A stochastic dominance analysis of yen carry trades

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Abstract

Yen carry trades have made headline news for over a decade. We examine the profitability of such trades for the period 2001–2009. Yen carry trades generated high mean returns and Sharpe ratios prior to the recent financial crisis. They continued to outperform major stock markets for the full sample period. Given the non-normality of carry trade returns, we apply non-parametric tests based on stochastic dominance (SD) to evaluate whether the high returns of yen carry trades are compatible with risk as reflected in returns on US and global stock market indices. We apply a general test for SD developed recently by Linton, Maasoumi and Whang (2005) to six currencies as well as portfolios of these currencies. For a large class of risk-averse investors, profits from yen carry trades cannot be attributed to risks.

Introduction

This paper examines the profitability of carry trades funded by the Japanese yen. A carry trade involves borrowing in low interest rate currencies to invest in high interest rate currencies. In efficient markets, uncovered interest parity (UIP) implies that such trades should not be profitable since currency changes will neutralize the interest rate differential. However, there is extensive evidence that currency markets violate UIP and that carry trades have been profitable for a very long time (see e.g., Fama, 1984, Burnside et al., 2006, Darvas, 2009).

Most carry trade studies focus on the US dollar or pound as the funding currency. In the last decade, however, yen carry trades have become very popular as interest rates in Japan fell to almost zero from around the late 1990s. Studies of yen carry trades have mainly been concerned about the size of yen carry trade positions and its implication for currency market stability (Gagnon and Chaboud, 2007, Hattori and Shin, 2009). A few studies have documented the profitability of yen carry trades over various sample periods. Darvas (2009) examines carry trade returns for all possible pairs of eleven currencies (including the yen) and eleven portfolios from January 1976 to April 2008. He finds that yen carry trades implemented on a portfolio of the other currencies did not produce statistically significant returns over this period, although carry trades funded by many other currencies were significantly profitable. Using more recent data from January 2001 to September 2007, Gyntelberg and Remonola (2007) report that yen carry trades generated much higher risk-adjusted returns compared to global stock markets. However, they did not indicate whether those risk-adjusted returns were statistically significant.

Understanding whether the profitability of carry trades is consistent with risk is of fundamental importance to researchers, regulators and market participants. For example, the profitability of carry trades is often viewed as prima facie evidence against market efficiency. This inference would be unwarranted if carry trade returns are a compensation for risk. On the other hand, if carry trade returns are too high to be explained by risk, then efforts to understand the root cause of this inefficiency would be useful in giving regulators a more informed basis to formulate policies to enhance market stability.

In this paper, we examine whether the profitability of yen carry trades in the last decade can be explained by risk. Our sample period is from January 2001 to June 2009, which includes the recent global financial crisis. The “zero interest rate” policy adopted by the Bank of Japan (BOJ) since early 1999 has been a key factor in motivating the yen carry trade. The starting date of our sample period gives some time for currency speculators to get accustomed to the BOJ’s easy credit regime.1

The empirical literature on carry trades has difficulty identifying clear risk factors that can explain carry trade returns. For example, Burnside et al. (2006) find that returns to carry trades are essentially uncorrelated with common risk factors. Formal asset pricing tests e.g., Lustig and Verdelhan (2007) also fail to find factor betas which are statistically significant. Typical of most asset pricing models, the preference parameters in these models indicate implausibly high levels of risk aversion for investors (De Santis and Fornari, 2008).

We use a nonparametric approach based on stochastic dominance to test the efficiency implications of yen carry trades. The main idea of our test is simple: if the distribution of carry trade returns is such that all expected utility maximizers prefer carry trades to an efficiently priced risky asset, then risk compensation is unlikely to be a compelling explanation for the profitability of yen carry trades. Since stochastic dominance analysis is nonparametric, statistical inferences based on stochastic dominance tests do not depend on any asset pricing model or require returns to be normally distributed. Following the literature, e.g., Burnside et al., 2006, Burnside et al., 2007, we use as efficient benchmarks, major stock market indices in our stochastic dominance tests. The fact that carry trade returns tend to be highly correlated with stock returns during times of global volatility lends plausibility to the interpretation of stock returns as a global risk factor.

