The Returns to Currency Speculation

Transcription

1 The Returns to Currency Speculation Craig Burnside Martin Eichenbaum Isaac Kleshchelski Sergio Rebelo May 6

2 Motivation Uncovered interest parity (UIP) is a key feature of linearized open-economy models. Problem: UIP is overwhelmingly rejected by the data. `Forward premium-depreciation anomaly' is a particularly egregious deviation from UIP Currencies that are at a forward premium tend to depreciate. Sell pound forward at F t (pesos per pound)

3 Traditional Reponses to this Problem Ignore rejection of UIP and hope that UIP isn t central to the predictions of the model. Add an UIP `risk premium shock.

4 What We Do Investigate whether deviations from UIP are economically important. We study excess returns to currency speculation strategies that exploit the failure of UIP. Carry trade: widely used by practitioners. Sell currencies that are at a forward premium. Buy currencies that are at a forward discount. Use a particular regression to forecast payoff to selling currencies forward.

5 Payoff Properties Strategies yield high Sharpe ratios which aren t a compensation for risk. Currency returns aren t correlated with risk factors such as consumption growth. Why don't investors massively exploit this strategies to point where Sharpe ratio falls to zero or Currency speculation payoffs become correlated with risk factors?

6 Price Pressure Payoff to betting Pound on currency speculation is very small. To make large profits you have to take a very large position. Microstructure frictions: price at which investors can buy or sell an asset depends on the quantity they wish to transact. Presence of `price pressure Limits the size of bets that agents can place on currency speculation strategies. Drives a wedge between average and marginal Sharpe ratios. Marginal Sharp Ratio is zero even though Average Sharp Ratio is positive. No Money is being left in table.

7 Price Pressure Benchmark calculations based on Lyons and Evans () Total expected profits from the carry trade are 3.8 million pounds per month on bets of 3 million pounds per month. So while statistical failure of UIP is very sharp, amount of money that can be made from this failure seems very small.

8 Forward Premium-Depreciation Anomaly Our trading strategies exploit this anomaly. Why is it there in the first place? We display a simple microstructure model that generates this anomaly. Central feature of the model Market makers face an adverse selection problem that s less severe when, based on public information, a currency is expected to appreciate. Generates a negative relationship between forward rates and expected appreciations.

9 Outline Canonical UIP model Brief review of statistical tests of UIP Forward Premium Depreciation Anomaly Study excess returns to currency speculation Strategies are motivated by how UIP fails; Requires data on actual bid-ask spreads. Allow for price pressure Accounting for the Forward Premium Depreciation Anomaly

10 Canonical Model maxu E t t u C t,m t /P t B t S t B t B t R t S t B t R t P t Y t M t M t x t F t S t P t C t C t : domestic consumption M t : domestic beginning-of-period money supply P t : domestic price level Y t : domestic output B t : domestic beginning-of-period bond B t : foreign beginning-of-period bond R t and R t : yield on domestic and foreign bond, respectively S t : spot exchange rate (US$/Pound) F t : forward exchange rate (US$/Pound) for contracts maturing at time t. x t : number of Pounds sold forward in previous period To simplify our notation, we abstract from state-contingent securities.

11 Parity Conditions Implied by the Model Covered Interest Parity (CIP) R t S t R t F t Uncovered Interest Parity (UIP) R t R t E t S t S t cov t t,s t /S t E t t CIP + UIP imply: Forward as Forecaster of Future Spot F t E t S t cov t t,s t E t t Under risk neutrality covariance terms are zero. t Lagrange multiplier associated with budget constraint (marginal utility per dollar)

12 Data Series Bid and ask interbank spot exchange rate, Foreign Currency/British Pound Bid and ask interbank -month forward exchange rate, Foreign Currency/British Pound Bid and ask interbank 3-month forward exchange rate, Foreign Currency/British Pound Bid and ask interbank interest rates in London at -month maturities Bid and ask interbank interest rates in London at 3-month maturities Frequency Daily converted into non-overlapping monthly observations Source Spot and forward exchange rates , from Financial Times Spot and forward exchange rates 994-5, from WM/Reuters Interest rates, 98-5 from Datastream Our quotes are indicative quotes for small trade sizes. Pound is the domestic currency.

