Portfolio Benchmarking under Drawdown Constraint and Stochastic Sharpe Ratio

TL;DR

This paper develops approximation methods for portfolio optimization under drawdown constraints in markets with local stochastic volatility, highlighting the impact of stochastic volatility on optimal strategies.

Contribution

It introduces a coefficient expansion technique to approximate value functions and strategies in a complex stochastic volatility setting, which was not previously available.

Findings

Optimal strategies differ significantly between constant and stochastic volatility models.

Approximate value functions can be effectively computed using the proposed numerical methods.

Stochastic volatility influences the portfolio choices based on current volatility levels.

Abstract

We consider an investor who seeks to maximize her expected utility derived from her terminal wealth relative to the maximum performance achieved over a fixed time horizon, and under a portfolio drawdown constraint, in a market with local stochastic volatility (LSV). In the absence of closed-form formulas for the value function and optimal portfolio strategy, we obtain approximations for these quantities through the use of a coefficient expansion technique and nonlinear transformations. We utilize regularity properties of the risk tolerance function to numerically compute the estimates for our approximations. In order to achieve similar value functions, we illustrate that, compared to a constant volatility model, the investor must deploy a quite different portfolio strategy which depends on the current level of volatility in the stochastic volatility model.