Option-Implied Currency Risk Premia - Princeton University

ξt i = ξ i −Ψ t·(rt,t+1 i −rUS t,t+1 ), and find a negative within-time-period/across pair association between the loadings
and interest rate differentials (Ψ t > 0). In addition to this, we observe a negative across-time/across-pair relation
between the value of ξ i and the unconditional mean interest rate differential (Table I, Panel A). This result is
qualitatively in line with the preferred (“unrestricted”) specification in Lustig, et al. (2011). Furthermore, the
calibration indicates that on average slightly more than 50% of the variance of the global shock in the pricing
kernel is accounted for by the non-Gaussian (jump) shock. On average, the distribution of the global innovation
has a skewness of -1.1 and kurtosis of 6.0 (Table I, Panel B). These values are consistent with the distributional
properties of returns to dollar-neutral portfolios of currency carry trades reported in Jurek (2013), which play the
role of empirical factor mimicking portfolios for the global shock. The preferred model calibration delivers a root
mean squared option pricing error – measured in volatility points – of 1.12, which is in line with typical bid-ask
spreads for exchange rate options (Table I, Panel C).
We aggregate the pair-level estimates of option-implied currency risk premia using portfolio weights used in
the construction of empirical factor mimicking portfolios, to produce the corresponding model-implied portfolio
risk premia. We examine the historical returns to conditional factor mimicking portfolios – sorted on the basis of
contemporaneous interest rates – and unconditional factor mimicking portfolios – sorted on the basis of backward
looking averages of interest rates. We find that option-implied risk premia for the conditional and unconditional
HML F X factor mimicking portfolios are 3.55% (3.44%) per annum, respectively (Table IV). Neither of these
quantities is statistically distinguishable from the corresponding mean realized returns of 4.96% and 3.32% per
annum; the t-statistics of the differences are equal to 0.43 and -0.16, respectively. We then decompose the modelimplied
HML F X risk into contributions stemming from Gaussian and non-Gaussian pricing kernel shocks, as
well as, across the moments of the pricing kernel innovations. The decomposition reveals that (on average) 58%
of the risk premium for the HML F X factor mimicking portfolio is due to non-Gaussian (jump) innovations in
the global factor. To explore the mechanism through which jumps contribute to the HML F X risk premium,
we decompose the risk-premium across the moments of the global pricing shock. This reveals a striking result.
Although non-Gaussian shocks are the dominant drivers of the HML F X risk premium, they exert their influence
primarily by contributing variance, rather than skewness, to the global innovation. Specifically, we find that (on
average) 85% of the total risk premium is attributed to the variance of the pricing kernel shocks, with only 10%
due to skewness of the shocks, and roughly 5% due to the higher moments. This parallels the empirical results
reported by Jurek (2013) based on an analysis of returns to crash-hedged G10 portfolios, and casts doubt whether
rare disaster models (Farhi and Gabaix (2011)) provide an accurate description of developed market currencies. 4
4 Our finding is inconsistent with Farhi, et al. (2013), who argue that “disaster risk accounts for more than a third of the currency
risk premia in developed economies,” and can be traced to two differences in the empirical identification strategies. First, Farhi, et al.
3