13 Covered Interest Parity Holds Almost Always (Taking Bid-Ask Spreads Into Account) Covered Interest Arbitrage at -Month Horizon Median return to Fraction of periods Median of positive borrowing covered in with positive returns returns to borrowing to borrowing covered in covered in Pounds FX Pounds FX Pounds FX Currency percent percent percent Belgium Canada France Germany Italy Japan Netherlands Switzerland USA Consistent with Taylor (987) which uses data collected at minute intervals for a three-day period, Taylor (989) which uses data with three daily observations for selected historical periods of market turbulence, and Clinton (JPE,988) who uses 6 months of daily data.

14 Deviations from CIP are Similar (slightly smaller) in the Last Years Covered Interest Arbitrage at -Month Horizon Currency Median return to Fraction of periods Median of positive borrowing covered in with positive returns returns to borrowing to borrowing covered in covered in Pounds FX Pounds FX Pounds FX percent percent percent Only for 994:-5: Belgium Canada France Germany Italy Japan Netherlands Switzerland USA

15 Statistical Tests of UIP Standard Case: F t S t E t S t S t Literature focuses on the regression: S t S t /S t F t S t /S t t. Results are similar if we use logs. S and F quoted as foreign currency/british pound.

16 UIP Regressions UIP Regressions, Month Regression 3 Month Regression R R Belgium (.) (.74) (.6) (.669) Canada (.) (.83) (.5) (.858) France (.) (.589) (.5) (.54) Germany (.3) (.74) (.8) (.65) Italy (.) (.45) (.6) (.39) Japan* (.5) (.94) (.4) (.7) Netherlands (.4) (.4) (.9) (.86) Switzerland (.3) (.533) (.8) (.536) USA (.) (.88) (.6) (.865) Regression of [S(t+)/S(t)-] on [F(t)/S(t)-] * Data for Japan begin 7/78 Data for Euro legacy currencies ends /98

17 Statistical Tests of UIP ln S t /S t ln F t /S t t Overwhelming evidence against =. For most countries, <. When the forward exceeds the spot (the pound is at a premium), the pound is expected to depreciate. `The forward premium depreciation anomaly.

18 Two Currency Speculation Strategies Carry Trade Sell forward currencies that are at a forward premium and buy currencies that are at a forward discount. BGT Suggested by Backus, Gregory and Telmer (993) Use the following regression to predict the returns to selling currency forward F t S t /S t a b F t S t /S t t

19 Carry Trade suggests: ln S t /S t ln F t /S t t Sell pounds forward when F t >S t. Buy pounds forward when F t <S t. This strategy is equivalent to: Borrow low interest rate currency; Lend high interest rate currency; Don t hedge the exchange rate risk. This strategy is also equivalent to using the current spot to forecast the future exchange rate. S and F quoted as foreign currency/british pound.

20 x t if F t S t, if F t S t. Payoff x t F t S t Suppose agent believes E t S t S t E t Payoff x t F t S t Risk neutral agent adopts carry-trade strategy

21 x t if F t S t, if F t S t. Payoff x t F t S t Suppose agent believes E t S t S t E t Payoff x t F t S t Risk neutral agent adopts carry-trade strategy

22 Carry Trade Strategy If R R borrow in Pounds and invest in foreign currency: Excess Return S t R t S t R t Strategy Sell Pound forward when the Pound is at a forward premium, i.e. F t S t Excess Return F t S t /S t. Using covered interest parity: R t S t R t /F t. Excess Return Excess Return R t S and F quoted as foreign currency/british pound. Here we are treating the pound as our home currency.

23 Carry Trade with Bid-Ask Spreads If F t S t Sell Pound Forward against Foreign Currency Payoff in Pounds F b a t /S t If F t S t Buy Pound Forward against Foreign Currency Payoff in Pounds F a b t /S t Symbol Definition Applies to S a Spot Ask Foreign Currency/Pound Exchange Rate Buying pounds spot S b Spot Bid Foreign Currency/Pound Exchange Rate Selling pounds spot F a Forward Ask Foreign Currency/Pound Exchange Rate Buying pounds forward F b Forward Bid Foreign Currency/Pound Exchange Rate Selling pounds forward

24 BGT Strategy Use the BGT regression to forecast the excess returns from selling pounds forward, F t -S t+ : F t S t /S t a b F t S t /S t t Sell pounds forward when: â b F t S t Buy pounds forward when: â b F t S t

25 BGT Regression F t S t /S t a b F t S t /S t t BGT Regressions, Month Regression 3 Month Regression a b R a b R Belgium (.) (.746) (.6) (.677) Canada (.) (.85) (.5) (.93) France (.) (.59) (.5) (.58) Germany (.3) (.7) (.9) (.68) Italy (.) (.44) (.6) (.43) Japan* (.5) (.957) (.5) (.6) Netherlands (.4) (.9) (.) (.849) Switzerland (.3) (.55) (.8) (.556) USA (.) (.9) (.6) (.94) Regression of [F(t)/S(t+)-] on [F(t)/S(t)-] * Data for Japan begin 7/78 Data for Euro legacy currencies ends /98 S and F quoted as foreign currency/british pound.

