We construct a panel of S&P 500 Index call and put option portfolios, daily adjusted to maintain targeted maturity, moneyness, and unit market beta, and test multi-factor pricing models. The standard linear factor methodology is applicable because the monthly portfolio returns have low skewness and are close to normal. We hypothesize that any one of crisis-related factors incorporating price jumps, volatility jumps, and liquidity (along with the market) explains the cross-sectional variation in returns. Our hypothesis is not rejected, even when the factor premia are constrained to equal the corresponding premia in the cross-section of equities. The alphas of short-maturity out-of-the-money puts become economically and statistically insignificant.

We investigate incentive effects of a typical hedge fund contract for a manager with power utility. With a one-year horizon, the manager displays risk taking that varies dramatically with fund value. We extend the model to multiple yearly evaluation periods and find that the manager's risk taking is rapidly moderated if the fund performs reasonably well. The most realistic approach to modeling fund closure uses an endogenous shutdown barrier where the manager optimally chooses to shut down. The manager increases risk taking as fund value approaches that barrier, and this boundary behavior persists strongly with multiyear horizons.

This article derives underlying asset risk‐neutral probability distributions of European options on the S&P 500 index. Nonparametric methods are used to choose probabilities that minimize an objective function subject to requiring that the probabilities are consistent with observed option and underlying asset prices. Alternative optimization specifications produce approximately the same implied distributions. A new and fast optimization technique for estimating probability distributions based on maximizing the smoothness of the resulting distribution is proposed. Since the crash, the risk‐neutral probability of a three (four) standard deviation decline in the index (about −36 percent (−46 percent) over a year) is about 10 (100) times more likely than under the assumption of lognormality.

Constructing portfolios based on second-order stochastic dominance (SSD) is theoretically attractive since all risk-averse investors would prefer a dominating portfolio. However, choosing among SSD efficient portfolios is a challenge without an obvious ranking metric. We explore particular choices based on Kuosmanen (2004) plus Kopa and Post (2011), comparing their performance to other SSD-related strategies and to standard portfolio choice approaches. These SSD-related choices outperform portfolios chosen based on their Sharpe ratio, information ratio, or using equal weights. Portfolios based on minimum variance that also match the benchmark’s mean return perform on a par with the SSD-related choices.

American options on the S&P 500 index futures that violate the stochastic dominance bounds of Constantinides and Perrakis (2009) from 1983 to 2006 are identified as potentially profitable trades. Call bid prices more frequently violate their upper bound than put bid prices do, while violations of the lower bounds by ask prices are infrequent. In out‐of‐sample tests of stochastic dominance, the writing of options that violate the upper bound increases the expected utility of any risk‐averse investor holding the market and cash, net of transaction costs and bid‐ask spreads. The results are economically significant and robust.

We document widespread violations of stochastic dominance by one-month S&P 500 index call options market over 1986-2006. These violations imply that a trader can improve her expected utility by engaging in a zero-net-cost trade. We allow the market to be incomplete and also imperfect by introducing transaction costs and bid-ask spreads. Even though pre-crash option prices conform to the Black-Scholes-Merton model reasonably well, they are incorrectly priced if the distribution of the index return is estimated from time-series data even with a variety of statistical adjustments. Even though there are fewer violations by OTM calls than by ITM calls, there are still substantial violations by OTM calls, contradicting the inference drawn from the observed implied volatility smile that the problem primarily lies with the left-hand tail of the index return distribution. Most of the violations by post-crash options are not due to the smile being too steep: options are underpriced over 1988-1995 and overpriced over 1997-2006. The decrease in violations over the post-crash period 1988-1995 is followed by a substantial increase in violations over 1997-2006. These results do not support the hypothesis that the options market is becoming more rational over time. Current draft: November 10, 2006 JEL classification: G13 Keywords: Derivative pricing; volatility smile, incomplete markets, transaction costs; index options; stochastic dominance bounds We thank workshop participants at the German Finance Society Meetings 2004, the Bachelier 2004 Congress, the EFA 2005 Meetings, the Frontiers of Finance conference 2006, the Alberta/Calgary 2006 conference, the Universities of Chicago, Iowa, Southern California, Maryland, Texas-Austin, Torino, Utah and Concordia, Laval, New York, Princeton and St. Gallen Universities and, in particular, Yacine Ait-Sahalia, David Bates, Duke Bristow, Larry Harris, Steve Heston, Jim Hodder, Mark Loewenstein, Matthew Richardson, Jeffrey Russell, Hersh Shefrin and Greg Willard for their insightful comments and constructive criticism. We also thank Michal Czerwonko for excellent research assistance. We remain responsible for errors and omissions. Constantinides acknowledges financial support from the Center for Research in Security Prices of the University of Chicago and Perrakis from the Social Sciences and Humanities Research Council of Canada. E-mail addresses: [email protected], [email protected], [email protected].