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Japanese yen currency dynamics are investigated in spot and futures markets. Maturity is proposed as a proxy for the time-varying risk premium. As the maturity of a yen futures contract nears, there is less uncertainty implying a small absolute risk premium. A longer maturity is associated with uncertainty about the economy, the underlying currency, and the contract; and implies a high risk premium. Models that include maturity in addition to the futures–spot basis as explanatory variables exhibit better empirical performance in explaining futures returns and spot returns. The results are robust to different sample periods, forecast horizons, and estimation techniques.

The Japanese foreign exchange market has seen an extraordinary growth after its liberalization in the 1980s and has become the second largest market in the world. The Japanese yen derivatives trading has a much greater volume than other currencies. There is also an increasing debate about whether the yen will emerge as a vehicle for other Asian currencies.1 In this financial environment, investors and monetary authorities show an increasing awareness of the risks connected with Japanese yen trading. In a risk-neutral world, the forward/futures rates are unbiased estimates of the future spot rates. This is called the Expectations Hypothesis (EH), or Uncovered Interest Parity (UIP). According to the EH, the expected currency return is equal to the difference between the futures rate and the current spot rate of the currency. This difference is called the futures–spot basis. The EH further states that, in a risk-neutral world, high interest rate currencies are expected to depreciate to maintain the equilibrium. However, numerous studies in the finance literature have found this not to be so (see, for example, Frankel and Froot, 1987 and Backus et al., 2001, and Inci & Lu, 2004). In other words, a regression of the change in the Japanese yen on the futures–spot basis (or the U.S.–Japanese interest rate difference according to covered interest parity) should produce a regression slope coefficient of 1.0. However, the coefficient is found to be significantly less than 1.0; in fact, often times negative. Fama (1984) named the phenomenon as the forward premium puzzle (FPP) and proposed a time-varying risk premium to account for it. The risk premium must be negatively correlated with the expected spot depreciation and must be more volatile than the expected spot depreciation to account for the FPP. Research since then has moved in two directions. The first direction has focused on developing sophisticated theoretical models to identify unobservable state factors (local and/or common) that drive the domestic and the foreign economies, as well as exchange rate movements that accommodate the FPP. The main problem with these models is that the state variables seldom have a meaningful economic interpretation. This paper introduces an economically meaningful variable to proxy for the time-varying part of the unobservable risk premium. The second direction the research has moved over the last two decades has focused on the persistence of the FPP with respect to different sample periods, or with respect to different estimation techniques. In general, studies using different currencies and sample periods find evidence of the FPP. However, some recent studies (such as Meredith and Chinn, 1998 and Baillie and Bollerslev, 2000, and Flood & Rose, 2002) claim that the puzzle has diminished slightly in recent years. On the other hand, some econometricians (such as Baxter, 1994) have developed different estimation methodologies to explore the FPP. The aim has been to filter out potential nonstationarities and to establish the actual relationship between currency movements and the basis. Hsieh (1993) and Bansal (1997) have found that the FPP is extensive in different futures/forward markets. Finally, Longstaff (2000) has shown that the validity of EH in term structure of interest rate literature can depend on the maturity of the investment. To address the concerns explored in this second line of research, the analyses in this study are performed on two subsamples. The original sample period of 1982 to 2001 is split into the 1980s and the 1990s to determine whether the puzzle has been as dominant in the recent decade. The nonstationarity problem is eliminated by taking the first difference of the currency data. Exchange rate movements are examined not only with traditional estimation techniques, but also with complex GARCH innovations. Both spot markets and futures markets for the Japanese yen are investigated. A model of the Japanese yen dynamics that includes a better measure for the time-varying portion of the risk premium should more accurately reveal the relationship between the currency return and the futures–spot basis and should have better goodness-of-fit measurements. Because the risk premium is not observable, the question becomes whether there is an observable variable that can proxy for the risk premium. This study introduces the maturity of the futures contracts as a candidate for the time-varying portion of the risk premium.2 One practical implication of using a model that includes a proxy for the time-varying risk premium is that such a model should have a better empirical performance in describing variables that have volatile dynamics.3 That has indeed been the case for the Japanese currency. Over the last twenty years, the Japanese yen has shown higher variability than other major currencies offering better profit opportunities if proper forecasting techniques and trading strategies are developed (Reszat, 1997). Any financial security tied to the yen will have this volatility embedded in its valuation as well. The novel approach in this study is to examine both the spot markets and the futures markets for the yen by taking into account the maturity structure of the futures contracts.4 Therefore, the main conjecture of this article is, when the maturity of the Japanese yen futures contract is near, investors face less uncertainty, therefore the risk premium is small. On the other hand, when maturity is longer, the risk premium is larger because investors face more economic uncertainty. To explore the implications of this proposition, a model with maturity as an additional explanatory variable is examined in the relationship between the yen returns and the futures–spot basis. The augmented model is compared to the original model with Akaike Information Criterion (AIC) and adjusted R-square value. Both measures indicate that the augmented model has a much better empirical fit. The coefficient for maturity is also statistically significant in the augmented model. The practical interpretation of the empirical results is clear-cut. For longer maturity contracts, investors demand a higher risk premium and this is reflected in higher overall spot returns. On the other hand, investors accept a lower risk premium and get lower returns for shorter maturity contracts. The study also examines the Japanese yen futures returns. The expected futures rate should be the same as the current futures rate in a risk-neutral world under the EH. Thus the expected futures return is zero. This implies that a regression of this return on a constant and on any variable, including the futures–spot basis, should produce coefficients that are statistically insignificant. However, the empirical investigation with maturity as the proxy for the time-varying portion of the risk premium indicates that the current futures rate is not an unbiased estimator of the expected futures rate. The augmented model with maturity explains futures returns better compared to the first model. 5 Furthermore, the estimates of all the variables in the augmented regressions are statistically significant. The rest of the article is organized as follows: Section 2 provides the layout and the methodology for the empirical tests. Section 3 explains the data and sample construction. Discussion of the results is in Section 4. Conclusion follows.

This study investigates the Japanese yen spot returns and futures returns. The well-known risk premium embedded in currency dynamics is proposed to be time varying and to be related to the maturity of the futures contract on the Japanese yen. To test this proposition, maturity is added as an explanatory variable to the regressions of the spot return on the futures–spot basis, and to the regressions of the futures return on the basis. Maturity is a good proxy for the risk premium as a linear rather than a nonlinear explanatory component. The coefficient on maturity is significant and of correct sign, indicating that longer maturity futures contracts have a higher risk premium. Addition of maturity increases the explanatory power of the regression models as measured by the adjusted R-square and by the AIC. However, the addition of maturity to the regressions does not eliminate the risk premium completely. The results are robust to different sample periods, to different forecast horizons for futures returns, and to GARCH(1,1) innovations in the estimates.