26 Why is `b so high? F t S t /S t a b F t S t /S t t Suppose /S t is a martingale. Then BGT regression is roughly equivalent to F t S t /S t a b F t S t /S t t. Can re-arrange this equation to show that a = - and b = in standard UIP regression. close to - implies b close to 3.

27 Carry Trade Versus BGT BGT Strategy Buy Pound Forward Sell Pound Forward Carry Trade Buy Pound Forward Sell Pound Forward -a/b S and F quoted as foreign currency/british pound. Pound Forward Premium (F t -S t )

28 Currency Speculation and Exchange Rate Forecasts Both currency speculation strategies rely implicitly on forecasts of future exchange rates. Carry trade ( random walk forecasts) E t S t S t Excess Return to Carry Trade F t S t S t. BGT E t S t b F t b a S t

29 The root-mean-square of the random walk forecasts are generally smaller than those of BGT Month Ahead Forecast Error Properties ROOT MEAN SQUARED ERROR Relative to Spot Rate Spot Rate Forward Rate Regression Rolling Regression Forward Rate Regression Rolling Regression Belgium Canada France Germany Italy Japan Netherlands Switzerland UK

30 The root-mean-square of the random walk forecasts are generally smaller than those of BGT 3 Month Ahead Forecast Error Properties ROOT MEAN SQUARED ERROR Relative to Spot Rate Spot Rate Forward Rate Regression Rolling Regression Forward Rate Regression Rolling Regression Belgium Canada France Germany Italy Japan Netherland Switzerland UK

31 Does it follow that the carry trade is a superior speculation strategy? When S t is normally distributed the strategy that minimizes RMSE also maximizes the Sharpe ratio When the distribution is not normal there is no clear connection between RMSE and the Sharpe ratio.

32 Returns to the Carry Trade Strategies 76:-5: No Transactions Costs With Transactions Costs Mean Standard Deviation Sharpe Ratio Mean Standard Deviation Sharpe Ratio Belgium* (.9) (.) (.68) (.5) (.) (.7) Canada (.8) (.) (.59) (.4) (.) (.55) France* (.6) (.) (.6) (.5) (.) (.66) Germany* (.8) (.) (.66) (.6) (.) (.65) Italy* (.7) (.) (.58) (.4) (.) (.57) Japan (.) (.3) (.63) (.) (.3) (.59) Netherlands* (.8) (.) (.68) (.5) (.) (.68) Switzerland (.7) (.) (.6) (.6) (.) (.58) USA (.7) (.) (.58) (.6) (.) (.59) Euro (.7) (.) (.83) (.3) (.) (.79) Average Equally-weighted portfolio (.9) (.) (.6) (.) (.) (.57) Optimally-weighted portfolio (.9) (.) (.59) (.) (.) (.53) Sharpe Ratio Average Excess Return Standard Deviation of Excess Returns

33 Returns to the BGT Strategies 76:-5: No Transations Costs With Transactions Costs Mean Standard Deviation Sharpe Ratio Mean Standard Deviation Sharpe Ratio Belgium* (.7) (.) (.66) (.7) (.) (.65) Canada (.7) (.) (.55) (.7) (.) (.57) France* (.8) (.) (.65) (.6) (.) (.73) Germany* (.9) (.) (.7) (.5) (.) (.67) Italy* (.7) (.) (.69) (.6) (.) (.69) Japan (.) (.3) (.58) (.7) (.3) (.58) Netherlands* (.8) (.) (.65) (.5) (.) (.67) Switzerland (.7) (.) (.56) (.5) (.) (.59) USA (.8) (.) (.64) (.7) (.3) (.64) Euro (.7) (.) (.83) (.5) (.) (.95) Average Equally-weighted portfolio (.8) (.) (.57) (.) (.) (.6) Optimally-weighted portfolio (.3) (.) (.67) (.3) (.) (.6) Sharpe Ratio Average Excess Return Standard Deviation of Excess Returns

34 Bid-Ask Spreads Have Large Impact on Excess Returns Average of Bid and Ask With Bid-Ask Spreads Equallyweighted portfolio Mean Standard Deviation Sharpe Ratio Mean Standard Deviation Sharpe Ratio Carry Trade BGT Bid-ask spreads are small If agent buys and sells one pound against the U.S. dollar in the spot market he loses on average S b -S a =.3 dollars. But payoff to the strategy is also small.

