Average Variance, Average Correlation, and Currency Returns

Transcription

1 Average Variance, Average Correlation, and Currency Returns Gino Cenedese, Bank of England Lucio Sarno, Cass Business School and CEPR Ilias Tsiakas, Tsiakas,University of Guelph Hannover, November 211

2 What is the Carry Trade? A currency trading strategy that invests in high-interest currencies by borrowing from low-interest currencies. Designed to exploit deviations from uncovered interest parity (UIP). If UIP holds: the interest rate differential will on average be offset by a commensurate depreciation of the investment currency, and the expected FX excess return will be zero. If instead UIP is violated, the carry trade will be profitable. Extensive empirical evidence dating back to Bilson (JB, 1981) and Fama (JME, 1984) shows that UIP is strongly empirically rejected. Cenedese, Sarno & Tsiakas (211) Risk and the Carry Trade 2 / 29

3 Historical Performance: Feb July 29 US Equally-Weighted Stock Market Carry Trade Mean St. Deviation Sharpe Ratio Skewness Kurtosis (Source: Burnside, Eichenbaum, Kleshchelski and Rebelo, RFS 211) Cenedese, Sarno & Tsiakas (211) Risk and the Carry Trade 3 / 29

4 What Justifies the Carry Trade Returns? Is the carry trade a free lunch or are investors compensated for bearing risk? Burnside (21): Traditional risk factors used to price the stock market fail to explain the returns to the carry trade. Menkhoff, Sarno, Schmeling and Schrimpf (JF forthcoming): the large average carry trade payoffs are compensation for exposure to global FX volatility. In times of high volatility, high-interest currencies deliver low return whereas low-interest currencies perform well. Lustig, Roussanov and Verdelhan (RFS forthcoming): identify a slope factor ( high-minus-low ) in the cross-section of FX portfolios (similar to Fama-French, JFE 1993). Cenedese, Sarno & Tsiakas (211) Risk and the Carry Trade 4 / 29

5 Is it Crash Risk? You go up the stairs, you go down the elevator Collecting pennies in front of a steamroller Burnside, Eichenbaum, Kleshchelski and Rebelo (RFS 211): high carry trade payoffs reflect a peso problem, which is a low probability of large negative payoffs that may not occur in sample. Find no evidence of peso events, but argue that investors still attach great importance to them and require compensation for them. Brunnermeier, Nagel and Pedersen (NBER Macro Annual 29): carry trades crash due to lack of funding liquidity in times of high volatility. Similar arguments made by Farhi, Fraiberger, Gabaix, Ranciere and Verdelhan (29) and Jurek (29). Cenedese, Sarno & Tsiakas (211) Risk and the Carry Trade 5 / 29

6 Our paper We investigate the intertemporal tradeoff between the carry trade return and FX risk. Can we predict when the carry trade becomes unprofitable just by conditioning on market volatility? We analyze the relation between risk and full distribution of future carry returns using quantile regressions. We define risk as the FX market variance, and We decompose the market variance into the product of average variance and average correlation (Pollet and Wilson, JFE 21). Assess the performance of a new version of the carry trade that conditions on FX risk. evaluate out of sample and account for transaction costs Cenedese, Sarno & Tsiakas (211) Risk and the Carry Trade 6 / 29

7 Merton s ICAPM (1973) Model Our analysis is loosely motivated by the intertemporal capital asset pricing model (ICAPM) of Merton (1973, 198): r M,t+1 = α + βe t [MV t+1 ] + ε t+1 where β > is the investors risk aversion. As systematic risk increases, risk-averse investors require a higher risk premium to hold aggregate wealth and the expected return must rise. An extensive literature on equity markets finds an insignificant (even negative) relation between risk and return. The ICAPM may be applied to the FX market as it holds for any risky asset in any market. Cenedese, Sarno & Tsiakas (211) Risk and the Carry Trade 7 / 29

8 The Carry Trade for Individual Currencies (I) A simple currency trading strategy: Buy a forward contract now for exchanging the domestic into foreign currency in the future (or vice versa), and then convert the proceeds of the forward contract into the domestic currency at future spot exchange rate. The log excess return of this strategy is: r j,t+1 = s j,t+1 f j,t for j = {1,..., N t } exchange rates, s j,t+1 is the log of the nominal spot exchange rate j at time t + 1; f j,t is the log of the one-period forward exchange rate j at time t. Cenedese, Sarno & Tsiakas (211) Risk and the Carry Trade 8 / 29

