ETG-ETL Portfolio Optimization

Abstract

Modern Portfolio Theory dates back to 1950s, when Markowitz proposed mean-variance portfolio optimization to construct portfolios. It provided a systematic approach to determine portfolio allocation when one is facing complicated risk structure that not only exists for individual assets but also across different assets. Since then there has been much research exploring better ways to quantify risk. In particular, asymmetric risk measures including the more recent downside risk measures. Here we use expected tail loss (ETL) as the risk measure which is a coherent risk measure, and define a reward measure, expected tail gain (ETG), to measure the upside return. We formulate the portfolio optimization problem using these two measures and developed an iterative algorithm to find its optimal solution.