Patterns in foreign-currency returns
The uncovered interest-rate parity states that if investors are risk-neutral and rational, they should be largely indifferent between investing at home and abroad. Theoretically, high-interest-rate currencies depreciate and low-interest-rate currencies appreciate until their returns roughly line up. The empirical evidence, however, seems to strongly contradict this view. Trillions of US dollars turn around on currency markets on a daily basis – and for a good reason. At least since the 1980s, trading in global currency portfolio investments systematically leads to making money. In particular, borrowing in low-interest-rate currencies and investing in high-interest-rate currencies promises a positive return to investors in foreign-exchange markets. The same logic applies to high versus low forward-discount currencies (i.e., the difference in forward and spot rates). Figure 1 plots the average annualised returns on six-monthly rebalanced forward discount-sorted currency portfolios over the sample period, from December 1983 to December 2010. The portfolios are constructed in such a way that portfolio ‘F1’ always consists of the lowest forward-discount currencies, while portfolio ‘F6’ always contains the highest forward-discount currencies. This data set is constructed by Lustig et al. (2011) and freely available on the website of Adrien Verdelhan (Verdelhan).
Figure 1. Six forward discount-sorted portfolios
A simple investment strategy which takes a long position in ‘F6’ and a short position in ‘F1’ promises roughly 5% per annum on average! Interestingly, risk premia of a similar order of magnitude have been observed on equity markets too. What hides behind the secret to making money? Why do currencies with different forward discounts earn vastly different returns? Standard asset pricing theory claims that high returns should reflect a risk premium for exposure to systematic sources of risk: poor performance in bad economic times should be rewarded with high returns. For instance, Menkhoff et al. 2011 argue that currency returns can be explained as compensation for the volatility of risk undertaken: high interest-rate currencies yield lower excess returns when global foreign-exchange volatility risk is high and vice versa.
What is the risk in foreign-currency returns?
In a recent paper we argue that there is a tight link between equity and foreign-exchange markets (Galsband and Nitschka 2013). This fact makes it possible to exploit currency bets as a hedge against unexpected economic downturns on equity markets, such as severe dividend shocks feared by risk-averse stockholders. More specifically, currencies that appreciate when the stock market falls might be a good investment since they provide a valuable insurance against unfavourable fluctuations on equity markets. On the other hand, currencies which depreciate in times of poor stock-market performance tend to further destabilise investors’ positions and should hence offer a premium for their risk. We find strong empirical support for our hypothesis.
To solve the mystery behind profitable currency trading, we build on Campbell and Vuolteenaho (2004) who point towards two sources of systematic risk in equity markets. The first is ‘bad’ long-lasting cash-flow news about poor future-market dividends or consumption stream. The second is ‘good’ short-lived news about future-market rates applied to discount these cash flows. We show that it is the former type of shocks that can explain a large part of risk premia reflected in foreign-currency returns. The distinction between cash-flow risks such as a sudden permanent drop in dividends and transitory discount-rate fluctuations such as an unexpected rise in interest rates is crucial in this respect.
We document a strong relation between currencies’ average returns and their sensitivities to cash-flow shocks in equity markets. High forward-discount currencies react strongly to stock-market cash flows while low forward-discount currencies are much more resilient in this regard.
Figure 2. Average returns and cash-flow premia
Figure 2 illustrates the portion of total return on foreign currency (in blue) that can be attributed to market cash-flow risks (in red). Statistical tests consistently support the view that cash-flow risk exposure increases monotonically from low to high forward-discount currencies and thus reminds strongly of the pattern in portfolio returns themselves. In turn, differences in returns (in blue) and cash-flow premia (in red) are often attributed to insignificant discount-rate premia and disturbance terms that cannot be explained by the theory.
What is the underlying mechanism?
To uncover the underlying mechanism that drives our main result, we exploit a fundamental insight from Backus et al. (2001): basic finance theory suggests that high forward-discount currencies depreciate when the ‘home’ stock market receives bad cash-flow news that is associated with capital losses, whereas low forward-discount currencies appreciate under the same conditions. Thus, holding high forward-discount currencies is risky for a stockholder, while investing in low forward-discount currencies can provide him a hedge.
Does this model do a good empirical job?
We think that it does. Depending on specification, our model can explain between 81% and 87% in total variation in average returns on foreign-currency portfolios. Figure 3 provides a graphical summary of the model performance. It plots the predicted average returns on six currency portfolios on the vertical axis against the actually-realised sample average returns on the horizontal axis. Under perfect fit, all points would fall on the 45° line displayed in red. Consistent with Figure 2, the largest pricing error is realised for portfolio ‘F4’ where the estimated cash-flow premium is too low to fit the observed return of slightly more than 2.5% per annum. In general, however, the model appears a stout tool to explain returns on foreign currencies. Moreover, we show that it has a joint explanatory power for both foreign currencies and equities.
Figure 3. Realised versus fitted returns
Currency trading has been strikingly profitable at least since the 1980s. Yet, the free-lunch hypothesis on foreign-exchange markets is strongly rejected by the data. We argue that making money on currency investments is tightly linked to bad news about future dividend payments on stock markets: high forward-discount currencies load more on cash-flow risk than their low forward-discount counterparts. This observation reflects a depreciation of high forward-discount currencies and an appreciation of low forward-discount currencies in hard times when home stock market experiences severe unexpected dividend cuts. Our results support the view that violations of the zero-profit conditions on foreign-exchange markets reveal compensation for risk and reinforce the importance of common risk sources across different asset classes. Eventually, recognising the risky nature of currency trading is the key to the construction of unbiased, optimally hedging portfolios by long-term investors.
Disclaimer: The views expressed here are those of the authors and do not necessarily represent those of the institutions with which they are affiliated.
Backus, D K, S Foresi, and C I Telmer (2001), “Affine Term Structure Models and the Forward Premium Anomaly”, Journal of Finance, 56, 279-304.
Campbell, J Y and T Vuolteenaho (2004), “Bad Beta, Good Beta”, The American Economic Review, 94, 1249-1275.
Galsband, V and T Nitschka (2013), “Foreign Currency Returns and Systematic Risks”, Journal of Financial and Quantitative Analysis, forthcoming.
Lustig, H, N Roussanov, and A Verdelhan (2011), “Common Risk Factors in Currency Markets”, Review of Financial Studies, 24, 3731-3777.
Menkhoff, L, L Sarno, M Schmeling, and A Schrimpf (2011), “The Risk in Carry Trades”, VoxEU.org, 23 March.
Verdelhan, Adrien http://web.mit.edu/adrienv/www/, mit.edu.