We're talking (briefly) about option payoffs in class this week. So, I was excited when I came across this piece titled "Why are Put Options So Expensive?", by Oleg Bondarenko of the University if Illinois at Chicago. In it, he provides some very interesting figures. First off, the abstract:
This paper studies the "overpriced puts puzzle" - the finding that historical prices of the S&P 500 put options have been too high and incompatible with the canonical asset-pricing models, such as CAPM and Rubinstein (1976) model. Simple trading strategies that involve selling at-the-money and out-of-the-money puts would have earned extraordinary profits. To investigate whether put returns could be rationalized by another, possibly nonstandard equilibrium model, we implement a new methodology. The methodology is "model-free" in the sense that it requires no parametric assumptions on investors' preferences. Furthermore, the methodology can be applied even when the sample is affected by certain selection biases (such as the Peso problem) and when investors' beliefs are incorrect.
We find that no model within a fairly broad class of models can possibly explain the put anomaly.
Writing put options should make consistent small profits,. but with a chance that the option writer will occasionally get really hosed. But by Bondareknko's analysis, markets consistently overvalue at the money [ATM] and out of the money options [OTM] that are "close" (i.e. within 6% of ATM). In fact, writing options seems to result in average returns of 39% per month, with returns for deep OTM options of almost double that. That's right - almost 40% per month.
So, how likely is the "hosing"? Does this merely reflect the risk of large losses? By his estimates, there would have to be a meltdown like the one in October 1987 1.3 times a year for the option writer to lose money.
So, why are put options so apparently overvalued? There are at least two possible explanations (other than something really funky/wrong with the data): one is that investors systematically overestimate the chance or severity of large market declines. The other is that option buyers have a utility function that is extremely risk averse. In either case, there's apparently an excess demand for insurance that option writers can benefit from (if they're willing to bear the risk).