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The Foreign Exchange Market
Barry W. Ickes
Econ 434 Fall 2006
- Introduction
The market for foreign exchange involves the purchase and sale of national currencies. A foreign exchange market exists because economies employ national currencies. If the world economy used a single currency there would be no need for foreign exchange markets. In Europe 11 economies have chosen to trade their individual currencies for a common currency. But the euro will still trade against other world currencies. For now, the foreign exchange market is a fact of life. The foreign exchange market is extremely active. It is primarily an over the counter market, the exchanges trade futures and option (more below) but most transactions are OTC. It is difficult to assess the actual size of the foreign exchange market because it is traded in many markets. For the US the Fed has estimated turnover (in traditional products) in 1998 to be $351 billion per day, after adjusting for double counting. This is a 43% increase over 1995, and about 60 times the turnover in 1977. The Bank of International Settlements did survey currency exchanges in 26 major centers and this provides some evidence. In figure 1 we present some evidence of the daily trading volume in the major cities. This shows the size and growth of the market. Daily trading volumes on the foreign exchange market often exceed $1 trillion,^1 which is much larger than volumes on the New York Stock Exchange (the total volume of trade on ”Black Monday” in 1987 was $21 billion). The annual volume of foreign exchange trading is some 60 times larger than annual world trade ($5.2 trillion), and even 10-12 times larger than world GNP (about $25-30 trillion in 1995). You can also verify from figure 1 that the UK still accounts for the largest share of actual trades, more than 31%. What accounts for this huge volume and its rapid growth? Although world trade has (^1) According to the BIS survey, in 1998 turnover in traditional products (spot, forwards, and fx swaps, but excluding futures, currency options, and currency swaps) was $1.49 trillion. This represented an 80% increase from 1992.
Figure 1: Foreign Exchange Turnover by Region and Currency
grown substantially — increasing 2.5 times since 1980 — this is far smaller than the growth in the foreign exchange market. International capital flows have increased more dramatically. This is related (causality is hard to infer) to increases in current account deficits is many counties, especially the US. Although the world current account must sum to zero, if the US has large deficits, other countries must have large surpluses, and this leads to an increase in international capital flows. Moreover, there has been an expansion in international securities markets. Banks have become more multinational and more bonds are issued internationally than before. This is evident in figure 2 which shows how dramatically these have increased. This is clearly related to increasing activities of multinational companies. Still there is a bit of a puzzle. The explanations for growth of the foreign exchange market are still too small to explain the huge volume. The reason is that the turnover in foreign exchange represents gross capital flows, but the explanations focus on net capital flows. Take the US case. Turnover is $351 billion per day, or about $87 trillion per year (assuming 250 work day). But US GDP is only about $10 trillion, and our current account deficit is "only" about 5% of that, or $500 billion. Gross transactions are thus a big multiple of net transactions. This reflects hedging behavior on the part of market participants. More below. The vast majority of transactions in the foreign exchange market involve dollars. In 1989 the share of total turnover that involved dollars was 90%. By 1995 this had fallen to 83%.
Trading in currencies is much larger now than it was prior to the demise of Bretton Woods. When exchange rates were fixed there was less reason to trade.
Figure 1: Daily Volume of Trading by Location (in billions of US$)
April 1989 April 1989 April 1995 April 1995 Pct change Country Turnover share Turnover share 1989- United Kingdom 184 25.6% 464 29.5% 60% United States 115 16.0 244 15.5 46 Japan 111 15.5 161 10.2 34 Singapore 55 7.7 105 6.7 43 Hong Kong 49 6.8 90 5.7 49 Switzerland 56 7.8 86 5.5 32 Germany (NA) 76 4.8 39 France 23 3.2 58 3.7 74 Australia 29 4.0 40 2.5 37 Others 96 13.4 248 15.8 36 Total 718 100 1,572 100 46 Adjustments less cross-border -184 - Net-net turnover 534 1,137 45 plus estimated gaps 56 53 = estimated global 590 1,190 45 plus futures and options 30 70 17 Grant Total 620 1,260 45 It turns out that foreign exchange trading is rather profitable. Commercial banks that engage in currency trading make rather large profits, though these are quite variable across banks and from year to year. Some evidence in table 1. The fact that many commercial banks earn large profits is rather curious. One might suspect that foreign exchange trading is a zero-sum game. Of course, traders might like to argue that these profits are due to their
expertise. Can we think of an economic explanation? One explanation for positive profits might be that the banks are providing a service for which they earn a positive return. Only the speculative activities of the banks ought to be zero sum. A back of the envelope calculation is informative. We have seen that the foreign exchange market amounts to about $1.19 trillion per day, or $300 trillion per year. Now suppose that customer trading is only 10% of total trades (actually it is larger than this) with speculative positions the remainder. Then if banks earn a fee of 2 basis points (.0002) per transaction, total profits would be $6 billion in spread income. Now a sample of the 14 largest commercial banks profits sums to about $2.1 billion. So it is quite likely that turnover income is the source of all profits, and that trading is actually a net loss. Another explanation that could account for the profits from foreign exchange trading could be the activities of central banks. Central banks may engage in foreign exchange transactions that lose money, as they unsuccessfully try to defend currencies. Thus the losses of the central banks could be the source of the profits of the commercial banks. Some studies have found these losses to be very large.