I argue that hazard models are more appropriate for forecasting bankruptcy than the single-period models used previously. Single-period bankruptcy models give biased and inconsistent probability estimates while hazard models produce consistent estimates. I describe a simple technique for estimating a discrete-time hazard model with a logit model estimation program.Applying my technique, I nd that about half of the accounting ratios that have been used in previous models are not statistically signi cant bankruptcy predictors. Moreover, several market-driven variables are strongly related to bankruptcy probability, including market size, past stock returns, and the idiosyncratic standard deviation of stock returns. I propose a model that uses a combination of accounting ratios and market-driven variables to produce more accurate out-of-sample forecasts than alternative models.I thank Chris Acito, Steve B o yce, John Cochrane, George Constantinides, Dennis Capozza, Kathryn Clark, Josh Coval, Eugene Fama, Chris Geczy, P aul Gompers, Steve Kaplan, Michael Parzen, Burt Porter, Ross Stevens, Kelly Welch, Sven Wilson, Arnold Zellner, Luigi Zingales, Mark Zmijewski, an anonymous referee, and seminar participants at the University of Chicago, Brigham Young University, and the University of Michigan for suggestions.

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This paper examines expected option returns in the context of mainstream assetpricing theory. Under mild assumptions, expected call returns exceed those of the underlying security and increase with the strike price. Likewise, expected put returns are below the risk-free rate and increase with the strike price. S&P index option returns consistently exhibit these characteristics. Under stronger assumptions, expected option returns vary linearly with option betas. However, zero-beta, at-the-money straddle positions produce average losses of approximately three percent per week. This suggests that some additional factor, such as systematic stochastic volatility, is priced in option returns.ASSET-PRICING THEORY CLAIMS that options, like all other risky securities in an economy, compensate their holders with expected returns that are in accordance with the systematic risks they require their holders to bear. Options which deliver payoffs in bad states of the world will earn lower returns than those that deliver their payoffs in good states. The enormous popularity of option contracts has arisen, in part, because options allow investors to precisely tailor their risks to their preferences. With this in mind, a study of option returns would appear to offer a unique opportunity in which to investigate what kinds of risks are priced in an economy. However, although researchers have paid substantial attention to the pricing of options conditional on the prices of their underlying securities, relatively little work has focused on understanding the nature of option returns.Understanding option returns is important because options have remarkable risk-return characteristics. Option risk can be thought of as consisting of two separable components. The first component is a leverage effect. Because an option allows investors to assume much of the risk of the option's underlying asset with a relatively small investment, options have characteristics similar to levered positions in the underlying asset. The BlackScholes model implies that this implicit leverage, which is ref lected in option betas, should be priced. We show that this leverage should be priced under

Psychological evidence and casual intuition predict that sunny weather is associated with upbeat mood. This paper examines the relationship between morning sunshine in the city of a country's leading stock exchange and daily market index returns across 26 countries from 1982 to 1997. Sunshine is strongly signi¢cantly correlated with stock returns. After controlling for sunshine, rain and snow are unrelated to returns. Substantial use of weatherbased strategies was optimal for a trader with very low transactions costs. However, because these strategies involve frequent trades, fairly modest costs eliminate the gains.These ¢ndings are di⁄cult to reconcile with fully rational price setting. SUNSHINE AFFECTS MOOD, as evidenced by song and verse, daily experience, and formal psychological studies. But does sunlight a¡ect the stock market?The traditional e⁄cient markets view says no, with minor quali¢cations. If sunlight a¡ects the weather, it can a¡ect agricultural and perhaps other weatherrelated ¢rms. But in modern economies in which agriculture plays a modest role, it seems unlikely that whether it is cloudy outside the stock exchange today should a¡ect the rational price of the nation's stock market index. (Even in countries where agriculture plays a large role, it is not clear that one day of sunshine versus cloud cover at the stock exchange should be very informative about harvest yield.)An alternative view is that sunlight a¡ects mood, and that people tend to evaluate future prospects more optimistically when they are in a good mood than when they are in a bad mood. A literature in psychology has found that mood a¡ects judgment and behavior. The psychological literature on sunlight, mood, and misattribution of mood is discussed in the next section. An important strand of this literature has provided evidence that mood contains valuable information

