Abstract
The Sharpe Ratio (SR) is a well-known metric for risk-adjusted returns, and is commonly used in gauging the performance of an investment strategy. How to construct an optimal portfolio to maximize its SR is a problem that is frequently faced by many portfolio managers. However, the SR optimization problem is not trivial to solve, due to the highly nonlinear form of the SR function. The commonly used approach is to replicate the Markowitz efficient frontier numerically by solving a mean variance optimization problem multiple times, and then compare all the numerical solutions and select the one with the greatest SR. In this article we introduce a mathematical technique that allows us to solve the SR maximization problem directly, without the need of computing a discrete version of the efficient frontier. The new approach can pinpoint the optimal solution by one optimization call, and hence is more efficient and accurate than the efficient frontier approach. We will:
- Introduce the new approach with a geometric interpretation as well as an analytical derivation. The analytical technique presented herein is useful even beyond the SR optimization problem.
- Demonstrate the application of the method by solving a SR maximization problem for a 130/30 portfolio construction using the Lehman Brothers Portfolio Web Bench Optimizer, which is fully integrated with the new approach.
- Introduce the new approach with a geometric interpretation as well as an analytical derivation. The analytical technique presented herein is useful even beyond the SR optimization problem.
- Demonstrate the application of the method by solving a SR maximization problem for a 130/30 portfolio construction using the Lehman Brothers Portfolio Web Bench Optimizer, which is fully integrated with the new approach.
| Original language | English |
|---|---|
| Publisher | Lehman Brothers |
| Publication status | Published - 2008 |