by traditional currency factors, equity factors, or the volatility carry factor proposed by Della Corte et al. (2017).
I use the dollar factor to study volatility risk premia in currencies because Verdelhan (2017) shows that the dollar factor accounts for a substantial part of the variation of bilateral exchange rates. Other natural candidate factors, i.e., the conditional and unconditional carry factors of Lustig et al. (2011), have a relatively small contribution in comparison for most exchange rates. The findings of Verdelhan (2017) therefore suggest that the carry factors, although priced in the cross-section of currency excess returns, play a smaller role as a source of exchange rate volatility. In contrast, the dollar factor appears intimately connected to foreign exchange volatility risk, even for exchange rates that do not involve the U.S. dollar. The methodology that I propose, however, can be used for any currency factor model including multi-factor models.
While most studies on volatility risk premia focus only on the difference between one-month realized and risk-neutral volatility, I also investigate if systematic variance risk is priced at longer horizons. Specifically, I empirically test if exposure to dollar factor variance risk is priced in the cross-section of excess returns on volatility swaps and forward volatility agreements (FVAs). The volatility swap pays at maturity the difference between realized volatility over the life of the contract and the spot implied volatility fixed at the inception of the contract (the swap rate). An FVA is a forward contract on spot implied volatility, i.e., it allows the holder to enter into a volatility swap at future point in time at a swap rate known today. The FVAs therefore contain information about the term structure of volatility risk premia, while volatility swaps are informative about the short-term volatility risk premia.
The market for currency volatility derivatives is enormous. For example, according to Della Corte, Kozhan, and Neuberger (2017), the market for FVAs has a daily average turnover of 254 billion USD and notional amounts outstanding of 11.7 trillion USD, as of April 2016, underlining a large demand from market participants to hedge against future currency volatility shocks.
Since my main objective is to study if dollar factor variance risk is an important source of volatility excess returns, I begin the empirical analysis by documenting some key properties of the volatility risk premia of the dollar factor. I show that the term structure of dollar
factor volatility is, on average, upward sloping and concave, i.e., it is particularly steep at the short end and flattens out at longer maturities. As a consequence, the average dollar factor volatility risk premia are negative with an upward sloping term structure. Intuitively, this implies that investors are willing to pay a higher price for insuring against short-term systematic variance risk compared to long-term systematic variance risk.
In order to test if dollar factor variance risk is priced in the cross-section volatility excess returns, I define a measure for the share of systematic variance risk (SYS) for each exchange rate as its systematic variance component divided by its total objective variance.
The systematic variance component is the product of the dollar factor variance and the squared dollar factor beta, both of which are inferred from cross-pair currency options as in Nielsen (2017). I justify that the SYS measure identifies systematic variance risk by showing that the cross-section of expected variance excess returns is solely explained by SYS under two assumptions. First, there is a negative variance risk premium on the systematic factor.
Second, idiosyncratic variance risk premia are equal across exchange rates per unit volatility (e.g., they are all zero).
Each month, I allocate volatility swaps into portfolios based on their SYS measures and document a strong negative relation between SYS and the portfolio excess returns. For example, at the 1-month horizon, a long-short portfolio that buys (sells) volatility swaps with low (high) SYS measures delivers a significant monthly mean excess return of 4.47%
and an annualized Sharpe ratio of 0.71. The mean excess returns of the long-short portfolios, however, decrease in maturity and are only significant for maturities of up to six months.
Furthermore, I find that the share of systematic variance is priced in the cross-section of FVA excess returns, in particular at shorter maturities. For example, when the forward contract and its underlying volatility both have a 1-month maturity, a long-short portfolio that buys (sells) FVAs with a low (high) share of systematic variance has a monthly mean excess return of 2.73% and an annualized Sharpe ratio of 0.95. At shorter maturities, the risk premia on the long-short portfolios based on systematic variance risk cannot be explained by exposure to the conditional dollar factor of Lustig et al. (2014), the G10 HML carry factor of Lustig et al. (2011), the G10 FX momentum factor of Asness et al. (2013), or the volatility carry factor of Della Corte et al. (2017). At longer maturities of the FVAs, however, the risk premia of the systematic variance risk portfolios are subsumed by the volatility carry
factor. However, this is partly explained by the fact that the volatility risk premia decrease in maturity.
There is a growing literature that studies volatility risk premia in currency markets (Della Corte, Kozhan, and Neuberger, 2017; Della Corte, Sarno, and Tsiakas, 2011; Londono and Zhou, 2017). But, to the best of my knowledge, there are no previous papers that directly estimate systematic versus idiosyncratic volatility risk premia in currencies, which is the main objective of this paper. Della Corte, Sarno, and Tsiakas (2011) show that forward volatility prices are biased predictors of future spot implied volatility. Building on this idea, Della Corte, Kozhan, and Neuberger (2017) document high mean excess returns on a long-short portfolio that buys (sells) FVAs that trade at a high (low) forward volatility discount, i.e., a volatility analogue to the traditional carry trade.
While Della Corte, Kozhan, and Neuberger (2017) focus on constructing portfolios of longer-term FVAs based on the slope of the volatility term structure, the systematic vari-ance risk that I identify is most significantly priced for FVAs at shorter maturities and for volatility swaps. In general, at shorter maturities of the forward contract, the volatility carry factor explains only a small part of the systematic forward volatility risk premia that I identify from FVAs. Moreover, the volatility carry factor based on volatility swaps does not explain the excess returns of the long-short portfolio of volatility swaps that I construct using the share of systematic variance measure.
The finding that systematic variance risk is priced in currency volatility excess returns appears consistent with a general phenomenon of investors requiring significantly larger risk premia for holding systematic variance vis-`a-vis diversifiable variance risk (Bollerslev, Tauchen, and Zhou, 2009; Carr and Wu, 2008; Duan and Wei, 2008). For instance, Carr and Wu (2008) find that variance risk premia on individual stocks are mostly explained by their exposure to the S&P 500 index variance, and Duan and Wei (2008) identify a positive relationship between the share of systematic variance for individual stocks and the level and slope of their implied volatility curve. Christoffersen, Fournier, and Jacobs (2017) construct a no-arbitrage option pricing model with a systematic factor in equity returns, and they uncover a positive relation between a stock’s beta with respect to the S&P 500 index and the level and slope of its implied volatility curve.