We study the dynamics of IPOs by examining the tradeoff between an entrepreneur's private benefits, which are lost whenever the firm is publicly traded, and the gains from diversification. We characterize the timing dimension of the decision to go public and its impact on firm value and the evolution of firm risk over time. By endogenizing the timing of the decision to go public, we explain the clustering of IPOs and buyouts in time, the industry concentration of IPO waves, the high incidence of reprivatization of recent IPOs, and the long-run underperformance of recently issued stock relative to the shares of longer-listed companies. r

n extensive body of recent research in futures markets has dealt with the A determination of the minimum variance hedging ratio.' The strength of these results is mitigated, however, by two factors: First, the researchers assume (implicitly or explicitly) that the hedger has a quadratic utility function. This is well-known to be a problematic assumption, since quadratic utility functions have many undesirable properties.2 Second, the hedge ratio which is determined is not an optimal hedge ratio, but rather one which minimizes the variance of the producer's income. Even if the hedger is assumed to have a quadratic utility function, there is no reason to believe that the utility will be maximized when the variance of the spot cum futures position is minimized?In this article we show that-when futures markets are assumed to be unbiasedthe minimum variance hedge position is also on optimal hedge ratio. Optimality holds irrespective of the hedger's utility function. Since existing research on futures prices appears to indicate that unbiasedness is a property of many futures markets, our results are considerably stronger than those of previous authors.In Section I of the article we set out our model and indicate the intuition behind 'The seminal papers are Johnson (1960) and Stein (1961). Interest in the problem was re-inspired by Ederington (1979), and much of the recent research has its roots in his paper. For papers which deal with the JohnsonlEderington model in various future markets, see Franckle (1980) and Hill and Schneeweis (1982).'For a discussion, see Baron (1977). 3The potential nonoptimality of the minimum variance hedge portfolio has been recognized by all of the authors who have dealt with the theoretical aspects of the problem, but this distinction has tended to become blurred in the empirical papers which have focussed on the determination of the hedge ratio.

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