Should an investor buy and hold a stock index? Hold the index plus a put on the index (portfolio insurance)? Or hold the index plus a short position in a call on the index (a covered write)? Which strategy will be the most efficient in terms of the tradeoff between risk and return? Which will offer the highest annual return? The highest long-term return?

Plots of the efficient frontiers of these strategies indicate that the covered write will dominate both the index and portfolio insurance. Yet portfolio insurance provides participation in up markets and protection against down markets, whereas covered writing provides participation in down markets while losing out relative to stocks in up markets. Obviously mean-variance analysis alone cannot make appropriate distinctions between these strategies.

Furthermore, the relative performances of the strategies as measured by their Sharpe ratios depend critically on the exercise prices of their options. As the natural habitat of buyers of portfolio insurance differs from that of covered writers, it is impossible to say which strategy will dominate the other when exercise price is taken into consideration.

Similar conclusions emerge from analyses of the strategies’ compound annual returns and long-term returns. Neither portfolio insurance nor covered writing dominates the other strategy when exercise price is a consideration. Furthermore, if only return is considered, the stock index will dominate either of the other strategies. The existence of portfolio insurance and covered writing implies that investors are concerned with more than long-term or compound annual return.