Dynamic Portfolio Allocation Under Market Incompleteness and Wealth Effects

Dynamic Portfolio Allocation Under Market Incompleteness and Wealth Effects In the paper “Dynamic portfolio allocation under market incompleteness and wealth effects,” a novel decomposition of an optimal dynamic portfolio is developed under general incomplete-market models and the wealth-dependent hyperbolic absolute risk aversion (HARA) utility. It shows that with hedgeable interest rate risk, the optimal portfolio consists of two parts: a pure constant relative risk aversion optimal portfolio and a financing bond portfolio for investor future subsistence requirements. Under such a structure, the wealth growth rate is always higher for HARA investors with more initial wealth, leading to increased wealth inequality regardless of the underlying model dynamics and realized market scenario. Using the decomposition, the authors solve the HARA optimal policy in closed form under an incomplete-market model with both stochastic interest rate and volatility. The wealth effect in the optimal portfolio has interesting implications. It generates a procyclical pattern in investor stock positions and time-varying risk aversion levels as well as a “buy high, sell low” market timing effect that may hurt HARA investors with low initial wealth.