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Economics of Money and Banking Part Two

25 January 2014 (latest update: 11 October 2014)

Lecturer: Professor Perry. G. Mehrling

Foreword

This document contains redacted course notes of the second part of the course Economics of Money and Banking by Professor Perry G. Mehrling of Columbia University in the United States that is available on Coursera.org. This course explains the basics behind money and banking that are essential in understanding the financial system. According to Professor Mehrling, the financial system is about balancing flexibility and discipline.

Professor Mehrling builds on his own background in the history of monetary economics and financial economics. He sees himself in the American tradition of monetary thought that is based on the tradition of British central banking thought. Each generation had to rethink the underlying issues for themselves in order to make sense of the conditions of their own time. The current challenge is to work out the implications of financial globalisation for money, banking and central banking.

Foreword

Contents

International money and banking
13. Chartalism, metallism and key currencies
13.1. Metallism
13.2. The current situation
13.3. Chartalism
13.4. Money view
13.5. Private and public money: from parallel systems to integrated systems
14. Money and the state: international
14.1. Introduction
14.2. Phase 1: confrontation of the FRS with the gold standard (1900-1933)
14.3. Phase 2: confrontation between Keynesian national management and the Bretton Woods fixed rate system (1933-1971)
14.4. Phase 3: Flexible exchange rates, learning from experience (1971-1999)
14.5. The global financial crisis
15. Banks and global liquidity
15.1. Introduction
15.2. Dealer model
15.3. Central bank defence
15.4. City of London and Bank of England defence
16. Foreign exchange
16.1. Economics of the dealer function
16.2. Central bank backstop

Banking as advance clearing
17. Direct and indirect finance
17.1. Introduction
17.2. The alchemy of banking and development finance
17.3. Payment versus funding
17.4. What is an intermediary?
17.5. Paradigmatic intermediaries: insurance and pension
17.6. Banks as intermediaries
17.7. The shadow banking system as intermediation
18. Forwards and futures
18.1. Introduction
18.2. Forwards and futures
18.3. Forwards
18.4. Futures
18.5. Monetary issues
19. Interest rate swaps
19.1. A swap is a swap of IOUs or a parallel loan
19.2. Swaps and other parallel loans
19.3. Comparative advantage as a reason to swap
19.4. Market making in swaps
19.5. Money market swaps
19.6. Significance
20. Credit derivatives
20.1. Introduction
20.2. Corporate bonds
20.3. CDS pricing
20.4. Market making
20.5. UBS example: market making and liquidity risk
20.6. Goldman Sachs example: hedging CDS with CDS
20.7. Goldman Abacus example: synthetic CDO as collateral prepayment

Banking and the real world
21. Shadow banking, central banking, and global finance
21.1. Shadow banking as market based credit
21.2. Immature liquidity backstop
21.3. Immature solvency backstop
21.4. Shadow banking as global banking
21.5. Shadow banking as modern finance
21.6. Definition of shadow banking
21.7. Key role of market-making institutions
21.8. Backstopping market-making institutions
21.9. Regulation of systemic risk
21.10. Regulation of collateral and payment flows
21.11. Private and public backstops
22. Touching the elephant: three views
22.1. Three world views
22.2. A world without money: commodity exchange
22.3. Imagine a world without money: risk
22.4. The education of Fischer Black
22.5. The future of banking

References

International money and banking

13. Chartalism, metallism and key currencies

13.1. Metallism

Under a gold standard, gold is the ultimate international money. Under a gold standard, each currency has its own mint par. The exchange rate is determined by the ratio of mint pars. The multiple national (state) systems relate to one another not directly (money to money) but only indirectly (credit to credit) through the international (private) system. Each national currency has an exchange rate with the international money and it is that pattern of exchange rates that sets up a pattern of exchange rates between national currencies.

Exchange rates in a metallic world

dollar = X oz.
deposits
securities

gold
S = X/Y

pound = Y oz.
deposits
securities

From this point of view, a central bank is a banker's bank, holding international reserves that keep the national payment system in more or less connection with the international system. The mint par ratio idea does not work exactly in practise because of the cost of shipping gold around. Sometimes the currency trades higher and sometimes lower. This can be rationalised within the metallist frame by using the Covered Interest Parity (CIP) relationship.

CIP: [1+R*(0,T)]S(0) = [1+R(0,T)]F(T)

where the cost of shipping gold as putting lower and upper bounds on S as follows:

X/Y – δ < S(0) < X/Y + δ

Spot rates and forward rates can move away from mint par. Also foreign and domestic interest rates can diverge a bit, all within the limits provided by the gold points. The Treynor model is operating behind the scenes here. At the moment there is no gold standard so an adequate theory should be able to explain the current situation.

13.2. The current situation

Currently the US dollar serves as world reserve currency and the foreign exchange market is largely the price of the dollar. The dollar in question is mostly the international private dollar, which is bank money and not state money. Furthermore, the hierarchical character of the FX market is more than the special role of the US dollar relative to everything else. There are major currencies that have high volume, liquid markets, with tight bid-ask spreads. All majors have the dollar as one leg: EUR/USD, GBP/USD, AUD/USD, USD/JPY, USD/CAD, USD/CHF. So-called cross-currency pairs have no dollar leg, but euro-crosses have a euro leg. The minors trade as cross-currency pairs with some major as the other leg. With only a few exceptions, minor cross-currency pairs do not trade.

The hierarchical organisation of spot FX markets carries over also into FX derivatives markets, such as forwards, futures, and options. Most derivative trades have the dollar as one leg, and most also involve other majors. By volume, the derivative market is larger than the spot market. Of the $4 trillion a day of FX trades, $1.5 trillion are spot transactions, while $1.8 trillion are FX swaps, and the remainder are outright forwards ($.5 trillion), options and exotics ($.2 trillion), and currency swaps ($43 billion). The overwhelming majority of the market is short term. The FX market is fundamentally a money market and not a capital market.

13.3. Chartalism

Joseph A. Schumpeter identified two traditions in monetary thought that he calls chartalism and metallism. Chartalism proceeds analytically by thinking of money as a creation of the state. The quintessential form of money is fiat currency, a piece of paper with the king's image on it that costs essentially nothing to produce. By contrast, Metallism proceeds analytically by thinking of money as a creation of private business. In this tradition, the quintessential form of money is some precious metal, not the liability of anyone, and all lesser monies are promises to pay that ultimate money.

Both traditions trace their origins to the distant past when there were two parallel monetary systems operating at the same time. Within nations, the hand-to-hand currency used by the common people was the king's money (and its credit derivatives). The chartalist tradition explains how that money worked. Between nations, the money used to facilitate international wholesale trade between businesses was a metallic currency (and its credit derivatives). The metallist tradition explains how that money worked. The exchange rate was a relative price between domestic and international currency that circulated side by side. There was no mint par to anchor the value of the domestic currency but yet it had value.

	public/retail	private/wholesale
money	state money (base)	international money (gold)
credit	domestic credit	international credit

Historically, domestic coinage was the king's prerogative. Given the undeveloped tax system, kings frequently used that prerogative as a source of funds to finance state projects. From a chartalist standpoint, the central bank is a creature of government finance or a government bank. In more recent history, domestic coinage has been the prerogative of the state. By monopolising the issue of currency, the government monopolises the cheapest source of funding in the nation.

Treasury

assets	liabilities
◦ (taxing) authority	◦ treasury bills, 5%

Government bank

assets	liabilities
◦ treasury bills, 5%	◦ currency

The government gains access to a further source of funds from depreciation of the value of the currency and any debt outstanding in the currency. The central bank is a way of issuing zero-interest debt that can be repudiated over time by inflation. For drawing out the full implications of this point of view, it may be helpful to take advantage of a certain affinity between the chartalist view of the money standard and the quantity theory of money (MV = PT).

The quantity theory of money does not question the ability of the government to assert what is money but it points to the limits of that power. If the government issues more money than people can use, any excess depreciates the value of money. If the volume of transactions T is determined by the patterns of real trade, and the velocity of money V is determined by monetary institutions, then an overissue of money can only show up in a rise in the price level. From this point of view, inflation (ΔP/P) is caused by and is a symptom of the government's irresponsible expansion of money, an overreaching of state power.

International exchange between states can be thought of as each country's price level being determined by the quantity of money issued in that country. The exchange rate between currencies can be seen as a relative price linking two essentially valueless currencies. Define S as the number of pounds that exchange for a dollar. The theory of purchasing power parity states that SP=P* or ΔS/S + ΔP/P = ΔP*/P*. Exchange rates reflect differential scarcity of two fiat monies, and changes in exchange rates reflect differential inflation rates, which arise from differential money growth rates. This way of looking at exchange rates makes sense with fiat currencies.

Exchange rates in a fiat money world with parallel national hierarchies

dollar
deposits
securities

S = P*/P

pound
deposits
securities

This theoretical structure does not seem to describe real economies very well, at least in the short run. There is a lot of slippage between M and P in the quantity equation, and even more in the purchasing power parity equation. Price levels move slowly but exchange rates and monetary quantities fluctuate rapidly. Advocates of chartalism argue that the theory is about the long run tendency of the system. But in the long run doubts arise about the direction of causation. Money and prices move together but maybe prices drive money, especially under modern conditions where most money is actually credit. Maybe exchange rate movements drive domestic prices.

13.4. Money view

Purchase Power Parity (PPP) sees the exchange rate as the relative price of goods, whereas CIP sees the exchange rate as the relative price of assets. Neither thinks of the exchange rate as the relative price of money, which is the money view. The survival constraint or reserve constraint focuses attention on the end-of-day clearing in a multilateral payments system. Every day payments go in and out, but at the end of the day net payments must be settled. If a country has sold more than it has bought, it is a surplus country. If a country has bought more than it has sold, it is a deficit country. The survival constraint is the requirement that deficit countries find a way to settle with surplus countries.

A deficit country needs to acquire reserve currencies. Possibly it has reserve currency holdings but often it will need to acquire reserve currency in world foreign exchange markets. This need to acquire dollars disciplines the behaviour of the deficit country. If it cannot acquire the necessary reserve currency, it will be unable to complete its purchases. The following example shows how a deficit country may acquire reserve currency via the private FX dealing system:

surplus country

assets	liabilities
+ $10 due from
- $10 due from + $10 spot

deficit country

assets	liabilities
	+ $10 due to
- 10S FX spot	- $10 due from

FX dealers

assets	liabilities

+ 10S FX spot + $10 term	+ $10 spot + $10S FX term

speculative dealers

assets	liabilities

+ $10S FX term	+ $10 term

The first row shows the net positions of the two countries before settlement. The second row shows how the FX dealer system facilitates settlement by creating credit, specifically a spot dollar liability which we suppose the deficit country buys from the dealer at the spot exchange rate using local currency, and then transfers to the surplus country. The consequence is expansion of the dealer's balance sheet on both sides, expansion that exposes the dealer to exchange risk, namely the risk that the dollar price of its new FX asset may fall.

As a hedge against this price risk, the the FX dealer enters into an offsetting forward exchange contract by borrowing term FX and lending term dollars, taking its cue from the Covered Interest Parity condition. At the end of the day the FX dealer has matched book. If the dollar price of its new FX spot asset falls, then so also will the dollar value of its new FX term liability. The FX dealer does still face liquidity risk since maintaining the hedge requires rolling over its spot dollar liability position until maturity of its term dollar asset position. The FX dealer may be a central bank for less liquid currencies.

A second speculative dealer provides the forward hedge to the FX dealer. This dealer does not have matched book and is exposed to exchange risk in the forward market, but not the spot market. In practise the speculative dealer may hedge with a futures position, or an FX options position, but that only shifts the risk to someone else. The second speculative dealer is engaged in a carry trade, paying the dollar interest rate and receiving the FX interest rate. If the realised spot rate is different from the forward rate, this speculation will make a profit or a loss.

13.5. Private and public money: from parallel systems to integrated systems

Both metallism and chartalism do not explain the modern money system very well. The modern money system is not a parallel money system but rather a hybrid or integrated system. Historically, wars have provided the opportunity for kings to discover the usefulness of the private money system. During wars, governments face a need for funds in order to pay for crucial war materials. Typically the kind of funds they need are metallic and not fiat. The private metallic system can provide gold since it runs on metallic reserves.

Suppose, as was usually the case, there is a banker's bank separate from the government bank, and suppose such a bank issues deposits against a 100% gold reserve. In that case there are parallel money systems, although the private gold money is better or higher in the hierarchy. The prewar parallel banking systems look like this:

government bank

assets	liabilities
◦ Treasury bills	◦ domestic currency

banker's bank

assets	liabilities
◦ gold ◦ private credit	◦ deposits

Then the government borrows from the private banking system and takes payment in gold. Consequently, the Wartime hybrid banking system changes like this:

government bank

assets	liabilities
◦ Treasury bills + gold	◦ domestic currency + loan

banker's bank

assets	liabilities
- gold + state loan	◦ deposits

When the government repays the loan in currency and bills, holding onto gold as the international reserves but requiring banks to use its own currency as domestic reserves, a postwar hybrid banking system emerges that looks like this:

central bank

assets	liabilities
◦ gold ◦ Treasury bills	◦ domestic currency

private banking system

assets	liabilities
+ domestic currency + Treasury bills	◦ deposits

In return for financing the war the bankers gained the right to issue forms of money that compete with the money of the state. It is a win-win. In the pre-war parallel system, domestic credit was tied to the inferior state money, and repressed with adverse economic effects. International credit was tied to the superior international money, but inaccessible to most people. The hybrid structure brought more credit to the state for war, and then more credit to the economy for peacetime expansion.

