Derivatives-based portfolio decisions. An expected utility insight

Abstract

This paper challenges the use of stocks in portfolio construction, instead we demonstrate that Asian derivatives, straddles, or baskets could be more convenient substitutes. Our results are obtained under the assumptions of the Black--Scholes--Merton setting, uncovering a hidden benefit of derivatives that complements their well-known gains for hedging, risk management, and to increase utility in market incompleteness. The new insights are also transferable to more advanced stochastic settings. The analysis relies on the infinite number of optimal choices of derivatives for a maximized expected utility (EUT) agent; we propose risk exposure minimization as an additional optimization criterion inspired by regulations. Working with two assets, for simplicity, we demonstrate that only two derivatives are needed to maximize utility while minimizing risky exposure. In a comparison among one-asset options, e.g. American, European, Asian, Calls and Puts, we demonstrate that the deepest out-of-the-money Asian products available are the best choices to minimize exposure. We also explore optimal selections among straddles, which are better practical choices than out-of-the-money Calls and Puts due to liquidity and rebalancing needs. The optimality of multi-asset derivatives is also considered, establishing that a basket option could be a better choice than one-asset Asian call/put in many realistic situations.