Data Mining Practical Machine Learning Tools and Techniques

We examine the pricing of aggregate volatility risk in the cross-section of stock returns. Consistent with theory, we find that stocks with high sensitivities to innovations in aggregate volatility have low average returns. In addition, we find that stocks with high idiosyncratic volatility relative to the Fama and French (1993) model have abysmally low average returns. This phenomenon cannot be explained by exposure to aggregate volatility risk. Size, book-to-market, momentum, and liquidity effects cannot account for either the low average returns earned by stocks with high exposure to systematic volatility risk or for the low average returns of stocks with high idiosyncratic volatility.

The Cross-Section of Volatility and Expected Returns

We examine the pricing of aggregate volatility risk in the cross-section of stock returns. Consistent with theory, we find that stocks with high sensitivities to innovations in aggregate volatility have low average returns. Stocks with high idiosyncratic volatility relative to the Fama and French (1993, Journal of Financial Economics 25, 2349) model have abysmally low average returns. This phenomenon cannot be explained by exposure to aggregate volatility risk. Size, book-to-market, momentum, and liquidity effects cannot account for either the low average returns earned by stocks with high exposure to systematic volatility risk or for the low average returns of stocks with high idiosyncratic volatility. IT IS WELL KNOWN THAT THE VOLATILITY OF STOCK RETURNS varies over time. While considerable research has examined the time-series relation between the volatility of the market and the expected return on the market (see, among others, Campbell and Hentschel (1992) and Glosten, Jagannathan, and Runkle (1993)), the question of how aggregate volatility affects the cross-section of expected stock returns has received less attention. Time-varying market volatility induces changes in the investment opportunity set by changing the expectation of future market returns, or by changing the risk-return trade-off. If the volatility of the market return is a systematic risk factor, the arbitrage pricing theory or a factor model predicts that aggregate volatility should also be priced in the cross-section of stocks. Hence, stocks with different sensitivities to innovations in aggregate volatility should have different expected returns. The first goal of this paper is to provide a systematic investigation of how the stochastic volatility of the market is priced in the cross-section of expected stock returns. We want to both determine whether the volatility of the market

https://www0.gsb.columbia.edu/faculty/rhodrick/crosssection.pdf

This bestselling and thoroughly classroom-tested textbook is a complete resource for finance students. A comprehensive and illustrated discussion of the most common empirical approaches in finance prepares students for using econometrics in practice, while detailed case studies help them understand how the techniques are used in relevant financial contexts. Worked examples from the latest version of the popular statistical software EViews guide students to implement their own models and interpret results. Learning outcomes, key concepts and end-of-chapter review questions (with full solutions online) highlight the main chapter takeaways and allow students to self-assess their understanding. Building on the successful data- and problem-driven approach of previous editions, this third edition has been updated with new data, extensive examples and additional introductory material on mathematics, making the book more accessible to students encountering econometrics for the first time. A companion website, with numerous student and instructor resources, completes the learning package.

Introductory Econometrics for Finance

If asset returns have systematic skewness, expected returns should include rewards for accepting this risk. We formalize this intuition with an asset pricing model that incorporates conditional skewness. Our results show that conditional skewness helps explain the cross-sectional variation of expected returns across assets and is significant even when factors based on size and book-to-market are included. Systematic skewness is economically important and commands a risk premium, on average, of 3.60 percent per year. Our results suggest that the momentum effect is related to systematic skewness. The low expected return momentum portfolios have higher skewness than high expected return portfolios.

/pdf/conditional-skewness-in-asset-pricing-tests-3bq6pue1a4.pdf

Conditional Skewness in Asset Pricing Tests

We examine a sample of 8,313 cases, between 1951 and 2001, where firms unexpectedly increase their research and development (R&D) expenditures by a significant amount. We find consistent evidence of a misreaction, as manifested in the significantly positive abnormal stock returns that our sample firms' shareholders experience following these increases. We also find consistent evidence that our sample firms experience significantly positive long-term abnormal operating performance following their R&D increases. Our findings suggest that R&D increases are beneficial investments, and that the market is slow to recognize the extent of this benefit (consistent with investor underreaction).

An Examination of Long-Term Abnormal Stock Returns and Operating Performance Following R&D Increases

We present a new methodology for estimating time-varying conditional skewness. Our model allows for changing means and variances, uses a maximum likelihood framework with instruments, and assumes a non-central t distribution. We apply this method to daily, weekly, and monthly stock returns, and find that conditional skewness is important. In particular, we show that the evidence of asymmetric variance is consistent with conditional skewness. Inclusion of conditional skewness also impacts the persistence in conditional variance.

Autoregressive conditional skewness

We present a framework for modeling and estimating dynamics of variance and skewness from time-series data using a maximum likelihood approach assuming that the errors from the mean have a non-central conditional t distribution. We parameterize conditional variance and conditional skewness in an autoregressive framework similar to that of GARCH models and estimate the parameters in a conditional noncentral t distribution. The likelihood function has two time-varying parameters, the degrees of freedom and the noncentrality parameter. We apply this methodology to daily and monthly equity returns data from the U.S., Germany and Japan, concurrently estimating conditional mean, variance and skewness. We find that there is significant conditional skewness. We then use this model to understand how the inclusion of conditional skewness affects some of the well-known stylized facts about conditional variance and the relation between returns and conditional variance. Two important stylized facts about conditional variance we examine are persistence and asymmetry in variance. Persistence refers to the tendency where high conditional variance is followed by high conditional variance. Asymmetry in variance, i.e., the observation that conditional variance depends on the sign of the innovation to the conditional mean has been documented in asymmetric variance models used in Glosten, Jagannathan, and Runkle (1993) and Engle and Ng (1993). We find that the evidence of asymmetric variance is really just conditional skewness. Inclusion of conditional skewness also impacts the persistence in conditional variance. However, we also find that there are significant seasonalities in variance and the results also depend on how the seasonal effects are accommodated in the estimation methodology. We also examine the relation between expected returns and volatility.

Autoregressive Conditional Skewness

If asset returns have systematic skewness, expected returns should include rewards for accepting this risk. We formalize this intuition with an asset pricing model which incorporates conditional skewness. Our results show that conditional skewness helps explain the cross-sectional variation of expected returns across assets and is significant even when factors based on size and book-to-market are included. Systematic skewness is economically important and commands a risk premium, on average, of 3.60 percent a year. Our results also suggest that the momentum effect is related to systematic skewness. The low expected return momentum portfolios have higher skewness than high expected return portfolios.

Akhtar R. Siddique

Papers

Conditional Skewness in Asset Pricing Tests

An Examination of Long-Term Abnormal Stock Returns and Operating Performance Following R&D Increases

Autoregressive conditional skewness

Autoregressive Conditional Skewness

Conditional Skewness in Asset Pricing Tests