9 The Carry Trade for Individual Currencies (II) An equivalent strategy: Buy a foreign bond and sell a domestic bond (or vice versa). The foreign bond yields a riskless return in the foreign currency but a risky return in the domestic currency. The log excess return to this strategy is: r j,t+1 = i j,t i t + s j,t+1 s j,t where i t and ij,t respectively. are the domestic and foreign nominal interest rates The return to the two strategies are exactly equal due to the covered interest parity (CIP) condition: f j,t s j,t = i t i j,t Cenedese, Sarno & Tsiakas (211) Risk and the Carry Trade 9 / 29

10 The Carry Trade Portfolio At the beginning of each month sort all currencies from high to low interest rates (or from low to high forward premium). Divide the total number of currencies available in that month in five portfolios (quintiles). Go long in portfolio 1 (highest interest rate currencies) Go short in portfolio 5 (lowest interest rate currencies). The monthly return on the carry trade portfolio is the excess return of going long on portfolio 1 and short on portfolio 5. If UIP is violated, the carry trade portfolio will deliver positive excess returns. Cenedese, Sarno & Tsiakas (211) Risk and the Carry Trade 1 / 29

11 FX Market Variance Define the excess return to the FX market portfolio: r M,t+1 = 1 N t N t r j,t+1. j=1 Estimate the monthly FX market variance using a realized measure based on daily excess returns: MV t+1 = k t r 2 k t 1 M,t+d /k t + 2 r M,t+d /kt r M,t+(d 1)/kt, d =1 d =1 where k t is the number of trading days in month t, typically k t = 21. Cenedese, Sarno & Tsiakas (211) Risk and the Carry Trade 11 / 29

12 Average Variance and Average Correlation Pollet and Wilson (JFE, 21) approximate decomposition: MV t = AV t AC t. where: and AV t+1 = 1 N t N t V j,t+1 j=1 V j,t+1 = k t r 2 k t 1 j,t+d /k t + 2 r j,t+d /kt r j,t+(d 1)/kt, d =1 d =1 AC t+1 = C ij,t+1 = 1 N t (N t 1) N t i=1 N t j =i V ij,t+1 Vi,t+1 Vj,t+1 C ij,t+1, Cenedese, Sarno & Tsiakas (211) Risk and the Carry Trade 12 / 29

13 Risk in the Equities Literature The risk measures implemented in our analysis have been the focus of recent intertemporal as well as cross-sectional studies of the equity market. The intertemporal role of average variance is examined by Goyal and Santa-Clara (JF, 23) and Bali, Cakici, Yan and Zhang (JF, 25). The intertemporal role of average correlation is examined by Pollet and Wilson (JFE, 21). In the cross-section of equity returns, the negative price of risk associated with market variance is examined by Ang, Hodrick, Xing and Zhang (JF, 26; JFE, 29). Chen and Petkova (21) examine the cross-sectional role of average variance and average correlation. Cenedese, Sarno & Tsiakas (211) Risk and the Carry Trade 13 / 29

14 Predictive OLS Regressions 1 Regression 1: r C,t+1 = α + βmv t + ε t+1, 2 Regression 2: r C,t+1 = α + β 1 AV t + β 2 AC t + ε t+1, For example, β < implies: high market variance predicts lower future carry trade returns and may lead to carry trade unwinding. OLS regressions estimate only the effect on the conditional mean of the distribution Cenedese, Sarno & Tsiakas (211) Risk and the Carry Trade 14 / 29

15 Predictive Quantile Regressions Using quantile regressions, we examine whether large gains or losses in FX are predictable by FX volatility τ-quantile conditional on MV: Q rc,t+1 (τ MV t ) = α (τ) + β (τ) MV t τ-quantile conditional on AV and AC: Q rc,t+1 (τ AV t, AC t ) = α (τ) + β 1 (τ) AV t + β 2 (τ) AC t Cenedese, Sarno & Tsiakas (211) Risk and the Carry Trade 15 / 29

16 Decomposing the Monthly FX Market Variance 33 currencies, Regressions for Monthly FX Market Variance (1) (2) (3) (4) Constant (.56) ( 2.324) ( 11.79) (1.473) Average Variance (9.993) (13.883) Average Correlation.15.1 (8.96) (13.784) (Average Variance) (Average Correlation).939 (24.281) R 2 (%) Cenedese, Sarno & Tsiakas (211) Risk and the Carry Trade 16 / 29

