Another Look at Portfolio Optimization under Tracking-Error Constraints

Abstract

Today, the use of a benchmark portfolio is common practice in the financial management industry. This setup allows the investor to evaluate the added value in line with the risks undertaken. But the relevant concept of risk is relative risk as defined by tracking-error volatility. The problem of minimizing the volatility of tracking error was originally solved by Roll (1992). He noticed that the optimal portfolios obtained have several undesirable properties and then suggested introducing an additional constraint on the beta of the portfolio. More recently, Jorion (2003) elegantly tackled this problem again, pointing out that constant-TEV portfolios are described by an ellipse. He showed that because of the flat shape of this ellipse, adding a constraint on total portfolio volatility can substantially improve the performance of the managed portfolio. This paper looks at the problem from another angle. Instead of considering constant TEV frontiers as Jorion does, we allow tracking error to vary but we fix the risk aversion. It is shown that the resulting optimal portfolios have several desirable properties.