Analyzing Variance Bounds of the Market Pricing Kernel

Abstract

The empirical analysis of the variance bounds for the market pricing kernel, i.e. of the bounds for the relationship between the first and the second unconditional moment of the market pricing kernel, covers the period 1968 to 1994 and proceeds in two steps. First, in section 7.1 the variance bounds are estimated employing different time series of asset returns. The sensitivity of the bounds with respect to changes in (1) the underlying set of assets, (2) the method of return calculation, (3) the taxation scenario applied, and (4) the length of the time intervals is analyzed. These analyses provide insights into the information content of different asset return data sets for testing parametric models of the market pricing kernel. Second, in section 7.2 different parametric models of the market pricing kernel are evaluated using the estimated variance bounds, i.e. the implications of the estimated variance bounds for the parameters of the parametric models of the market pricing kernel are analyzed. The investigated parametric models are those derived from the consumption-based asset pricing model alternatively assuming time-additive expected utility with constant relative risk aversion, time-additive expected logarithmic utility and recursive non-expected utility. Notice that the purpose of this analysis is to visualize the models’ capability to jointly price different assets and to illustrate how this capability is affected by changes in the models’ parameters but not to formally test the parametric models of the market pricing kernel. For formal tests sampling errors in the variance bounds and the means and standard deviations of the parametrized market pricing kernel must be considered in addition. But, as discussed in section 3.3.3, even then the variance bound approach is an unsatisfactory tool for formally testing parametrized market pricing kernels.