Optimal Dynamic Portfolio with Mean-CVaR Criterion

TL;DR

This paper develops an analytical solution for dynamic portfolio optimization using the Mean-CVaR criterion, revealing that optimal portfolios can take three values under certain constraints, unlike traditional binary solutions.

Contribution

It introduces a novel analytical solution for the Mean-CVaR portfolio problem in a dynamic setting, extending beyond Neyman-Pearson binary solutions.

Findings

Optimal portfolios can take three values with an upper bound constraint.

Without an upper bound, the optimal portfolio does not exist, but a three-level sub-optimal solution is possible.

The solution generalizes the Neyman-Pearson type binary solution to a three-value solution.

Abstract

Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) are popular risk measures from academic, industrial and regulatory perspectives. The problem of minimizing CVaR is theoretically known to be of Neyman-Pearson type binary solution. We add a constraint on expected return to investigate the Mean-CVaR portfolio selection problem in a dynamic setting: the investor is faced with a Markowitz type of risk reward problem at final horizon where variance as a measure of risk is replaced by CVaR. Based on the complete market assumption, we give an analytical solution in general. The novelty of our solution is that it is no longer Neyman-Pearson type where the final optimal portfolio takes only two values. Instead, in the case where the portfolio value is required to be bounded from above, the optimal solution takes three values; while in the case where there is no upper bound, the optimal investment portfolio does not exist, though a three-level portfolio still provides a sub-optimal solution.