This paper presents evidence that the foreign exchange appreciation is predictable by the currency variance risk premium at a medium 6-month horizon and by the stock variance risk premium at a short 1-month horizon. Although currency variance risk premiums are highly correlated with each other over longer horizons, their correlations with stock variance risk premiums are quite low. Interestingly the currency variance risk premium has no predictive power for stock returns. We rationalize these findings in a consumption-based asset pricing model with orthogonal local and global economic uncertainties. In our model the market is incomplete in the sense that the global uncertainty is not priced by local stock markets and is therefore a forex-specific phenomenon-the currency uncertainty's effects on the expected stock return are offsetting between the cash flow channel and the volatility channel.JEL Classification: G12, G15, F31. Keywords: Forward premium puzzle, currency variance risk premium, stock variance risk premium, unspanned currency uncertainty, forex return predictability. * We would like to thank Craig Burnside, Darrell Duffie, Andrea Vedolin, and Adrien Verdelhan for helpful discussions. We would also like to thank the participants at the Federal Reserve Board Finance Forum for their valuable comments and Michael Zdinak for outstanding research assistance. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. Variance Risk Premiums and the Forward Premium PuzzleAbstract This paper presents evidence that the foreign exchange appreciation is predictable by the currency variance risk premium at a medium 6-month horizon and by the stock variance risk premium at a short 1-month horizon. Although currency variance risk premiums are highly correlated with each other over longer horizons, their correlations with stock variance risk premiums are quite low. Interestingly the currency variance risk premium has no predictive power for stock returns. We rationalize these findings in a consumption-based asset pricing model with orthogonal local and global economic uncertainties. In our model the market is incomplete in the sense that the global uncertainty is not priced by local stock markets and is therefore a forex-specific phenomenon-the currency uncertainty's effects on the expected stock return are offsetting between the cash flow channel and the volatility channel.JEL Classification: G12, G15, F31.
Recent empirical evidence suggests that the variance risk premium, or the difference between risk-neutral and statistical expectations of the future return variation, predicts aggregate stock market returns, with the predictability especially strong at the 2-4 month horizons. We provide extensive Monte Carlo simulation evidence that statistical finite sample biases in the overlapping return regressions underlying these findings can not "explain" this apparent predictability. Further corroborating the existing empirical evidence, we show that the patterns in the predictability across different return horizons estimated from country specific regressions for France, Germany, Japan, Switzerland and the U.K. are remarkably similar to the pattern previously documented for the U.S. Defining a "global" variance risk premium, we uncover even stronger predictability and almost identical crosscountry patterns through the use of panel regressions that effectively restrict the compensation for worldwide variance risk to be the same across countries. Our findings are broadly consistent with the implications from a stylized two-country general equilibrium model explicitly incorporating the effects of worldwide time-varying economic uncertainty.
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