Motivated by the behavior of asset prices, trading volume and price volatility during historical episodes of asset price bubbles, we present a continuous time equilibrium model where overconfidence generates disagreements among agents regarding asset fundamentals. With short-sale constraints, an asset owner has an option to sell the asset to other overconfident agents when they have more optimistic beliefs. As in Harrison and Kreps (1978), this re-sale option has a recursive structure, that is, a buyer of the asset gets the option to resell it. Agents pay prices that exceed their own valuation of future dividends because they believe that in the future they will find a buyer willing to pay even more. This causes a significant bubble component in asset prices even when small differences of beliefs are sufficient to generate a trade. In equilibrium, large bubbles are accompanied by large trading volume and high price volatility. Our model has an explicit solution, which allows for several comparative statics exercises. Our analysis shows that while Tobin’s tax can substantially reduce speculative trading when transaction costs are small, it has only a limited impact on the size of the bubble or on price volatility. We also give an example where the price of a subsidiary is larger than its parent firm. This paper was previously circulated under the title “Overconfidence, Short-Sale Constraints and Bubbles.”

Abstract: We develop a model of stock prices in which there are both differences of opinion among investors as well as short-sales constraints. The key insight that emerges is that breadth of ownership is a valuation indicator. When breadth is low i.e., when few investors have long positions in the stock this signals that the short-sales constraint is binding tightly, implying that prices are high relative to fundamentals and that expected returns are therefore low. Thus reductions in breadth should forecast lower returns, while increases in breadth should forecast higher returns. Using quarterly data on mutual fund holdings over the period 1979-1998, we find evidence supportive of this prediction: stocks whose change in breadth in the prior quarter places them in the lowest decile of the sample underperform those in the top change-in-breadth decile by 6.38 % in the first twelve months after portfolio formation. After adjusting for size, book-tomarket and momentum, the corresponding figure is 4.95%.

Abstract: This paper is an investigation into the determinants of asymmetries in stock returns. We develop a series of cross-sectional regression specifications which attempt to forecast skewness in the daily returns of individual stocks. Negative skewness is most pronounced in stocks that have experienced: 1) an increase in trading volume relative to trend over the prior six months; and 2) positive returns over the prior thirty-six months. The first finding is consistent with the model of Hong and Stein (1999), which predicts that negative asymmetries are more likely to occur when there are large differences of opinion among investors. The latter finding fits with a number of theories, most notably Blanchard and Watson’s (1982) rendition of stockprice bubbles. Analogous results also obtain when we attempt to forecast the skewness of the aggregate stock market, though our statistical power in this case is limited.

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We present a model in which an asset bubble can persist despite the presence of rational arbitrageurs. The resilience of the bubble stems from the inability of arbitrageurs to temporarily coordinate their selling strategies. This synchronization problem together with the individual incentive to time the market results in the persistence of bubbles over a substantial period. Since the derived trading equilibrium is unique, our model rationalizes the existence of bubbles in a strong sense. The model also provides a natural setting in which news events, by enabling synchronization, can have a disproportionate impact relative to their intrinsic informational content.

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Financial crises are widely argued to be due to herd behavior. Yet recently developed models of herd behavior have been subjected to two critiques which seem to make them inapplicable to financial crises. Herds disappear from these models if two of their unappealing assumptions are modified: if their zero-one investment decisions are made continuous and if their investors are allowed to trade assets with market-determined prices. However, both critiques are overturned–herds reappear in these models–once another of their unappealing assumptions is modified: if, instead of moving in aprespecified order, investors can move whenever they choose.

We present a model of asset valuation in which short-selling is achieved by searching for security lenders and by bargaining over the terms of the lending fee. If lendable securities are difficult to locate, then the price of the security is initially elevated, and expected to decline over time. This price decline is to be anticipated, for example, after an initial public offering (IPO), among other cases, and is increasing in the degree of heterogeneity of beliefs of investors about the likely future value of the security. The prospect of lending fees may push the initial price of a security above even the most optimistic buyer’s valuation of the security’s future dividends. A higher price can thus be obtained with some shorting than if shorting is disallowed.

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Motivated by the behavior of internet stock prices in 1998-2000, we present a continuous time equilibrium model of bubbles where overconfidence generates agreements to disagree among agents about asset fundamentals. With a short-sale constraint, an asset owner has an option to sell the asset to other agents when they have more optimistic beliefs. This re-sale option has a recursive structure, that is a buyer of the asset gets the option to resell it, causing a significant bubble component in asset prices even when small differences of beliefs are sufficient to generate a trade. The model generates prices that are above fundamentals, excessive trading, and excess volatility. We also give an example where the price of a subsidiary is larger than its parent firm. Our analysis shows that while Tobin's tax can substantially reduce speculative trading when transaction costs are small, it has only a limited impact on the size of the bubble or on price volatility.