Psychological evidence and casual intuition predict that sunny weather is associated with upbeat mood. This paper examines the relation between morning sunshine at a country's leading stock exchange and market index stock returns that day at 26 stock exchanges internationally from 1982-97. Sunshine is strongly significantly correlated with daily stock returns. After controlling for sunshine, rain and snow are unrelated to returns. There were positive net-of-transaction costs profits to be made from substantial use of weather-based strategies, but the magnitude of the gains was fairly modest. These findings are difficult to reconcile with fully rational price-setting. I need to laugh, and when the sun is out, I've got something I can laugh about. I feel good in a special way; I'm in love and it's a sunny day. Good Day Sunshine, Good Day Sunshine, Good Day Sunshine We take a walk, the sun is shining down, Burns my feet as they touch the ground.

I document a delisting bias in the stock return data base maintained by the Center for Research in Security Prices (CRSP). I find that delists for bankruptcy and other negative reasons are generally surprises and that correct delisting returns are not available for most of the stocks that have been delisted for negative reasons since 1962. Using over‐the‐counter price data, I show that the omitted delisting returns are large. Implications of the bias are discussed.

We investigate the bias in CRSP's Nasdaq data due to missing returns for delisted stocks. We find that the missing returns are large and negative on average, and that delisted stocks experience a substantial decrease in liquidity. We estimate that using a corrected return of Ϫ55 percent for missing performance-related delisting returns corrects the bias. We revisit previous work which finds a size effect among Nasdaq stocks. After correcting for the delisting bias, there is no evidence that there ever was a size effect on Nasdaq. Our results are inconsistent with most risk-based explanations of the size effect.EACH YEAR, MANY OF THE STOCKS TRADED on Nasdaq are delisted from the system and cease to be traded there. Delistings occur for a number of reasons including merger and acquisition, bankruptcy, liquidation, or migration to another exchange. They usually coincide with significant firm-specific events, so the returns associated with delistings are often sizable. Further, a stock's liquidity can change dramatically upon delisting, affecting the price at which shareholders can sell their shares. The Center for Research in Security Prices CRSP! attempts to systematically collect delisting returns; however, the task is difficult, and many returns are not collected. Some categories are missed more often than others. Specifically, delisting returns associated with poor firm performance~e.g., bankruptcy or failure to meet capital requirements! are missed much more often than returns associated with neutral or good firm performance~e.g., merger, acquisition, or migration to another exchange!. Since most of the missing delisting returns are associated with negative events, a significant bias exists in the data.We study this delisting bias in two ways. First, we document the magnitude of the bias. We investigate when and how often delisting returns are not collected by CRSP, and we estimate the average size of the missing returns. In this way, we extend to Nasdaq the work of Shumway~1997! which examines the delisting bias in CRSP's NYSE and AMEX data. The bias in the Nasdaq data is much larger-on average, 1.2 percent of NYSE and AMEX stocks are delisted for poor performance each year but 5.6 percent of Nasdaq stocks are delisted each year for similar reasons. Delistings are most fre-* University of Michigan Business School. We thank Dmitry Davydov for superb research assistance. We also thank Gene Fama, Mark Mitchell, René Stulz, an anonymous referee, and participants at a seminar at the University of Michigan for helpful comments.

I argue that hazard models are more appropriate for forecasting bankruptcy than the single-period models used previously. Single-period bankruptcy models give biased and inconsistent probability estimates while hazard models produce consistent estimates. I describe a simple technique for estimating a discrete-time hazard model with a logit model estimation program.Applying my technique, I nd that about half of the accounting ratios that have been used in previous models are not statistically signi cant bankruptcy predictors. Moreover, several market-driven variables are strongly related to bankruptcy probability, including market size, past stock returns, and the idiosyncratic standard deviation of stock returns. I propose a model that uses a combination of accounting ratios and market-driven variables to produce more accurate out-of-sample forecasts than alternative models.I thank Chris Acito, Steve B o yce, John Cochrane, George Constantinides, Dennis Capozza, Kathryn Clark, Josh Coval, Eugene Fama, Chris Geczy, P aul Gompers, Steve Kaplan, Michael Parzen, Burt Porter, Ross Stevens, Kelly Welch, Sven Wilson, Arnold Zellner, Luigi Zingales, Mark Zmijewski, an anonymous referee, and seminar participants at the University of Chicago, Brigham Young University, and the University of Michigan for suggestions.