What’s the relationship between stock returns and exchange rates?

The relationship between stock and currency returns

If a country’s equity market is expected to outperform that of other countries, should we expect its currency to appreciate or depreciate? The answer to this ques­tion matters to international equity investors, policymakers and, of course, aca­demics. An investor holding foreign equities is naturally exposed to exchange rate fluctuations. Both portfolio performance and the decision regarding whether to hedge foreign exchange (FX) risk will depend, amongst other things, on the relationship be­tween equity and currency returns. Policymakers care about this relation as valuation changes – induced by foreign exchange and equity returns – generate significant swings in international investment positions. However, while there is a vast literature on the link between interest rate differentials and exchange rates across countries, little is known about the relation between exchange rates and international equity returns (see Burnside et al. 2011, Lustig et al. 2011, and Menkhoff et al. 2012 for recent contributions).

The first paper to provide theoretical guidance on this relation is by Hau and Rey (2006). In a recent paper (Cenedese et al. 2015), we shed new light on this topic.

How should stock and currency returns be related?

From a simple asset pricing viewpoint, it is straightforward to show that the correlation between exchange rates and equity returns can take any sign; the sign depends on the covariance between returns and currency and stock market risk premia. Recent theory (notably Hau and Rey 2006) suggests that foreign exchange and equity market returns should be negatively correlated because of portfolio rebalancing. To see the mechanism, consider a US portfolio manager with money invested in Japan. When the Japanese stock market rises relative to the US, the manager is overweight with Japanese equities and, to return to a neutral position, sells Japanese stock and then sells the Japanese yen proceeds for US dollars. The sale of yen for dollars causes the yen to depreciate at the same time that the Japanese stock market is outperforming. This is the essence of the uncovered equity parity (UEP) condition whose statistical validity is assessed in various studies (e.g. Hau and Rey 2006, Melvis and Prins 2015 and the references therein).

Are equity and currency returns related at all?

We look again at this correlation, but from the cross-sectional perspective that is typical in empirical finance research. We consider an investor who builds a portfolio strategy designed to capture differences in future predicted returns across international equity markets in local currency, without hedging foreign exchange risk at all. We measure the returns from this strategy, and how they decompose into an equity market and foreign exchange component. This allows us to evaluate the economic importance of the uncovered equity parity deviations directly, and also measure the correlation between equity and currency returns in a broad cross-section of countries.

Our analysis is based on data for over 40 country-level equity indices observed over the past 30 years. In line with a vast literature on stock market predictability, we make forecasts of individual stock market returns using conventional predictors, such as aggregate dividend yields, momentum returns, and yield curve term spreads. The portfolio strategy we consider goes long markets that are predicted to rise and short markets that are predicted to fall (or to rise less). This strategy earns excess US dollar gross returns ranging between 7% and 12% per annum, depending on which of the three predictors we use. We therefore find that there are significant rewards available to international equity investors from betting on markets that are expected to perform well. This says something interesting about the correlation between foreign exchange and equity markets as when we compute the contributions of foreign exchange movements to the strategy returns we find that they are essentially zero.

• On average, across the three predictors, foreign exchange changes neither erode nor enhance the returns from the portfolio strategy, suggesting that there is no systematic relationship between local currency equity returns and currency returns.

Figure 1 shows the cumulative returns from the strategy that predicts stock market returns using momentum returns. The total return over 28 years is around 350%, and this is composed of 300% originating from local market equity returns and 50% due to currency returns. Clearly, in this case, currency returns are not working against investors.

Figure 1. Cumulative returns from the international momentum strategy

What do we learn about risk premia?

After providing evidence on the economic significance of the correlation between foreign exchange and stock market returns, we explore the logical question of whether the large positive returns from our portfolio strategy are merely a compensation for bearing risk. Using techniques that are routinely implemented in cross-sectional asset-pricing studies, we show that the average volatility of international stock markets prices the cross-section of returns from our international strategy fairly well. Portfolios that generate high expected returns do so partly because they tend to pay off when global stock volatility is low, and they perform poorly when global stock volatility is high.¹

However, we also show that exposure to global stock market volatility does not tell the full story for our cross-section of stock market returns. In fact, even after having accounted for risk, significant differences in portfolio returns remain; investors can run a long-short strategy based on predicted stock market returns and obtain significant excess returns which are on a par with or better than those from conventional domestic and international stock market strategies.

Conclusion

Overall, stock returns seem to tell us little, if anything, about the behaviour of ex­change rates. If there is a relationship between stock market and currency returns, this should be searched for at individual country level, and the above results do not rule out that the correlation may not be zero or vary over time for certain countries or in response to specific shocks. However, on average, across a broad set of countries, their correlation is essentially zero.

References

Ang, A, R J Hodrick, Y Xing, and X Zhang (2006), “The cross-section of volatility and expected returns”, Journal of Finance 61, 259–299.

Burnside, C, M Eichenbaum, I Kleshchelski, and S Rebelo (2011), “Do peso prob­lems explain the returns to the carry trade?” Review of Financial Studies 24, 853–891.

Cenedese, G, R Payne, L Sarno and G Valente (2015), “What Do Stock Markets Tell Us About Exchange Rates?” CEPR Discussion Paper No. 10685, forthcoming in Review of Finance.

Hau, H and H Rey (2006), “Exchange rates, equity prices, and capital flows”, Review of Financial Studies 19, 273–317.

Lustig, H, N Roussanov, and A Verdelhan (2011), “Common risk factors in currency markets”,Review of Financial Studies 24, 3731–3777.

Melvin, M and J Prins (2015), “Equity hedging and exchange rates at the London 4p.m. fix”, Journal of Financial Markets 22, 50–72.

Menkhoff, L, L Sarno, M Schmeling, and A Schrimpf (2012), “Carry trades and global foreign exchange volatility”, Journal of Finance 67, 681–718.

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