^3 The Fed has been rather successful since the mid 1980’s,^4 but there have been some quite notable losses, most famous, perhaps, the Bank of England defending the pound in the early 1990’s. The Bank of Japan similarly lost quite a lot of money trying to prevent the yen from appreciating against the dollar during 2003 and 2004. (^3) One study found that major central banks lost $16 billion on currency trading during the 1970’s. (^4) The US was even more successful when it sold Carter bonds in the late 1970’s. These were US debt denominated in foreign currencies. For example, the Fed sold debt denominated in DM in 1978. The interest rate on this debt was about 3% less than similar dollar-denominated debt. The reason was fear of dollar depreciation. When the debt matured, however, the dollar had appreciated, so the US earned a capital gain as well as the lower interest. You can think of this as trading on your inside information that monetary policy will be tighter than believed by the market.
the number of dollars per Euro, because for the US the Euro is foreign exchange. Often, we will simply treat the rest of the world as one country, and hence we will simply refer to foreign exchange rather than specify the specific country. In that case the exchange rate, e, is just the domestic currency price of foreign exchange:
e = domestic currencyforeign exchange
The spot (or nominal) exchange rate refers to the current price of foreign exchange. It is a contract for immediate delivery, though that might actually take a day or two. A forward contract refers to a transaction for delivery of foreign exchange at some specified date in the future. Suppose, for example, that a US company, say Ford Motors, expects to receive Eu 100 , 000 60 days from now. The value of these receipts will vary with the actual value of the spot exchange rate in the future. The firm may wish, however, to hedge. It may wish to reduce the risk that the dollar will appreciate during these 60 days. Consequently, it signs a contract to deliver Eu 100 , 000 in 60 days at the current exchange rate. The company has locked in the current rate and hedged the exchange rate risk. Similarly, if Microsoft commits to invest GBP 1 m in 6 months time, it may wish to fix the dollar amount of this investment now. Hence, it could purchase a contract today to deliver pounds six months from now. Suppose that the forward price of pounds in this transaction is $1.637.^7 Then Microsoft pays $1,637,000 today to obtain GBP 1 m in 6 months time. If the pound appreciates this is a profitable transaction.^8 Even if it does not, Microsoft has reduced its risk. So far we have only analyzed Microsoft’s interest. But the risk that Microsoft has hedged the bank has absorbed. But the bank actually is acting like a dealer. Simultaneously, it will be looking for other agents who need to hedge against the dollar depreciating. For example, suppose that Coca Cola expects to earn GBP 1 m in six months from exports to the UK. It will then have to convert the pounds into dollars. To avoid the currency risk Coca Cola would (^7) The spot price on September 21, 2003 was 1.6479. (^8) For example, if the pound happened to trade at $1.73 in six months, then Microsofts hedge would have saved them $93,000 minus transactions fees.
like to sell the pounds forward: accept dollars today for the commitment to deliver pounds in six months. Notice that Coke is hedging against the risk that the pound will depreciate, while Microsoft is hedging the risk that the pound will appreciate. Trade is thus mutually beneficial; the bank is merely the intermediary.^9 In this example, the intentions of Coke and Microsoft exactly balance. More typically, a bank will have many clients whose interests differ. The intention of the bank is to balance the two sides of the market and profit from the fees. Notice that the forward price of a currency need not be equal to the spot price. If the market expects that the franc will depreciate over the next 6 months, the forward price will be lower than the spot price. The forward premium is a measure of the market’s expectation, and it can be expressed as:
fm = Fm^ e− e (2)
where m is the number of days from today and Fm is the forward exchange rate. Clearly, if fm > 0 it means that more dollars will be required to purchase foreign exchange m days from now than today. Forward contracts are usually offered by commercial banks, and this helps to explain the difference with futures contracts. Banks offer their important customers forward contracts as part of their business relationship. It enables firms to engage in international trade with limited exposure to foreign currency risk. Now in the late 1960’s many observers expected the British government to devalue the pound. Milton Friedman wanted to bet on this, and he tried to purchase forward contracts to sell the pound short; that is, he would receive dollars today for the obligation to deliver pounds in several months time. If the pound were devalued he would be able to purchase the pounds for fewer dollars in the future, and hence would profit (^9) Notice that there is no need for Coke and Microsoft to have different expectations for this trade to be profitable if the firms are risk averse. Risk averse agents are willing to pay to obtain certain future outcomes. If the firms were risk neutral, on the other hand, then for trade to occur they would need to have different expectations about the future value of the pound. Thus, if Coke expected depreciation and Microsoft expected appreciation, they would both prefer to hedge, even if they were risk neutral. This would not be the case for risk lovers. In that case some differences in expectations are needed for trade. To see this, consider betting on sports events. If everyone believed the outcome of the game would bethe same, no one would bet.
