Who Should Buy Portfolio Insurance?

Abstract

THE EXISTENCE OF OPTIONS markets can generate new opportunities for portfolio management. As Ross [1976] has shown, a complete set of options markets on a reference stock or portfolio will enable investors to achieve any desired pattern of returns conditional on the terminal value of the reference asset. While buyand-hold equity strategies allow investors to achieve returns proportional to the terminal value of a reference portfolio, buy-and-hold option strategies permit nonproportional returns to be achieved. A nonproportional return of particular interest to some investors is that which provides portfolio insurance. Equivalent to a put option on the reference portfolio, portfolio insurance enables an investor to avoid losses, but capture gains, at the cost of a fixed premium. Unfortunately, options markets do not currently exist for portfolios of securities, and a portfolio of options is not equivalent to an option on a portfolio. Even when options markets do not exist, however, investors may be able to achieve nonproportional returns on terminal asset values by following dynamic investment strategies. If security returns are lognormally distributed at any future time, and continuous trading is possible, Black and Scholes [1973] show that the returns to any option on an asset can be duplicated by an appropriate trading strategy involving, the asset and a riskless security. This implies that, in a BlackScholes world, there exists a dynamic investment strategy which can generate insured portfolio values. The investment strategy involves trading only in the securities of the portfolio and in the riskless asset; no options need exist to achieve insured values. While the theory of option pricing suggests how to value options, and therefore how to value portfolio insurance, it does not suggest the nature of investors who would benefit from purchasing options or insurance. Unlike traditional insurance, in which everyone can benefit from a pooling of independent risks, portfolio insurance involves hedging against a common (market) risk. For every investor buying portfolio insurance, some other investor(s) must be selling it, either by writing the appropriate put option, or by following the inverse dynamic trading strategy. Who should buy, and who should sell? In this paper, we provide a characterization of investors who will benefit from purchasing portfolio insurance. Indeed, our results are considerably more general: we characterize investors who demand arbitrary nonproportional patterns of returns on a reference portfolio, and thereby characterize the nature of investors