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Foreign Exchange. Purchase and sale of national currencies Huge market $4 trillion per day (April 2007), much growth recently Compared with US Treasury market = $300 billion NYSE < $10 billion Comprised of $1.005 trillion $2.076 trillion in derivatives , ie
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Foreign Exchange • Purchase and sale of national currencies • Huge market • $4 trillion per day (April 2007), much growth recently • Compared with US Treasury market = $300 billion • NYSE < $10 billion • Comprised of • $1.005 trillion • $2.076 trillion in derivatives, ie • $362 billion in outright forwards • $1.714 trillion in forex swaps • Concentrated in few centers and few currencies
Global Foreign Exchange Market Turnover(average daily turnover)
Exchange Rates • Spot versus forward exchange rates • Nominal exchange rate • A forward contract refers to a transaction for delivery of foreign exchange at some specified date in the future. • Used to hedge currency risk • Forward premium
Forward versus futures • Forwards sold by commercial banks, otc • Futures sold in organized exchanges • Originated in 1972 in the Merc • Clearinghouse, currencies need not be delivered • Contracts settled in cash • Forward markets larger but futures markets more liquid • Options • Right to buy or sell at set price (strike price)
Covered Interest Parity • Covered transactions eliminate currency risk • Let i and i* be the domestic and foreign interest rate • Let etand Ft be the spot and forward rate at t • Suppose we want to invest in foreign currency • We face currency risk when we repatriate earning • But we can hedge the risk by purchasing euros forward today at Ft • One dollar invested in euros yields euros • 3 months from now I have euros • So 3 months hence I have dollars
Covered Interest Parity • Arbitrage requires that • Which is called CIPC • This implies • or • If not equal there are arbitrage profits to be made • Thus, a positive interest differential implies a forward premium • Interest must compensate for capital loss
CIPC • Take logs of both sides of CIPC • or, for small i • Most studies show that CIPC holds • Notice that there is no currency risk • Forward price signals markets expectation
Riskless Arbitrage: Covered Interest Parity • Arbitrage profit? • Considers the German deutschmark (GER) relative to the British pound (UK), 1970-1994. • Determine whether foreign exchange traders could earn a profit through establishing forward and spot contracts • The profit from this type of arrangement is:
Uncovered Interest Parity • Suppose we do not hedge our investment • Again we invest one dollar • Let be the expected future spot rate • In 3 months we earn • Arbitrage requires • UIPC, thus
CIPC and UIPC compared • The two conditions differ only in one term • versus • CIPC involves no currency risk • UIPC bears currency risk • Holds only if agents are risk neutral • Risk averse agents may require a risk premium • Notice that if then UIPC holds • This would be cool => markets reveal expectations • We can test for this
Efficient Markets • Example of Efficient Markets Hypothesis • Investors use available information efficiently • Does not mean they are ex post correct, only that prices reflect all available current information in an efficient manner • Unbiased errors • If I am efficient my error pattern looks like that of Tiger Woods • Of course, the variance of my pattern is greater, but we are both on target on average
Testing for UIPC • We have data on F but not on • Rational expectations implies that forecast errors are unbiased • Then should be an unbiased predictor of • That is, guesses are on average correct • UIPC implies that • Thus, if REH and UIPC holds, then should be an unbiased predictor of • => market is efficient!!! • What does unbiased mean? • If I have a lot of observations, then the average value of Ft should differ from et+1 only by a random error • Hiawatha’s Last Arrow
Testing UIPC • So if I estimate • where is any variable you can think of, and is a random error • I should find • That is, all the information valuable for predicting is incorporated in the market price,
Testing UIPC • Typically one actually regresses changes, so • With null hypotheses • Notice this is a joint test • REH and UIPC • So rejection could mean either • Expectations are not rational • UIPC does not hold (perhaps agents are not risk neutral) • Visual inspection does not vindicate UIPC
Tests of UICP • Most tests find forward premium puzzle • Not only is in the data, it is often negative • If UIPC held, the pound should, on average, appreciate when it is at a forward premium, i.e., f > 0 • The negative point estimates of β imply that the pound actually tends to depreciate when it is at a forward premium. • UK interest rates exceed US by 2.41% on average, but sterling appreciates by 22.25%
Forward Premium Puzzle • If UICP fails there are two possibilities • Markets are not efficient • risk premium is missing • We are testing a joint hypothesis • If marginal agents are risk averse ignoring this could explain the forward puzzle • If income is volatile perhaps risk premium varies • Or it could be Central Bank Behavior
Central Banks • Central Banks move exchange rates in short run • They could set policy based on observations of F • E.g., intervene when risk premium rises • Seems that when CB’s intervene heavily the forward discount increases • Forward discount is larger in floating rate regimes • Forward discount larger at shorter horizons • Interesting because CB’s can only move e over short periods • Less risk at longer horizons
Risk Premium • But time varying risk premia hard to observe • To explain risk premium must be more volatile than • Why would this be the case (assertion, see notes for explanation)? • We don’t seem to be able to find such a risk premium • Why is forward discount larger for industrialized economies? • Unlike major currencies, which generally show a coefficient significantly less than zero, suggesting that the forward rate actually points in the wrong direction, the coefficient for emerging market currencies is on average slightly above zero, and even when negative is rarely significantly less than zero. • Hard to reconcile with risk premium explanation • Emerging markets appear riskier but have a smaller risk premium????