35 Bid-Ask Spreads Spot Median Bid-Ask Spreads month Forward 3 month Forward Spot month Forward 3 month Forward x ln(ask/bid) foreign currency units Units Full Sample Period Dates Belgium Centimes 76:-98: Canada Cents 76:-5: France Centimes 76:-98: Germany Pfennig 76:-98: Italy Lire 76:-98: Japan Yen 78:6-5: Netherlands Cents 76:-98: Switzerland Centimes 76:-5: USA Cents 76:-5: Euro* Cents 99:-5: Canada Cents Japan Yen Switzerland Centimes USA Cents Euro* Cents Results are based on daily data *Euro quotes are Euro/USD, whereas other quotes are originally in FCU/British pound

36 Bid-ask Spreads Bid-ask spreads fell significantly with the advent of two screen-based electronic foreign-exchange dealing and brokering systems Reuters' Dealing - Dealing System, launched in 99 Electronic Broking Service, launched in 993

37 Bid-Ask Spreads in the Spot Market (percent) Belgium Canada France Germany Italy Japan Netherlands Switzerland USA

38 Bid-Ask Spreads in the Month Forward Market (percent) Belgium Canada France Germany Italy Japan Netherlands Switzerland USA

39 Bid-Ask Spreads in the 3 Month Forward Market (percent) Belgium Canada France Germany Italy Japan Netherlands Switzerland USA

40 Bid-Ask Spreads in the Spot Market 3 Belgium Canada 4 France Centimes Cents.5.5 Centimes Germany Italy 3 Japan Pfennig Lire 5 Yen Netherlands 4 Switzerland USA Cents Centimes 3 Cents

41 Bid-Ask Spreads in the Month Forward Market 6 Belgium Canada 6 France Centimes 4 Cents.5.5 Centimes Germany 3 Italy 3 Japan Pfennig 3 Lire Yen Netherlands 6 Switzerland USA Cents 3 Centimes 4 Cents

42 Bid-Ask Spreads in the 3 Month Forward Market 6 Belgium Canada 6 France Centimes 4 Cents.5.5 Centimes Germany 3 Italy 3 Japan Pfennig 3 Lire Yen Netherlands 6 Switzerland USA Cents 3 Centimes 4 Cents

43 There are Large Diversification Gains from Combining Country Strategies Carry Trade With Bid-Ask Spreads Mean Standard Deviation Sharpe Ratio Average Equally-weighted portfolio BGT Average Equally-weighted portfolio

44 Mean-Variance-Efficient Portfolios At each point in time there is a portfolio of strategies for individual currencies that maximizes the Sharpe ratio. At each point in time we compute the optimal portfolio currencies using recursive estimates of the covariance matrix. We impose the constraints that weights must be positive.

45 Comparing the Sharpe Ratios of the Portfolio Strategies over a Common Sample (79:-5:) Equal Weighted Optimally Weighted Difference Carry trade (.6) (.56) (.33) BGT (.6) (.6) (.3) Difference.34.7 (.69) (.67) The difference between the Sharpe ratios of optimally-weighted and equally-weighted portfolios is statistically significant. The Sharpe Ratios of the carry trade and BGT are not statistically different.

46 Realized Sharpe Ratio: Three Year Rolling Window.8 Carry Trade, Equally-Weighted Portfolio.8 Carry Trade, Optimally-Weighted Portfolio.6.6 Sharpe Ratio.4. Sharpe Ratio BGT Strategy, Optimally-Weighted Portfolio.8 S&P Sharpe Ratio.4. Sharpe Ratio

47 Weights for Carry Trade Efficient Portfolio Belgium Canada France Germany/Euro Italy Japan Netherlands Switzerland USA

48 Weights for BGT Strategy Efficient Portfolio Belgium Canada France Germany/Euro Italy Japan Netherlands Switzerland USA