tures contract. Microsoft would be paying some dollars today for the right to purchase francs within some future period at the pre-arranged exchange rate. A call option, for example, would provide Microsoft the right to purchase francs at the pre-arranged price during the life of the option. If the value of the franc increased holding the option would benefit Microsoft. If the value of the franc decreased, Microsoft would choose not to exercise the option. It would lose what it paid for the option, but it would not have locked itself into an unprofitable transaction. An option contract thus includes a measure of insurance. It allows the investor to avoid potential losses that would accompany unfavorable movements in currencies.
2.1. Covered Interest Parity
The existence of forward markets for foreign exchange benefits not only firms that expect to have foreign currency transactions in the future, but also investors who wish to invest in foreign currencies. Suppose that the domestic interest rate (on say, 3 month T-bills to provide specificity) is given by i, and that the foreign interest rate is i∗, and that i∗^ > i. I might wish to invest in foreign assets rather than domestic assets. But if I do so, I would face the risk that 3 months from now the dollar may appreciate, so that when I convert my foreign currency into dollars I would take a capital loss. The forward market allow an alternative, called a covered transaction, which eliminates currency risk.^11 Letting et be the spot exchange rate (dollars per euro) and Ft the current forward price for euro three months hence, I could hedge my risk by purchasing a forward contract. Specifically, assume that I choose to invest a dollar. I can convert this into (^) e^1 t euro. I then invest this, and at the end of three months I have (^) e^1 t (1 + i∗) euro. Because I purchased the forward contract, this yields me F ett (1 + i∗) dollars. This transaction is called covered because I have already closed the transaction. The covered transaction indicates the dollar return to investing in (^11) Notice that a covered transaction implies no currency risk. So arbitrage will equalize returns even if agents are risk averse. This is certainly true for US and German transactions. But in the summer of 1998 ruble forward transactions were anything but certain. And for good reason; most sellers of forward contracts (in dollars) were unable to honor their contracts. Because of high ruble yields on Russian T-bills (called GKO’s) foreign investors flocked to Russia and purchased forward contracts to convert profits back into dollars. But in the wake of the currency crisis, the banks could not buy the dollars needed to honor the contracts.
foreign assets. Of course, I could always invest in domestic assets and earn (1 + i). Hence, arbitrage should insure that
1 + i = F ett (1 + i∗) (3)
which is called the covered interest parity condition (CIPC).^12 A host of studies have shown the high degree to which this condition is satisfied by market rates. The CIPC can be used to reveal an interesting relationship between interest rates and the exchange rates, by using the expression for the forward premium (2). From the definition of fm it follows that
1 + i 1 + i∗^ =^
Ft − et et^ + 1 =^ fm^ + 1.^ (4) In other words, when the forward premium is positive domestic interest rates are higher than foreign interest rates, and vice versa. The forward premium reflects the capital gain on my covered transaction, and by arbitrage, this must equal the difference in interest rates in the two countries. It is easier to interpret (4) if we take logs of (3) to obtain:
log(1 + i) = log Ft − log et + log(1 + i∗)
and then use the fact that for small x, log(1 + x) ≈ x,^13 we obtain:
i = log Ft − log et + i∗ (^12) In practice this is an approximation, because of transaction costs. (^13) This follows from taking a first-order Taylor approximation to x, which yields: x − x 22 + x 33 − x 44 + ... ≈ x.
risk, hence arbitrage occurs whether or not agents are risk averse. Uncovered interest parity, on the other hand, results only if agents are risk neutral.^17 If agents are risk averse, then they will demand a risk premium to hold the risky return. In this case the only differential risk is the currency risk associated with holding foreign assets. Hence, arbitrage would result not in (6), but rather in:
1 + i = bet e+1t (1 + i∗) + ρt (8)
where ρt is the risk premium. Finally, notice that if expected future exchange rates are equal to forward rates (i.e., Ft = bet+1) it follows that the UIPC must hold. It is an important item of research to test for this. Although we often assume it, in practice UIPC tends not to be supported by the data. If risk premia are important, then the forward rate is not equal to the expected exchange rate. Rather we have ft = δt + ρt. The forward premium differs from the expected rate of currency depreciation by the risk premium. In this case we cannot recover the market’s expectation about the exchange rate directly from interest rate differentials.^18 We will return to this later.
