Portfolio Selection with Return Predictability and Periodically Observable Predictive Variables

Abstract

We consider the optimal portfolio selection problem for a constant relative risk aversion (CRRA) investor who derives utility from his terminal wealth. The stock returns are predictable, but the predictive variables are only periodically observable with noise. We obtain the investor's value function in an explicit form. The theoretical results are then used to study an empirical model after calibration. We show that lack of continuous or precise observation of the predictive variables has a large impact on the optimal trading strategy. We demonstrate how information value changes with risk aversion, investment horizon, observation error volatility and other parameters. In addition, we find that although the benefit of incorporating predictability is significantly reduced due to the periodic and noisy observation, the cost of ignoring predictability is still substantial.