49 Expected Returns to Currency Speculation, Carry Trade: Equally-Weighted Portfolio Carry Trade: Efficient Portfolio BGT Strategy: Equally-Weighted Portfolio.5 BGT Strategy: Efficient Portfolio Monthly payoffs (not annualized)

50 . Realized Returns to Currency Speculation, Carry Trade: Equally-Weighted Portfolio Carry Trade: Efficient Portfolio BGT Strategy: Equally-Weighted Portfolio. BGT Strategy: Efficient Portfolio Monthly payoffs (not annualized)

51 Realized Returns to Currency Speculation ( month MA) Carry Trade: Equally-Weighted Portfolio Carry Trade: Efficient Portfolio BGT Strategy: Equally-Weighted Portfolio.3 BGT Strategy: Efficient Portfolio Monthly payoffs (not annualized)

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54 Why is the Sharpe ratio so high? Risk Fat tails Price pressure

55 Are Excess Returns Correlated with Risk Factors? We use mid-point quotes against the US dollar to compute dollar payoffs at a three-month horizon. We regress these payoffs on several risk factors and on macro variables.

56 Are Excess Returns Correlated with Risk Factors? (No!) Carry Trade

57 Are Excess Returns Correlated with Risk Factors? (No!) BGT

58 Are Excess Returns Correlated with Macro Factors? (No!) Carry Trade

59 Are Excess Returns Correlated with Macro Factors? BGT Note: Fed funds and inflation enter significantly into BGT return regression.

60 S&P 5 versus Currency Speculation Payoffs..5.8 Carry Trade Equally Weighted Carry Trade Optimally Weighted S&P S&P 5 BGT Trade Equally Weighted S&P 5 BGT Trade Optimally Weighted S&P 5

61 Fat Tails Payoffs to speculation in individual currencies have fat tails. These fat tails are reduced once currencies are combined into either equally-weighted or optimal portfolio.

62 Payoff to Carry Trade 5 Belgium (.4) (Percentage of periods with no trade in parenthesis) Canada (.33) (%) (%) France (.3) Germany (.7) (%) 5 (%) Italy (.3) 5 Japan (.) (%) 5 (%) Netherlands (.34) Switzerland (.7) (%) 5 (%) USA (.) Euro (.38) (%) 5 (%)

63 Payoff to BGT Strategy Belgium (.8) (Percentage of periods with no trade in parenthesis) Canada (.9) (%) 5 (%) France (.8) 5 Germany (.35) (%) (%) Italy (.8) 5 Japan (.5) (%) (%) The Netherlands (.) Switzerland (.3) (%) 5 (%) USA (.) Euro (.37) (%) 5 (%)

64 7 Equally Weighted Carry Trade 7 Optimally Weighted Carry Trade (%) 3 (%) Equally Weighted BGT Trade 8 Optimally Weighted BGT Trade (%) 3 (%)

65 Skewness, Kurtosis and Normality Test Returns to Carry Trade Returns to BGT Strategy With Transactions Costs With Transactions Costs Skewness Excess Kurtosis Jarque-Bera Test Skewness Excess Kurtosis Jarque-Bera Test Belgium* (.498) (.) (.) (.535) (.3) (.) Canada (.38) (.59) (.) (.7) (.34) (.47) France* (.34) (.69) (.) (.35) (.64) (.) Germany* (.78) (.85) (.) (.695) (3.68) (.) Italy* (.389) (.5) (.) (.37) (.93) (.) Japan (.539) (.4) (.) (.947) (3.56) (.) Netherlands* (.34) (.98) (.) (.6) (3.39) (.) Switzerland (.8) (.83) (.) (.444) (.7) (.) USA (.53) (.77) (.) (.563) (.9) (.) Euro (.54) (.4) (.) (.7) (.75) (.44) Average Equally-weighted portfolio (.47) (.8) (.) (.75) (.76) (.) Optimally-weighted portfolio (.) (.37) (.) (.365) (.5) (.)

66 Are Fat Tails Large Enough to Deter Investors? U E Y t t t t C t s C t Y t X ts r ts X tc r tc X t C t - consumption Y t - endowment income (assumed to grow at an annual rate of.9 percent) X ts - end of time t investment in the S&P r ts - returns to stocks purchased at time t X tc - end of time t investment in currency speculation strategy r tc - payoff to currency speculation strategy implemented at time t

67 Fat Tails Assume are generated by joint empirical distribution of returns to S&P 5 and to optimally-weighted carry trade. r t c and r t s Define x t s X t s /Y t x t c X t c /Y t We impose that agent uses a time invariant strategy for these ratios.