14. Money and the state: international

14.1. Introduction

Mundell sees the 20th century as a long excursion away from the gold standard and back again. The discipline that is imposed by the gold standard is a payments discipline. Countries settle payments ultimately in gold, although there are myriad opportunities to delay net settlement for a while in anticipation that some offsetting payment will arrive. This discipline not only polices the behaviour of individual nations, but also knits the entire collection of nations into a more or less unified, integrated, and stable money flow system.¹

Individual states and their central banks may not be willing to submit to the discipline. If they could coordinate with other states, either to revalue gold or to create accepted substitutes for gold such as the SDR, they could relax the discipline somewhat by increasing the amount of gold and gold substitutes in circulation relative to the amount of credit. In practise they have not been able to coordinate because individual states and their central banks are often generally not satisfied with the place assigned to them in the system, and always looking to improve their position.

As a consequence, 20th century monetary history is not about gold and but about the behaviour of the dominant nation (the US) and its central bank (the Fed). Mundell blames monetary mistakes for most of the travails of the twentieth century, not only deflation and inflation but also wars, social unrest, Communism and Nazism. Mundell's account of the 20th century has three phases, which are the confrontation of the Federal Reserve System with the Gold Standard (1900-1933), contradiction between Keynesian national management and the Bretton Woods fixed rate system (1933-1971), flexible exchange rates (1971-1999).

14.2. Phase 1: confrontation of the FRS with the gold standard (1900-1933)

The Federal Reserve System was established in 1913 on the eve of WWI. Only the US remained on gold during the war, but that was no great feat because throughout the war gold flowed in to pay for war material. At the end of the war, most of the world's gold was in the US, and the international monetary system was comprised of national currencies, none of which was properly convertible into gold. Nevertheless, the decision was made to move in the direction of a return to the international gold standard which had been the system before the war.

Almost no one prepared for the deflationary consequences of doing so without revaluing gold. Over the next decade, the value of gold would increase with every country that returned to gold, simply because of the increased monetary demand for gold, and the consequence would be downward pressure on other prices in gold throughout the world. France was a partial exception because France devalued its own currency against gold, and so got a fresh start.

Added to this structural deflationary tendency there was some mismanagement by the Fed, which were the ingredients for a real disaster. Mundell identifies the key mistake in 1931. Instead of pumping liquidity into the system, the Fed chose to defend the gold standard by raising the rediscount rate from 1½ to 3½ percent. Thus the Fed compounded the secular deflationary tendency with an explicitly deflationary policy of its own.

The Fed was defending the position of the dollar relative to the better international money gold. According to Mundell, this was the wrong thing to do for two reasons. First, the whole point of raising the rediscount rate was to attract gold, but that just increased the upward pressure on the price of gold, which means the downward pressure on prices generally, and on other currencies. In the event the pressure was too much for the weaker currencies to stand, and they simply abandoned gold, as did the United States itself eventually, and the end result was the collapse of the international monetary system, and along with it much of international commerce.

Second, Mundel stated that by defending the dollar against gold, the Fed was in effect leaving domestic banks on their own to defend the par value of bank deposits against the national dollar. Falling agricultural prices meant widespread loan default, and tight central bank policy added liquidity pressure. The result was widespread domestic bank failure, which added a further impulse to domestic deflation.

Mundell further suggested that the right policy would have been a worldwide revaluation of gold, which means a worldwide depreciation of currencies against gold. Mundel also suggested that if the price of gold had been raised in the late 1920s, or had the major central banks pursued policies of price stability instead of adhering to the gold standard, there would have been no Great Depression, no Nazi revolution, and no World War II.

14.3. Phase 2: confrontation between Keynesian national management and the Bretton Woods fixed rate system (1933-1971)

At the Bretton Woods conference, most gold was once again in the US, and the international system once again involved a collection of national currencies that were not convertible into gold. This time, unlike World War I, there was no thought of trying to return to the gold standard. Instead there were several proposals for fundamental reform, most notably Keynes' bancor plan which would have created an elastic international money supply.

deficit countries

assets	liabilities
	◦ Bancor loans

international bank

assets	liabilities
◦ Bancor loans	◦ Bancor deposits

surplus countries

assets	liabilities
◦ Bancor deposits

A key feature of this plan was an attempt to create symmetry between the deficit and surplus countries, which means weakening the discipline of the survival constraint that binds on the deficit countries but not the surplus countries. Countries with large and persistent surpluses were to be penalised, and so provided with incentives for spending the surpluses (on goods or capital from the deficit countries) rather than save them. At that time, the US was the only surplus country as everyone else was rebuilding from wartime damage, so the US did not like this feature and instead put forward a plan that fixed the quantity of international money.

International Monetary Fund

assets	liabilities
+ gold + national currencies	+ SDR's

member central banks

assets	liabilities
- gold + SDR's	+ national currency

This rather harsh discipline at the international level could have caused problems. The US dollar was convertible into gold, and all other currencies were convertible into the US dollar, the so-called anchored dollar system, and the quantity of dollars was elastic because the United States (not just the Fed) was the world's bank.²

United States

assets	liabilities
◦ gold ◦ long term bonds	◦ short term US dollar deposits

rest of the world

assets	liabilities
◦ short term US dollar deposits	◦ long term bonds

In these balance sheets there is an expansion of dollar reserves for the rest of the world that does not require the US to be running a trade deficit. Instead they are just the liability counterparts of gross capital outflows to finance the redevelopment of the rest of the world. So long as the rest of the world accepts dollar deposits as if they were gold, the system works fine, but it comes under unsustainable pressure if gold becomes undervalued, so that holders of dollars ask for the promised convertibility. Over time, in the 1960s, this started to happen with increased frequency.

The problem could have been fixed by revaluing gold. Mundell wrote that Arthur Burns was trying to get Nixon to do that. Another way was to increase the supply of gold, or rather of SDR's (Special Drawing Rights) or paper gold by the IMF. This was attempted in 1967 but it was too little too late. Mundell suggests that if more had been issued, so that central banks could have substituted SDRs for gold reserves, that would have reduced worldwide demand for gold, lowering its price relative to the dollar, and taking the pressure off. Instead, the pressure continued and in 1971 the US simply went off the gold standard.

14.4. Phase 3: Flexible exchange rates, learning from experience (1971-1999)

When the United Stated unilaterally broke the connection with gold, even the weak discipline of the gold anchor was lost. The rationale for other currencies to peg to the dollar was therefore lost, and they broke away. A system of national currencies and floating exchange rates emerged. A system of national currencies is typical in war time, when commerce is typically severely restricted, but quite unusual in peace time.

Some economists like Milton Friedman argued that flexible rates actually work better, on the grounds that market prices tend to work better than administered prices. He may have thought that price stability domestically would inevitably result in exchange rate stability internationally, through the mechanism of Purchasing Power Parity. In reality, this did not happen.

The result was inflation and stagnation simultaneously until the 1980s when some discipline entered the system again, and an ordering around a few key currencies. The discipline came from commitment by central banks to a regime of inflation targeting domestically, even when there was no international disciplining device. Such regimes were very successful in producing price stability. But internal price stability did not translate into international exchange stability. Currency exchange rates remained volatile.

One important legacy of the period of disorder was the rise of currency futures markets for hedging exchange rate risk. These markets remain extremely important to this day. Mundell does not speak much about speculative currency markets as he may have expected the emergence of a fixed exchange system. One of the things he missed was that the world funding market is basically a US dollar funding market, not euro or yen. The US dollar is very much the dominant player as has been proven in the global financial crisis.

14.5. The global financial crisis

During the financial crisis, one of the big problems was a shortage of dollar funding for US dollar assets held outside the United States. When the system was working, there was an unregulated international dollar market that worked like this:

global shadow bank

assets	liabilities
◦ RMBS	◦ money market funding

money market mutual fund

assets	liabilities
◦ money market funding	◦ shares

When the crisis started, money market funding dried up as money market mutual funds refused to roll over their loans to the shadow banks and demanded high quality money market assets such as Treasury bills. In the aftermath of Lehman and AIG, the funding problem was fixed temporarily by means of liquidity swaps between central banks. The Fed lent US dollars to foreign central banks, which in turn lent those US dollars to the shadow banks located in their countries. The central banks replaced the collapsing money markets. The action looks as follows:

shadow bank

assets	liabilities
◦ RMBS	+ US dollar loan from ECB

ECB

assets	liabilities
+ US dollar deposit (swap) - US dollar deposit + US dollar loan to shadow bank	+ euro deposit (swap)

Fed

assets	liabilities
+ euro deposit (swap)	+ US dollar deposit (swap)

US Treasury

assets	liabilities
+ US dollar deposit	+ Treasury bills

money market mutual fund

assets	liabilities
+ Treasury bills	◦ shares

Ultimately the money market mutual fund deposits still fund the Shadow Bank holding of mortgage backed securities. But there is no direct lending from the money market mutual fund to the Shadow Bank. Rather the money market mutual fund lends to Treasury, which lends to Fed, which lends to ECB, which lends to the Shadow Bank. In the aftermath, this temporary construction was dismantled by taking mortgage backed securities back to the US where it was easier to realise dollar funding directly. Over a trillion US dollars of MBS have been placed on the balance sheet of the Fed as follows:

Fed

assets	liabilities
◦ mortgage backed securities	◦ reserves

banks

assets	liabilities
◦ reserves	◦ deposits or other funding

money market mutual fund

assets	liabilities
◦ deposits or other funding	◦ shares

This was a reversal of globalisation of the financial system similar to the end of the 1920s. The US dollar is used as a global currency while it is also the national currency of the United States. This makes the United States vulnerable to issues in the global financial system.

15. Banks and global liquidity

15.1. Introduction

The dealer model can be adapted to the foreign exchange market under a gold standard. At the time of Bagehot there were bills of exchange, discounting banks, and a central bank as liquidity backstop. The discussion of international money starts by specifying that the firms issuing and accepting bills are both outside England, while the discounting banks and the central bank are inside England.

surplus firm/country

assets	liabilities
- goods + bill - bill + notes

City of London banks

assets	liabilities
+ bill - notes
- bill + notes

deficit firm/country

assets	liabilities
+ goods	+ bill
- goods + notes - notes	+ bill - bill

The surplus firm discounting bills for sterling pound notes, which are not the domestic currency for the surplus firm. The deficit firm pays the bill with sterling pound notes, which are not the domestic currency for the deficit firm either. The surplus firm has to exchange pound sterling for its domestic currency, and the deficit firm has to exchange domestic currency for pound sterling. These are two different currencies, and the exchanges happen at two different times. Foreign exchange dealers make two-way markets in the various currencies by quoting prices and absorbing the resulting order flow on their own balance sheet as follows:

surplus dealer/bank

assets	liabilities
+ notes/gold - domestic currency

Bank of England

assets	liabilities
+/- gold	+/- notes

deficit dealer/bank

assets	liabilities
- notes/gold + domestic currency

At the inception of the trade, the surplus dealer is creating domestic currency and building up inventories of international reserves. At maturity, the deficit dealer is destroying domestic currency and drawing down inventories of international reserves. And at any point in between, either dealer may decide to hold reserves in gold or in pound sterling, and go to the Bank of England for that purpose. So there are three markets.

15.2. Dealer model

Under the gold standard, the analysis is fairly straightforward. There is a mint par, defined as a quantity of gold that private agents can take to the mint and get pounds sterling. Because there is some cost of transporting gold abroad, the exchange rate for pounds sterling can move a bit away from the mint par, on either side, without creating incentive to convert pounds into gold. These gold points are the outside spread, established by the central bank, within which the private dealers make markets, establishing the inside spread.

The exchange rate S = £/$ = x/y, ratio of mint pars, so actual exchange rate fluctuates between gold points, so x/y – δ < S < x/y + δ. Dealers are willing to add to their inventories of foreign exchange if they can get them at a cheap price, but once that price falls to the gold point they are unwilling to add any more. At that point, anyone who wants to sell foreign exchange must sell it to the central bank who pays gold (mint par) for them.

Taylor model for gold standard currencies

The diagram shows the economics of a dealer who is taking on liquidity risk by shedding international reserves (pounds) and holding instead dollars. This is a position similar to the deficit dealer. The dealer is willing to bear a certain amount of liquidity risk, but when it gets too much, the exchange rate falls to the gold points, the dealer stops and the central bank steps in.

15.3. Central bank defence

Under the gold standard, central banks are committed to maintaining a fixed exchange rate. Upward pressure on the currency can be met by issuing the currency to buy foreign reserves. This is not a problem. Downward pressure must be met by buying currency, which can be a big problem. There are three basic methods toward this end. First, the central bank can buy in domestic currency with its holding of international reserves, which is exactly what the deficit dealer was doing. The net effect is a contraction of the balance sheet, since the currency purchased is the central bank's own liability. But this works only as long as the central bank has reserves.

central bank

assets	liabilities
- gold reserves + currency - currency	- currency

Second, the central bank could sell some assets, presumably the most liquid ones, for example the public debt. This results in a contraction of the balance sheet, but also possible downward pressure on Treasury bill price, hence an upward pressure on interest rates. This may be large upward pressure if speculators fear devaluation. Central banks can offer interest bearing securities in exchange for currency, in the hope that the interest will prove sufficient incentive to prevent asset holders from demanding payment in international reserves.

central bank

assets	liabilities
- Treasury bills + currency - currency	- currency

Third, if the central bank has no more reserves and is unwilling to push interest rates higher, one further possibility is to rely on lines of credit with other central banks or the IMF. These borrowed reserves then can be sold for US dollars.

central bank

assets	liabilities
+ reserves - reserves + currency - currency	+ borrowed reserves - monetary base

The third method amounts to a portfolio adjustment on the liability side. The balance sheet stays the same but some of the monetary base that was in private hands shifts to other central banks. These examples make clear in what sense a contraction of the money supply supports the international value of the currency. Central banks can enter the market as buyers of their own currency, but since currencies are the liability of central banks, a purchase of their own currency by central banks is a contraction of their balance sheet.

