Must an Optimal Buy and Hold Portfolio Contain any Derivative?

Abstract: Consider a portfolio choice problem maximizing the expected return and simultaneously minimizing a general (and frequently coherent) risk measure. This paper shows that every stock (or stock index) is often outperformed by a buy and hold strategy containing some of its derivatives and the underlying stock itself. As a consequence, every investment only containing international benchmarks will not be efficient, and the investors must properly add some derivatives. Though there is still a controversy, this finding had been pointed out in dynamic frameworks, but the novelty is that one does not need to rebalance the portfolio of derivatives before their expiration date. This is very important in practice because transaction costs are sometimes significant when trading derivatives.