17 OLS Predictive Regressions (conditional mean) Regressions for the Carry Trade Return (1) (2) Constant (5.939) (3.888) [.122] [.64] Market Variance ( 2.6) [.46] Average Variance ( 1.972) [.51] Average Correlation.7 (.936) [.35] R 2 (%) Cenedese, Sarno & Tsiakas (211) Risk and the Carry Trade 17 / 29

18 α β Quantile Regressions: Market Variance.5 Constant 1 Market Variance Quantile Quantile Figure: Carry Return on MV Cenedese, Sarno & Tsiakas (211) Risk and the Carry Trade 18 / 29

19 Quantile Regressions: Ave. Variance and Ave. Correlation 5 Average Variance.3 Average Correlation β 1 1 β Quantile Quantile Figure: Carry Return on AV and AC Cenedese, Sarno & Tsiakas (211) Risk and the Carry Trade 19 / 29

20 Quantile Regressions: The Exchange Rate Component 5 Exchange Rate Component: Average Variance.5 Exchange Rate Component: Average Correlation 5 β 1 1 β Quantile Quantile Figure: The Exchange Rate Component on AV and AC Cenedese, Sarno & Tsiakas (211) Risk and the Carry Trade 2 / 29

21 Augmented Carry Trade: Condition on AV We assess the economic significance of the quantile regression results by designing three augmented carry trade strategies: AV strategy: at time t: for the carry trade returns that are lower than the τ-quantile of the distribution, if AV has increased from t 1 to t, we close the carry trade positions and thus receive an excess return of zero; otherwise we execute the standard carry trade Cenedese, Sarno & Tsiakas (211) Risk and the Carry Trade 21 / 29

22 Augmented Carry Trade: Condition on AC AC strategy: at time t: for the carry trade returns that are higher than the τ-quantile of the distribution, if AC has decreased from t 1 to t, we double the carry trade positions and thus receive twice the carry return otherwise we execute the standard carry trade Combined strategy: condition on both AV and AC at the same time Cenedese, Sarno & Tsiakas (211) Risk and the Carry Trade 22 / 29

23 Trading Strategies (with Transaction Costs) Carry Trade Average Variance Strategy Quantile Mean St. Dev Sharpe ratio Turnover Average Correlation Strategy Mean St. Dev Sharpe ratio Turnover Combined Average Variance and Average Correlation Strategy Mean St. Dev Sharpe ratio Turnover Cenedese, Sarno & Tsiakas (211) Risk and the Carry Trade 23 / 29

24 β β Robustness: VIX and VXY.15 VIX.8 VXY Quantile Quantile Figure: The Carry Return on VIX and VXY Cenedese, Sarno & Tsiakas (211) Risk and the Carry Trade 24 / 29

25 Robustness: Additional Predictive Variables 5 Average Variance.2 Average Correlation β 1 β Quantile 1.5 Interest differential Quantile.6 Lagged Carry Return β 3 β Quantile Quantile Cenedese, Sarno & Tsiakas (211) Risk and the Carry Trade 25 / 29

26 Robustness: The Numeraire Effect 1 Weighted Average Variance.8 Weighted Average Correlation β 1 1 β Quantile Quantile Numeraire Effect. Weighted variables use the IMF Special Drawing Rights weights: 41.9% on USD, 37.4% on the EUR, 11.3% on GBP, and 9.4% on JPY. Cenedese, Sarno & Tsiakas (211) Risk and the Carry Trade 26 / 29

27 Conditional Skewness We can use the quantile regressions to compute a conditional skewness measure that is robust to outliers. We use a conditional version of the Bowley (192) coeffi cient of skewness (e.g., Cenesizoglu and Timmermann, 21): SK t = Q.75,t + Q.25,t 2 Q.5,t Q.75,t Q.25,t, We find that conditional skewness of carry returns has diminished in last part of the sample. This is indicative of a surge in crash risk in recent years. Cenedese, Sarno & Tsiakas (211) Risk and the Carry Trade 27 / 29

28 Conditional Skewness Cenedese, Sarno & Tsiakas (211) Risk and the Carry Trade 28 / 29

29 Conclusions There is an intertemporal risk-return tradeoff in the FX market: Focusing on the full distribution of carry returns and decomposing the FX market variance is critical in establishing this relation. Higher AV is significantly related to future carry trade losses. Higher AC is significantly related to future carry trade gains. Conditioning on AV and AC improves the performance of the carry trade. Hence AV and AC can predict returns when it matters the most. Cenedese, Sarno & Tsiakas (211) Risk and the Carry Trade 29 / 29