Optimization of covered calls under uncertainty
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Optimization of covered calls under uncertainty Mauricio Diaz1,2 · Roy H. Kwon1 Received: 3 August 2019 / Revised: 15 February 2020 / Accepted: 16 February 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract We present a two-stage stochastic program with recourse to construct covered call portfolios. To maximize the expected utility of a covered call portfolio, the model selects equity positions and call option overwriting weights for varying strike prices and expiry dates. Since the model has linear constraints and risk-averse utility functions are concave, the optimization problem is convex. The model is tested using 67 U.S. large-cap equities and optimizing the quadratic, negative exponential, and power utility functions. The expected utility is modeled as the average utility of the portfolio in a number of scenarios. Scenarios are first generated randomly then moment matching is employed, allowing the model to produce high quality results with a relatively small number of scenarios. To improve solution times we use a progressive hedging decomposition. Keywords Covered call · Options · Portfolio optimization · Utility optimization · Stochastic programming · Progressive hedging
1 Introduction A covered call or buy-write strategy is formed by selling call options while holding units of the option’s underlying asset. The short call produces a liability which decreases returns in up-side cases while the premium from selling the call provides a buffer for losses. Thus the short call position helps to regulate the return of the underlying equity, and many authors note improved risk-return efficiency using covered calls versus the underlying long position. Whaley (2002), Feldman and Roy (2004), and Callan Associates (2006) found that the Chicago Board * Roy H. Kwon [email protected] Mauricio Diaz [email protected] 1
Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto, ON M5S 3G8, Canada
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IHS Markit, 365 Bloor St. E. Suite 801, Toronto, ON M4W 3L4, Canada
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M. Diaz, R. H. Kwon
Options Exchange (CBOE) S&P 500 BuyWrite Index had higher risk-adjusted returns than a simple long position in the S&P 500. Board et al. (2000) and McIntyre and Jackson (2007) reported similarly for covered call strategies formed using the Financial Times Stock Exchange (FTSE) 100 Index. Kapadia and Szado (2007) found that a covered call overlay improved the risk-return efficiency of the Russell 2000 Index. Covered calls may also be beneficial purely from a return perspective. Figelman (2008) and Diaz and Kwon (2017) showed that the expected return of a covered call strategy is related to the call price less the expected option payoff computed under the real-world probability measure. The option price is dictated by the market, but estimating the expected payoff under the real world measure is highly subjective and ultimately depends upon an investor’s world view. We must also consider the existence of the vo
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