Optim Lett DOI 10.1007/s11590-016-1083-8 ORIGINAL PAPER Optimization of covered call strategies Mauricio Diaz 1,2 · Roy H. Kwon 1 Received: 13 October 2015 / Accepted: 14 September 2016 © Springer-Verlag Berlin Heidelberg 2016 Abstract We present a risk-return optimization framework to select strike prices and quantities of call options to sell in a covered call strategy. Covered calls of a general form are considered where call options with different strike prices can be sold simul- taneously. Tractable formulations are developed using variance, semivariance, VaR, and CVaR as risk measures. Sample expected return and sample risk are formulated by simulating the price of the underlying asset. We use option market price data to perform the optimization and analyze the structure of optimal covered call portfolios using the S&P 500 as the underlying. The optimal solution is shown to be directly linked to the options’ call risk premiums. We find that from a risk-return perspective it is often optimal to simultaneously sell call options of different strike prices for all risk measures considered. Keywords Portfolio optimization · Call options · Covered call writing 1 Introduction Covered call or buy-write strategies involve shorting a European call option until maturity while holding a long position in the underlying asset. Asset return beyond the strike price of the shorted call is sacrificed in exchange for gaining the call B Roy H. Kwon rkwon@mie.utoronto.ca Mauricio Diaz mauricio.diaz@mail.utoronto.ca 1 Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto, ON M5S 3G8, Canada 2 Manulife Asset Management, 200 Bloor St. E., NT-5, Toronto, ON M4W 1E5, Canada 123