The deficit entity is forced to adjust, but the deficit entity is not necessarily below the Bank of England in the hierarchy. The deficit entity could be the Bank of England itself, if the pound drops to the gold points, for example when the dollar rises to the point where gold flows from the Bank of England in defence of its mint par.

15.4. City of London and Bank of England defence

The global discount business in the City of London involved daily note outflow, and also note inflow as discounts reach maturity. Each individual bank is watching the balance between outflow and inflow, and adjusting its discount rate in order to bring them into line. A higher rate discourages new discount, thus stemming outflow for a while until inflow restores liquidity. All banks were doing this, and competition between them established the market rate of interest, which fluctuates over time depending on the aggregate note outflow and inflow between the banking system and the rest of the world.

Taylor model for gold standard interest rates

This discount system can be understood using the dealer model. Banks are willing to take on additional liquidity risk, by continuing to discount even when note reserves are falling, if they get compensated by a higher interest rate. But at some point, they have enough, market rates rise to bank rate (the discount rate quoted by the Bank of England) and the Bank of England takes over. It may discount (or rediscount) bills and pay out notes, just like the private banks. But it may also discount bills by creating deposits, which are promises to pay notes, insofar as banks are willing to accept deposits as substitutes for notes.

Bank of England Banking Department

assets	liabilities
+ bills - notes + bills	+ deposits

This kind of lender of last resort activity, which is lending freely but at a high rate against good security, can stem an internal drain, meaning a net outflow of notes from the banking system into circulation. This does not help much when there is an external drain, meaning a net outflow of notes to the rest of the world. The rest of the world doesn't want notes, it wants gold, so if it finds itself with excess notes it just takes them to the issue department of the Bank and exchanges them.

Bank of England Issue Department

assets	liabilities
- gold	- notes

The Bank of England can face the same problem that a deficit country central bank faces. It can pay out gold for a while, but reserves inevitably fall short. The next step can be raising Bank Rate. This discourages the world from bringing bills to London for discount, and allowing repayment of maturing bills to restore gold reserves. The problem with this policy is that it inevitably raises domestic interest rates as well, even though domestic credit was not the source of the problem. The Bank of England may borrow from other central banks that have larger gold reserves or suspending specie payments.

This latter is the "nuclear option" but the Bank of England historically was forced to resort to it on numerous occasions. Obviously once the Bank of England suspends gold payments, the gold point story about determination of exchange rates no longer operates.

Central banks were crucial for the operation of the gold standard. They established two critical outside spreads that provide bounds on the system within which profit maximising dealers could operate to make markets. One bound is on the exchange rate, or the gold points. The other is on the interest rate, or Bank Rate, which is a term interest rate. In modern exchange rate systems, neither of these bounds is effective. Nonetheless, the analysis can be adapted to explain how things work nowadays.

Keynes wrote in his Tract on Monetary Reform, where he referred to the gold standard as a barbarous relic, and emphasised the role of Ministers of Finance in discovering how to operate national currencies without the discipline of gold. He urged them to focus their efforts on stabilising domestic pricing, hoping that such stability will also, through Purchasing Power Parity (PPP), stabilise exchange rates. It turned out that price stability is not enough, as Mundell emphasises. There is need of a theory of exchange that does not come from Purchasing Power Parity (PPP), but rather from Covered Interest Parity (CIP).

16. Foreign exchange

16.1. Economics of the dealer function

It is possible to develop a more general theory of exchange rate determination without a gold standard anchor. The example from paragraph 13.4 shows how a deficit country can acquire US dollars using the private FX dealing system. The speculative dealer is concerned about price risk. This dealer is only willing to accept more price risk if the forward rate for FX depreciates relative to expected spot, so there is a larger expected profit. This depreciation is represented as a downward sloping forward curve in the Taylor model.

The economics of the speculative dealer function require violation of Uncovered Interest Parity (UIP). The expected profit that lures the dealer into a naked forward position is a deviation between forward and expected spot. The expected spot plays the role, in a flexible exchange rate system, that the mint par ratio plays in a gold standard system. Deviations from mint par create opportunities for dealer profit, so long as there is some expectation that the system will at some time return to mint par.

In a flexible exchange rate system, there is no long run anchor for expected spot. If people believe UIP then they believe that forward rates are unbiased forecasts of future spot rates, so depreciation of forward rates which arises to encourage dealers to absorb imbalances can easily be interpreted instead as a sign that future spot rates will also involve depreciation. This is a source of potential volatility in the flexible exchange rate system.

A matched book dealer faces dollar liquidity risk. The larger the dealer's book, the larger the risk. The dealer is buying FX spot and selling FX forward. He is willing to enlarge his book, and hence his liquidity exposure, but will insist on buying spot relatively more cheaply than forward, so F/S increases with the size of the book. S goes up, but F goes up more. Spot depreciates but forward depreciates more.

By contrast to the gold standard case, the outside spread is not set by the central bank, at least not directly. Modern central banks typically operate on the overnight interest rate, not the term rate. Supposing the US and foreign country maintain constant overnight interest rates, that still leaves scope for payments pressure to move around term rates. Because of CIP, F/S=(1+R*)/(1+R), so as positions build up term interest rates have to move apart as well. Assuming that the dollar rate is unaffected, that means FX term rates rise.

Central banks are involved indirectly because of the expectations hypothesis of the term structure, which states that term rates should be the same as the expected result from rolling over a series of short term deposits. The expectations hypothesis fails empirically because the implied arbitrage (borrowing short and lending long) exposes to liquidity risk. FX dealers are borrowing short and lending long in dollars, hence exposed to liquidity risk, and they are willing to do more of it only if they are compensated. One way to compensate the dealers is to keep overnight rates low even as term rates rise.

16.2. Central bank backstop

There is a limit to this. If private dealers hit their limits, and the central bank is still not willing to let the overnight rate go, the central bank itself can get into the speculative dealer business, selling the hedges that the matched book dealers want. The central bank can get into the matched book business too by doing liquidity swaps with other central banks. The way that a central bank's commitment to target overnight rates implies FX intervention whenever the F/S ratio moves to the extreme end of the possible range. Central banks that target overnight interest rates are inevitably drawn into serving as FX dealers of last resort.

In some cases the deficit central bank borrows reserves from the surplus central bank for a certain term at interest rate R^g, trades those reserves with the private citizen at the spot rate s^g, and then sterilises the consequent domestic monetary contraction by buying a domestic Treasury bill. The surplus central bank lends term reserves by creating a spot deposit to the credit of the deficit central bank, which winds up in the hands of its own private citizen, and then sterilises the consequent domestic monetary expansion by selling a domestic Treasury bill. For simplicity, the private citizen counterparts to both sterilisation operations are not shown.

private citizen, surplus country

assets	liabilities
◦ $10 due from + $10 spot - $10 due from

central bank, surplus country

assets	liabilities
+ $10 term, R^g (swap) - $10 Treasury bill (sterilisation)	+ $10 spot (swap) - $10 spot, deficit central bank + $10 spot, private citizen - $10 spot (sterilisation)

central bank, deficit country

assets	liabilities
+ $10 spot (swap) - $10 spot + 10S^g FX spot + 10S^g FX term (sterilisation)	+ $10 term, R^g (swap) + 10S^g FX spot (sterilisation)

private citizen, deficit country

assets	liabilities
+ $10 spot, central bank - 10S^g FX spot, central bank - $10 spot	◦ $10 due to - $10 due to

At the end of the day, the deficit country central bank is borrowing dollars term and lending FX term, which is essentially a naked forward position analogous to the position a speculative private dealer was induced to take by the expectation of private profit. A central bank does not need and probably does not expect to profit from this speculation.

The interest rate at which it borrowed from the surplus central bank does not need and probably does not match the term funding rate in private credit markets. And the spot rate at which it sold dollars to its own citizen does not need and probably does not match the spot rate in private FX markets. These are both policy rates, which can be expected to reflect the non-commercial relationship between one central bank and another internationally, and the non-commercial relationship between the central bank and the private citizen domestically.

At the end of the day, the surplus country central bank is lending dollars term to a foreign central bank, instead of to its parent government. This is very unlikely to be a move about which the parent government is neutral, hence our characterisation of it as a limiting case. Counterparties other than the surplus country central bank, could also help. There are sources of reserves other than the Fed, sources such as regional liquidity pooling arrangements or the International Monetary Fund which do not depend on the goodwill of the surplus country's government.

Once it is recognised that deficit country dealer of last resort involves willingness to take on a naked forward position when no one else will, it becomes clear that the whole operation does not need to involve another central bank as counterparty at all. The deficit country central bank could, if it choses so, instead facilitate private matched-book dealing by serving as the speculative dealer to enable forward hedging of spot exposures. It could go even further by facilitating the term dollar borrowing of its own private citizens by directly offering them forward hedges, so taking their exchange risk onto its own balance sheet.

All of this is policy, so pricing of these forward contracts does not need to be, and probably will not be on commercial terms. The limiting case along these lines comes when central banks offer forward cover to all comers at the same rate as current spot exchange, in effect fixing the exchange rate as a matter of policy.

The danger is that whenever a trade is offered at non-commercial prices, arbitrage opportunities for speculators are offered. The positive case for doing so must therefore rest on an argument that commercial prices are in some sense wrong. One consequence of the view that the exchange rate is the relative price of money is to draw attention to the way that order flow can push prices around for reasons that are not fundamental. The potential problem is that private agents may take these distorted prices as parametric for their economic decisions, and may make distorted decisions.

This is a potential argument for central bank intervention, certainly in extreme cases to prevent breakdown of the payments system, but also in less extreme situations where, for one reason or another, private markets are not making markets at all, or only reluctantly doing so at the cost of substantial price distortion. But it is an argument that applies only under specific conditions, not universally. The exchange rate is not a free variable left open for state choice, but neither is it a market price that always fully reflects fundamental valuation.

Banking as advance clearing

17. Direct and indirect finance

17.1. Introduction

It is common practise to treat capital markets in finance courses, and money markets in banking courses. In reality the two markets are completely integrated, most obviously in the shadow banking system, which is money market funding of capital market lending. The intellectual habit to treat them separately is outdated. The tight integration of the two has historical and institutional roots.

When Bagehot lived, the two were much more separate than now. Banking was about discounting of short term bills that financed goods on their way toward sale. Bank liquidity was assured by creating a portfolio of bills maturing at different times in the future, so that cash inflows meet possible cash outflows, either from deposit withdrawal or from new discounts. On the other hand, there was a capital market, for government and corporate bonds, and also equities.

primary borrowers (businesses)

assets	liabilities
	◦ bills
	◦ bonds ◦ equities

banks

assets	liabilities
◦ bills	◦ deposits

primary lenders (households)

assets	liabilities
◦ deposits
◦ bonds ◦ equities

The first line is the money market, while the second line is the capital market. Households buy bonds and equities by transferring their bank deposits to businesses, that spend them on investments. But for the most part banks did not buy bonds or equities as they were thought to be inappropriate assets for banks because they were not self-liquidating. Economic historians argue whether British excellence in money markets held back the capital development of the nation by emphasising short term finance at the expense of long term finance.

In the United States, which was a developing country compared to Britain at that time, the need for long term finance caused the banking system to regularly hold long term bonds. Even some of the purported short term loans were really long term, since they were intended simply to roll over at maturity. As a consequence, banks did not have regular cash inflows to provide liquidity and had to devise another method. Instead of self-liquidating short term assets, banks in the United States held substantial cash reserves, including correspondent balances, and devised elaborate mechanisms of secured interbank borrowing using their bond holdings as collateral.

deficit bank

assets	liabilities
◦ bonds ◦ loans ◦ cash ◦ banker's balances - cash reserves - banker's balances	◦ deposits + interbank borrowing (repo)

surplus bank

assets	liabilities
◦ bonds ◦ loans ◦ cash + cash reserves + interbank borrowing (repo)	◦ deposits ◦ banker's balances - banker's balances

This also explains why the United States was the first country to have bond rating services. A bank in need of funds needed to sell some of its bond holdings to another bank or to put it up as collateral. There was no time to investigate the value of the bonds so they relied on rating agencies.

In the American system, liquidity was all about shiftability or salability. Shiftability means market liquidity, or the ability to buy and sell. The net effect of this system was to mobilise bank deposits as a source of funding for long term capital finance, by using the repo market and not the real bills discount mechanism as a source of liquidity. The founders of the Fed saw this shiftability system as a source of instability and tried to replace it with proper real bills discount banking.

One way of understanding the banking collapse of the 1930s is that it was a run on the shadow banking system of the time, namely this system of private funding liquidity using repo on non-Treasury security. The Fed refused to support it, so it collapsed. The consequence was that the government had to take on responsibility for long term lending itself through various mechanisms, most famously the Reconstruction Finance Corporation. In the United States, securities markets and money markets have always been intertwined.