68 Are Fat Tails Large Enough to Deter Investors? (No) Risk aversion = 5 Portfolio Weights On S&P 5 On Carry Trade strategy Belgian franc Canadian dollar French franc German mark Italian lira Japanese yen Netherlands guilder Swiss franc.59.6 US dollar Portfolios Equally-weighted Optimally-weighted Agents are willing to place large bets in the carry strategies, especially if they are combined into portfolios.

69 A Challenge There s currency speculation strategies that yield higher Sharpe ratios than the S&P 5. Payoffs are uncorrelated with standard risk factors. Investors can significantly increase their expected return, for a given level of the variance of returns, by combining currency speculation with a passive strategy of holding the S&P 5. Why don't they massively exploit this opportunity to the point where either the Sharpe ratio falls to zero or currency speculation payoffs become correlated with risk factors.

70 Our Argument Use evidence from microstructure literature to argue that, while currency speculators do make profits, there is little if any money left on the table. While the average Sharpe ratio to our currency strategies is positive, the marginal Sharpe ratio is zero.

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73 Breaking Up Orders A trader who places an order for z pounds at the beginning of t+ pays zs t e bz If trader divides this order into infinitesimal orders and net order flow is zero while execution occurs, then trader pays z St e bw dw S t e bz /b zs t e bz

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76 To Summarize All trades at marginal exchange rate Marginal and average exchange rates coincide Marginal Sharpe should be driven to zero implying average Sharpe is also zero. This implication is inconsistent with our Sharpe ratio estimates. Breaking up trades: Marginal exchange rates > average exchange rates Marginal Sharpe is driven to zero Average Sharpe is positive

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78 Profits from Carry Trade with Price Pressure, Bets set Marginal Sharpe = Bet Size (millions pounds) Standard Mean Deviation Profits (millions pounds) Standard Deviation Sharpe Ratio Country results use b=.54 Mean Belgium* Canada France* Germany* Italy* Japan Netherlands* Switzerland USA Euro Sum across all currencies using b= (85) (56) (4.) (8.6) (.5) using b= (37) (3) (8.) (7.3) (.5) using b= (739) (64) (6.) (34.5) (.5) using b= No limits were imposed on bet sizes (478) (48) (3.5) (69.) (.5)

79 Number of Pounds Sold Forward Against Each Currency 3 Belgium 3 Canada 3 France pounds (billions) - pounds (billions) - pounds (billions) Germany/Euro 3 Italy 3 Japan pounds (billions) - pounds (billions) - pounds (billions) Netherlands 3 Switzerland 3 USA pounds (billions) - pounds (billions) - pounds (billions)

80 8 Total Number of Pounds Sold Forward Against All Currencies 6 4 pounds (billions)

81 Expected Total Profits from Speculative Trading on Each Currency Belgium Canada 4 France pounds (millions) 5 5 pounds (millions) 5 pounds (millions) Germany/Euro 4 Italy 6 Japan pounds (millions) 5 5 pounds (millions) 3 pounds (millions) Netherlands 3 Switzerland 3 USA pounds (millions) pounds (millions) pounds (millions)

82 Actual Total Profits from Speculative Trading on Each Currency 5 Belgium Canada France pounds (millions) 5 pounds (millions) pounds (millions) Germany/Euro Italy Japan pounds (millions) 5-5 pounds (millions) pounds (millions) Netherlands Switzerland USA pounds (millions) pounds (millions) - pounds (millions)

83 8 Expected Total Profits from Speculative Trading on All Currencies pounds (millions)

84 6 Actual Total Profits from Speculative Trading on All Currencies pounds (millions)

85 5 Cumulated Total Profits from Speculative Trading on All Currencies 4 3 pounds (millions)

86 .4 Realized Sharpe Ratio Computed up to Each Date.35.3 Sharpe Ratio

87 Key Question Why does the Forward Premium Depreciation anomaly arise in the first place? There s a huge literature on this question Monetary policy: McCallum (994) Risk premia: Fama (984) Statistical problems Peso problem : Lewis (995) Random walk/cointegration : Roll and Yan () Maynard (3) Learning: Lewis (995) Expectation biases: Frankel and Rose (994) Endogenous market segmentation: Alvarez, Atkeson, and Kehoe (6) Rational Inattention: Bachetta and van Wincoop (6).

