Currency Risk And Pricing Kernel Volatility

A basic tenet of lognormal asset pricing models is that a risky currency is associated with a low pricing kernel volatility. Empirical evidence implies that a risky currency is associated with a relatively high interest rate. Taken together, these two statements associate high-interest-rate currencies with low pricing kernel volatility. We document evidence suggesting that the opposite is true. We approximate the volatility of the pricing kernel with the volatility of the short-term interest rate. We find that, across currencies, relatively high interest rate volatility is associated with relatively high interest rates. This contradicts the prediction of lognormal models. One possible reason is that our approximation of the volatility of the pricing kernel is inadequate. We argue that this is unlikely, in particular for questions involving currencies. We conclude that lognormal models of the pricing kernel are inadequate for explaining currency risk.

Large fundamental imbalances persist in the global economy, with potential exchange rate implications. This paper assesses whether exchange rate risk is priced across G-7 stock markets. Given the multitude of hedging instruments available, theory suggests that stock market investors should not be compensated for currency risk. However, data covering 33 industry portfolios across seven major stock markets suggest that not only is exchange rate risk priced in many markets, but that it is time-varying and sensitive to currency-specific shocks. With stock market investors typically exhibiting "home bias," this suggests that investors are using equity asset proxies to hedge the exchange rate risks to consumption.

Relations between foreign exchange risk premia, exchange rate volatility, and the volatilities of the pricing kernels for the underlying currencies, are derived under the assumption of integrated capital markets. As predicted, the volatility of exchange rates is significantly associated with the estimated volatility of the relevant pricing kernels, and foreign exchange risk premia are significantly related to both the estimated volatility of the pricing kernels and the volatility of exchange rates. The estimated foreign exchange risk premia mostly satisfy Fama's (1984) necessary conditions for explaining the forward premium puzzle, but the puzzle remains in several cases even after taking account of the pricing kernel volatilities.

The relation between the volatilities of pricing kernels associated with different currencies and the volatility of the exchange rate between the currencies is derived under the assumption of integrated capital markets, and the volatilities of the pricing kernels are related to the foreign exchange risk premium. Time series of pricing kernel volatilities are estimated from panel data on bond yields for five major currencies using a parsimonious term structure model that allows for time varying pricing kernel volatilities. The resulting estimates are used to test hypotheses about the relation between the volatilities of the pricing kernels in different currencies and the volatility of the exchange rate. As predicted, time variation in foreign exchange risk premia is found to be related to time variation in both the volatility of the pricing kernels and the volatility of exchange rates: the estimated pricing kernel volatilities can account for the forward premium puzzle in an 'average' sense across exchange rates.

I investigate a pricing kernel in which coskewness and the market volatility risk factors are endogenously determined. I show that the price of coskewness and market volatility risk are restricted by investor risk aversion and skewness preference. The risk aversion is estimated to be between two and five and significant. The price of volatility risk ranges from -1.5% to -0.15% per year. Consistent with theory, I find that the pricing kernel is decreasing in the aggregate wealth and increasing in the market volatility. When I project my estimated pricing kernel on a polynomial function of the market return, doing so produces the puzzling behaviors observed in pricing kernel. Using pricing kernels, I examine the sources of the idiosyncratic volatility premium. I find that nonzero risk aversion and firms' non-systematic coskewness determine the premium on idiosyncratic volatility risk. When I control for the non-systematic coskewness factor, I find no significant relation between idiosyncratic volatility and stock expected returns. My results are robust across different sample periods, different measures of market volatility and firm characteristics.

We study a large currency cross section using asset pricing methods which account for omitted-variable and measurement-error biases. First, we show that the pricing kernel includes at least three latent factors which resemble (but are not identical to) a strong U.S. “Dollar” factor, and two weak, high Sharpe ratio “Carry” and “Momentum” slope factors. Evidence for an additional “Value” factor is weaker. Second, using this pricing kernel, we find that only a small fraction of the over 100 nontradable candidate factors considered have a statistically significant risk premium -- mostly relating to volatility, uncertainty and liquidity conditions, rather than macro variables.

Episodes of increased global risk aversion, also known as risk-off episodes, have become more frequent and severe since 2007. During these episodes, currency markets exhibit recurrent patterns, as the Japanese yen, Swiss franc, and U.S. dollar appreciate against other G-10 and emerging market currencies. The pattern of these moves can be explained by a combination of fundamental factors, such as the nominal interest rate, the international investment position and measures of exchange rate misalignment, and market-liquidity factors, such as bid-offer spreads and restrictions on international capital flows. We also find that currency performance in a risk-off episode has become more related to a currency?s yield and relationship to broader risks in recent years.

Episodes of increased global risk aversion, also known as risk-off episodes, have become more frequent and severe since 2007. During these episodes, currency markets exhibit recurrent patterns, as the Japanese yen, Swiss franc, and U.S. dollar appreciate against other G-10 and emerging market currencies. The pattern of these moves can be explained by a combination of fundamental factors, such as the nominal interest rate, the international investment position and measures of exchange rate misalignment, and market-liquidity factors, such as bid-offer spreads and restrictions on international capital flows. We also find that currency performance in a risk-off episode has become more related to a currency?s yield and relationship to broader risks in recent years.