We compare and contrast some existing ordinary least squares (OLS)- and generalized method of moments (GMM)-based tests of asset pricing models with a new more general test. This new test is valid under the assumption that returns are elliptically distributed, a necessary and sufficient assumption of the linear capital asset pricing model (CAPM). This new test fails to reject the CAPM on a dataset of stocks sorted by market valuations, whereas similar tests constructed from OLS and GMM estimation methods reject the linear CAPM. We also find that outliers reduce the OLS-estimated mispricing of the linear CAPM on monthly returns sorted by previous performance, that is, momentum. Monte Carlo evidence supports superior size and power properties of the new test relative to OLS- and GMM-based tests. Copyright 2003, Oxford University Press.

We compare and contrast some existing ordinary least squares (OLS)- and generalized method of moments (GMM)-based tests of asset pricing models with a new more general test. This new test is valid under the assumption that returns are elliptically distributed, a necessary and sufficient assumption of the linear capital asset pricing model (CAPM). This new test fails to reject the CAPM on a dataset of stocks sorted by market valuations, whereas similar tests constructed from OLS and GMM estimation methods reject the linear CAPM. We also find that outliers reduce the OLS-estimated mispricing of the linear CAPM on monthly returns sorted by previous performance, that is, momentum. Monte Carlo evidence supports superior size and power properties of the new test relative to OLS- and GMM-based tests.

A diversified firm can trade at a discount to a matched portfolio of single-segment firms if the diversified firm has either lower expected cash flows or higher expected returns than the single-segment firms. We study whether firms with diversification discounts have higher expected returns in order to compensate investors for offering less upside potential (or skewness exposure) than focused firms. Our empirical tests support this hypothesis. First, we find that focused firms offer greater skewness exposure than diversified firms. Second, we find that diversified firms have significantly larger discounts when the diversified firm offers less skewness than matched single-segment firms. Finally, we find that up to 53% of the excess returns received on diversification-discount firms relative to diversification-premium firms can be explained by differences in exposure to skewness.

We develop a one-period model of investor asset holdings where investors have heterogeneous preference for skewness. Introducing heterogeneous preference for skewness allows the model's investors, in equilibrium, to underdiversify. We find support for our model's three key implications using a dataset of 60,000 individual investor accounts. First, we document that the portfolio returns of underdiversified investors are substantially more positively skewed than those of diversified investors. Second, we show that the apparent mean-variance inefficiency of underdiversified investors can be largely explained by the fact that investors sacrifice mean-variance efficiency for higher skewness exposure. Furthermore, we show that idiosyncratic skewness, and not just coskewness, can impact equilibrium prices. Third, the underdiversification of investors does not appear to be coincidentally related to skewness. Stocks most often selected by underdiversified investors have substantially higher average skewness—especially idiosyncratic skewness—than stocks most often selected by diversified investors.

[We develop a one-period model of investor asset holdings where investors have heterogeneous preference for skewness. Introducing heterogeneous preference for skewness allows the model's investors, in equilibrium, to underdiversify. We find support for our model's three key implications using a dataset of 60,000 individual investor accounts. First, we document that the portfolio returns of underdiversified investors are substantially more positively skewed than those of diversified investors. Second, we show that the apparent mean-variance inefficiency of underdiversified investors can be largely explained by the fact that investors sacrifice mean-variance efficiency for higher skewness exposure. Furthermore, we show that idiosyncratic skewness, and not just coskewness, can impact equilibrium prices. Third, the underdiversification of investors does not appear to be coincidentally related to skewness. Stocks most often selected by underdiversified investors have substantially higher average skewness-especially idiosyncratic skewness-than stocks most often selected by diversified investors.]

We develop a preference-based equilibrium asset pricing model that explains low-frequency conditional volatility. Similar to Barberis, Huang, and Santos (2001), agents in our model care about wealth changes, experience loss aversion, and keep a mental scorecard that affects their level of risk aversion. A new feature of our model is that when perturbed by unexpected returns, investors become temporarily more sensitive to news. Gradually investors become accustomed to the new level of wealth, restoring prior levels of risk aversion and news sensitivity. The state-dependent sensitivity to news creates the type of volatility clustering found in low-frequency stock returns. We find empirical support for our model's predictions that relate the scorecard to conditional volatility and skewness.

We develop a preference-based equilibrium asset pricing model that explains low-frequency conditional volatility. Similar to Barberis, Huang, and Santos (2001), agents in our model care about wealth changes, experience loss aversion, and keep a mental scorecard that affects their level of risk aversion. A new feature of our model is that when perturbed by unexpected returns, investors become temporarily more sensitive to news. Gradually investors become accustomed to the new level of wealth, restoring prior levels of risk aversion and news sensitivity. The state-dependent sensitivity to news creates the type of volatility clustering found in low-frequency stock returns. We find empirical support for our model's predictions that relate the scorecard to conditional volatility and skewness.

We test the prediction of recent theories that stocks with high idiosyncratic skewness should have low expected returns. Because lagged skewness alone does not adequately forecast skewness, we estimate a cross-sectional model of expected skewness that uses additional predictive variables. Consistent with recent theories, we find that expected idiosyncratic skewness and returns are negatively correlated. Specifically, the Fama-French alpha of a low-expected-skewness quintile exceeds the alpha of a high-expected-skewness quintile by 1.00% per month. Furthermore, the coefficients on expected skewness in Fama-MacBeth cross-sectional regressions are negative and significant. In addition, we find that expected skewness helps explain the phenomenon that stocks with high idiosyncratic volatility have low expected returns.

[We test the prediction of recent theories that stocks with high idiosyncratic skewness should have low expected returns. Because lagged skewness alone does not adequately forecast skewness, we estimate a cross-sectional model of expected skewness that uses additional predictive variables. Consistent with recent theories, we find that expected idiosyncratic skewness and returns are negatively correlated. Specifically, the Fama-French alpha of a low-expected-skewness quintile exceeds the alpha of a high-expected-skewness quintile by 1.00% per month. Furthermore, the coefficients on expected skewness in Fama-MacBeth cross-sectional regressions are negative and significant. In addition, we find that expected skewness helps explain the phenomenon that stocks with high idiosyncratic volatility have low expected returns.]

The proposition that investors are overconfident about their valuation and trading skills can explain high observed trading volume. With biased self-attribution, the level of investor overconfidence and thus trading volume varies with past returns. We test the trading volume predictions of formal overconfidence models and find that share turnover is positively related to lagged returns for many months. The relationship holds for both market-wide and individual security turnover, which we interpret as evidence of investor overconfidence and the disposition effect, respectively. Security volume is more responsive to market return shocks than to security return shocks, and both relationships are more pronounced in small-cap stocks and in earlier periods where individual investors hold a greater proportion of shares.