Is 40% Per Month Shorting Index Puts a Fair Return?

September 10, 2007 • Posted in Equity Options

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 futures for 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.

A reader wrote:

“Unless I have misunderstood, there is a serious flaw in this study.

“The paper assumes that a put seller’s capital requirement is equal to the initial cost of the put. However, a put seller has a much larger capital requirement, assuming the seller of the puts plans to continue selling puts after one of the infrequent but very large losses. Specifically, any put seller after October 1987 would know there is a possibility the S&P 500 Index could loose 18% of its value in a month and so must maintain at least 18% of the value of the underlying in cash reserves. Thus, based upon recent prices for puts on S&P Depository Receipts (SPY), the minimum capital requirement of the put seller reduces the 39%/month average profit to about 6%/month.

“An optimistic put seller who wants to continue selling puts after a major market crash might set the required capital reserve at 2x the worst payout or 38% of the underlying, which reduces average monthly return to about 3%. A more conservative put seller might go with 3x the worst payout which implies a monthly return of just under 2%.

“More generally, the paper assumes that there is a remarkable anomaly involving why put buyers are willing to lose 40%/month and why more traders do not become put sellers to obtain 40%/month profit, and thereby increase competition which would reduce profits from writing such puts to more reasonable levels. These two puzzles exist only as long as one assumes the buyers and the sellers of the puts have their eyes on the PREMIUM which changes hands. However, my view is that both the sellers and buyers of the puts have their eyes on the rare but very real possibility that a very large sum of money might change changes if the underlying index experiences a significant decline during the life of the put contracts. Once one considers the cash reserves necessary to meet margin calls in such rare but real cases, the amount of monthly profit drops significantly in percentage terms and no longer appears irrational. In fact it appears rather normal.

“Even if the anomaly truly exists and could be profitably exploited, the profit potential is relatively small, at least for private investors. Let’s consider an example in which an investor devotes 5% of his total portfolio to selling at-the-money put options on S&P 500 Index futures via the conservative scenario above, earning about 2%/month on that 5%. The net impact at the portfolio level would be 2% of 5% or about 0. 1%/month (ignoring interest earned on the 5% of the portfolio sitting in cash as a reserve to meet whatever margin calls might come during the life of the puts). I don’t see the point in doing any more due diligence on this put writing strategy.”

You have made a good argument that the methodology in the referenced study is careless with portfolio-level calculations, despite the sanguine assertion in the paper (page 12) that:

“Because the magnitude of the mispricing of puts is so large, introducing reasonable market imperfections (trading costs, bid-ask spreads, price impact, costs associated with maintaining the margin requirements, etc.) have a relatively small effect on the average returns.”

You may be too hard on the 5%-of-portfolio put-selling alternative, for which you assume that the 5% part of the portfolio allocated to put-selling must be a self-contained portfolio within a portfolio (i.e., it must stand alone and never draw on the rest of the portfolio). Applying instead the constraint that the initial margin requirement for the puts as you sell them each month is 5% of the portfolio, the average return to the portfolio would be substantial (however, the portfolio would be exposed to fairly large, but readily survivable, drawdowns in the event of an equity market crash).

Perhaps the most reasonable way to view these transactions is that put sellers are selling insurance policies, and put buyers are buying them. A premium is reasonable for the service offered by the sellers. Points of interest/caution are:

  • Results for put sellers would probably be especially good (bad) when transitioning from high (low) volatility market states to low (high) volatility market states.
  • Going out of the money boosts the average percentage of premium retained at expiration, but could affect ratio of premium to margin requirement.
  • Despite inclusion of 1987, the test period of the original study may be biased in favor of selling puts (the stock market more bullish than should be expected in the future).
  • The distribution of returns from put writing may be wild; hence, normal statistics (mean monthly return and standard deviation of monthly returns) are inherently unreliable measures of expectations.

Based on the body of research on options premiums and corroboration from asymmetric fear-greed outcomes derived from psychological experiments, it seems there might be a systematically exploitable edge.

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