Testing for Uncovered Interest Parity How can one test whether the UIPC holds? Notice that if both conditions held it follows that Ft = bet+1. We have data on the former but not on the expected spot rate. To form a test, we therefore need an hypothesis about exchange rates. Hence, to test for UIPC we then impose the rational expectations hypothesis. This says that the expected value of a variable is given by the conditional expectation of that variable using the appropriate economic model. For our purposes the key implication is that expectations will be unbiased. This implies that bet+1 will be an unbiased predictor of et+1. Now we can test for UIPC. If UIPC and rational expectations hold, then Ft should be an unbiased predictor of et+1. I can always collect a time series of spot and future exchange (^17) At the margin. (^18) This also explains why investors demand a large premium to hold Brazilian reals (in February 1999) even when the real has severely depreciated. Presently, interest differentials are close to 36%, while the real has probably reached a trough relative to the dollar. But investors are worried that Brazil may default on its debt, so a large risk premium is required to induce agents to hold Brazilian assets.
rates. A regression of the form:
et+1 = α + βFt + γXt + εt (9)
should, according to our hypotheses result in estimates of αb = 0, bγ = 0 and bβ = 1, where Xt are any other variables we may include in the regression. Tests usually reject this hypothesis, typically finding bβ < 1. For technical reasons — the fact that e and F have a common trend — it is preferable to test this in a different manner. Note that UIPC implies that bet+1 − et = i − i∗. From CIPC we can replace the interest differential with Ft − et. Hence, we have bet+1 − et = Ft − et. Of course we still cannot observe bet+1, but rational expectations implies that et+1 − bet+1 ≡ εt+ (the forecast error) will be uncorrelated with any information known at time t. Hence, we can write et+1 − εt+1 − et = Ft − et
which can be tested by estimating
et+1 − et = α + β(Ft − et) + γXt + εt+1 (10)
where the null is that αb = bγ = 0 and βb = 1. Notice that this is then a joint test: we are testing the assumption that the forward rate is an unbiased estimator of the spot rate — i.e., that agents have rational expectations — and that agents are risk neutral. A rejection of the hypothesis could thus arise from one of two reasons.
- expectations are not rational
- risk neutrality One way to view the evidence is to look at a plot of Ft and et+1. According to the hypothesis the difference between these two variable should be random error. But the plot shows in fact that the differences are systematic. Indeed, the spot rate seems to lead the forward rate. This is evident in figure 3 which plots the Yen forward and spot rate versus the dollar.
and when i < i∗^ I follow the opposite route. My profits in this case are:
p−^ = −
μ (1 + i) − (1 + i∗)et e+1t
; i − i∗^ < 0
Figure 4: Realized exchange rates and the forward premium
Another version of the carry trade would be to sell domestic currency forward (going short on domestic currency) whenever there is a forward premium (Ft > et) and buying the domestic currency forward (going long on domestic currency) whenever it is at a forward discount (Ft < et). That is,
xt =
0 if Ft > et < 0 if Ft < et
where xt is the number of dollars sold forward. The payoff to this strategy is
xt
μ (^) Ft et+1^ −^1
If UIPC holds, then this strategy (13) yields positive profits whenever the conventional carry trade (11) yields positive profits, and vice versa. This might be more profitable, however, as there are fewer transactions costs. Suppose you followed this strategy (this is sometimes called the carry trade). Would you make money? Suppose you did this from September 1993 to August 2003. Bet each month for
Figure 5:
the ten years, so you have 120 observations. Turns out you would make money. The average value of p =. 0041. We can plot the distributions of realized profits in figure 6. You can see that they are volatile, but you do make money. But the profits are risky. The standard deviation of p =. 033 , which implies that the Sharpe ratio (meanstd ) is 0. 12.^19 This appears risky; the Sharpe ratio for the S&P 500 is about. 06. LTCM and Tiger Management Fund made this type of bet and lost in 1998:8 and 1998:9.^20 Were they unlucky? Here are the numbers. We use covered forward interest parity for the interest differential since that does hold. In August 1998 the monthly interest rate in the US was 0.1% higher than in Japan. So invest in the US. Bad move, the dollar depreciated by 7% (yen appreciated 7%) and LTCM lost 6.4% (a 2 std. deviation event) on the bet.^21 And September was even worse. The interest differential was 0.4% in favor of the US, but the dollar depreciated by 13% (yen appreciated 13%,) and LTCM lost 12%, ( a 3.5 std. deviation outlier, and the minimum profit in the sample). The estimate is that Tiger lost $2 billion on one day in October on such trades. Suppose that we find that βb < 1.