Learning and Portfolio Decisions for HARA Investors

TL;DR

This paper derives explicit optimal investment strategies for HARA investors facing an unobservable market risk, analyzing how learning influences portfolio choices and hedging demands.

Contribution

It provides explicit formulas for optimal portfolios under partial information and compares them with myopic policies, highlighting the impact of learning and risk tolerance.

Findings

Portfolio ratio increases with risk tolerance for constant sign market risk.

Partial observation portfolios differ significantly from myopic ones based on risk tolerance.

Learning about market risk induces specific hedging demands.

Abstract

We maximize the expected utility from terminal wealth for an HARA investor when the market price of risk is an unobservable random variable. We compute the optimal portfolio explicitly and explore the effects of learning by comparing it with the corresponding myopic policy. In particular, we show that, for a market price of risk constant in sign, the ratio between the portfolio under partial observation and its myopic counterpart increases with respect to risk tolerance. As a consequence, the absolute value of the partial observation case is larger (smaller) than the myopic one if the investor is more (less) risk tolerant than the logarithmic investor. Moreover, our explicit computations enable to study in details the so called hedging demand induced by learning about market price of risk.