Nº 20-22: Dynamic Portfolio Allocation under Market Incompleteness and Wealth Effects

This paper develops a novel decomposition of optimal dynamic portfolio choice under flexible incomplete market models and the wealth-dependent HARA utility. The decomposition reveals the fundamental impacts of market incompleteness and wealth effect in portfolio allocation. With hedgeable interest rate risk, we can decompose the optimal portfolio under HARA utility into a pure CRRA optimal portfolio and a financing portfolio for the investor future subsistence requirements. In this case, the wealth growth rate is always higher for HARA investors with higher initial wealth levels, leading to increased wealth inequality. As an application of our decomposition, we solve the HARA optimal policy in closed-form under an incomplete market model with both stochastic interest rate and volatility. Using parameters calibrated from U.S. market data, we find that the wealth effect generates a procyclical pattern in investor stock positions and time-varying risk aversion levels in different market regimes. Moreover, we identify a novel “buy-high-sell-low” effect that may hurt the HARA investors with low initial wealth.