In this paper we develop an approach to asset pricing in incomplete markets that gives the modeller the flexibility to control the tradeoff between the precision of equilibrium models and the credibility of no-arbitrage methods. We rule out the existence of investment opportunities that are very attractive to a benchmark investor. The key feature of our approach is the measure of attractiveness employed: the gain-loss ratio. The gain (loss) of a portfolio is the expectation, under a benchmark risk-adjusted probability measure, of the positive (negative) part of the portfolio's excess payoff. The benchmark risk-adjusted probability measure incorporates valuable prior information about investor preferences and portfolio holdings. A restriction on the maximum gain-loss ratio in the economy has a dual representation in terms of admissible pricing kernels: it is equivalent to a bound on the ratio of extreme deviations from the benchmark pricing kernel. Price bounds are derived by computing all prices which do not permit the formation of portfolios with gain-loss ratios in excess of some prespecified level. We give an example where we bound the price of an option on a non-traded asset that is correlated with a traded asset. The resulting bounds lie strictly between the Black-Scholes price and the no-arbitrage bounds, and they are sharper when (i) the maximum allowable gain-loss ratio is lower, (ii) the correlation between the non-traded and traded asset is higher, and (iii) the volatility of the non-traded asset is lower. This has implications for pricing real options and executive stock options, and for performance evaluation of portfolio managers who use derivatives.

This paper explains why seemingly irrational overcon dent behavior can persist. Information aggregation is poor in groups in which most individuals herd. By ignoring the herd, the actions of overcon dent individuals ("entrepreneurs") convey their private information. However, entrepreneurs make mistakes and thus die more frequently. The socially optimal proportion of entrepreneurs trades off the positive information externality against high attrition rates of entrepreneurs, and depends on the size of the group, on the degree of overcon dence, and on the accuracy of individuals' private information. The stationary distribution trades off the tness of the group against the tness of overcon dent individuals.Starting any company is really hard to do, so you can't be so smart that it occurs to you that it can't be done.

We model a run on a financial market, in which each risk-neutral investor fears having to liquidate shares after a run, but before prices can recover back to fundamental values. To avoid having to possibly liquidate shares at the marginal postrun price-in which case the risk-averse market-making sector will already hold a lot of share inventory and thus be more reluctant to absorb additional shares-each investor may prefer selling today at the average in-run price, thereby causing the run itself. Liquidity runs and crises are not caused by liquidity shocks per se, but by the fear of future liquidity shocks.In contrast to the financial institutions literature (e.g., Diamond and Dybvig [1983]), runs on financial markets have not been a prime subject of inquiry. Our paper offers such a model, in which investors fear (but do not necessarily experience) future liquidity shocks. This creates two scenarios. In the good scenario, a risk-neutral public holds most of the risky shares. Investors hit by a liquidity shock in the future will sell to the risk-averse market-making sector at a "low-inventory price," which will be close to the risk-neutral value of the asset. In the good scenario, the market-making sector provides the public with low-cost insurance against liquidity shocks.In the bad scenario, every investor conjectures that other investors intend to sell today, thus causing a "run." By joining the pool of selling requests today, an individual investor can expect to receive the average price that is necessary to induce the marketmaking sector to absorb all tendered shares today. The investor's alternative is to not enter the pool and instead to hold onto the shares. In making this decision, this investor is better off if he can wait out the storm and realize the eventual expected asset value. However, if he were randomly hit by the possible liquidity shock, this investor would need to sell his shares behind the rest of the public. But, with the market-making sector already holding the shares of other investors who had joined the run, this postrun price will be worse than the average in-run price today. If the average in-run price is greater than the expected payoff achieved by waiting, this investor will join the herd and also sell into the run. If other investors act alike, the conjecture that other inves-* We would like to thank Markus Bronnermeier, Douglas Diamond, Harry Mamaysky, José Scheinkman, and Matthew Spiegel for helpful comments.

The types of investments a firm undertakes will depend in part on what it expects the outcome of those investments to reveal about its skills, capabilities, and assets (i.e., its resources). We predict that a firm will specialize when young, then experiment in a new line of business for some time, and then either expand into a large, multisegment business or focus and scale up its specialized business. We derive several empirical implications for firm valuations and the reaction of stock prices to news about firm prospects. We also offer a novel explanation for the well-documented ''diversification'' discount. r 2002 Published by Elsevier Science B.V.

This paper explains why seemingly irrational overcon dent behavior can persist. Information aggregation is poor in groups in which most individuals herd. By ignoring the herd, the actions of overcon dent individuals ("entrepreneurs") convey their private information. However, entrepreneurs make mistakes and thus die more frequently. The socially optimal proportion of entrepreneurs trades off the positive information externality against high attrition rates of entrepreneurs, and depends on the size of the group, on the degree of overcon dence, and on the accuracy of individuals' private information. The stationary distribution trades off the tness of the group against the tness of overcon dent individuals.Starting any company is really hard to do, so you can't be so smart that it occurs to you that it can't be done.