The Cross Section of Foreign Currency Risk Premia and Consumption Growth Risk
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The Cross Section of Foreign Currency Risk Premia and Consumption Growth Risk By HANNO LUSTIG AND ADRIEN VERDELHAN* Aggregate consumption growth risk explains why low interest rate currencies do not appreciate as much as the interest rate differential and why high interest rate currencies do not depreciate as much as the interest rate differential. Domestic investors earn negative excess returns on low interest rate currency portfolios and positive excess returns on high interest rate currency portfolios. Because high interest rate currencies depreciate on average when domestic consumption growth is low and low interest rate currencies appreciate under the same conditions, low interest rate currencies provide domestic investors with a hedge against domestic aggregate consumption growth risk. (JEL E21, E43, F31, G11) When the foreign interest rate is higher than rate currencies, on average, depreciate against the US interest rate, risk-neutral and rational US the dollar when US consumption growth is low, investors should expect the foreign currency to while low foreign interest rate currencies do depreciate against the dollar by the difference not. The textbook logic we use for any other between the two interest rates. This way, bor- asset can be applied to exchange rates, and it rowing at home and lending abroad, or vice works. If an asset offers low returns when the versa, produces a zero return in excess of the investor’s consumption growth is low, it is US short-term interest rate. This is known as the risky, and the investor wants to be compensated uncovered interest rate parity (UIP) condition, through a positive excess return. and it is violated in the data, except in the case To uncover the link between exchange rates of very high inflation currencies. In the data, and consumption growth, we build eight port- higher foreign interest rates almost always pre- folios of foreign currency excess returns on the dict higher excess returns for a US investor in basis of the foreign interest rates, because in- foreign currency markets. vestors know these predict excess returns. Port- We show that these excess returns compen- folios are rebalanced every period, so the first sate the US investor for taking on more US portfolio always contains the lowest interest rate consumption growth risk. High foreign interest currencies and the last portfolio always contains the highest interest rate currencies. This is the key innovation in our paper. Over the last three decades, in empirical asset * Lustig: Department of Economics, UCLA, Box 951477, Los Angeles, CA 90095, and National Bureau of pricing, the focus has shifted from explaining Economic Research (e-mail: [email protected]); Ver- individual stock returns to explaining the re- delhan: Department of Economics, Boston University, 270 turns on portfolios of stocks, sorted on variables Bay State Road, Boston, MA 02215, and Centre de recher- that we know predict returns (e.g., size and ches de la Banque de France, 29 rue Croix des petits 1 champs, Paris 75049 France (e-mail: [email protected]). The au- book-to-market ratio). This procedure elimi- thors especially thank two anonymous referees, Andy At- nates the diversifiable, stock-specific compo- keson, John Cochrane, Lars Hansen, and Anil Kashyap for nent of returns that is not of interest, thus detailed comments. We would also like to thank Ravi Ban- producing much sharper estimates of the risk- sal, Craig Burnside, Hal Cole, Virgine Coudert, Franc¸ois return trade-off in equity markets. Similarly, for Gourio, Martin Eichenbaum, John Heaton, Patrick Kehoe, Isaac Kleshchelski, Chris Lundbladd, Lee Ohanian, Fabri- currencies, by sorting these into portfolios, we zio Perri, Sergio Rebelo, Stijn Van Nieuwerburgh, and abstract from the currency-specific component seminar participants at various institutions and conferences. The views in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views 1 See Eugene F. Fama (1976), one of the initial advo- of the Bank of France. cates of building portfolios, for a clear exposition. 