A number of studies have presented evidence rejecting the validity of the Sharpe-Lintner capital asset pricing model (CAPM). Possible alternatives include risk-based models, such as multifactor asset pricing models, or nonrisk-based models which address biases in empirical methodology, the existence of market frictions, or the presence of irrational investors. Distinguishing between the alternatives is important for applications such as cost of capital estimation. This paper develops a framework which shows that, ex ante, CAPM deviations due to missing risk factors will be very difficult to detect empirically, whereas deviations resulting from nonrisk-based sources are easily detectable. The results suggest that multifactor pricing models alone do not entirely resolve CAPM deviations.

This paper evaluates the power of multivariate tests of the Capital Asset Pricing Model. The results indicate that when employing an unspecified alternative hypothesis, the ability of the tests to distinguish between the CAPM and other pricing models is poor. An upper bound is derived for the distance the alternative distribution of the test statistic can be from the null distribution when the deviations from the CAPM are due to missing factors. This upper bound explains the low power of the tests.

We develop and estimate an econometric model of limit-order execution times using survival analysis and actual limit-order data. We estimate versions for time-to-first-fill and time-to-completion for both buy and sell limit orders, and incorporate the effects of explanatory variables such as the limit price, limit size, bid/offer spread, and market volatility. Execution times are very sensitive to the limit price, but are not sensitive to limit size. Hypothetical limit-order executions, constructed either theoretically from first-passage times or empirically from transactions data, are very poor proxies for actual limit-order executions.

We estimate the conditional distribution of trade-to-trade price changes using ordered probit, a statistical model for discrete random variables. This approach recognizes that transaction price changes occur in discrete increments, typically eighths of a dollar, and occur at irregularly-spaced time intervals. Unlike existing models of discrete transactions prices, ordered probit can quantify the effects of other economic variables like volume, past price changes, and the time between trades on price changes. Using 1988 transactions data for over 100 randomly chosen U.S. stocks, we estimate the ordered probit model via maximum likelihood and use the parameter estimates to measure several transaction-related quantities, such as the price impact of trades of a given size, the tendency towards price reversals from one transaction to the next, and the empirical significance of price discreteness.