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.
