Handbook of Exchange Rates

10.5 Time-Varying Risk and Rare Events

I concluded, in Section 10.4.1, that standard risk models do not explain the returns to the carry trade. There we saw that the beta of the HML carry-trade portfolio with respect to the CAPM factor is statistically significant, but is much too small (0.163) to explain the risk premium of the carry trade. To explain the roughly 6% risk premium of the HML carry portfolio, the beta would need to be about six times as large. Lustig et al. (-NIL-) agree on this assessment, arguing that “the average beta of HML_FX with the US stock market return is too small to explain carry trade risk premia.” However, they argue that the beta of the carry trade with respect to the stock market increases during times of financial market distress. Certainly, during the recent mortgage crisis my HML carry-trade factor displayed more correlation than usual with the stock market. However, it seems unlikely that a simple conditional beta story can explain the returns to the carry trade. There are two reasons favoring this conclusion. First, as Figure 10.1 reveals, in historical data, there is no systematic relationship between distress in the stock market (measured by periods of sharp decline) and currency crashes (measured by the period of big losses to the carry trade). Second, time variation in the carry trade's stock market beta, while significant, is quantitatively not large enough. To see this, consider Figure 10.2, which plots betas of the daily returns of the ...