Optimal omega-ratio portfolio performance constrained by tracking error

Abstract

The mean-variance framework coupled with the Sharpe ratio identifies optimal portfolios under the passive investment style. Optimal portfolio identification under active investment approaches, where performance is measured relative to a benchmark, is less well-known. Active portfolios subject to tracking error (TE) constraints lie on distorted elliptical frontiers in return/risk space. Identifying optimal active portfolios, however defined, have only recently begun to be explored. The Ω – ratio considers both down and upside portfolio potential. Recent work has established a technique to determine optimal Ω – ratio portfolios under the passive investment approach. The authors apply the identification of optimal Ω – ratio portfolios to the active arena (i.e., to portfolios constrained by a TE) and find that while passive managers should always invest in maximum Ω – ratio portfolios, active managers should first establish market conditions (which determine the sign of the main axis slope of the constant TE frontier). Maximum Sharpe ratio portfolios should be engaged when this slope is > 0 and maximum Ω – ratios when < 0.

Is the omega ratio a good portfolio optimization criterion?

“…The Omega ratio is used in the same way for passive portfolio management as for active portfolio management. Gunning & Van (2020) use the volatility of the return spread (tracking error, i.e., portfolio return minus target return) to measure market conditions and to be able to restrict portfolio construction and include short sales in their strategy. Another use is the evaluation of portfolio performance for specific investor profiles.…”