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 hyperbolic absolute risk aversion (HARA) utility. The decomposition reveals the fundamental impacts of market incompleteness and wealth effect in portfolio allocation. With hedgeable interest rate risk, we show that the optimal portfolio under HARA utility can be decomposed into a pure constant relative risk aversion optimal portfolio and a financing bond portfolio that matches the investor future subsistence requirements. In this case, the wealth growth rate is always higher for HARA investors with more initial wealth, leading to increased wealth inequality regardless of the market scenario. 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. Moreover, the wealth effect in investor utility and the increased risk premium in a stressed market combined lead to a novel “buy high, sell low” channel that may hurt HARA investors with low initial wealth.

Funding: The research of Y. Shen was supported by the Hong Kong University of Science and Technology [Grant B000-0172-R9281]. The research of C. Li was supported by the Guanghua School of Management, the Center for Statistical Science, the High-Performance Computing Platform, and the Key Laboratory of Mathematical Economics and Quantitative Finance (Ministry of Education) at Peking University as well as the National Natural Science Foundation of China [Grant 72173003].

Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results, are available at https://doi.org/10.1287/opre.2024.0976.