Portfolio Performance and Risk Penalty Measurement with Differential Return

Abstract

In very recent times, some investment companies are using the Differential Return Approach to measure the performance of various individual risky assets as well as portfolio performance compared to a benchmark return. This approach of differential return was proposed by Simpson (2014). The differential return of a portfolio is simply the difference between its risk-adjusted return and that of another portfolio known as the benchmark/reference return. Risk-adjusted excess return of a portfolio can be obtained by dividing the observed return by its level of risk, such as . The equation proposed by Simpson to derive this risk-adjusted excess return can be based on Treynor Index or Sharpe Index (or even Jenson depending on how an investor wants to measure the risk associated with an asset or a portfolio, denoted by . However, the formulation of Simpson subtract risk-free rate which is not on the basis of any mathematical logic. In addition, it does not take into account the efficiency of the differential returns. The present study elaborates the formulation of Simpson and then adjust the differential return by using relative risks of the portfolio and the benchmark return. Finally the study using the relative risk ratio determines the equilibrium efficient differential return of a portfolio compared to a benchmark return.