17.2. The alchemy of banking and development finance

Schumpeter understood the importance of banking for development finance. His experience was with the banking system in continental Europe. As early as his PhD thesis he insisted on the importance of bank deposit creation as a mechanism for development finance, a way of giving purchasing power to entrepreneurs who do not have it, without requiring individual savers to cough up saved funds.

development bank

assets	liabilities
+ capital loans	+ deposits

The ability to create money from nothing is often seen as the work of monetary cranks as economics often seems to imply that there is no such thing as a free lunch. But monetary matters there is a free lunch. Adam Smith promoted the adoption of a paper money system as a way of economising on the use of gold. Gold can be traded for real capital assets, which is a trade of a sterile commodity for a productive resource. In a way that is what has been happening ever since, moving toward a pure credit economy.

The key is the use of banking to mobilise unused resources. If entrepreneurs use their new deposits to buy things that otherwise would have been unsold, this does not raise prices and increases economic activity. Schumpeter emphasised technological change. Others have emphasised other margins of mobilisation. The Lewis model on economic development emphasises the role of banks in mobilising underemployed labour, moving it from the traditional subsistence sector to modern manufacturing sector.

17.3. Payment versus funding

If a corporation is borrowing in order to purchase some physical capital asset such as a machine or a building, this involves the corporation in current expenditures far in excess of current receipts, and it is only over the long lifetime of the capital asset that the corporation expects to reverse that imbalance. Society's problem thus is to find someone to hold that illiquid asset over its entire productive lifetime.

The issue at stake is the distinction between payment versus funding. A corporation can acquire means of payment simply by swapping its own IOU with that of a bank. The corporation can be using that means of payment to acquire a physical asset from society. Then the question arises whether society as a whole is happy with the asset portfolio implied by the swap.

corporation (borrower)

assets	liabilities
+ deposit - deposit + machine	+ bank loan

bank

assets	liabilities
+ loan to corporation	+ deposit

society (lender)

assets	liabilities
+ deposit - machine

If society is happy holding money rather than the physical asset then the new capital is funded by an increase in outstanding money balances. This is a tricky matter because money is a promise to pay on demand, while the capital asset cannot be turned into payment except over a long time. There is significant mismatch between commitments and cash flows, which can be a cause for crisis. If will be safer when the financing matches better the characteristics of the asset being financed. This is the funding problem.

If society is not happy acquiring additional money balances, then the recipients will attempt to use those balances to buy a different financial asset. This will drive up the price of alternatives to money and so provide an incentive to issue such alternatives. One way this all can work out is the following. Suppose that the bank loan was only bridge financing until the capital asset is up and running. Once its ability to produce revenue is proven, the corporation can pursue permanent financing in the form of bonds. The proceeds of that bond offering are then used to pay off the bank loan.

corporation (borrower)

assets	liabilities
	- bank loan + bond

bank

assets	liabilities
- loan to corporation	- deposit

society (lender)

assets	liabilities
- deposit + bond

The bridge financing by deposit expansion is a kind of indirect finance, while the takeout financing by bond issue is a kind of direct finance. The Gurley and Shaw point of view emphasised the use of intermediaries as sources of indirect finance for the capital development of the nation.

17.4. What is an intermediary?

An intermediary is a financial institution that mediates between the primary borrower and primary lender of funds, holding as assets the liabilities that the borrower issues, and issuing as its own liabilities the assets that the creditor holds. Standard banking texts (such as Mishkin) make a big point about the empirical importance of such indirect finance by contrast with direct finance in which borrower and lender meet directly, as by the direct issue and holding of stocks and bonds.

corporations (primary borrowers)

assets	liabilities
	Direct finance: ◦ stocks ◦ bonds
	Indirect finance: ◦ stocks ◦ bonds ◦ loans

intermediaries

assets	liabilities

Indirect finance: ◦ stocks ◦ bonds ◦ loans	Indirect finance: ◦ pensions ◦ insurances ◦ money

households (primary lenders)

assets	liabilities
Direct finance: ◦ stocks ◦ bonds
Indirect finance: ◦ pensions ◦ insurances ◦ money

Gurley and Shaw, in their classic Money in a Theory of Finance (1960), made a big point about the importance of such financial intermediation. They argued that intermediaries help to facilitate economic growth by bridging any potential mismatch between the kind of liabilities that borrowers want to issue and the kind of assets that creditors want to hold. It is by changes in the quantity of indirect finance that capital markets equilibrate, and channel funds from savers to investors.

Modern finance, by contrast, emphasises that no risk is eliminated in the process of intermediation, only transferred, and sometimes quite opaquely. By changes in price capital markets equilibrate. Attempts to avoid this by indirect finance only create arbitrage opportunities that over time have transformed the system.

17.5. Paradigmatic intermediaries: insurance and pension

In idealised form, these intermediaries hold the following balance sheets:

insurance corporation

assets	liabilities
◦ bonds	◦ policies

pension fund

assets	liabilities
◦ stocks	◦ pension plans

Insurance corporations and pension funds are intermediaries, since their assets are of a different kind than their liabilities. Bonds pay regular coupons no matter what happens. Insurance policies pay only if some insurable event occurs. Stocks pay dividends and capital gains. Pension plans pay when owners retire, an amount depending on final wage, inflation, job tenure and the like (for defined benefit plans).

One of the trends in insurance is replacement of the traditional whole life insurance policy, which included a savings component, with term insurance. One of the trends in pensions is replacement of the traditional defined benefit plan with the defined contribution plan, such as a 401(k). Both trends reflect the rise of mutual funds as competitors to traditional indirect finance.

bond mutual fund

assets	liabilities
◦ bonds	◦ shares

stock mutual fund

assets	liabilities
◦ stocks	◦ shares

The shares have the same risk properties as the underlying pool of bonds or stocks. There is some benefit for the mutual fund shareholder from diversification and management services. There is also some liquidity benefit perhaps, because open end funds typically promise to buy back shares at Near Asset Value (NAV). That means that mutual funds have to keep cash or lines of credit for the purpose, both of which will lower the return and hence are paid for by shareholders.

Bond mutual funds have replaced the saving component of whole life insurance policies, and also bank time deposits, as fixed income saving instruments. Stock mutual funds have replaced defined benefit plans as retirement income savings instruments. This change reduces the degree of transformation in financial intermediation. Nowadays, mismatch between the preferences of borrowers and the preferences of lenders is increasingly resolved by price changes rather than by traditional intermediation.

17.6. Banks as intermediaries

Banks have a special role in the liquidity hierarchy because their liabilities (bank deposits) are means of payment. Thus banks are able to turn private debts into purchasing power by accepting them, in effect swapping IOUs. Individual households and firms in the economy not only want to make payments (flow), they also want to hold means of payment (stock). This makes room for the banking system as a whole to issue a permanent short position in cash. The role of banks as intermediaries comes from their use of this short position to fund long positions in non-cash assets.

The liquidity of bank liabilities does not require liquidity of bank assets, except on the margin. To achieve liquidity on the margin, it is sufficient that the banking system hold some cash reserves, and have the ability to replenish those reserves. For this latter purpose, individual banks depend on access to the FF market and discount loans at the Fed, and on holding of some easily sold secondary reserve assets. After liquidity needs are taken care of, there will be some fraction of total deposits left over which can be invested in less liquid assets.

stock mutual fund

assets	liabilities
◦ cash reserves ◦ secondary reserves ◦ loans	◦ deposits ◦ net worth

Because bank deposits are substitutes for currency, and because currency typically pays no interest, deposits typically pay zero or low interest as well. This makes it profitable for banks to make loans at relatively attractive rates. Not surprising, there is considerable competition to get access to this cheap money. Historically, the biggest player in this competition is the government. In times of war, bank balance sheets are filled up with loans to the government or to government-favoured enterprises. Similarly, for countries trying to jumpstart a development process, it is tempting to begin by trying to mobilise idle balances on the balance sheets of domestic banks.

In the United States, politics resulted in a division of the spoils of this cheap source of funds during peacetime. Until recently, the central bank has invested almost entirely in government debt. Commercial banks historically specialise in making commercial and industrial loans, though they do other things as well. Savings and loans historically specialise in mortgage lending and they issue shares which have come to look more and more like deposits.

central bank

assets	liabilities
◦ Treasury securities	◦ high powered money

commercial bank

assets	liabilities
◦ consumer and investment loans	◦ deposits

savings and loan

assets	liabilities
◦ mortgage loans	◦ shares

If a certain portion of deposits are permanent, there are still considerable risks involved in using those deposits to fund consumer loans, investment loans, and mortgages. Liquidity risk is one of them, but also solvency risk. Main sources of solvency risk are interest rate risk and credit risk. Again the financial revolution has transformed banking, most dramatically in the transformation from traditional banking to shadow banking.

17.7. The shadow banking system as intermediation

From a finance point of view, an intermediary that offers liabilities with different risk characteristics than its assets must itself be bearing the risk of that transformation. This means that its stockholders (or the government), presumably primary lenders, must be bearing that risk, so the transformation of risk is illusory. Risk is just getting moved around, not eliminated.

The illusion that risk is being eliminated comes from the fact that risk is not being (directly) priced. The answer is to strip out every risk exposure and price it separately. From the finance point of view, any mismatch between the kind of liabilities that borrowers want to issue and the kind of assets that creditors want to hold is equilibrated not by changes in quantity but by changes in price. Creditors bid up the price of assets they like, and bid down the price of assets they don't like, until the price exactly compensates for the risk.

18. Forwards and futures

18.1. Introduction

At any moment, a particular inter temporal pattern of cash flows and cash commitments resolves itself into a particular pattern of clearing and settlement at a moment in time. Deficit agents buy cash (borrow) today to delay settlement, and the elastic availability of loans is the essential source of elasticity in the payments system. By means of credit, current imbalances in the pattern of cash inflows and outflows are pushed into the future where, hopefully, they can be offset against a pattern of imbalances going the other way.

The cost of pushing those imbalances into the future is the current money rate of interest, which operates as a symptom of the degree of imbalance but also as an incentive to pay up soon. This provides the discipline in the system. A financial crisis arises when those delaying tactics no longer work. This is an extreme form of discipline.

Advance clearing is the way in which emerging imbalances in the future show up as cash flow imbalances in the present, again with the money rate of interest serving as a symptom, and discipline. In finance, the future determines the present, but no one knows the future, so there can be multiple views of what the future will look like. How does it happen that diverse views get coordinated? One way is by market pricing of different views, and by the effect of that pricing on behaviour that operates through the survival constraint.

At one extreme, if the market changes its mind about someone's view of the future, he or she may have difficulty rolling over his or her funding. The current survival constraint is thus a key mechanism through which one future path gets chosen over all the others. But there are subtler paths at work as well, through which ideas about the future cause changes in cash flows today, which make the survival constraint looser for some people and tighter for others. Changes in futures prices have cash flow consequences in the present.

18.2. Forwards and futures

Suppose a firm has ordered a machine for delivery three months from now. The firm plans to pay for the machine by borrowing, but is concerned that interest rates three months from now may be higher. The firm can lock in a borrowing rate by engaging in a forward contract with a bank. That forward contract can be seen as a swap of IOUs as follows:

Firm A

assets	liabilities
◦ 3 month deposit	◦ 6 month loan

bank

assets	liabilities
◦ 6 month loan	◦ 3 month deposit

The swap of IOUs will have zero present value if the deposit and the loan both pay the forward rate of interest F[3,6] defined by forward interest parity (1+R[0,3])(1+F[3,6]) = (1+R[0,6]). Because of the failure of the expectations hypothesis, in general F[3,6] > E₀R[3,6]. This provides incentive for the bank to enter into the forward contract. The forward loan is more profitable on average than the spot loan.

This swap of IOUs solves the problem of the firm, but creates a problem for the bank, since in three months the bank will have to come up with the money to lend to the firm, and at that moment it is entirely possible that R[3,6] will be greater than F[3,6], so leaving the bank with a loss. Ideally the bank (or the banking system as a whole) has another client with exactly offsetting needs, for example a firm that wants to lock in a lending rate by engaging in an opposite forward contract.

Firm B

assets	liabilities
◦ 6 month deposit	◦ 3 month loan

bank

assets	liabilities
◦ 3 month loan	◦ 6 month deposit

These two contracts exactly offset each other on the balance sheet of the bank. This combination of forward contracts have essentially cleared today a future payment from Firm B (the ultimate lender) to Firm A (the ultimate borrower). In this way the forward market performs advance clearing. There will be cash flows in three months between surplus and deficit firms, but they are all pre-arranged.

There is no reason to expect that forward contracts all net out on the balance sheet of any single bank. Even when banks trade their forward exposure with one another (using FRAs), there is no reason to expect that forward contracts all net out in the banking system as a whole. That means that the banking system will be left with a net exposure to the risk that the future spot rate of interest will be higher than the current forward rate. Banks will not hold this risk unless they are compensated by an expectation of profit. The source of this profit is movement in the forward rate away from expected spot.

This is one possible explanation for the empirical failure of the expectations theory of the term structure. The difference between the current forward rate and the current expectation of the future spot rate is just the expected profit from an unhedged forward exposure. The point is that the imbalance between future cash flows and cash commitments shows up as distortion of the current forward interest rate away from the expected future spot interest rate.