88 Basic Microstructure Model Based on Glosten and Milgrom (985) Exchange rates are quoted as US$/Pound. The spot exchange rate follows: S t S t t t Variable t represents a predictable change in the exchange rate that is public information at time t. t with probability / with probability / t with probability / with probability /

89 Trading and Traders Market maker draws one trader per period from a continuum Chosen trader can submit an order of fixed size x to buy or sell pounds forward. Probability a trader will trade a second time is zero (rules out strategic considerations) Informed traders Measure They know t+ (We only require that informed traders receive a time t signal that is informative about t+) Uninformed traders Measure (- They buy the pound forward when t >. They sell the pound forward when t <. We only require that uninformed traders are more likely to buy pound forward when t >.

90 Market Maker All trade takes place with risk neutral market makers Market makers decide at time zero on price setting rules for bid and ask forward rates. Abstract from bid-ask spreads associated with spot rates Market maker makes zero expected profits (potential Bertrand competition) The market maker doesn t know t+. But he can condition the price on the order flow, i.e. on whether the order is a buy or a sell.

91 Market Maker Market maker knows t but doesn t know t+ at time t. Forms expectation of t+ based on t and on whether he receives a buy or a sell order from the trader. There are two states of the world, t =, t = - In each of these states, market maker must quote a bid and an ask forward rate. So we have to compute F t a, F t b, F t a, F t b

92 Example: Ask Forward Rate when t > F a E S t buy, t S t t E t buy, t ) Pr buy t, t Pr buy t, t Using Bayes rule: Pr t buy, t Pr buy t, t Pr t Pr buy t, t Pr t Pr buy t, t Pr t Pr t buy, t Pr t buy, t E t buy, t Pr t buy, t Pr t buy, t F a S t t

93 Forward Rates If t, If t, F t a S t F t b S t F t a S t F t b S t The pound is expected to appreciate based on public information. Uninformed agents buy the pound forward. The pound is expected to depreciate based on public information. Uninformed agents sell the pound forward.

94 Proposition Suppose /. Consider the regression S t S t /S t F t S t / S t t. Plim of in regression computed with data generated from our model economy is negative This results holds regardless of whether the regression is conducted using ask, bid or average of bid and ask forward rates.

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98 S t S t All Traders are Informed ( =) F ta S t Fa is the forward rate at which traders buy currency from market maker. When all agents are informed the market maker knows that a buy order means that

99 S t S t All Traders are Informed ( =) F ta S t

100 S t S t All Traders are Informed ( =) Slope= F ta S t

101 S t S t Informed and Uninformed Traders ( <) When the pound is expected to appreciate based on public information, the uninformed agents buy the pound forward, so there is less adverse selection from the standpoint of the market maker. As a result F a is low when the peso is expected to appreciate! F ta S t A negative slope requires: / The component of exchange predictable on the basis of public information must be lower than the change in exchange rates that is unpredictable based on public information.

102 Trader Profits Informed traders Uninformed traders E i E u Profits of the two groups weighted by their sizes in the population add to zero. Suppose the number of informed traders is very small ( close to zero) Each informed trader makes a large profit; Each uninformed trader makes a very small loss.

103 Introducing Price Pressure Price pressure can be introduced as in Easley and O Hara (987). Suppose that there are two trade sizes, High (X) and low (x). Uninformed traders chose high or low size with probability ½. Informed traders prefer larger trade sizes (when bid-ask are the same for both sizes) Bid-ask spread for small orders is zero, reflecting the fact that only uninformed traders introduce small orders. Bid-ask spread for large orders is positive, reflecting the fact that both informed and uninformed submit large orders.

104 Other Issues The slope of the UIP regression is higher for high inflation countries The model generates this if the condition is violated. / This means that changes in the exchange rate predictable with public information is larger than the unpredictable component. This pattern is consistent with what Calvo and Reinhart describe as fear of floating Developing country currencies depreciate on average. These currencies are heavily managed so, outside crises periods that exhibit very low volatility

105 Conclusion There are currency speculation strategies that yield high expected excess returns and have high Sharpe ratios. In addition, the excess returns to these strategies are uncorrelated with standard risk factors. Why don t agents massively invest in these strategies and eliminate the high Sharpe ratios? The payoff to currency speculation strategies is small, so making significant profits requires betting large amounts. There is significant price pressure in currency markets, so as speculators bet large amounts the prices move against them.