Blog - Investing Notes

September 8, 2009 - Serious Flaw with the "Highest Alpha Ever" Strategy?

A reader wrote:

"Unless I have misunderstood, there is a serious flaw in the research paper 'Why are Put Options So Expensive?' (reported in your 'Is 40% Per Month Shorting Index Puts a Fair Return?' and referenced in your 'The Strategy with the Highest Alpha Ever?').

"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.

For a live, out-of-sample test of allocating part of a portfolio to selling put options on a broad equity index, see Strategy Test (but the initial round of testing has too many moving parts). The current test rules are perhaps roughly comparable to the 5%-of-portfolio example above, but performed with index options (higher margin requirement/less leverage). The strategy has features intended to mitigate the loss side via: (1) using the turn-of-the-month effect to avoid a part of the month that historical samples suggest are unusually bearish; and, (2) employing a bias toward out-of-the-money opening positions.