Thinking About Theta: An Analysis of Time Decay, Early Unwind and Closeout Feedback Effects

Abstract

Near-the-money options experience a rapid decline in time value over the weeks leading up to the expiry date. A possible strategy to alleviate the impact of the time decay effect is to unwind the hedge prior to expiry. However, appreciable time value is present for a reason: it is an indication that the final expiry value the option is uncertain and that there is a chance that the option could increase further in value. In this work, historical data is examined in order to determine whether or not a South African equity index exhibits any abnormal behaviour prior to expiry that would affect one’s view on the likelihood of a hedge expiring in-the-money. We present the results of analyses for two types of expiry-related effect in the local market, namely abnormal returns for periods immediately prior to expiry and price clustering where the underlying exhibits a higher probability of closing near a strike price on an expiry date. We also discuss the historical performance of a strategy aimed at reducing exposure to time decay in a systematic manner in which a derivative strategy is rolled well before the expiry date. It is shown that for the period analysed, an investor who wished to roll a hedge every 3 months achieved an appreciable increase in realised return for a moderate increase in risk by rolling a longer term option every 3 months compared to holding a 3 month option for the full term.