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Table 7 Second-stage regression—subsamples

From: The Swiss franc safety premium

\(r^{*}_{f,t+1}+E_{t}\left [\triangle e_{t+1}\right ]-r_{f,t+1}\) \(E_{t}\left [\triangle e_{t+1}\right ] = \triangle e_{t+1}\) \(E_{t}\left [\triangle e_{t+1}\right ] = 0 \) \(E_{t}\left [\triangle e_{t+1}\right ] = \widehat {E_{t}\left [\triangle e_{t+1}\right ]} \)
\( + \frac {1}{2} \widetilde {Var_{t}} \left (\triangle e_{t+1} \right)\) CHF Index EUR/CHF CHF Index EUR/CHF CHF Index EUR/CHF
Subperiod 1  
\(\widetilde {Cov_{t}} \left (r_{t+1}^{\omega }, \triangle e_{t+1} \right)\) −5.972 −7.086* 0.637*** 0.718** 4.260*** 2.482**
  [4.902] [4.538] [0.234] [0.365] [1.462] [1.230]
Cons 0.001 0.002* 0.002*** 0.002*** 0.001* 0.001***
  [0.002] [0.001] [0.000] [0.000] [0.001] [0.000]
J-statistic 3.745 2.804 5.887 4.561 6.225 4.632
p value 0.442 0.591 0.208 0.335 0.183 0.327
Subperiod 2  
\(\widetilde {Cov_{t}} \left (r_{t+1}^{\omega }, \triangle e_{t+1} \right)\) −0.101 −1.530 0.050 0.328** 2.610* 3.211***
  [3.789] [4.463] [0.198] [0.150] [1.881] [0.926]
Cons 0.000 0.000 0.001*** 0.001*** −0.001*** −0.001***
  [0.001] [0.001] [0.000] [0.000] [0.000] [0.000]
J-statistic 3.761 4.808 3.394 4.417 5.148 5.536
p value 0.439 0.308 0.494 0.353 0.272 0.237
  1. Notes: This table reports the results of the second-stage regression for the case of no time variation in the price of risk (see Eq. (13)). 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 first by the actual exchange rate change, then by zero, and finally by the fitted value of the zero stage regression. The regressors are a constant and the estimate of the conditional covariance between stock returns and exchange rate changes from the first stage regression. The set of instruments Z t 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. 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 model is estimated for each subsample separately. The first subsample (January 1990 to December 1998) consists of 107 observations and the second subsample (January 1999 to August 2011) consists of 152 observations. The standard errors are reported in square brackets
  2. ***, **, * denote significance levels of 1, 5, and 10%, respectively