Can we make money? • If UIPC fails, can we make money? • One can pursue carry trade: borrow low invest high • Let y be the amount of money borrowed, then • With payoff • So if my profit would be
Carry Trade • Suppose we did this via dollar-yen • September 1993 till August 2003 • Bet once a month for ten years, we have 120 observations • We would earn money, average profits positive = .0041 • Profits are volatile • Sharpe ratio = 0.12 < than for S&P 500 • Carry trade is a bet against arbitrage, on lower volatility • Sometimes carry trade leads to big losses, unexpected currency movements • Like selling puts out of the money • Why don’t investors arbitragers bet against it? • Incentive problem for fund managers • Rational inattention
Example • Example: Japanese yen and Australian dollar • 2001: steady increase in profits from carry trades. • Despite several months of positive carry profits, the yen did not sufficiently appreciate against the Australian dollar to offset these profits. • Leverage and margin • Example: You have $2,000 and borrow an additional $48,000 in yen from a bank in Japan. • You have borrowed 25 times your own $2,000 capital, a leverage ratio of 25. You conduct carry trade, investing $50,000 in the Australian dollar. • If you lose 4% on the trade, you’ve lost your initial capital investment. This initial capital put up by the investor of 4% of the total investment is known as a margin.
Summary • Obviously if large institutions do this losses could be huge. Duh! • Even if expected returns from arbitrage are equal to zero, actual profits are often not equal to zero. • Returns (profits/losses) are persistent. • Returns are volatile/risky.
Price Pressure • Bid-ask spreads reduce size of profits • Large amounts of speculation needed to earn money • Speculator who be one pound on an equally-weighted portfolio of carry-trade strategies (across the USA, Canada, Belgium, France, Germany, Japan, Netherlands, Switzerland and the euro) from 1976 to 2005 would earn an monthly payoff of 0.0025 pounds. • To earn an average annual payoff of 1 million pounds would require a bet of 33.33 million pounds per month. • Is there an effect of such large trades? • Would they survive such speculation? • Prices rise with order flow • Could eat profits • You could break up trades, but this chews up profits as well • The marginal expected payoff can be zero, even when the average payoff is positive • Speculators make profits but no money is left on the table
Risk versus Reward • Idea: Examine traders’ strategies and other finance theories to study tradeoff between risk and return. • Data: Positive 1% interest differential is associated with only a 0.23% appreciation in the currency, implying a 0.77% profit. • Problem: despite the existence of profits: • Profits do not rise/fall linearly, line is a poor fit for the data. At higher differentials, variance in return higher. • Variance around the line is high in general, creating uncertainty for investors.
Test of Efficient Markets • Not the high variance of observations around the line of best fit • Observations do not cluster around the line of best fit • For the same interest differential there are vastly different actual rates of depreciation observed
Limits of Arbitrage • Returns positive for currencies • Very high volatility of returns • Sharpe ratios < 1 • Equal to 0.5 – 0.6 for market portfolio of currencies • Differs little from stock market • Puzzle like the equity premium puzzle
Predictability and Nonlinearity • Linear model may be the problem • Nonlinear models reveal that low interest differentials are associated with very low profits. • At high differentials, investors engage in carry trades, bidding up the currency, sometimes causing reversals (and losses). • At the extreme ends, arbitrage appears to work, so what is happening for moderate interest differentials? • Investors are willing to take on some risk, if the return is large enough.
