Strategic asset allocation with generalized homothetic robust Epstein-Zin utility under a quadratic model

This study proposes generalized homothetic robust Epstein-Zin (GHREZ) utility in which the coefficient of relative ambiguity aversion in homothetic the robust Epstein-Zin (HREZ) utility is generalized to a positive-definite “relative ambiguity aversion matrix.” We analyze a robust consumption–investment problem with the GHREZ utility under a quadratic security market model. We demonstrate that the volatility of the optimal robust portfolio can be expressed as a weighted average of the market price of risk and the “investor hedging value of intertemporal uncertainty.” We derive an approximate optimal robust portfolio and quantitatively analyze the relationship between the approximate optimal robust portfolios and relative ambiguity aversion matrices. Numerical analysis reveals that as deviations from the relative ambiguity aversion matrix under the HREZ utility increase, deviations from the approximate optimal asset allocation under the HREZ utility increase, and this sensitivity is significant. This finding suggests that the GHREZ utility is promising for solving the equity home bias puzzle.