Foreign Exchange Volatility Is Priced in Equities

Article excerpt

This paper finds that standard asset pricing models fail to explain the significantly negative delta hedging errors that occur as a result of the purchase of options on foreign exchange futures. Foreign exchange volatility does influence stock returns, however. The volatility of the JPY/USD exchange rate predicts the time series of stock returns and is priced in the cross-section of stock returns.

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Research has consistently found that Black-Scholes implied volatility is a conditionally biased predictor of realized volatility across asset markets. That is, risk-neutral implied volatility exceeds realized volatility. The most popular explanation for this robust phenomenon is that volatility risk is priced, which is very plausible for options on stock market indices. (1) Merton's (1973) intertemporal capital asset pricing model (ICAPM) predicts that investors want to hedge their exposure to stock market volatility because increasing volatility indicates lower quality investment opportunities. (2) Moreover, recent authors, for example, Chen (2003), Guo (2006b), and Ang, Hodrick, Xing, and Zhang (2006), have estimated variants of Merton's ICAPM and found that equity volatility risk is significantly priced in the US stock market.

Black-Scholes implied volatility is also biased for nonequity assets, however, including foreign exchange. This suggests that foreign exchange volatility is also priced in options markets. Why might foreign exchange volatility risk be priced in equilibrium? Priced foreign exchange volatility risk might be related to priced foreign exchange level risk, as documented by Dumas and Solnik (1995), De Santis and Gerard (1998), Choi, Hiraki, and Takezawa (1998), and Ng (2004). (3) If the level of foreign exchange is a risk factor, as it is in the international ICAPM, its volatility should forecast stock market returns and thus degrade investment opportunities by raising volatility. Presumably, higher foreign exchange volatility indicates poorer investment opportunities because it makes hedging foreign exchange level risk more difficult (e.g., Coval and Shumway, 2001). (4) Therefore, one would expect that foreign exchange volatility risk would carry a negative premium.

This research is related to Bakshi and Kapadia (2003, hereafter BK) and Low and Zhang (2005, hereafter LZ), who characterize delta hedging errors in equity and foreign exchange markets, respectively. BK concentrated on showing that the price of volatility risk--as opposed to jump risk--is the source of S&P 500 hedging returns. LZ likewise considered the source of delta hedging profits in foreign exchange markets, as well as how the volatility term structure influenced the risk premium.

We also characterize delta hedging profits, but our motivation and methods differ fundamentally from BK and LZ. The negative premium on foreign exchange volatility should affect other asset markets, including equity markets, as pointed out by Detemple and Selden (1991), Coval and Shumway (2001), and Vanden (2004). We test this idea in three ways. First, we investigate whether standard asset pricing models (APMs) explain the delta hedging errors, which mainly reflect volatility risk, as argued by BK and LZ. We find that the risk adjusted profit from buying and delta hedging call options on foreign exchange futures is significantly negative. By contrast, this profit attenuates substantially (becomes smaller in absolute value) after controlling for loadings on realized foreign exchange volatility. Therefore, the failure of conventional risk adjustment to eliminate the significant delta hedging errors reflects the deficiency of APMs to explain volatility risk.

Second, consistent with the prediction of the international ICAPM, we show that realized foreign exchange volatility--especially that of the Japanese yen/US dollar rate--forecasts stock returns in both US and international markets. …