Optimal portfolio with options

Abstract

We propose a parsimonious framework to analyze the optimal asset allocation problem for a mean–variance investor who incorporates options into the portfolio. Building on the key insight that risk-neutral volatility often differs from physical volatility, we derive closed-form expressions for the optimal portfolio weights with options. The resulting economic gains are substantial and remain robust even when solvency constraints and transaction costs are considered. We then take the model to the data and show that the framework delivers superior out-of-sample performance for an investor trading the S&P 500 index and its options. Our approach underscores the importance of accounting for differences between physical and risk-neutral volatilities when constructing an optimal portfolio that includes options.

Valuation Insight: A firm’s issue of options, other than benefiting the firm’s financial position, adds value by providing investors with an investment alternative that is not duplicated by holding the firm’s stock. The additional investment value from options occurs when basic assumptions leading to Black-Scholes options pricing are violated causing variability implied by the model to differ from actual volatility. The paper shows, in this realistic scenario, that investors may benefit substantially from adding options to their stock portfolio.