 <?page no="155"?> ,! 7ID8C5-cfffch! ISBN 978-3-8252-5552-7 Wirtschaftswissenschaften Dies ist ein utb-Band aus dem UVK Verlag. utb ist eine Kooperation von Verlagen mit einem gemeinsamen Ziel: Lehrbücher und Lernmedien für das erfolgreiche Studium zu veröffentlichen. utb-shop.de QR-Code für mehr Infos und Bewertungen zu diesem Titel Die Autoren diskutieren verschiedene Formen des Finanzkapitals und zeigen mithilfe einfacher Modelle deren Funktionsweisen auf. Daran anknüpfend entwickeln sie einen formalen Rahmen, der dabei hilft, die relativ zur Realwirtschaft überproportionale Expansion und zunehmend ungleiche Verteilung des finanziellen Reichtums zu verstehen. The authors consider different forms of financial capital and discuss their functioning by using simple models. They then develop a formal framework that helps to understand the dramatic expansion of financial wealth (both money and financial capital) and its increasingly unequal distribution. Englischsprachiges Lehrbuch