Blog - Investing Notes

September 10, 2007 - Is 40% Per Month Shorting Index Puts a Fair Return?

Selling put options, with limited upside and potentially very large downside, seems very risky. Are actual returns from selling puts commensurate with the risk? In the May 2004 version of his paper entitled "Why are Put Options So Expensive?", Oleg Bondarenko confirms large returns for shorting puts options on a broad market index and investigates whether these large returns: (1) represent normal risk premiums; (2) are reasonably priced protection against market crashes; or, (3) indicate incorrect investor beliefs about the probability of negative market returns (crashes). Using a flexible testing methodology and daily price data for put options on S&P 500 index futures during 8/87-12/00, he concludes that:

• Selling put options makes a small profit most of the time (when markets are steady or rising), but takes a big loss once in a while (when markets crash).
• Systematically selling one-month-to-expiration, unhedged index puts generates extraordinary profits: 39% (95%) per month for at-the-money (deep out-of-the-money) puts.
• The Jensen's alpha for selling at-the-money index puts is a highly significant 23% per month. Other widely used methods of risk adjustment also indicate that put prices are very high.
• Buyers of S&P 500 index futures put options transferred $18 billion of wealth to sellers over the studied period.
• For buyers of at-the-money puts to break even, October 1987-like crashes would have to occur 1.3 times per year.
• No reasonable range of parameters supports any of the alternate explanations for the large return for shorting index put options.

The following chart, taken from the paper, shows the level of the S&P 500 index and the annualized one-month at-the-money implied volatility over the sample period. It also shows the average monthly returns for one-month-to-expiration S&P 500 index futures put options that are roughly 4% out-of-the-money (black bars), 2% out-of-the-money, at-the-money, 2% in-the-money and 4% in-the-money (white bars) over four subperiods: 8/87–6/90, 7/90–12/93, 1/94–6/97 and 7/97–12/00. The worst subperiod for selling puts is the first one, which includes the October 1987 market crash. However, even for that subperiod, selling puts yields average monthly returns of 12% to 27%. For the next three subperiods, average returns for selling puts are much higher, particularly for the strong stock markets of the second and third subperiods.

In summary, investors are willing to pay very high premiums, perhaps irrationally high, to insure against large losses in their stock portfolios. Sellers of this insurance can earn high average returns.

These results seem counter to the black swan investing approach outlined by Nassim Taleb in Fooled by Randomness (see our blog entry of 9/26/05).

For related research, see Blog Synthesis: Equity Options.