Our main findings are as follows. First, yen carry trades were highly profitable during the pre-crisis period from January 2001 to June 2007, generating Sharpe ratios that were well above those of global stock markets. Second, despite the financial crisis, all currencies outperformed stock markets in terms of cumulative returns and Sharpe ratios over the full sample period to June 2009. Third, stochastic dominance tests reveal that yen carry trades generally dominate stock market benchmarks. This result holds for individual currencies as well as for carry trade portfolios. Finally, we find mixed evidence that liquidity risk as proxied by implied volatility on S&P 500 index options (the VIX) explains yen carry trade returns. Removing the influence of the VIX does little to change our main result that yen carry trades stochastically dominate equities for a large class of risk-averse speculators.

This rest of the paper is organized as follows. Section 2 reviews related literature on carry trades. Section 3 describes our dataset. Section 4 presents summary statistics of yen carry trade returns. Stochastic dominance is introduced in Section 5, followed by a discussion of our test strategy. Results of the stochastic dominance tests are discussed in Section 6. In Section 7, we examine the role of risk aversion and liquidity in explaining yen carry trade returns. Section 8 concludes with a summary of our main findings.

Section snippets

Related literature

There is widespread consensus that the behavior of exchange rates violates UIP. Currencies exhibit a “forward rate bias” in which high interest rate currencies tend to appreciate than depreciate, contrary to the predictions of UIP.

Data

Our sample period is from January 2001 to June 2009. This period includes possibly the worst global financial crisis since the great depression of the 1930s. We study yen carry trades against six major currencies: Australian dollar, Canadian dollar, euro, pound, New Zealand dollar and the US dollar. We consider returns for individual currencies as well as portfolios comprising these currencies and focus on monthly returns to facilitate comparisons with other studies of carry trades, e.g.,

The distribution of yen carry trade returns

Table 1 reports summary statistics of monthly returns of yen carry trades. Statistics are shown for individual currencies and two portfolios. “Highest Carry” refers to a strategy that invests in the currency with the highest interest rate differential at the beginning of each month. “EW” is a portfolio that invests equal amounts in each currency in every period. “PW” is a proportional-weighted portfolio that weights each currency by the ratio of the currency’s interest rate differential to the

Stochastic dominance

Stochastic dominance analysis provides an utility-based framework for evaluating choices under uncertainty.7

As an example, suppose an investor is choosing between two risky prospects, A and B, whose distributions may be highly non-normal. Suppose A’s returns always exceed that of B. In this case, no investor

Results of stochastic dominance tests

This section reports the results of the LMW test for individual currencies and portfolios. Fig. 3 plots the cumulative distribution function for each currency relative to the US stock market (plots for the MSCI World Index are very similar and are not shown). The plots confirm that there is no FSD-dominance for any of the currencies. We therefore focus on the SSD and TSD tests.

Results of the SSD test are in shown Panel A of Table 3. The null hypothesis H01:YjZ is not rejected for all cases,

Liquidity and yen carry trades

Recent research on carry trades has focused on the role of funding liquidity in generating currency bubbles (Plaintin and Shin, 2008, Brunnermeier et al., 2008, Brunnermeier and Pedersen, 2009a. In particular, speculators who use leverage to fund carry trades face the risk of liquidity squeeze in bad times when banks become highly risk-averse. Platin and Shin (2008) show theoretically that the pro-cyclical nature of bank lending can lead to exchange rates that “go up by the escalator and come

Conclusions

Yen carry trades have made headline news over the last decade. We document the profitability of such trades over the period 2001–2009 when Japanese interest rates were extremely low relative to other currencies. Over this period, yen carry trades generated very high mean returns and Sharpe ratios relative to stock markets despite the adverse impact of the US sub-prime crisis. As carry trade returns are usually accompanied by high downside risk, we employ non-parametric tests based on stochastic

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