If the forward imbalance is large, then the current price distortion will be large, so the expected profit from an unhedged forward exposure will be large. This expected profit can be expected to attract speculators outside the banking system to hold the exposure that the banks cannot or are unwilling to bear. The futures market is often the place where the banking system sells off its excess forward exposure to speculators. Futures are forwards that are marked to market daily, with any changes in value settled daily. Distortions that affect forward rates will also affect futures rates, and hence current cash flows.

chain of hedges

client	bank	banking system	futures exchange	speculator
F[3,6]	forward contract	FRA	futures	ER[3,6]

Because of the failure of Expectations Hypothesis, forward interest rates tend to be upward biased forecasts of future spot rates. The bias is often seen as a liquidity premium. It is difficult to explain what risk that premium is compensating for. More generally, it can be observed that forward rate > futures rate > expected spot. This pattern provides a profit incentive to enter into the trade.

18.3. Forwards

Forward contracts are promises to deliver goods at future time T at a given price K. The classic example is that of the wheat farmer who has a natural long position in wheat and the baker who has a natural short position. Both face price risk. If they can arrange a forward contract, they can lock in the future price of wheat, and both may be better off. They each hedge their natural forward exposure by taking an opposite position in a forward contract.

When the time comes to settle, the spot price of wheat is likely to be different from the contracted delivery price. In this sense one side wins ex post. These winnings over the life of the contract can be tracked as the value of the contract changes. In forward contracts these winnings are only notional. No matter what happens to the spot price, at delivery date the short delivers the contracted good to the long, and the long delivers the contracted price to the short in money.

The underlying does not have to be a physical commodity like wheat. It can be a financial instrument like a Treasury bond. It is the easiest to understand if the underlying is a zero coupon riskless bond that yields no cash income and has no carrying cost. In that case the Forward Interest Parity condition in price terms is:

[1/1+F(3,6)] = [1/1+R(0,6)][1+R(0,3)]

The first term is the forward delivery price, the second is the current spot price, and the third the interest rate between now and the forward date. The forward price changes over time. The previous equation is the forward rate at time zero. At time 1, 2, 3, the following equations apply:

[1/1+F1(3,6)] = [1/1+R(1,6)][1+R(1,3)],

[1/1+F2(3,6)] = [1/1+R(2,6)][1+R(2,3)] and

[1/1+F3(3,6)] = [1/1+R(3,6)].

There is no reason to expect that these forward rates are the same as the period zero forward rate. That means that the forward contract established at time zero will change in value throughout time. To reflect that change, and to connect with standard finance treatments, it will be useful to recast the discussion in continuous time by introducing some new notation. At time zero when the contract is written, the following formula relates the forward delivery price K to the current spot price S₀:

K = S₀e^rT (1).

This is another version of the forward interest parity condition. The forward price K = 1/(1+F[3,6]), the spot price S₀ = 1/(1+R[0,6]) and the interest rate term e^rT = (1+R[0,3]). This is an arbitrage condition as it would be possible to make money if the condition did not hold.

If K > S₀e^rT then it is profitable to buy the bond spot and sell it forward. In this way it is possible to lock in a rate of return greater than the rate of interest r at which money can be borrowed to finance the trade. If K < S₀e^rT then it is profitable to sell the bond spot and buy it forward. In this way it is possible to lock in a borrowing rate lower than the rate of interest r at which the money received from selling the bond can be lent out.

For forward contracts, the delivery price K is fixed for the life of the contract. Hence, over the life of the contract, the value of the forward contract will change as follows:

f_t = S_t - Ke^-r(T-t), for 0 < t < T (2).

There is a time subscript on both f and S, but K is fixed. At t = 0, S₀ = Ke^-rT, so f₀ = 0 when the forward contract is signed. At t = T, f_T = S_T – K. This is the notional gain or loss. In between time 0 and time T, the value of the forward contract fluctuates, depending mainly on the fluctuating spot price of the underlying zero coupon bond.

In most forward contracts, at the final date the long side pays the short side the agreed price K and receives the agreed underlying, which is worth S_T. In interest rate forward contracts however, cash settlement is the rule. Instead of delivering the bond for K, the short side delivers the current spot price of the bond in return for the payment K. This means net cash payment of the final value f_T = S_T - K from short to long if positive and from long to short if negative. In cash settlement, the notional winnings become real cash flows at time T.

18.4. Futures

A futures contract is like a forward except that all changes in the value of the contract f_t are instead absorbed in changes in the delivery price, which is the futures price, F_t. F_t is reset every day so that f_t is zero. The futures price is that price at which the analogous forward contract has a current value of zero, or:

0 = S_t - F_te^-r(T-t)

F_t = S_te^r(T-t).

This equation is sometimes called future-spot parity. At expiry the futures price is equal to the spot price. In algebra this means that at t = 0, F_t = K, and at t = T, F_T = S_T. The big difference between forwards and futures is that the wins and losses that come from changing spot prices are paid out daily over the life of the contract, which is called mark to market. In a forward contract, the only payment flow is at the end, and the amount of that payment is fixed by the contract from the beginning.

Both the long and short side of a futures contract have to put up margin, because at the moment the contract is entered, both are in a sense equally likely to lose and so equally likely to have to make a payment to the other side. These margin accounts are similar to bank deposits, but the clearinghouse will also accept liquid securities. At the end of the day the securities are re-priced to reflect any change during the day. Thus the collateral underlying the futures contract as well as the futures contract itself are both marked to market every day.

The cumulative payment on the futures is the same as the final payment on the forward, but for the futures the cash flows come about every day during the life of the contract. This is the way in which views about the future are settled in the present.

18.5. Monetary issues

Stigum discusses a trade involving spot 6 month bills, the 3 month ahead futures contract on the bills, and the 3 month risk free repo rate.³ It starts with buying the 6 month bill for spot price S₀ using money borrowed at the repo rate r. Borrowing short term in order to lend long term creates an exposure to price risk, since the future rate at which the second three months of the bill must be financed are unknown. To hedge that price risk, 3 month Treasury bill futures can be shorted at the futures price F_t. Then, whatever happens to the Tbill price is exactly countered by whatever happens to the futures price. In this way all price risk is hedged. The question then is, given that all price risk is hedged, why would there ever be an expected profit from this trade, and hence why would anyone do it?

One way to understand this trade is that the trader is long a forward contract (the combo of the Treasury bill and repo) and short the corresponding futures contract. To see why such a trade might be profitable, the relationship between futures and current spot prices, or futures-spot parity, is of interest. Stigum calls this relationship full carry pricing. Deviations from full carry pricing offer opportunities for arbitrage profit.

If F_t = S_te^r(T-t) then there is full carry pricing and no arbitrage profit.

If F_t > S_te^r(T-t) then it is profitable to do a cash and carry arbitrage, which is being short futures, long underlying at S₀, financed by borrowing at rate r. At futures expiry, the underlying is delivered for spot S_T and the loan is repaid.

If F_t < S_te^r(T-t) then it is profitable to do a reverse cash and carry arbitrage, which is being long futures, short underlying at S₀, while the proceeds are invested at rate r. At futures expiry, the underlying is purchased for spot S_T.

Stigum uses a different language when she talks about the difference between an implied repo rate and the actual repo rate. The actual repo rate is the rate paid on the short term repo (the carry part of the trade) that is used to purchase the Treasury bill (the cash part of the trade). The implied repo rate is the short term return that is locked in by the combination of the cash bill and the short futures position. The price at which the bill can be bought and sold are known in the futures price.

Define the implied repo rate by the equation F_t = S_te^ρ(T-t). The implied repo rate ρ is the borrowing rate that would have to hold in order for futures prices to satisfy full carry pricing. Now it is possible to express the arbitrage opportunities as a deviation of the implied repo rate from the actual repo rate. If ρ = r then there is full carry pricing and no arbitrage profit. If ρ > r then cash and carry arbitrage is profitable. If ρ < r then reverse cash and carry arbitrage is profitable.

The arbitrage profit in the cash and carry trade arises from the fact that it is possible to borrow at a lower rate than it is possible to lend. Put that way, it is remarkable that such a relationship would ever hold for more than an instant. Why does not everyone do the trade to eliminate the arbitrage?

The cash and carry arbitrage is long forward and short futures. What is the risk in that position that might command a premium for bearing it? If the forward rate is typically greater than the expected spot, that means we can expect to gain by borrowing short and lending long. The long forward interest rate position should be increasing in value. At the same time the short futures interest rate position should be decreasing in value. These two positions more or less net out in terms of value, but not in terms of cash flow.

Futures are marked to market whereas forwards are not so the cash and carry trade typically involves negative cash flows throughout the life of the contract, plus a large positive cash flow at maturity. The profit comes from the fact that the positive cash flow is larger than all the negative flows added up, but the timing is inconvenient. The volatility of the spot price of the underlying bill creates liquidity risk for the cash and carry trade. The profitability of the cash and carry trade may be a reward for bearing liquidity risk.

19. Interest rate swaps

19.1. A swap is a swap of IOUs or a parallel loan

Stigum also discusses interest rate swaps.⁴ Suppose that there are two counterparties, Corporation AA and Corporation BBB. One is able to borrow at a fixed rate but wants to borrow at a floating rate, the other is able to borrow at a floating rate but wants to borrow at a fixed rate. They can help one another by swapping IOUs, fixed for floating, in a parallel loan structure.

Corporation AA
(seller of swap, short swap, payor of floating)

assets	liabilities
◦ [fixed parallel loan]	◦ original fixed rate borrowing ◦ [floating parallel loan] ◦ swap

Corporation BBB
(buyer of swap, long swap, payor of fixed)

assets	liabilities
◦ [floating parallel loan] ◦ swap	◦ original floating rate borrowing ◦ [fixed parallel loan]

In the parallel loan arrangement AA still pays its original creditor a fixed rate over the life of its original loan, and BBB still pays its original creditor a floating rate over the life of its original loan. The swap of IOUs between AA and BBB means that AA receives a fixed rate payment from BBB, while BBB receives a floating rate payment from AA. These receipts match the promised payments on their original loans. In this way AA achieves floating rate financing while BBB achieves fixed rate financing.

The parallel loan structure solves the problem for the two companies, but it does so by expanding both balance sheets as well as the apparent leverage and counterparty risk exposure. Since money is going both ways, it is natural to net the two payments and pay only the net, from AA to BBB or from BBB to AA, whichever is larger. In most cases, BBB will be paying AA because the short term interest rate is lower than the long term interest rate. This netting goes some way toward reducing counterparty risk.

The swap contract goes even further by netting the principal payments as well, both at the beginning and at the end of the contract. The net payment flows on a swap contract are the same as in the parallel loan structure, but now everything is off-balance sheet. In the swap arrangement, there are market linguistic conventions. A long swap position pays fixed and receives flexible. A short swap position is just the opposite. Contrary to market lingo, long swap positions are treated as assets and short swap positions as liabilities in this discussion.

19.2. Swaps and other parallel loans

It may be helpful to think of selling a swap, or taking a short swap position, as like buying a five-year fixed rate bond and financing the position by borrowing short term, using the bond as collateral for the loan. From this point of view, the swap is similar to a repo. The difference is that swaps deal with corporate liabilities and not governments, and also with much longer maturities both of the bond (for example, five years rather than 3 month Treasury bill) and of the financing (for example, 6 month LIBOR rather than overnight repo).

It is common in the finance literature to analyse the swap as a strip of forward interest rate contracts, one for every time-dated payment on the underlying notional fixed rate loan. The swap refers to forwards, and not to futures contracts, because payments are periodic and not marked to market. BBB is in effect locking in the a future borrowing rate, and AA is in effect locking in a future lending rate. Being long a swap is like being short a portfolio of forwards, so a long swap can be hedged with long future. The parallel loan interpretation can help to allay any confusion. A forward can be understood as a parallel loan as follows:

long forward

assets	liabilities
◦ 6 month loan R(0,6)	◦ 3 month deposit R(0,3)

short forward

assets	liabilities
◦ 3 month deposit R(0,3)	◦ 6 month loan R(0,6)

Compared to the parallel loan interpretation of the interest rate swap, the exposure on the first payment of the short swap is just like the long forward. The later swap payments are analogously like more distant forwards.

19.3. Comparative advantage as a reason to swap

Stigum provides an example where BBB borrows floating and AA borrows fixed, and then swap.⁵ The reason they do this is that by assumption BBB can borrow relatively more cheaply in floating, and AA can borrow relatively more cheaply in fixed, though absolutely more cheaply in all markets. Each would like to borrow in the market that is relatively more expensive. Here is the structure of rates Stigum assumes:

	floating loan terms	5 year fixed Eurobond
BBB	6 month LIBOR + 1/4	5.85
AA	6 month LIBOR + 1/8	5.375
difference	12.5 bp	47.5 bp

There are 35 basis points to play with (47.5 - 12.5). In Stigum's example AA gets 25 of them and so achieves LIBOR – 1/8 (original floating – 25 bp), and BBB gets 10 and so achieves 5.75 Eurobond (original fixed – 10 bp). This can be understood better by putting those numbers into a parallel loan interpretation, as follows:

assets	liabilities
◦ [5 yr fixed, 5.50]	◦ 5 yr bond, 5.375 ◦ [LIBOR]

BBB

assets	liabilities
◦ [LIBOR]	◦ LIBOR + 1/4 ◦ [5 yr fixed, 5.50]

One reason for this apparent free lunch to exist, is market imperfection. Stigum tells the story about British capital controls that were evaded by parallel loans which were in effect currency swaps. Stigum also notes that US interest rate swaps have their origin in 1981, in the midst of the Volcker tight money period, when some lesser credits would have been locked out of certain markets completely.

