The Impact of Large Portfolio Insurers on Asset Prices

We develop a simple model in which the presence of portfolio insurers in a market of risk-averse traders leads to multiple equilibria for the pricing of financial assets and can cause an increase in volatility, including insurance-induced price drops. We demonstrate, however, that centralized portfolio insurance firms may actually reduce, not increase, volatility, even if the existence of these firms increases the total amount of funds under insurance. A PORTFOLIO INSURER TYPICALLY sells equity as stock prices fall, in order to limit the losses from holding equity in a declining market, and buys equity as prices rise. This can be accomplished directly by switching between stocks and cash, or indirectly by taking a position in derivative securities whose payoffs are tied to stock market performance.1 The general effects of such dynamic hedging strategies have been studied by authors such as Grossman (1988), Brennan and Schwartz (1989), and Gennotte and Leland (1990). Gammill and Marsh (1988), Shiller (1989), Jacklin, Kleidon, and Pfleiderer (1992), and others have studied the role of portfolio insurance in the crash of 1987. Since these papers do not differentiate between an economy in which a group of atomistic investors follow their own individual insurance strategies and an economy in which large portfolio insurance firms act on behalf of investors who wish to insure, however, the specific price effects of large portfolio insurance firms are yet to be investigated. This is the purpose of our paper. Section I develops a rudimentary asset-pricing model with two types of traders: atomistic portfolio insurers and atomistic ordinary traders. This model is essentially a simplified version of Gennotte and Leland (1990) in which we focus on the stop-loss basics of portfolio insurance. Like Gennotte and Leland, we demonstrate that the existence of atomistic portfolio insurers increases the variance of possible equilibrium prices (i.e., volatility) and can lead to situations in which there are many potential equilibrium prices for a single set of fundamentals. Section II extends the model by allowing some, *Donaldson is from the University of British Columbia and Uhlig is from Princeton University. This is a revised version of a paper previously entitled "Portfolio Insurance and Asset Prices." For helpful comments and suggestions we thank Jonathan Berk, Ruth Freedman, Ron Giammarino, Alan Kraus, an anonymous associate editor of this journal, the managing editor Rene Stulz, and especially an anonymous referee. Any errors are, of course, our own. 1 See, for example, Leland and Rubinstein (1981).