Portfolio optimization when expected stock returns are determined by exposure to risk

TL;DR

This paper proposes a modified Black-Scholes model with a new parametrization of stock return drifts, leading to a stable, high-performing portfolio strategy that outperforms traditional methods in empirical tests.

Contribution

It introduces a novel parametrization of drift rates in a Black-Scholes framework and derives a stable, out-of-sample optimal portfolio strategy with improved Sharpe ratios.

Findings

Portfolio weights are stable over time.

Strategy achieves higher Sharpe ratio than classical 1/n approach.

Out-of-sample application confirms robustness.

Abstract

It is widely recognized that when classical optimal strategies are applied with parameters estimated from data, the resulting portfolio weights are remarkably volatile and unstable over time. The predominant explanation for this is the difficulty of estimating expected returns accurately. In this paper, we modify the $n$ stock Black--Scholes model by introducing a new parametrization of the drift rates. We solve Markowitz' continuous time portfolio problem in this framework. The optimal portfolio weights correspond to keeping $1/n$ of the wealth invested in stocks in each of the $n$ Brownian motions. The strategy is applied out-of-sample to a large data set. The portfolio weights are stable over time and obtain a significantly higher Sharpe ratio than the classical $1/n$ strategy.