Bubbles and Panics in a Frictionless Market with Heterogeneous Expectations

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Abstract
When investors have differences of opinion about the payoffs of a stock, Harrison and Kreps (1978) demonstrate the existence of a speculative bubble in the stock price, that is, the stock price can exceed the valuation of the most optimistic investor. A crucial condition that supports this result in their model is that investors are not allowed to short sell the stock. This paper demonstrates that speculative bubbles may arise without the short sales constraint. The paper also demonstrates that a panic of the stock price may arise, that is, the stock price may be lower than the valuations of all individual investors. In particular, even if the short sales constraint binds, panics can still arise. In the case of a bubble, our model generalizes the Harrison-Kreps notion of a resale option, namely, investors believe that they can resell the stock later at a higher price. In the case of a panic, our model develops the notion of a buy-back option, namely, investors believe that they can sell the stock now and buy back the stock later at a lower price. We further show that panics can arise even when investors face a binding short sales constraint. Intuitive sufficient conditions for both bubbles and panics are developed, and it is shown that under certain conditions, bubbles and panics can arise even when investors have almost homogeneous expectations.

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