Portfolio optimization based on the Treynor ratio

Abstract

Purpose and subject of research

The aim of the study is to develop a model of portfolio optimization allowance Traynor (ratio of return and systematic risk) and a corresponding algorithm.

Research methodology

The approach optimizing the ratio of return and risk, which was first proposed by Markowitz, but in this article instead of the full risk of the criterion of optimization and utility function for the Beta. The problem is solved by the proposed algorithm quadratic programming.

Value results

This study is based on the efficient market hypothesis, and that the stock market is developed and liquid. Most research in this area focused on optimizing the full risk and, in this paper we consider the systematic risk, this risk is rewarded by investors in developed markets. Optimization of the norm Traynor can be used to manage a well-diversified portfolio that is usually relevant for institutional investors.

Conclusions

The optimal portfolio in the area of return-beta are on convex polygons, as opposed to parabolic boundary effective in-plane yield risk. But when a large number of assets in the portfolio at a rate Traynor optimal portfolio is close to the optimum allowance Sharpe.