Another possible reason for this structure of rates is counterparty risk. That suggests that the lunch may not be free. A bank may be willing to lend short term to Triple B because it thinks it can reassess the situation every 6 months, perhaps raising the markup over LIBOR if BBB gets into trouble. The higher markup for longer term lending compensates for the fact that there is a lot more that can go wrong in five years than in six months. The swap gives Triple B long term financing, but leaves AA holding the credit risk. If things go bad for Triple B, it will roll over its term loan at higher and higher markups over LIBOR, but it is receiving only LIBOR flat.

19.4. Market making in swaps

The 35 basis points attract not only AA and BBB, but also brokers and dealers who take a few of the basis points to set up and manage the swap. AA could borrow in the Eurobond market and swap fixed for floating by selling a swap to a dealer. Triple B likewise could borrow in the floating market and swap floating for fixed by buying a swap. The dealer would take 1bp each way, subject to credit check. Dealers make markets in swaps by taking positions and hedging them, either by taking opposite positions in the same or similar swaps or by taking opposite positions in related instruments like forwards and futures.

assets	liabilities
	◦ AA swap

investment bank

assets	liabilities
◦ AA swap	◦ BBB swap

BBB

assets	liabilities
◦ BBB swap

In general dealers will not be able to match longs and shorts perfectly with the business that naturally comes to them, so they must resort to imperfect hedging. The kind of position that is used as a hedge gives further insight into the nature of the swap contract.

Stigum thinks of a swap as a synthetic corporate bond. A short position in interest rate swaps is similar to a long bond position financed by repo. Such a position can be hedged with a short bond position. Treasuries or Euros are the most liquid instruments, so there may be a hedge there, either in the cash market or the futures markets. Such a hedge involves continued exposure to basis risk because the swap rate is a corporate bond not a government bond rate. Also, the dealer faces counterparty risk on both sides. Other hedges will be necessary to shelter from basis and counterparty risk.

If the position can be hedged satisfactorily, then the swap dealer is doing essentially the same thing as a government bond security dealer, but in corporate bonds instead of government bonds. There is a term structure in swaps, as a markup over Treasuries. At every maturity there is a rate of interest determined in the private credit markets and there is one determined in the government credit market. Speculators on the spread at various maturities keep the markets in touch.

The swap market is now larger than the bond market itself as measured by size of notional swap principal. The question raised by the enormous success of this market is whether in some sense it is coming to replace the government market. In good times, there is just as much liquidity in swaps as in governments, but in bad times (tight liquidity) the hierarchical structure is restored. Swap dealers are apparently market makers at a lower level in the hierarchy of money than government bond dealers, who are themselves below the banks that make markets in money, who are themselves below central banks.

19.5. Money market swaps

The short term swap market is more of an interbank (rather than intercorporate) market. For example, Bank AA may take in a one-year deposit and swap fixed for 3 month LIBOR, by selling the money market swap.⁶ Morgan buys the swap (and hence is short fixed) and immediately hedges with a long futures position. The reason for this hedge is the nature of a swap. A swap is a strip of FRAs, and a FRA is a single-set swap. A swap is like a portfolio of financial forward contracts. Because they are forwards and not futures, the futures hedge involves exposure to liquidity risk.

The futures contract is there only temporarily as a hedge, until Morgan can, for example, make a one year loan to an LBO and close out the futures contract. LBO borrows at 3 month LIBOR, swaps flex for fixed, and the problem is solved. In this way the one-year fixed rate deposit winds up financing Morgan's one year flex rate loan. The swap between the banks hedges interest rate exposure as follows:

Bank AA

assets	liabilities
◦ [1 year fixed]	◦ 1 year deposit ◦ [3 month floating] ◦ swap at 4.44

Morgan

assets	liabilities
◦ [3 month floating] ◦ swap at 4.44 ◦ [1 year fixed]	◦ [1 year fixed] ◦ [3 month floating] ◦ swap at 4.47

LBO

assets	liabilities
◦ [3 month floating] ◦ swap at 4.47	◦ [3 month floating] ◦ [1 year fixed]

The first swap is between AA and Morgan. The implicit parallel loan in brackets above the swap. Then there is a second swap between LBO and Morgan. The temporary futures hedge is left out. AA is borrowing fixed but wants to borrow flex, and LBO is borrowing flex but wants to borrow fixed. Instead of doing a swap with each other, they each separately do a swap with Morgan. Morgan winds up with equal and opposite swap exposures, and has matched book.

Morgan makes money by being short a swap at 4.47 and long a swap at 4.44. The parallel loan interpretation makes this clear. Morgan is paying LIBOR and receiving LIBOR, so these flows net out. On its long swap it is paying 4.44 fixed and on its short swap it is receiving 4.47 fixed. This is a 3 bp net profit.

19.6. Significance

There are many borrowers and lenders, each with their own preferences about maturity and currency, and each with their own market access. In the swap market they are each finding the lowest cost financing by matching up their needs with the market as a whole. The swap market spreads stresses in one place and at one time, across the system and across time, and unites the individual markets into one big market. In this way, any imperfections in the markets caused by regulation or intervention can be evaded. If central banks raise short rates in one area, making it unattractive for short term lending, borrowing can happen elsewhere by swapping into the desired currency.

According to Stigum, money market swaps occur in arbitrage land. Traders arbitrage swaps against futures, swaps against cash, swaps against FRAs, FRAs against futures, and so on. Arbitrage opportunities keep arising because these related markets are constantly affected by many different events. Maybe an Asian bank does a big cash-and-swap arbitrage, which drives up the swap market. This creates profit in the swap-FRA arbitrage, so someone does the swap-FRA arbitrage, which drives up FRAs. This creates profit in the FRA-futures arbitrage, so someone does the FRA-futures arbitrage, which drives up futures. An event that moves one rate causes a rate ripple that creates some basis points for every play except may the futures player if he is an unhedged speculative player in the futures pit.⁷

The sequence of trades have a hierarchical structure: swap market (OTC) to FRA (interbank forward) to futures. The flexibility of this system depends on ability to hedge immediately in highly liquid futures markets. Although in one sense the system works to spread stresses, in another sense it concentrates stresses into the futures.

20. Credit derivatives

20.1. Introduction

Fischer Black wrote in 1970 that a long term corporate bond could actually be sold to three separate persons. One would supply the money for the bond, one would bear the interest rate risk, and one would bear the risk of default. The last two would not have to put up any capital for the bonds, although they may have to post some sort of collateral. He already was thinking about the kind of world that we live in today. The latter two instruments he mentions are today's interest rate swaps and credit default swaps, and the collateral he mentions is the margin that participants in these markets may have to post to ensure performance.

Credit default swaps (CDS) and collateralised debt obligations (CDO) arose initially to handle problems of corporate credit risk, so the underlying assets were corporate bonds and bank loans. There are extensions to the case where the underlying assets are sovereign bonds and loans, and commercial and household mortgages. It is the latter extension that is important to understand for the subprime mortgage crisis. From a finance point of view, which is Fischer Black's approach, the key idea for understanding credit derivatives is:

price of risky asset + price of insurance on risky asset = price of risk free asset

or:

yield on risky asset = yield on risk free asset + credit risk premium.

From this perspective, credit default swaps look like a kind of credit risk insurance. From a money view, the instruments look somewhat different. By translating Fischer Black into a parallel loan balance sheet construction, it is possible to see how credit default swaps enter the picture analogously to interest rate swaps:

buyer of insurance
(long swap, short credit risk)

assets	liabilities
◦ corporate bond ◦ [Treasury bond] ◦ [Treasury bill] ◦ credit default swap ◦ interest rate swap	◦ [corporate bond] ◦ [Treasury bond]

seller of insurance
(short swap, long credit risk)

assets	liabilities
◦ [corporate bond] ◦ [Treasury bond]	◦ [Treasury bond] ◦ [Treasury bill] ◦ credit default swap ◦ interest rate swap

The parallel loan construction is shown in brackets. One side promises to make the same payments the corporation makes, and to miss the same payments the corporation misses, while the other side promises to make the same payments that the Treasury makes on a bond of the same maturity. As long as the corporate bond does not default, this swap of IOUs involves a net cash flow from the long swap to the short swap, simply because the coupon on the corporate bond is larger than the coupon on the Treasury. In the event the corporate bond defaults, there is a large cash flow in the opposite direction. In effect the long swap delivers the defaulted bond to the short swap, and receives in return a Treasury bond.

20.2. Corporate bonds

It is the easiest to introduce the basic ideas while thinking of the underlying as a corporate bond. Such bonds are often complicated instruments, because of the various warrants attached (call provisions and protection). It is better to abstract from those provisions and think of corporate bonds as promises to pay a certain coupon at regular intervals over the life of the bond, and the face value upon maturity. Standard valuation considerations suggest that the price of such a bond can be thought of in present value terms as

P(0) = Σδ^tC_t + δ^TF_T

where C is the coupon, F is the face value, and δ is a discount factor that that can be thought of as (1/1+R) where R is some risk-adjusted interest rate. The formula shows that there is an inverse relationship between R and P. Fluctuations in the price of the bond after issue can be thought of as fluctuations in the risk-adjusted interest rate. Reasons for those fluctuations are fluctuations in the risk-free interest rate, changes in the price of credit risk and, changes in the quantity of credit risk.

Bonds are typically rated by one of the various rating agencies. Ratings go from AAA to B-, to NR. Lower rated bonds sell at a discount, which means that the risk-adjusted interest rate is higher. Usually however there is an attempt to set the coupon at a level that counteracts this effect so that, at least when the bond is issued, bonds of various ratings all sell near par.

At any moment in time, there is a pattern of credit spreads over Treasuries, or perhaps over the swap rate. These are small spreads for AAA and larger spreads for lower ratings. These spreads fluctuate over time, which is one source of risk (price), and individual bond ratings can also change over time, which is a second source of risk (quantity). The basic idea of credit derivatives is to create an instrument that will allow these sources of risk to be carved off of the bond and priced (and sold) separately.

20.3. CDS pricing

Suppose that Person A owns a bond that promises to pay a constant coupon C for 10 years. Suppose further that Person A buys an interest rate swap in which he pays fixed and receives LIBOR. In effect, his combined portfolio now pays LIBOR + S%, where S is the credit spread over the fixed rate on the swap. Now Person A thinks about selling off the credit risk.

Person A

assets	liabilities
◦ corporate bond (LIBOR + S%) If no default: ◦ [LIBOR] If default: ◦ [face value of bond, F]	◦ [LIBOR + U%] ◦ [liquidation price of bond, P]

A credit default swap can be understood as a swap of IOUs. Person A issues an IOU that promises to make periodic payments of LIBOR+U% on the face value of the bond, as long as the bond issuer keeps up his own payments. In the event of default, he promises to pay the liquidation value of the bond. The IOU can be called a mirror bond because the time pattern of payments exactly mirrors the corporate bond Person A is holding. In return for this promise, Person A accepts an IOU that promises to pay LIBOR as long as the bond issuer keeps up his payments, and the full face value of the bond in the event of default. Thus on net Person A is paying U until default, and then receives the difference between the full face value of the bond and its liquidation value.

Here are the net cash flows from the swap of IOU's, assuming default at period 5:

1	2	3	4	5
-U*F	-U*F	-U*F	-U*F	+F-P(5)

U is a number that makes the present value of the small payments exactly equal to the present value of the large payment, so that at inception the swap is a zero value instrument. It is a swap of IOUs that have the same exact value. In the finance view, U is a kind of insurance premium. As long as Person A pays U, he is insured against the risk of default on the bond he holds. If there is default, then the liquidation value of the bond is P(5), but the swap of IOUs pays F - P(5), so on net Person A recovers F, the full face value of the bond.

Any change in the credit spread S%, whether market-wide or specific to the bond, will change the value of the CDS. In theory, the value moves inversely to the value of the underlying bond. In this way, CDS is not so much insurance against eventual default as it is insurance against change in the credit spread.

20.4. Market making

The seller of insurance may be a bank or an investment bank. The seller receives a stream of small payments but faces the possibility of having to make a single large payment in the event of default. It is possible to create portfolios of such swaps, which pool the individual default risks so that the risk of the pool is less than the risk of any component. This depends on the correlation of the individual risks. The less correlation, the better. This pooling then allows the seller of the swap to charge a lower spread to the buyer.

buyer of insurance

assets	liabilities
◦ risky bond CDS_i

dealer

assets	liabilities
◦ CDS on index CDS	◦ CDS_i ◦ CDS_j ◦ CDS_k

seller of insurance

assets	liabilities
	◦ CDS on index CDS

This pooling is important. The incentive to create a swap comes from mispricing of credit risk in the original corporate bond. It should be expected that the creation of a flourishing swap market will reduce the price of credit risk overall. That is exactly what happened. Diversification reduces risk, but does not eliminate it. If the seller seeks matched book, this pool of OTC swaps may then be hedged against a general bond index, perhaps by trading an exchange traded swap such as CDX with a hedge fund.