^22 What does this mean? It is important to recall that (^19) The Sharpe ratio is the excess return on an asset divided by the standard deviation of the excess return. Thus, let RA be the return on asset A and let Rb be the return on a benchmark (risk-free asset). The the Sharpe ratio of asset A is given by SA = E^ (RA σ^ −^ Rb) where E is the expectations operator, and σ is the standard deviation of excess returns, σ = (var(RA − Rb))^1 /^2. Note that if assetmeasure of excess return. Suppose you have two assets with the same expected excess return. If one of the b is really risk-free then σ = (var(RA))^1 /^2. Thus the Sharpe ratio is a risk-adjustment assets has less volatile returns its Sharpe ratio will be higher. You can think of it as reward per unit of risk. 20 21 Many of LTCM’s bets were swaps, but Tiger seems to have engaged in the pure carry trade. It seems that the central banks of both governments decided to intervene to prop up the yen that summer — this was unexpected by the markets. 22 This is referred to as forward rate bias — the forward rate over-predicts the future spot rate.
Most studies are unable to find such a systematic relationship. Indeed, it turns out that some of the X variables are useful for explaining forecast errors. This is surprising. For example, historic forecast errors seem to be significant in explaining current forward rate forecasting errors. This inefficiency is important. If markets were efficient then the case for intervention in currency markets would be much weaker. Of course the converse is not necessarily true — intervention could still be counter-productive. But it does open the door. So it is important to know why markets are inefficient. What explains this inefficiency? One explanation could be that noise traders can cause the deviation from fundamental values. This could result from insufficient speculation. If arbi- tragers are liquidity constrained they may be unable to profit from short selling "overvalued" assets. Now this may seem surprising given how large these markets are. But many of the participants may not be interested in short-run profits. Why? Banks tend to close out their positions each night. And corporations, though they hold for long periods, may not be able to re-adjust their hedges in response to shocks due to their financial policies. They may be informed, but they may be unable to make speculative transactions when market prices stray from fundamentals. Economists prefer to think that markets are efficient, so the typical explanation centers on the risk premium, ρ, as in expression (8). In particular, it is thought that this may vary over time. Why would risk matter? Risks arise because the future value of currencies are uncertain. If you engage in currency arbitrage, for example, you do not know what the value of the exchange rate will be when you have to convert your interest earnings back to your home currency. If currencies are volatile then such risks are larger. If agents do not like risk (if they are risk averse) then they will pay to reduce them — that means they are willing to sacrifice some income to avoid the risk — we observe that people buy insurance, after all. This means that they will demand a premium to bear a risk. To see this, consider figure 7 where we plot income against utility. U(y) is concave because the individual is risk averse: certain incomes are preferred to uncertain ones. Suppose that
an individual is presented with an uncertain income stream. Specifically, with probability α income will equal y 1 and with probability (1 − α) income will be y 2. Then average income will be by = αy 1 + (1 − α)y 2. The utility an individual obtains from this gamble is u(by). Compare this to the utility that the individual obtains from the certain level of income y 3 < by, that is u(y 3 ). Because U(y) is concave — that is because the agent is risk averse — u(y 3 ) > u(yb). This means that the individual prefers to have a lower level of income with certainty to the uncertain gamble. The individual would pay to reduce risk. Notice that the maximum amount that the agent would pay to reduce the risk is equal to y 4 , which is referred to as the certainty equivalent level of income. Clearly the individual would be willing to pay any amount up to by − y 4 to be relieved of this uncertainty. Alternatively, one can think of this amount as the risk premium that the agent demands to go from the certain prospect y 4 to the uncertain prospect yb. Utility
U(y)
y (^) 1 y 2 y ˆ y (^) =α y 1 +( 1 − α) y 2
u ( ˆ y )
y 3
u ( y 3 )
u ( y 1 )
u ( y 2 )
y 4
Figure 7: Certain and Uncertain Income We can note two important points about the risk premium from figure 7.
- First, the size of the risk premium clearly depends on the extent of volatility. To see this simply make the difference between y 1 and y 2 smaller without changing yb. You can see for yourself that the size of the risk premium that will be demanded will fall. So one
