The standard “carry trade” is a popular currency speculation strategy that invests in high-interest currencies by borrowing in low-interest currencies. This strategy works well if, for example, spot exchange rates are unpredictable. There is ample empirical evidence pointing in that direction or, in academic jargon, showing that exchange rates follow a random walk (Meese and Rogoff 1983). In this case, investors engaging in carry trading will on average earn the difference in interest rates without having to worry about movements in exchange rates. The return to currency speculation can be substantial over time. It should be no surprise, therefore, that the carry trade has attracted considerable attention from academics and practitioners over the years.

# Speculating on volatility

In recent years, investors have been able to speculate not only on the value of currencies but also on the level of volatility of these currencies. This has become possible by trading a contract called the forward volatility agreement (FVA), which effectively allows investors to trade volatility. Technically speaking, the FVA is a forward contract on future spot implied volatility, which for a one dollar investment delivers the difference between future spot implied volatility and forward implied volatility. To make our terminology clear, implied volatility is a measure of expected volatility, which is directly quoted in traded currency options (Jorion 1995). When we say “spot” implied volatility we mean the implied volatility for an interval starting today and ending in the future (e.g., starting today and ending one month from now). “Forward” implied volatility is the implied volatility determined today for an interval starting in the future and ending further in the future (e.g., starting in one month and ending in two months from now).

The main point of the FVA is that it allows investors to speculate on the level of future volatility. Then, the “carry trade in volatility” is a speculation strategy that buys and sells FVAs, where investors try to make money by guessing the level of future spot implied volatility. Similar to the standard carry trade, the carry trade in volatility works well if spot implied volatility is unpredictable. Then, investors engaging in this new carry trade will on average earn the difference between spot and forward volatility without having to worry about movements in exchange rates.

# Is forward volatility a good predictor of future volatility?

The FVA sets a forward implied volatility by making a guess about future spot implied volatility. For example, today it might set a forward volatility of 10% for the period starting in one month and ending in two months from now. This forward volatility is meant to be an unbiased predictor of the future spot implied volatility for the same period, which may end up being higher or lower than 10%. As any forward contract, the FVA is designed so that on average the ex ante forward volatility matches the spot volatility that happens ex post.^{1} If these two volatilities end up being very similar, buying and selling FVAs will not be profitable and the carry trade in volatility will not work. In this case, speculating on volatility will not generate profits. But is this the case?

In a recent paper (Della Corte et al. 2010), we investigate the systematic relation between spot and forward volatility in foreign exchange by estimating the volatility analogue to the famous Fama regression (Fama 1984). Using a number of currencies, alternative measures of volatility, and different estimation techniques, we find a fairly robust result. Forward volatility is a poor predictor of future spot implied volatility. This is called the “forward volatility bias.” In fact, for some cases, the relation between spot and forward volatility is practically non-existent, which implies that spot volatility may be close to a random walk. This is a strong result with important implications.

# Is volatility speculation profitable?

If forward volatility is a poor predictor of future spot implied volatility, buying and selling FVAs can be very profitable. For example, buying (selling) FVAs when forward implied volatility is lower (higher) than current spot implied volatility will consistently generate excess returns over time. Even better, we show that investors can design simple dynamic asset allocation strategies that exploit the forward volatility bias. These strategies can consistently generate high profits even when the transaction cost of trading FVAs is rather high. Similar strategies assuming that spot volatility follows a random walk generate equally high profits.

Another important result is that the returns to the standard carry trade in currency and the carry trade in volatility tend to be uncorrelated over time. This point can be seen clearly in Figure 1, which shows the annualised out-of-sample Sharpe ratios for the standard carry trade in currency and the carry trade in volatility, labelled CTC and CTV respectively. The Sharpe ratio is simply defined as the excess return of each strategy per unit of risk. The CTV strategy tends to perform better at the beginning and end of the sample, whereas the CTC is better in the middle period. Moreover, it is interesting to note that for the last two years of the sample the Sharpe ratio of the CTV strategy is rising but that of the CTC is falling. This indicates that the CTV strategy has done well during the recent credit crunch when the CTC has not.

**Figure 1.**

# Conclusion

There is money to be made in trading foreign-exchange volatility. If there is a bias in the way the market sets forward volatility, then the carry trade in volatility strategy will be profitable. We find strong statistical and economic evidence that this is indeed the case. Hence, there is a new carry trade. Finally, our empirical findings on volatility speculation can provide valuable insight to market participants and policymakers who can benefit from taking a stance on the future volatility in currencies.

# References

Della Corte, P, L Sarno, and I Tsiakas (2010), “Spot and Forward Volatility in Foreign Exchange”, *Journal of Financial Economics*, forthcoming. Centre for Economic Policy Research Discussion Paper 7893.

Fama, EF (1984), “Forward and Spot Exchange Rates”, *Journal of Monetary Economics*, 14:319-338.

Jorion, P (1995), “Predicting Volatility in the Foreign Exchange Market”, *Journal of Finance*, 50:507-528.

Meese, RA and K Rogoff (1983), “Empirical Exchange Rate Models of the Seventies: Do They Fit Out of Sample?”, *Journal of International Economics*, 14:3-24.

^{1} Technically speaking, as any forward contract, the FVA’s net market value at entry must be equal to zero. Therefore, its exercise price (forward implied volatility) represents the risk-neutral expected value of future spot implied volatility. Hence the former must be an unbiased predictor of the latter.