Option-Implied Currency Risk Premia - Princeton University

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Table IV Option-Implied Currency Risk Premia: Empirical factor mimicking portfolio returns The table compares the historical (realized) returns to factor mimicking portfolios, with the corresponding model-implied risk premia. The data span the period from January 1999 to June 2012 (N = 162 months). Realized returns are computed on the basis of monthly buy-and-hold returns. The conditional HML F X factor mimicking portfolios is a dollar-neutral portfolio formed by sorting currencies into long and short portfolios on the basis of their prevailing one-month LIBOR rates. Within each portfolio currencies are spread weighted, on the basis of the distance of their respective interest rates to the mean of the interest rates in countries with ranks five and six. The unconditional HML F X portfolios is formed on the basis of the historical interest rate differentials computed using an expanding window starting in January 1990. The conditional short USD factor mimicking goes long (short) the U.S. dollar when the prevailing U.S. dollar interest rate is above (below) the prevailing average of the nine other G10 interest rates. The unconditional short USD factor mimicking portfolio is long an equal-weighted basket of G10 currencies against the U.S. dollar. Model risk premia are computed on the basis of Specification I. We report the moments of various quantities of interest, the p-values of the Jarque-Bera test for the realized portfolio returns, and comparisons of the mean realized and model-implied risk premia (t-stats in square brackets). Portfolio ξ L and ξ S report the time-series mean of the global factor loading for the long and short leg of the portfolio. Panel A: HML F X Factor Mimicking Portfolio Conditional Unconditional Difference Realized Mean 4.96 3.32 1.63 [1.92] [1.32] [1.99] Volatility 9.51 9.26 Skewness -1.07 -0.89 Kurtosis 7.03 6.90 JB (returns) 0.00 0.00 JB (Z-scores) 0.00 0.00 Carry 4.57 3.69 0.88 t-stat [60.81] [51.65] [27.95] Model Total (λ) 3.55 3.44 0.11 [8.72] [8.37] [2.63] HML (global, (λ HML ) 3.55 3.44 0.11 [8.72] [8.37] [2.63] Short USD (λ USD ) 0.00 0.00 0.00 - - - Portfolio ξ L (long) 0.83 0.87 Portfolio ξ S (short) 1.06 1.07 Difference Mean 1.41 -0.11 1.53 t-stat [0.53] [-0.04] [1.86] Panel B: Short USD Factor Mimicking Portfolio Conditional Unconditional Difference Realized Mean 4.93 3.12 1.81 [2.05] [1.29] [0.78] Volatility 8.84 8.90 Skewness -0.45 -0.17 Kurtosis 3.96 3.72 JB (returns) 0.01 0.09 JB (Z-scores) 0.00 0.00 Model Total (λ) 0.76 1.69 -0.93 [4.38] [13.46] [-7.61] HML (global, (λ HML ) 0.37 0.94 -0.57 [3.10] [9.53] [-6.32] Short USD (λ USD ) 0.38 0.74 -0.36 [3.19] [22.73] [-8.93] Portfolio ξ L (long) 0.96 0.94 Portfolio ξ S (short) 0.98 1.00 Difference Mean 4.18 1.44 2.74 t-stat [1.73] [0.59] [1.17]
Table V Option-Implied Currency Risk Premia: Individual currency pairs The table reports the results of a regression analysis of realized carry trade returns for individual currency pairs on option-implied currency risk premia and interest rate differentials. The returns are measured using 21-day non-overlapping intervals, and the explanatory variables are assumed to be measured as of the last day preceding that interval. We report two sets of results. The first is based on repeated cross-sectional regressions (Fama-MacBeth); the second, is based on a pooled panel regression. The reported coefficients are time series averages and standard errors are computed on the basis of the time series of estimates. Adj. R 2 reports the average cross-sectional adjusted R 2 . Standard errors of coefficient estimates are reported in parentheses (N = 167). The second set of regressions is based on pooled panel regressions with currency-pair fixed effects (N = 24 · 167 = 4008). For panel regressions, standard errors are adjusted for cross-sectional correlation and time series auto- and cross-correlations using the methodology from Thompson (2011) with three lags. The panel regression is run with country-fixed effects; however, the adjusted R 2 is reported net of the explanatory power of the fixed effects. Finally, we report the p-value for two hypothesis tests. The first hypothesis asserts that the model is correctly specified, such that the regression intercept (respectively, fixed effects) is zero and the slope coefficients on the model-implied risk premia are one (H 0 ). When additional regressors are included, the model predicts a zero coefficient on those variables; if no model-implied variables are included in the regression, we do not report the result of the test. The second hypothesis (H 1 ) is that the included variables have no explanatory power (i.e. all the coefficients with the exception of the intercept are zero). Cross-sectional Panel (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) Intercept 0.00 -0.00 0.00 -0.00 -0.00 FE FE FE FE FE (0.00) (0.00) (0.00) (0.00) (0.00) λ ji t 2.09 0.73 -0.22 -0.21 (1.31) (1.44) (0.72) (0.74) λ ji,hml t 2.50 0.75 -0.15 -0.11 (1.42) (1.46) (0.72) (0.75) λ ji,refF X t 6.01 6.74 -5.25 -6.61 (4.03) (4.53) (4.81) (4.68) r j t − ri t 0.14 0.11 0.08 0.06 0.05 0.07 (0.05) (0.06) (0.06) (0.07) (0.08) (0.08) Adj. R 2 0.30 0.47 0.26 0.43 0.57 0.00 0.00 0.00 0.00 0.00 (0.02) (0.02) (0.02) (0.02) (0.02) - - - - - N 167 167 167 167 167 4008 4008 4008 4008 4,008 H 0 p-value [%] 68.90 45.22 - 27.76 32.35 0.00 0.00 - 0.00 0.00 H 1 p-value [%] 11.01 11.88 0.51 6.20 17.07 75.47 53.86 44.01 68.28 46.25
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Option-Implied Currency Risk Premia
Page 3 and 4: a closed-form expression for the ge
Page 5 and 6: We conduct a similar analysis for r
Page 7 and 8: the determination of currency risk
Page 9 and 10: Y j t parameter can be interpreted
Page 11 and 12: where S ji t is the currency exchan
Page 13 and 14: where V g t = κ2 L g and S g t =
Page 15 and 16: coupon bond in country i; otherwise
Page 17 and 18: 2 Data and Model Calibration We cal
Page 19 and 20: How does the identification intuiti
Page 21 and 22: account for the fact that the avera
Page 23 and 24: √ δ requires loadings to range f
Page 25 and 26: volatilities (blue) and their fitte
Page 27 and 28: isk premium can be computed on the
Page 29 and 30: 3.2.1 Slope (carry) factor To const
Page 31 and 32: 3.2.2 Short U.S. dollar factor Lust
Page 33 and 34: Figure 7 contrasts the ability of o
Page 35 and 36: in fact, largely orthogonal to fact
Page 37 and 38: etter than under Specification I. T
Page 39 and 40: A Cumulant Generating Functions of
Page 41 and 42: References [1] Ang, A. and J. Chen,
Page 43 and 44: [27] Ghysels, Eric, Pedro Santa-Cla
Page 45 and 46: Figure 2. Cross-Sectional Relation
Page 47 and 48: Figure 4. Returns to Empirical Fact
Page 49 and 50: Figure 6. Option-Implied Currency R
Page 51 and 52: Table I Calibrated Model Parameters
Page 53: Table III Model Short Reference Cur
Page 57 and 58: Table A.I State-variable Dynamics a
Page 59 and 60: Table A.III Option-Implied Currency
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