Dynamic Portfolio Selection Under Quantile Maximization

Although maximizing quantiles is intuitively appealing and has an axiomatic foundation, it is difficult to find the optimal portfolio strategy because of time inconsistency. Using an intrapersonal equilibrium approach and focusing on the class of time-varying affine strategies, we find that the only viable outcome is from the median maximization because for other quantiles, either the equilibrium does not exist or there is no investment in risky assets. We also prove that maximizing the median endogenizes the use of portfolio insurance. The calibration of the model uncovers a new empirical phenomenon: “portfolio share smile.” This paper was accepted by Giesecke Kay, finance. Funding: This research was supported by the General Research Fund of the Research Grants Council of Hong Kong SAR [Grant 14207620], Early Career Scheme of the Research Grants Council of Hong Kong SAR [Grant 25213424], the National Natural Science Foundation of China [Grant 12401622], and the Hong Kong Polytechnic University [Grant P0042708]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.03182 .