The Impact of Options on Investment Portfolios in the Short-Run and the Long-Run, with a Focus on Downside Protection and Call Overwriting

Abstract

In this article, we analyse the impact of the introduction of options on an investment portfolio. Our first objective is to derive closed-form formulae for the standard measures of portfolio efficiency: risk premium, risk, Sharpe ratio, and beta, of any portfolio containing any combination of options. Using these formulae on three examples of simple option strategies (call overwriting, put protection, and collars), we show how these statistics are altered by the inclusion of an option overlay in a portfolio. Our second objective is to show that if an option strategy is repeated over multiple investment time periods, the long-run return becomes normally distributed. Our motivation is to provide investors with the mathematics to measure the impact of the introduction of options on portfolio efficiency and encourage a potential portfolio rebalance to account for this impact. Then, we highlight that whilst options can create asymmetric non-normal outcomes, their repeated use may not alter the long-run portfolio return in the desired way and thus to encourage investors to assess if an option overlay will deliver the desired long-run outcome.