Portfolio Selection with Options∗

I introduce dynamic option trading and non-linear views into the classical portfolio selection problem. The optimal dynamic option portfolio is characterized explicitly in terms of its expected sensitivities (Greeks) and the role of the meanvariance efficient portfolio is played by the “Greek-efficient” portfolio. This is the portfolio that has the optimal sensitivities to chosen risk factors. I test these portfolios empirically and find that options significantly improve the risk-return profile due to predictability of powers (and other non-linear functions) of returns which allows for optimal management of non-linear views. To test the effects of higher moments on portfolio choice, I compute (both analytically and numerically) the Greek efficient portfolios for a CRRA investor and find that accounting for higher moments may have ambiguous effects on the optimal tail risk. In fact, even Greek efficient portfolios for a mean-variance investor already offer a highly attractive skewness-kurtosis profile. In the presence of transactions costs that depend on an option’s moneyness and maturity, optimal state-contingent option portfolios are characterized in terms of state prices Greeks as well as a new object, the transactions costs Greeks.