Another Look at Portfolio Optimization under Tracking-Error Constraints

Research has shown that adding constraints to total portfolio volatility can substantially improve the performance of managed portfolios. Although other work has considered constant tracking-error volatility frontiers, in this study tracking error was allowed to vary but the risk aversion was fixed. The resulting optimal portfolios have several desirable properties.Today, the use of benchmark portfolios to evaluate the relative performance of portfolio managers is common practice in the financial management industry. This setup allows the investor to evaluate the added value in line with the risks taken. The relevant concept of risk is the relative risk as defined by the tracking-error volatility (TEV).The problem of minimizing the volatility of tracking error was originally solved in 1992. The optimal portfolios obtained had several undesirable properties, however, and introducing an additional constraint on the beta of the portfolio was suggested.In 2003, the problem was again tackled, this time in a study that pointed out that constant-TEV portfolios are described by an ellipse. 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 article looks at the problem from another angle. Instead of considering constant-TEV frontiers, the author allowed tracking error to vary but fixed the risk aversion. He found that the resulting optimal portfolios have several desirable properties.