Measures of cross-sectional dispersion in international stock returns

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Type and Duration

internes Projekt, June 2015 until June 2018


Chair in Finance

Main Research

Wealth Management

Field of Research

Asset Pricing


Time-series volatility is a long standing and well established measure of risk for both individual stocks and the market as such. However, the fact that volatility is time variant is not the sole set of available information. Especially during periods of high time-series volatility, the level of idiosyncratic risk can vary significantly in the cross-section of stock returns. This fact is well-known and implicitly embedded in many style investing approaches. So far cross-sectional volatility of returns (return dispersion) has grown in importance on behalf of both academics and practitioners regarding explanatory power in terms of empirical asset pricing and forecasting. The advantage of cross-sectional risk measures over classical option-implied or sample-dependent historical volatility measures is that they are simple to derive, are model free and can be calculated for any frequency without the drawbacks of other volatility measures (liquid derivative markets, loss of observations, …).

The purpose of this project is twofold: First of all, we aim to construct a database including a variety of cross-sectional market factors based on the longest available timeseries of international stock returns for academic and practical application in financial economics and portfolio management, such as asset pricing.

Secondly, we evaluate these factors in the context of explaining and forecasting asset prices (cf., Fama & French 2012, 2014; Welch & Goyal, 2007) and test them as measures of market opportunity in the context of investment management (Cremers and Petajisto, 2009).

Factors (all equally- and value-weighted):
  • Return dispersion (cross-sectional volatility)
  • Alpha and beta dispersion (for Academic and Practitioners)
  • Non-market dispersion
  • Cross-sectional covariance
  • Cross-sectional skewness
  • Cross-sectional kurtosis


Cross-sectional volatility, Return dispersion, Alpha dispersion, Beta dispersion, Cross-sectional skewness, Cross-sectional kurtosis, Cross-sectional covariance, Non-market dispersion, International stock returns

Project Leader

  • Chair in Business Administration, Banking and Financial Management
  • Chair in Finance


  • Stöckl, S., & Kaiser, L. (2021). Higher Moments Matter! Cross-sectional (higher) Moments and the Predictability of Stock Returns. Review of Financial Economics, 39(4), 455-481. (ABDC_2022: B; ABS_2021: 1; VHB_3: B)

  • Stöckl, S., & Kaiser, L. (2017). Higher Moments Matter! Cross-Sectional (Higher) Moments and the Predictability of Stock Returns. Presented at the SGF Conference 2017, Zurich, Switzerland.