The results are quite illuminating. Although a naïve carry trade strategy had produced persistently positive returns over the previous five years, such a strategy would have suffered considerably during the March 2005-2009 period, with a negative 4.51% return and negative skew of -0.99. In part this is explained by the high error- rate in picking the long-short positions for the carry trade with only 42.3% of positions correctly called. In contrast, our simple linear models perform rather well and the inclusion of VX clearly improves their performance. All exhibit positive returns and positive skews although the Sharpe ratios suggest that carry trade strategies based on these models would be rather risky. The nonlinear threshold model performs best, with an annualized rate of return of 5.43%; a Sharpe ratio of 0.50, positive skew of 1.05 and correctly calling the long-short position 57.9% of the time.

Although these results look very promising, we ask ourselves whether they might be the result of a lucky sequence of draws or whether they truly reflect a statistically measurable improvement in performance. As we explained in section 3.2 our focus is not based on traditional measures of forecasting performance based on RMSE but instead investment performance measures that reflect the type of predictive ability and investor may be most interested in. Thus table 6, panel (b) summarizes the ability to predict the long-short direction correctly by comparing actual returns with the returns that would have been realized using our candidate models to determine the long-short position as described in expression (6). All these tests consider are the null model the random walk model. The results suggest that except for the VAR model, all alternatives dominate the random walk in a statistically significant way although differences across these models are probably small.

But is this realistic enough? Presumably investors do not consider individual bilateral trades but a portfolio and to the extent that a portfolio helps diversify risk, we may expect to improve on some of the bilateral results just reported. To this aim, we consider three types of portfolios: (1) a portfolio that invests an equal amount across all currencies in our sample against the dollar, which we call the equal-weights (EW) portfolio; (2) a portfolio where the weights are determined dynamically in proportion to the expected returns to the carry for each currency against the dollar, which we call the returns-weighted (RW) portfolio; and (3) a portfolio that invests in the three

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