On the Optimality of Long–Short Strategies

We consider the optimality of portfolios not subject to short-selling constraints and derive conditions that a universe of securities must satisfy for an optimal active portfolio to be dollar neutral or beta neutral. We find that following the common practice of constraining long–short portfolios to have zero net holdings or zero betas is generally suboptimal. Only under specific unlikely conditions will such constrained portfolios optimize an investor's utility function. We also derive precise formulas for optimally equitizing an active long–short portfolio using exposure to a benchmark security. The relative sizes of the active and benchmark exposures depend on the investor's desired residual risk relative to the residual risk of a typical portfolio and on the expected risk-adjusted excess return of a minimum-variance active portfolio. We demonstrate that optimal portfolios demand the use of integrated optimizations.