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Table 8 Second-stage regression—time-varying price of risk

From: The Swiss franc safety premium

\(r^{*}_{f,t+1}+\widehat {E_{t}\left [\triangle e_{t+1}\right ]}-r_{f,t+1}\) All T<1999 T≥1999
\( + \frac {1}{2} \widetilde {Var_{t}} \left (\triangle e_{t+1} \right)\) USD Index CHF Index EUR/CHF CHF Index EUR/CHF CHF Index EUR/CHF
\(\widetilde {Cov_{t}} \left (r_{t+1}^{\omega }, \triangle e_{t+1} \right)\) 238.052* −69.980 −111.617 −82.002 −55.257 −434.596* −33.416
  [155.262] [103.549] [110.291] [112.052] [108.330] [290.049] [88.693]
\(\widetilde {Cov_{t}} \left (r_{t+1}^{\omega }, \triangle e_{t+1} \right)*{dp}_{t}\) 58.169* −12.174 −25.785 −23.436 −14.114 −123.582* −8.220
  [37.989] [23.571] [24.536] [26.110] [23.680] [79.216] [23.181]
\(\widetilde {Cov_{t}} \left (r_{t+1}^{\omega }, \triangle e_{t+1} \right)*d.{ys}_{t}\) −1245.245 −1533.296 −2908.650* 1235.988 3613.389** −6344.461* −832.865
  [1677.153] [3471.034] [2199.215] [1388.052] [1660.386] [4052.069] [905.723]
\(\widetilde {Cov_{t}} \left (r_{t+1}^{\omega }, \triangle e_{t+1} \right)*d.r_{f,t}\) −1727.834* −4939.896* −2991.115 −2342.645 5548.407*** −4157.170 94.303
  [1283.600] [3510.700] [3678.825] [2073.427] [1957.128] [3612.278] [967.194]
\(\widetilde {Cov_{t}} \left (r_{t+1}^{\omega }, \triangle e_{t+1} \right)* baa\mathrm {\_}{aaa}_{t}\) −1776.649* 866.314 698.838 −2345.300 784.905 −382.272 202.512
  [1188.008] [2014.862] [1490.346] [2138.844] [2459.814] [1902.112] [556.533]
Cons 0.001 0.002 −0.000 0.002*** 0.002*** −0.008** −0.001
  [0.001] [0.002] [0.001] [0.001] [0.001] [0.004] [0.001]
J-statistic 1.142 4.532 3.373 4.474 2.480 3.932 5.919
p value (J-stat.) 0.767 0.209 0.338 0.215 0.479 0.269 0.116
χ2-statistic 5.194 4.624 7.656 9.964 15.077 2.881 5.603
p value (χ2-stat.) 0.268 0.328 0.105 0.041 0.005 0.578 0.231
  1. Notes: This table reports the results of the second-stage regression allowing for time variation in the price of risk. The dependent variables are the USD and CHF safety premium, respectively, defined as the expected excess return of investing in the foreign risk-free asset by shorting the home risk-free asset. The expected exchange rate change used to calculate this expected excess return is proxied by the fitted value of the zero stage regression. The regressors are a constant, the estimate of the conditional covariance between stock returns and exchange rate changes from the first stage regression, as well as four terms where the conditional covariance is interacted with the dividend price ratio, the yield spread between long- and short-term bonds, the change in the home risk free interest rate and the yield difference between BAA- and AAA-rated bonds. The set of instruments consists of a constant, the dividend-price ratio, the lagged equity return, plus a measure for the lagged equity return variance, exchange rate return variance, and their covariance as well as the yield spread, the change in the home risk free interest rate and the yield difference, which are included for technical reasons. The second-stage regression is estimated jointly with the zero stage regression by GMM which allows the standard errors of the second-stage regression to incorporate not only the uncertainty deriving from the first-stage regression, but also the one from the zero stage regression. The standard errors are based on the Newey-West estimate of the covariance matrix with maximum lag order set equal to T1/2. The J-statistic (Hansen 1982) plus the according p value are reported for the null hypothesis that the model is well-specified and the moment conditions do hold. The Wald χ2 test plus the according p value are reported for the null hypothesis that all four coefficients on the interaction terms are jointly equal to zero. The number of observations is 259 for the full sample, 107 for the first subsample and 152 for the second subsample. The standard errors are reported in square brackets
  2. ***, **, * denote significance levels of 1, 5, and 10%, respectively