20.5. UBS example: market making and liquidity risk

If U < S, then the buyer of the swap can swap out the credit risk and wind up with an investment that pays a small spread (S-U) over LIBOR. That is what UBS was doing in its most important risk arbitrage trade, as follows:

assets	liabilities
◦ AAA CDO tranche, floating rate ◦ credit default swap (AIG)	◦ money market funding (ABCP, RP)

UBS was doing something it called a Negative Basis Trade in which it paid AIG 11 bp for 100% credit protection on a supersenior CDO tranche, and financed its holding of that tranche in the wholesale money market. In its report to shareholders, to explain why it lost so much money, it states that this trade netted an apparently risk free arbitrage profit of 20 bp. Because it was apparently riskfree, they did massive amounts of it. The risk turned out to be liquidity risk, when money market funding dried up and they could not sell their AAA tranche. Their CDS hedge did them no good since they could not use it to raise funding. To make matters worse, the CDS hedge was typically only against the first 2% loss, leaving UBS exposed for everything more than that.⁸

20.6. Goldman Sachs example: hedging CDS with CDS

The recent SIGTARP report on AIG explains the relationship between Goldman and AIG, which can be translate into balance sheets as follows:⁹

Goldman Sachs

assets	liabilities
◦ CDS, AIG	◦ CDS, clients

AIG

assets	liabilities
	◦ CDS

Goldman Sachs was acting as a CDS dealer, selling protection to clients but buying protection from AIG. AIG was a naked seller of protection. When the referenced risky asset started to fall in price, the value of the insurance rose. This is a liability of AIG, so it cut into their capital buffer. AIG had no dedicated reserves against these CDS because it thought they were essentially risk free. Not only that, but AIG had agreed to post collateral, and mark the CDS to market, so these losses were not just book losses but involved payments into a segregated account that Goldman Sachs controlled, about 30 billion at the time AIG failed.

AIG failed because it was no longer able to meet these collateral calls. Instead the government took over AIG, lending 85 billion. There has been a lot of loose talk about how the government paid off Goldman at par instead of forcing Goldman to take a loss. This is not exactly what happened. Rather, because the CDS was marked to market, Goldman already had possession of the collateral and had already been paid. The government money was used to acquire the referenced securities at liquidation value in order to end the swap. In terms of our algebraic example, AIG had already paid F-P(5). What the government did was to lend AIG money to pay P(5) for the bond which the government then took onto the Fed's balance sheet.

20.7. Goldman Abacus example: synthetic CDO as collateral prepayment

Paulson, the hedge fund manager, paid Goldman to help him bet against subprime, and the way he did it was by establishing a so-called synthetic CDO.¹⁰ The very first CDS was established in this way for JP Morgan to hedge tail risk its portfolio of corporate loans. A simplified version of the balance sheets is:

Paulson

assets	liabilities
◦ CDS on RMBS

Abacus

assets	liabilities
◦ Treasury bills	◦ CDO tranche ◦ CDS on RMBS

IKB

assets	liabilities
◦ CDO tranche

Abacus is a synthetic CDO, not a cash CDO, because its exposure to credit risk comes from its CDS position, not from any actual holdings of RMBS (residential mortgage backed securities). It sells that exposure to IKB in the form of bonds (CDO tranche), and invests the proceeds in Treasury bills. The combination of long risk free securities and short CDS is equivalent to an outright position in the referenced risky security.

As long as the RMBS was not in default, Paulson paid a regular premium to Abacus, which added that premium to the Treasury bill return to pay interest to IKB on its bond holding. Once the RMBS was in default, Abacus paid Paulson by delivering its holding of Treasury bills, while Paulson delivered the underlying RMBS which he bought at liquidation value. The difference between face value and liquidation value is absorbed in the value of the CDO tranche bonds owned by IKB.

The Abacus arrangement went one step further than the AIG mark to market CDS. In the AIG case, the falling value of the referenced securities forced collateral payments to Goldman Sachs. In the Abacus case, the collateral payments were all made at the very inception of the contract when IKB bought the bonds, so IKB did not have to come up with any additional collateral (which it could have refused). Instead, the falling value of the referenced securities merely caused a transfer of the collateral, already collected, from Abacus to Paulson.

Banking and the real world

21. Shadow banking, central banking, and global finance

21.1. Shadow banking as market based credit

Shadow banking can be seen as market based credit. It is a wholesale market between financial institutions, but ultimately deposits fund loans.

securitisation

assets	liabilities
◦ RMBS	◦ hi tranche ◦ mid tranche ◦ lo tranche

shadow bank

assets	liabilities
◦ hi tranche	◦ repo

money market mutual fund

assets	liabilities
◦ repo	◦ deposits

21.2. Immature liquidity backstop

The traditional banking system has liquidity backstops in the form of reserve requirements and the Federal Reserve, but the liquidity backstops in the shadow banking system are immature. Those liquidity backstops are assets of the shadow banking system, but liabilities of the traditional banking system. In this way trouble in the shadow banking system became the problem of the traditional banking system. Ulitmately it became the problem of the government.

securitisation

assets	liabilities
◦ RMBS	◦ hi tranche ◦ mid tranche ◦ lo tranche

shadow bank

assets	liabilities
◦ hi tranche ◦ liquidity put	◦ repo

money market mutual fund

assets	liabilities
◦ repo ◦ liquidity put	◦ deposits

traditional bank

assets	liabilities
◦ loans ◦ reserves	◦ deposits ◦ capital ◦ liquidity put

21.3. Immature solvency backstop

The traditional banking system has solvency backstops in the form of capital requirements, but the solvency backstops in the shadow banking system were immature. Credit Default Swaps (CDS) were used to maintain the solvency of the shadow banks. Shadow banks often held the hi trance of RMBS, whereas pension funds held the mid tranche with mid CDS and hedge funds held the lo tranche with lo CDS. Investment banks made markets in CDS. They were often long hi CDS and short mid CDS and lo CDS (probably mostly for clients as they were dealers). AIG insured the hi CDS and expected that the risk was low.

CDO

assets	liabilities
◦ RMBS	◦ hi tranche ◦ mid tranche ◦ lo tranche

investment bank

assets	liabilities
◦ hi CDS ◦ loans	◦ mid CDS ◦ lo CDS

insurance

assets	liabilities
	◦ hi CDS ◦ capital

shadow bank

assets	liabilities
◦ hi tranche ◦ hi CDS	◦ money market funding

pension/insurance

assets	liabilities
◦ mid tranche ◦ mid CDS	◦ DB/annuity ◦ capital

hedge fund

assets	liabilities
◦ lo tranche ◦ lo CDS	◦ loans ◦ capital

21.4. Shadow banking as global banking

Shadow banking can be seen as global finance. The global markets are mainly US dollar markets because the US dollar is the global currency. If there is a banking crisis, there may be a currency crisis that hurts emerging economies as they may experience US dollar funding problems. Over time there has been some experience with this phenomenon.

Korean bank

assets	liabilities
◦ domestic currency loans ◦ FX swaps ◦ dollar reserves	◦ dollar funding

global bank

assets	liabilities
◦ dollar lending	◦ wholesale money market

dollar bank

assets	liabilities
◦ wholesale money market	◦ deposits

The shadow banking system used the same global US dollar funding system. Because lending as well as funding was in US dollars, there appeared to be no currency risk. The shadow banking system was using a mature global US dollar funding system for a new purpose, but the system to transfer risk via CDS was immature. Funding was easy but transferring risk was not. Because the global funding system was used, the crisis in the shadow banking system became a global crisis as the shadow banking system was mainly in Europe and funded globally using the Eurodollar market.

RMBS

assets	liabilities
◦ mortgage loans	◦ hi tranche ◦ mid tranche ◦ lo tranche

shadow bank

assets	liabilities
◦ hi tranche	◦ ABCP

money market mutual fund

assets	liabilities
◦ ABCP	◦ deposits

21.5. Shadow banking as modern finance

Shadow Banking was making use of new developments in modern finance, such as securitisation. Securitisation came along with financial globalisation. Individual loans cannot easily be bought and sold, but once they are packaged together into bonds, and they have a market price, foreign asset managers can buy and sell them. At the same time the global capital market emerged with derivatives to tranfer risk. Asset managers can get exposure for their customer capital entirely by holding derivatives that are equivalent to holding the securities. Shadow banks tried to strip the risk from their holdings and transfer it. Professor Mehrling believes this is what the future of shadow banking is going to look like.

shadow bank

assets	liabilities
◦ RMBS ◦ derivatives	◦ money

asset manager

assets	liabilities
◦ money	◦ capital ◦ derivatives

21.6. Definition of shadow banking

Shadow banking is money market funding of capital market lending. Shadow banking has the following features that traditional banking does not have:
- there is market pricing for both money and capital;
- there is global funding of local lending;
- there is a key role of market-making institutions.

Despite the failure of the shadow banking system in the financial crisis, shadow banking probably will become more important the future. The failures are the consequences of the historical evolution of the financial system. In the future, the system most likely will be improved. New regulation is needed but using the same regulation as now exists for traditional banks is not a good solution.

21.7. Key role of market-making institutions

Professor Merhling thinks that market-making institutions will play a major role in tranferring risk and funding. Until now, investment banks had this role. He envisions the existence of money dealers and derivative dealers that act as intermediaries between asset managers and shadow banks (capital funding banks). The dealers are crucial in this system and regulation should focus on them. The funding system is mature but the risk transfer system is not. There is need of a central clearing house for derivatives to ensure proper pricing.

capital funding bank

assets	liabilities
◦ RMBS ◦ CDS ◦ IRS ◦ FXS	◦ money market funding

global money dealer

assets	liabilities
◦ money market funding	◦ deposits

derivative dealer

assets	liabilities
◦ credit default swaps ◦ interest rate swaps ◦ foreign exchange swaps	◦ credit default swaps ◦ interest rate swaps ◦ foreign exchange swaps

asset manager

assets	liabilities
◦ deposits	◦ capital ◦ CDS ◦ IRS ◦ FXS

Because the risk is transferred, the capital needs to be on the balance sheet of the asset manager. For that reason, dealers and capital funding banks may not need much capital.

21.8. Backstopping market-making institutions

According Professor Mehrling, central banks should provide a liquidity backstop to the shadow banking system. Because the shadow banking system is a global system, a consortium of central banks should be responsible for providing the liquidity backstop. This is exactly what the Fed did during the financial crisis. This has transformed the balance sheet of the Fed.

global money dealer (funding)

assets	liabilities
◦ money market funding ◦ liquidity put (funding)	◦ deposits

derivative dealer

assets	liabilities
◦ credit default swaps ◦ interest rate swaps ◦ foreign exchange swaps ;◦ liquidity put (risk)	◦ credit default swaps ◦ interest rate swaps ◦ foreign exchange swaps

asset manager

assets	liabilities
◦ liquidity put (funding) ◦ liquidity put (risk)

21.9. Regulation of systemic risk

When regulating systemic risk, the inherent instability of credit should be acknowledged. Crucial in understanding the instability is the dealer model. During a boom phase, asset managers want more money substitutes and risk exposure than the shadow banks can absorb, pushing down yields and risk premiums. Prices are distorted by the order flows, and shadow banks seem highly profitable, so more of them are instituted.

During the bust, asset managers want less money substitutes and risk exposure than the shadow banks need, pushing up yields and risk premiums. Prices are distorted by the order flows, and shadow banks suddenly seem highly unprofitable, so they run into trouble. Also dealers experience funding stress, and if they are exposed to losses, they can absorb less risk, making the stress in the system worse.

21.10. Regulation of collateral and payment flows

During normal times, collateral flows are important. The capital funding bank may hold residential mortgage backed securites (RMBS) and use them as collateral for money market lending, for example repo or asset backed commercial paper (ABCP). The collateral may pass through the money market dealer to the asset manager. Derivative position can be valued at zero when they are set up. The asset manager has exposure to risk but has sufficient capital. If the shadow bank loses money, the asset manager may need to transfer deposits to the derivatives dealer who pays out the shadow bank.

capital funding bank

assets

liabilities

◦ RMBS
◦ CDS
◦ IRS

100
0
0

◦ money market funding

100

global money dealer

assets

liabilities

◦ money market funding

100

◦ deposits

100

derivative dealer

assets

liabilities

◦ CDS
◦ IRS

0
0

◦ CDS
◦ IRS

0
0

asset manager

assets

liabilities

◦ deposits

100

◦ capital
◦ CDS
◦ IRS

100
0
0

There is no counterparty risk. The shadow bank is hedging its positions, while the asset manager has sufficient capital. There is liquidity risk however. Prices of the RMBS may drop, for example from 100 to 90. At such a moment, it may be important to block a liquidity crunch, and a firesale of RMBS because of collateral problems. Collateral flows can backstop the losing positions of shadow banks. It must be possible to use the CDS, or the collateral that is coming from the CDS, to use as collateral for money market funding.

capital funding bank

assets

liabilities

◦ RMBS
◦ CDS
◦ IRS

90
10
0

◦ money market funding

100

global money dealer

assets

liabilities

◦ money market funding

100

◦ deposits

100

derivative dealer

assets

liabilities

◦ CDS
◦ IRS

10
0

◦ CDS
◦ IRS

10
0

asset manager

assets

liabilities

◦ deposits

100

◦ capital
◦ CDS
◦ IRS

90
10
0

At some point losses may need to be recognised and paid out. There should be no payment problems as in a liquidity crunch different parties depend on the payment of others to make their own payments. If someone does not make a payment, then other payments may not be made as well. Collateral flows as well as payment flows are needed to make sure that normal fluctuations in value cause a crisis. The private sector should deal with those problems as much as possible ortherwise you may get moral hazard problems.

