Portfolio optimization with covered calls

Covered calls are traditionally formed as an overlay on an existing portfolio. Our analysis suggests that covered calls formed in two steps by first optimizing underlying equity positions and then selecting call overwriting weights are not risk-return optimal in general. We introduce an optimization framework which simultaneously selects underlying asset positions and call options to sell to form risk-return optimal covered call portfolios. Call option market prices form a critical part of the expected return and risk expressions. Variance of the return, semivariance of the return, and conditional value-at-risk are used as risk measures. The model was first tested by forming covered call portfolios composed of three indices and then by forming portfolios using 92 U.S. equities. We find that selling call options not only reduces risk, but when selected optimally can also benefit the expected return.