Index Options Realized Returns Distributions from Passive Investment Strategies

Abstract

Few papers provide research about options returns, and the few available are focused in the analysis from the perspective of the long side of the option contract, i.e. the buyer that pays the price and her expected and realized option return.

The main point of our research work is to provide a simple metric to analyze option returns from the perspective of the short side of the contract, the seller, where at the time of the sale of naked options, capital is committed in the form of a guarantee or margin (similar to net worth). We estimate realized returns from passive investment strategies, by assuming puts and calls are kept until the expiration of the maturity.

To that purpose we develop an appropriate algorithm which is applied on real historic data. Our result is a distribution of realized option returns (ex-ante prices and ex-post cash flows whether the options end up in or out-of-the-money with respect to margin requirements) for the seller point of view, as if the seller was an insurer seeking to calculate how profitable the insurance activity is.

From the results we can see that selling puts is more profitable than selling calls, without adjusting for the return of the underlying asset and for the risk free rate of return, something in line with what was expected, but we also find that the risk is approximately the same. We also find that time tends to increase the realized returns, measured everything on annual basis.

Keywords: Ex post returns, distribution, realized returns, option pricing

JEL Classification: C1, C3, N2, G11