Option-Implied Currency Risk Premia - Princeton University

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Table A.II Model HML F X Factor Risk Premium Decomposition: Equal-weighted portfolios This table uses the calibrated pricing kernel model to compute and decompose the HML F X factor risk premium from the perspective of a U.S. dollar investor. We compute the model-implied HML F X factor risk premium by constructing a hypothetical, dollar-neutral factor mimicking portfolio on the basis of the calibrated time series of the global factor loadings, ξ i t. At each point in time, we sort the G10 currencies – excluding the U.S. dollar – into long and short portfolios on the basis of their prevailing loadings, and equal-weight the currencies within each portfolio. The model risk premia are computed daily and span from January 1999 to June 2012 (T = 3520 days). We report the global factor loadings of the high and low interest rate portfolios (ξ H and ξ L ), as well as, the mean portfolio risk premium (λ HML ; % per annum). We then decompose the portfolio risk premium into contributions from the Gaussian and non-Gaussian components of the global factor innovation, L g Z t . Finally, we evaluate the mechanism through which jumps contribute to equilibrium currency risk premia by decomposing risk premia across the moments of the pricing kernel innovations (variance, skewness, etc.). For each quantity, we report its time-series mean, volatility, and range. Results are reported for each of the four specifications reported in Table A.I. Loadings Risk premium By Shock Type By Moment Specification ξ H ξ L λ HML Gaussian Non-Gaussian Variance Skewness Other I Mean 0.87 1.04 2.66 42.28 57.72 85.78 9.32 4.90 Volatility 0.04 0.03 3.16 18.18 18.18 10.54 5.13 5.88 Min. 0.62 0.96 0.11 0.01 0.18 39.08 0.01 0.00 Max. 0.92 1.34 37.48 99.82 99.99 99.99 26.00 36.10 II Mean 0.88 1.04 2.82 40.41 59.59 85.68 9.94 4.38 Volatility 0.00 0.00 3.53 17.17 17.17 9.33 4.73 5.01 Min. 0.88 1.04 0.13 0.01 5.08 37.90 0.08 0.00 Max. 0.88 1.04 42.18 94.92 99.99 99.92 25.89 37.24 III Mean 0.88 1.09 1.95 42.12 57.88 87.64 8.79 3.57 Volatility 0.05 0.05 2.20 20.38 20.38 10.28 5.50 5.31 Min. 0.66 1.00 0.04 0.00 0.16 25.49 0.02 0.00 Max. 0.95 1.45 25.60 99.84 100.00 99.97 26.59 54.47 IV Mean 0.93 1.07 2.12 41.26 58.74 85.70 10.24 4.06 Volatility 0.00 0.00 2.32 18.83 18.83 9.50 5.16 4.76 Min. 0.93 1.07 0.07 0.00 5.84 30.50 0.67 0.06 Max. 0.93 1.07 29.20 94.16 100.00 99.25 26.67 45.74
Table A.III Option-Implied Currency Risk Premia: Empirical factor mimicking portfolio returns (Specification II; constant global factor loadings) 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 II. 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). 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) 3.81 3.73 0.08 [8.97] [8.54] [1.74] HML (global, (λ HML ) 3.81 3.73 0.08 [8.97] [8.54] [1.74] Short USD (λ USD ) 0.00 0.00 0.00 - - - Portfolio ξ H 0.85 0.88 Portfolio ξ L 1.06 1.08 Difference Mean 1.14 -0.41 1.55 t-stat [0.43] [-0.16] [1.89] 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 8.56 Skewness -0.45 -0.17 -0.62 Kurtosis 3.96 3.72 8.07 JB (returns) 0.01 0.09 0.00 JB (Z-scores) 0.00 0.00 0.00 Model Total (λ) 0.84 1.59 -0.74 [5.35] [13.59] [-8.30] HML (global, (λ HML ) 0.46 0.81 -0.35 [4.47] [9.21] [-6.81] Short USD (λ USD ) 0.39 0.78 -0.39 [3.76] [22.96] [-8.88] Portfolio ξ H 0.97 0.95 Portfolio ξ L 0.98 1.00 Difference Mean 4.09 1.54 2.56 [1.70] [0.63] [1.09]
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Option-Implied Currency Risk Premia
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a closed-form expression for the ge
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We conduct a similar analysis for r
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Page 17 and 18: 2 Data and Model Calibration We cal
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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
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Page 51 and 52: Table I Calibrated Model Parameters
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