Volatility risk premia – differences between implied and realized volatility – are plausible and empirically validated predictors of directional foreign exchange returns, particularly for EM currencies. The intuition is that excess implied volatility typically results from elevated risk aversion, which should be indicative of undershooting. When calculating the volatility risk premium it is important to compare short-term implied volatility with realized volatility of that same period. One would expect positive returns on currencies whose very recent volatility has been less than feared.

*The post ties in with this site’s lecture on implicit subsidies paid in financial markets, particularly the sections on foreign exchange and volatility markets.*

*The below are excerpts from the paper. Emphasis and cursive text have been added.*

### The intuition behind volatility risk premia

“Volatility risk premium (VRP)…[*is*] __the difference between an implied and a realized volatility__…[*In*] a stylized general equilibrium model…the risky asset…can be forecasted by its volatility risk premium…When the market anticipates high (low) volatility going forward, there is a discount (premium) built into prices, resulting in high (low) futures returns…An emerging market currency can be considered the risky asset for an US-based investor. Even small developed markets can be viewed as a risky asset.”

“The intuition is that, when risk aversion sentiment increases, the market quickly discounts the [*risky*] currency, and later this discount is accrued, leading to currency positive returns over a month or even more time.”

*On the role of volatility risk premia for FX overshooting also view post here.*

“The predictive ability of the VRP does not mean necessarily some sort of market inefficiency. The __higher returns following a higher VRP can be seen as a compensation for a higher risk aversion, a higher perceived future risk, or both__.”

*N.B.: Volatility risk premium and variance risk premium are synonymous. In equity markets the variance risk premium is viewed as compensation for hedges against variations in future realized volatility and particularly against downside risk (view post here).*

### The calculation of volatility risk premia for FX

“In order to calculate the volatility risk premium, we need a measure of implied (risk-neutral) volatility and a measure of realized (physical) volatility… The use of high-frequency intraday data for calculating the realized volatility generally affords much more accurate ex post observations on the actual return variation than the more traditional sample variances based on daily or coarser frequency returns…I argue that __risk premia calculated using short-term windows and intraday data are a more accurate measure of the actual premia than those using large windows of daily data__.”

“__I compare the option-implied volatility with the realized volatility for the same period of the option__. The traditional method compares implied volatility with the past realized volatility, assuming, thus, a unit autocorrelation. The novel method outperforms the traditional method in forecasting exercises in most of the cases…However, the cost of this approach is that the risk-neutral volatility information will be some periods ‘old’.”

“My empirical investigation is based on two samples. The first sample uses a daily time series of options with maturity in one month, thus there is a strong overlapping. The second sample has one-week options with no overlapping structure. The realized volatility is based on intraday returns of 30- and 5-minute respectively. While the second sample goes back to 2003, and has option data from only six currencies, the first starts in 2007 and has option data from 20 currencies – 10 developed and 10 emerging markets…[*The table below*] summarizes the characteristics of the samples.

### Empirical evidence for the predictive power of volatility risk premia

“I document a __positive relationship between volatility risk premium…and future currency returns__, using one-week and one-month options and realized volatilities calculated using intraday returns. This is the same relationship found [*in previous research*]…for developed equity markets.”

“Using the Global currency VRP (average VRP of all currencies) provides better results than regional or specific VRP, especially for emerging markets. Averaging across many currencies seems to reduce estimation error of individual currencies, giving robustness to the predictive ability.”

“The Global currency VRP – an equally weighted average of all VRPs with data available – shows predictive ability over an equally weighted average of returns from all currencies. When grouping by geographic region, results are stronger for currencies from Latin America and Asia-Pacific…__Results for the forward VRP approach are much stronger__ [*than for the backward VRP approach*]. It shows statistically significant coefficients for the overall case, the global VRP, and for developed markets. When grouping by geographical region in the forward approach, Europe is the only region with no statistical significance.”

“The __regression estimates suggests that one percentage point of annualized currency VRP leads to a 0.28% currency appreciation on average over the next month for the first sample and 0.16% over the next week for the second sample__…The only currency with statistically negative VRP coefficient is the Japanese Yen, meaning that investors favor the Yen when risk sentiment increases.”

“The coefficients [*describing the relation between VRP and FX returns*] decrease with the horizon almost monotonically. It is statistically significant with 95% confidence interval up to four months approximately…Overall, results suggests that the VRP effect on returns fades in a few months.”