89 90 THE AMERICAN ECONOMIC REVIEW MARCH 2007 Characteristics of the eight portfolios (excess returns) 2 0 Mean −2 1 2 3 4 5 6 7 8 10 Std 5 0 1 2 3 4 5 6 7 8 0.4 0.2 0 −0.2 Sharpe ratio −0.4 1 2 3 4 5 6 7 8 FIGURE 1. EIGHT CURRENCY PORTFOLIOS Notes: This figure presents means, standard deviations (in percentages), and Sharpe ratios of real excess returns on eight annually rebalanced currency portfolios for a US investor. The data are annual and the sample is 1953–2002. These portfolios were constructed by sorting currencies into eight groups at time t based on the nominal interest rate differential with the home country at the end of period t Ϫ 1. Portfolio 1 contains currencies with the lowest interest rates. Portfolio 8 contains currencies with the highest interest rates. of exchange rate changes that is not related to these portfolios keep the number of covariances changes in the interest rate. This isolates the that must be estimated low, while allowing us to source of variation in excess returns that inter- continuously expand the number of countries ests us, and it creates a large average spread of studied as financial markets open up to interna- up to five hundred basis points between low and tional investors. This enables us to include data high interest rate portfolios. This spread is an from the largest possible set of countries. order of magnitude larger than the average To show that the excess returns on these spread for any two given countries. As one portfolios are due to currency risk, we start from would expect from the empirical literature on the US investor’s Euler equation and use con- UIP, US investors earn on average negative sumption-based pricing factors. We test the excess returns on low interest rate currencies of model on annual data for the periods 1953–2002 minus 2.3 percent and large, positive excess and 1971–2002. returns on high interest rate currencies of up to Consumption-based models explain up to 80 3 percent. The relation is almost monotonic, as percent of the variation in currency excess re- shown in Figure 1. These returns are large even turns across these eight currency portfolios. Are when measured per unit of risk. The Sharpe the parameter estimates reasonable? Our results ratio (defined as the ratio of the average excess are not consistent with what most economists return to its standard deviation) on the high view as plausible values of risk aversion, but interest rate portfolio is close to 40 percent, only they are consistent with the evidence from other slightly lower than the Sharpe ratio on US eq- assets. The estimated coefficient of risk aver- uity, while the same ratio is minus 40 percent sion is around 100, and the estimated price of for the lowest interest rate portfolio. In addition, US consumption growth risk is about 2 percent VOL. 97 NO. 1 LUSTIG AND VERDELHAN: CURRENCY RISK PREMIA 91 per annum for nondurables and 4.5 percent for I. Foreign Currency Excess Returns durables. Consumption-based models can ex- plain the risk premia in currency markets only if This section first defines the excess returns on we are willing to entertain high levels of risk foreign T-Bill investments and details the con- aversion, as is the case in other asset markets. In struction and characteristics of the currency fact, currency risk seems to be priced much like portfolios. We then turn to the US investor’s equity risk. If we estimate the model on US Euler equation and show how consumption risk domestic bond portfolios (sorted by maturity) can explain the average excess returns on these and stock portfolios (sorted by book-to-market currency portfolios. and size) in addition to the currency portfolios, the risk aversion estimate does not change. Our A. Why Build Portfolios of Currencies? currency portfolios really allow for an “out-of- sample” test of consumption-based models, be- We focus on a US investor who invests in cause the low interest rate currency portfolios foreign T-Bills or equivalent instruments. These have negative average excess returns, unlike bills are claims to a unit of foreign currency one i most of the test assets in the empirical asset period from today in all states of the world. Rtϩ1 pricing literature, and the returns on the cur- denotes the risky dollar return from buying a rency portfolios are not strongly correlated with foreign T-Bill in country i, selling it after one bond and stock returns. period, and converting the proceeds back into i ϭ i,£ i i i Consumption-based models can explain the dollars: Rtϩ1 Rt (Etϩ1/Et), where Et is the cross-section of currency excess returns if and exchange rate in dollar per unit of foreign cur- i,£ only if high interest rate currencies typically rency, and Rt is the risk-free one-period return 3 depreciate when real US consumption growth is in units of foreign currency i. We use Pt to low, while low interest rate currencies appreci- denote the dollar price of the US consumption i,e ϭ i Ϫ $ ate. This is exactly the pattern we find in the basket. Finally, Rtϩ1 (Rtϩ1 Rt )(Pt/Ptϩ1)is data. We can restate this result in standard fi- the real excess return from investing in foreign $ nance language using the consumption growth T-Bills, and Rt is the nominal risk-free rate in beta of a currency. The consumption growth US currency. Below, we use lowercase symbols beta of a currency measures the sensitivity of to denote the log of a variable.