Options Portfolio Selection with Position Limits

This paper examines the performance from 1996 to 2020 of mean-variance efficient portfolios of monthly options with all available strikes on each of the S&P 500, Nasdaq 100, and Dow Jones indexes, using a constrained optimization approach that incorporates position limits, transaction costs, and volatility persistence. The Sharpe ratios of index-neutral strategies is between one and two for the S&P 500 and Nasdaq 100, but less than half for the Dow Jones. Constraining portfolios to be solvent on all past index' returns reduces Sharpe ratios by a third in the S&P 500 and Nasdaq 100 and by two thirds in the Dow Jones. All strategies suffer significant losses from the coronavirus shock of 2020, underscoring their vulnerability to rare events.