By Professor George Skiadopoulos, Queen Mary University of London and University of Piraeus
A common finding when it comes to options trading is that selling index put option contracts (such as those written on the S&P 500) tends to offer average returns and Sharpe ratios which seem to be excessive when compared to equities.
Academic literature has well documented that selling index put options yields high average returns. This is also well known among practitioners: these trades have been highly profitable, except in instances where sales coincide with spikes in volatility, such as when Lehman Brothers crashed, or in the initial heat of the pandemic in March 2020.
This raises the question whether seemingly high average put option returns are abnormal, or they can be justified when taking into account the risks of these option strategies. The answer to this long-standing question is not trivial: one needs to account for all possible risks, and measure them accurately. This task becomes more difficult in the case of options compared to equities, because option returns are related to risks in a non-linear fashion. For instance, option price is not a linear function of the underlying put price. The price of a put option on the S&P 500 increases when the S&P 500 price goes down, yet the relationship is not linear.
This has been a puzzle for academics and practitioners for years. To date, the economic sources driving this abnormal behavior have remained relatively unexplored; until now.
In the paper, “Learning and Index Option Returns,” researchers Alejandro Bernales from University of Chile; Gonzalo Cortazar and Luka Salamunic, both from Pontificia Universidad Católica de Chile, and I, George Skiadopoulos from Queen Mary University of London and University of Piraeus, offer a new economic explanation for what appear to be factors contributing to perceived high abnormal risk/return performance in selling put index option contracts.
We provide a new option pricing model that incorporates learning for economic fundamentals. In our model, the agent learns about how the average growth rate of dividends evolves over time, as the growth rate of dividends may change abruptly from time to time due to the occurrence of shocks. Our model extends the Black-Scholes model to explain the observed empirical patterns in the average returns of short index put options. The proposed economic mechanism encompasses risks which affect option returns, and it also takes into account the non-linear relation of option returns and their risk factors. Learning is modeled in a Bayesian setting, where the investor formulates an initial belief about what the expected dividend growth may be, and then he/she updates her initial belief as he/she receives more information.
To verify that our model can generate the empirically observed patterns in average short index put options, we first computed the average returns for index put options using actual option data on the S&P 500 across different strikes. To this end, we used IvyDB US Optionmetrics.
While there are many sources one can use when it comes to performing academic research, we, have done considerable work with OptionMetrics’ IvyDB US database, and it appears to be the most commonly used database for academic research on U.S. index and stock option markets over the past two decades.
We, then, compute returns for the same set of strikes with the learning model. Finally, we compare the calculated average returns from the learning model to the average returns from the historical data.
What we find is that the patterns calculated with our learning model are similar to the ones obtained from the historical data from OptionMetrics. This showcases that the empirically observed patterns in short index option returns can be generated by learning about fundamentals.
What should institutional investors take from this research? How should they apply it to their work today?
The main implication of this study is that participants in option markets, including traders, institutional investors, and policy makers, should be cautious in asserting that specific option strategies provide abnormal returns. To make this claim, one needs to take all risks and non-linearities into account. One way to do this is with the learning model.
To see the full paper, please visit https://doi.org/10.1080/07350015.2018.1505629.
George Skiadopoulos is Professor of Finance in the School of Economics and Finance, Queen Mary University of London, and in the Department of Banking and Financial Management, University of Piraeus. He is also Director of the Institute of Finance and Financial Regulation (www.iffr.gr) and an Honorary Senior Visiting Fellow at Business School, City University of London.