21.11. Private and public backstops

Matched book dealers do not need much capital but they do need liquidity, so liquidity reserves are important for the matched book part of the dealer system. Speculative dealers need capital to be able to absorb losses, so capital reserves are important for the speculative part of the dealer system. This is true for money market dealers as well as derivatives dealers.

capital funding bank

assets	liabilities
◦ RMBS ◦ CDS ◦ IRS	◦ money market funding

global money dealer

assets	liabilities
◦ money market funding ◦ liquidity reserves	◦ deposits ◦ capital reserves

derivative dealer

assets	liabilities
◦ CDS ◦ IRS ◦ liquidity reserves	◦ CDS ◦ IRS ◦ capital reserves

asset manager

assets	liabilities
◦ deposits	◦ capital ◦ CDS ◦ IRS

With regard to liquidity and solvency risk and regulations, the following observations can be made:
- the key players in a market-based credit system are the dealers and not the shadow banks;
- the key backstop for matched book dealers is liquidity and not capital;
- the key backstop for speculative dealers is capital and not liquidity;
- the survival constraint is also about collateral flows and not just payment flows.

Professor Mehrling sees a role for central banks in creating an outside spread, which means that central banks act as a value based trader. Furthermore, central banks should act decisively, and not in a piecemeal way as they did during the financial crisis of 2008-2011. Intervention should be predictable. Intervention should also be expensive for private parties in order to create an incentive for private parties to deal with the issue themselves.

22. Touching the elephant: three views

22.1. Three world views

The money view looks at a world where the present determines the present, in the sense that cash inflows must be adequate to meet cash outflows over the period of a single day. This is a period much too short for there to be any elasticity in production or consumption, the usual subject matter of economics, so this is not taken into consideration.

The economics view looks at a world where the past determines the present, in the sense that the current flow of goods being produced is the consequence of capital investments made over many generations in the past. The sale of those goods is the source of current income, most of which is consumed but some of which is saved in the form of additions to the capital stock available for future production.

Production: Y = F(K,L)

Capital Accumulation: K_t = K_t-1 + I_t

The finance view looks at the world where the future determines the present, in the sense that current capital values are a consequence of ideas about future income flows, which are discounted back to the present. Changing ideas cannot change the physical quantity of capital currently in existence, but they can very easily change the valuation of that capital, as well as the valuation of capital investments not yet made.

Capital valuation: P_K = E₀Σ(1/1+r)^tC_t

The economics view and the finance view meet each other in the present, but the present is the realm of the money view. Cash flows emerging from past production meet cash commitments engaged with an eye on future production, and the balance or imbalance between the two poses the problem that is solved every day by the monetary system. Most of the history of monetary thought is about the conversation between the money view, which emerges organically from experience with the monetary system, and the economics view in the academy. Finance challenged economics mainly, and the big story of the last thirty years has been economics versus finance.

22.2. A world without money: commodity exchange

When economists build theories about why goods have the prices they do, they typically abstract from money. This practise has allowed economists to build the Walrasian general equilibrium theory of value, but it is a theory without any place for money. The static two-good equilibrium suggests that production possibilities and consumer preferences jointly determining the relative price of two goods. If the price of oranges is p_o and the price of apples p_a then the slope of the budget line is –p_o/p_a, which is the relative price of the two goods.

Money is not mentioned. The matter of money and prices is addressed in the quantity equation

MV = PQ, or MV = p_aq_a + p_oq_o.

The right hand side represents the value of goods sold, and the left hand side represents how money turnover facilitated that sale. The equation as stated is an identity, but economists have always been tempted to read causality into it. One theory is that the quantity of money determines the price level. Another theory is that the scale of transactions determines the scale of money flow, including elastic credit substitutes.

Irving Fisher moved debate in a more constructive direction by including the idea of inter temporal exchange, resulting in the one-good two-period equilibrium. Production possibilities and consumer preferences together determine the relative price of two goods. The rate of interest acts as the relative price of goods between two different time periods. That rate of interest has nothing to do with money. Denoting production by {C1, C2}, the wealth of the representative consumer can be written as:

W = p₁C₁ + [p₂/(1+r)]C₂.

In equilibrium, the price ratio p₁/[p₂/(1+r)] will be equal to the marginal rate of substitution for each consumer, and also the marginal rate of transformation for each producer.

Also in this model, nothing is said about money or the price level. The quantity equation is not very helpful as future consumption is not exchanged today, so it is not possible to put it in the equation together with present consumption. Fisher's realised that the market for securities is a current market with current prices where claims for future consumption are exchanged.

To make room for loans (credit), it is assumed that there are two kinds of people in this world, both with the same production possibilities. One group prefers consumption today and one group prefers consumption tomorrow. In equilibrium, both groups of people produce the current and future consumption goods in the same proportions, but the present-oriented consume more of the present good and the future-oriented consume more of the future good.

The relative price of goods today and goods tomorrow includes the rate of interest, which looks like the pure price of time. Instead of thinking of the two consumers as trading goods across time, what happens in period 1 is considered separate from what happens in period 2. In period 1, the present-oriented consumer A consumes more of the present good than he produces, and in period 2 the future-oriented consumer B consumes more of the future good than he produces.

This is achieved by borrowing and lending at the rate of interest. The quantity of outstanding credit then depends on the difference between people. Maybe people use these credit balances to make payments, but this does not affect prices.

One-good two-period equilibrium with credit

In this way the quantity theory is expanded to an inter temporal equilibrium, but money is still out of the picture. It is possible to to add securities transactions and the prices at which they are made to the commodity transactions and the prices at which they are made. This is represented in Irving Fisher's transactions version of the quantity theory:

MV = PT = p_cC + (1/1+r)F

where F denotes financial transactions.

Again this identity is sometimes seen as a causal equation, and there is dispute about whether causation flows from left to right or right to left. The left to right view suggests that monetary manipulation by the central bank affects not only the price level (price of goods) but also the price of assets, P_K, and hence the rate of interest r. This is the origin of the idea expressed in the Hicks-Samuelson IS-LM model that the monetary authority can affect the real economy by changing the money supply.¹¹

22.3. Imagine a world without money: risk

Fischer Black viewed the world from the perspective of securities, not commodities, and from the Capital Asset Pricing Model (CAPM). He had a finance view. Irving Fisher can be seen as a transitional figure between the economics view and the finance view. CAPM adds risk to the Fisher model. In standard general equilibrium theory, this is done by distinguishing future states of the world and treating goods produced in each possible future state as different goods with different prices. From a financial point of view, the relative price of goods today and goods tomorrow includes not just the price of time but also the price of risk.

The Capital Asset Pricing Model makes it possible to separate out these two prices. Suppose there are capital assets, each of which can be characterised by the mean and variance of its return over a short interval of time. Consider the set of expected returns and variances that can be achieved by holding a portfolio of these assets. Assume that there are two kinds of people, one quite risk tolerant and the other less risk tolerant.

In equilibrium, everyone holds the same portfolio of the risky capital assets, but the risk tolerant hold more and the less tolerant hold less. This allocation is achieved by having the more tolerant borrow from the less tolerant, at the risk free rate of interest. The interaction of these two types determines two prices, the risk free rate R_f, and the price of risk ER_m - R_f, which is the expected return on the market portfolio minus the risk free rate. In equilibrium, the CAPM equation applies:

Security Market Line:¹² ER_i = R_f + (ER_m - R_f)β_i,

Capital Market Line:¹³ ER_p = R_f + (ER_m - R_f)σ_p/σ_M.

Starting from CAPM, Fischer Black proposes that banks are essentially intermediaries between the risk tolerant and the less risk tolerant. Bank assets are the loans to the risk tolerant, and bank liabilities are the assets of the less tolerant. If each has wealth of 100, the risk tolerant may borrow 50 in order to invest 150 in the risky portfolio, and the less risk tolerant may lend 50 to the risk tolerant in order to invest 50 in the risky portfolio. The outstanding quantity of bank assets and liabilities is determined by private supply and demand, and the same is true of the interest rate. From a CAPM view, monetary policy determines neither the quantity of money nor the price of money. Both are determined by private borrowing and lending.

From the viewpoint of the quantity equation, financial equilibrium requires to think of the causation passing from right (PT) to left (MV). If the price of the market rises, risk tolerant people want to borrow to buy more, while risk averse people want to sell to lend more, so both loans and deposits change whenever the stock market changes.

risk tolerant

assets	liabilities
◦ 150 market	◦ 50 loan

bank

assets	liabilities
◦ 50 loan	◦ 50 deposit

risk averse

assets	liabilities
◦ 50 market ◦ 50 deposit

From his point of view, the quantity of money (bank deposits) must be allowed to fluctuate freely to allow people to adjust their risk exposure as stock prices fluctuate. Similarly, the price of money (rate of interest) must be allowed to fluctuate freely to allow the market for riskless borrowing and lending to clear. In both respects there is no place for money or monetary policy.

From his point of view, there is no role for government policy to control the money supply. Fischer Black stated that there is nothing that can be called the quantity of money, and hence there is nothing to control. It is equally true that there is no role for government policy to control the rate of interest. Of course the government has, historically, tried to control both of these things. Fischer Black's position seemed that such efforts produce inefficiency at the very least. In a financially developed economy, they don't even do that, since there will be multiple ways to evade control.

22.4. The education of Fischer Black

Fischer Black observed that, once people use banks as their source of risk free borrowing and lending for investment purposes, it is inevitable that they would use them as means of payment as well. People who need to make payments to one another do so simply by making book entries in the banking system. What is more, payments from a negative account (loan) seem just as possible as payments from a positive account (deposit). Such patterns of payments will affect the quantity of bank assets and liabilities, but not their price because the payments system is efficient.

If a holder of a positive account in one bank makes a payment to a holder of a positive account in another bank, the quantity of outstanding bank credit does not change. But if a holder of a negative account makes a payment to a holder of a positive account, credit expands. And if a holder of a positive account makes a payment to a holder of a negative account, credit contracts. In the finance view, the elasticity of the payments system arises from the elasticity of credit in capital markets, not vice versa as in the money view.

For Fischer Black, the only constraint is wealth, which people allocate between different assets depending on their tolerance for risk, in a market where price is efficient and there is no trouble adjusting portfolios at the margin. He did not consider the survival constraint, or the role of dealers in marking markets. Professor Mehrling sees a few lessons he would like to teach Fischer Black if he were still alive.

The first lesson is that market liquidity depends on the dealer system. CAPM abstracts from liquidity. The model assumes that all securities can be bought and sold in perfectly liquid markets, but this would be true only if the outside spread, established by the value trader, was as tight as the inside spread, established by the dealer. The second lesson is that the ability of dealers to provide market liquidity depends on their own funding liquidity. The collapse of LTCM in 1998 taught this. The strategy of LTCM was loading up on liquidity risk. When liquidity dried up they could not refinance their position. The third lesson is that he ultimate source of funding liquidity is the central bank because ultimate means of payment is the liability of that bank which it can expand or contract.

22.5. The future of banking

Banking can be seen as selective enforcement (discipline) and relaxation (elasticity) of the survival constraint. The importance of this function is two-fold. On the one hand it means that agents who have accumulated obligations to pay that they cannot now meet can, if the banking system lets them, put off the problem until some time in the future when perhaps they will be better able to meet their obligations. On the other hand it means that agents who have plans for the future they cannot now realise for lack of spending power can, if the banking system lets them, issue obligations to pay in the future.

In helping to postpone realisation of failure, and to anticipate realisation of success, banks take on risk. They make the payments that the agents are not (yet) themselves able to make. In this sense, the core of the banking function is the selective bearing of liquidity risk. As long as there is liquidity risk, there will be a crucial role for banks.

From a policy perspective, the question of regulation revolves around externalities, which are all the ways in which private profit motive for selective bearing of liquidity risk deviates from the larger social good. The problem is that, the more liquidity risk banks bear, the more they charge for an additional unit, until ultimately they are unwilling to bear any more and the system breaks down. Central banks can help by serving and lender and dealer of last resort. It follows that they can also help by intervening earlier on when the deviation between private and social begins to widen.

References

1. A Reconsideration of the Twentieth Century, Robert A. Mundell, The American Economic Review, Vol. 90, No 3, 2000
2. The dollar and world liquidity, Emile Depres, Charles P. Kindleberger, and Walter S. Salant, The Economist, 5 Feburary 1966, p. 526-529
3. Stigum's Money Market Fourth Edition, Marcia Stigum, Anthony Crescenzi, 2007, p. 718-722
4. Stigum's Money Market Fourth Edition, Marcia Stigum, Anthony Crescenzi, 2007, p. 869-921
5. Stigum's Money Market Fourth Edition, Marcia Stigum, Anthony Crescenzi, 2007, p. 874-875
6. Stigum's Money Market Fourth Edition, Marcia Stigum, Anthony Crescenzi, 2007, p. 895-897
7. Stigum's Money Market Fourth Edition, Marcia Stigum, Anthony Crescenzi, 2007, p. 900
8. Transparency report to the shareholders of UBS AG, UBS AG, Zurich and Basel, Switzerland, 2010
9. Factors Affecting Efforts to Limit Payments to AIG Counterparties, SIGTARP, 2009
10. The Greatest Trade Ever, Gregory Zuckerman, 2010
11. IS–LM model - Wikipedia (as on 4 February 2014): http://www.naturalmoney.org/islmmodel.html; current version: http://en.wikipedia.org/wiki/IS%E2%80%93LM_model
12. Security market line - Wikipedia (as on 8 February 2014): http://www.naturalmoney.org/securitymarketline.html; current version: http://en.wikipedia.org/wiki/Security_market_line
13. Capital market line - Wikipedia (as on 8 February 2014): http://www.naturalmoney.org/capitalmarketline.html; current version: http://en.wikipedia.org/wiki/Capital_market_line