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1 January 1985 Financial Analysts Journal Volume 41, Issue 1

Problems in Evaluating the Performance of Portfolios with Options

  1. Richard Bookstaber
  2. Roger G. Clarke

As call options are written on a stock portfolio, the portfolio’s return distribution shifts to the right, reflecting the receipt of premiums from writing the calls; the portfolio’s upside return potential, however, becomes more limited as increasing percentages of the stock become callable. The addition of protective puts shifts a portfolio’s return distribution to the left, reflecting the cost of buying the options, but reduces undesirable downside risk.

A portfolio with written calls will appear to outperform a stock-only portfolio in bear markets, as option premiums more than compensate for poor overall performance. Written calls will, however, limit the optioned portfolio’s ability to respond to rising market returns, and the portfolio will appear inferior to a stock-only portfolio when market returns are high. Puts will have substantially the opposite effects.

In order to evaluate optioned portfolios, it is necessary to determine their return distributions given a realized value for the market return and to establish probability ranges that distinguish significant departures from expected performance. In general, the probability ranges for portfolios with either calls or puts will be tighter, or closer to the mean, than those for the underlying stock-only portfolio. The right-hand bound marking superior performance for a portfolio with written calls will be closer to the mean than the left-hand bound marking significant inferior performance. The reverse will hold for portfolios with protective puts.

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