Conditional strike prices of covered call and uncovered put strategies

Abstract

This article investigates the Stochastic Dominance (SD) of investment strategies which combine a long position in a stock index with a short position in options written on that index. Two main issues are analysed here: First, exercise prices are analysed which are conditioned on proxies of expected returns. Second, next to the well-known covered call strategies, the SD of uncovered put strategies is also investigated. Empirical analysis of strategies on the Dow Jones EURO STOXX 50 Index shows that covered call strategies dominate an index investment at the second and third degrees, while uncovered put strategies fail to do so. It can be observed that strategies with conditional exercise prices are stochastically dominant to strategies with unconditional exercise prices.

Keywords:

• covered call strategies
• uncovered put strategies
• conditional strike prices
• stochastic dominance

JEL Classification::

• G11
• G13

Notes

¹ For example, on 18 September 2006, STOXX Ltd. launched the Dow Jones EURO STOXX 50 BuyWrite Index (Stoxx, 2008a). Also in 2006, Deutsche Börse launched the DAXplus Covered Call Index. In the US, the S&P BuyWrite Index has been listed since 2003 (Feldman and Roy, 2005).

² Early studies which investigate the return of option strategies are those by Merton et al. (1978, 1982).

³ Alternatively, the number of options that are sold could be conditioned on the proxy for the expected return. Considering the example of Fig. 1 with μ(c) > μ(u), the number of call options then has to be reduced, while the number of put options has to be increased.

⁴ Additionally, the number of options that are sold (e.g. delta-hedging strategy) could also be varied. This choice, however, will not be investigated by this article.

⁵ The monthly volatility of the investigated index, DJ EURO STOXX 50, is about 6% per month over the sample period. Therefore, an exercise price of 3% above the current future price corresponds to approximately a half SD. Assuming a normal distribution for index returns implies, then, that the probability of a call option with an exercise price of 103% finishing in-the-money is about 30%. However, the results presented in the empirical section are robust to a choice of exercise prices different from 103%–100%–97% within a reasonable range.

⁶ See Levy (1992) for an overview of the SD approach.

⁷ Ederington and Guan (2002) derived the option smile from S&P 500 options for a maturity of between 2 and 6 weeks and various exercise prices. It is assumed that the smile effect of the S&P 500 options is similar to that of Dow Jones STOXX 50 options.