A Two Period Model with Portfolio Choice: Understanding Results from Different Solution Methods

Using a stylized two period model we obtain portfolio solutions from two solution approaches that belong to the class of local approximation methods – the approach of Judd and Guu (2001, hereafter ’JG’) and the approach of Devereux and Sutherland (2010, 2011, hereafter ’DS’) – and compare them with the true portfolio solution. We parameterize the model to match mean, standard deviation, skewness and kurtosis of return data on aggregate MSCI stock market indices. The optimal equity holdings in the true solution depend on the size of uncertainty, and the precise form of this relationship is determined by the distributional properties of equity returns. While the DS method and the JG approach provide the same portfolio solution as the size of uncertainty goes to zero, else the two solutions can differ substantially. Because under the DS method portfolio holdings are never approximated in the direction of the size of uncertainty, even higher-order approximations lead to the (zero-order) constant solution in our example model. In contrast, the JG solution generally varies as the size of uncertainty changes, and already a second-order JG solution can account for effects of skewness and kurtosis of equity returns.