High risk, high return? A study on idiosyncratic volatility

The study presented in the following, sets out to investigate the effect of idiosyncratic risk on expected returns. In traditional financial literature, risk and return are positively related to each other. If theory holds, greater risk results in higher expected returns. Furthermore, the CAPM states that only systematic risk matters, while unsystematic (=idiosyncratic) risk can be diversified away. However, several studies identified that investors do not always hold fully diversified portfolios and, therefore, systematic risk is not necessarily the only risk factor to be considered.

In fact, in markets where not every investor is able to hold the market portfolio, investors might as well require a premium for bearing idiosyncratic risk. Previous empirical evidence on the relation between idiosyncratic risk and expected returns is diverse. While many researchers find a significant positive relation, others do not find any or even a significant negative relation.

Shedding light on the darkness with a meta-analysis.  
Although the literature provides a large number of empirical studies on idiosyncratic volatility, a comprehensive overview is still missing. The study “A Review of the Cross-Section of Volatility and Expected Returns” by Dr. Sebastian Seidens helps to reconcile the conflicting empirical evidence by investigating different proxies of idiosyncratic risk, both from an empirical and a meta-perspective. Furthermore, the meta-analysis investigates the differences in the reported coefficients and a set of study-specific parameters that may be able to explain the conflicting empirical findings.
 

The study presents an overall picture of previous empirical findings across different measures and markets. Therefore, an extensive collection of 45 articles and 101 observations is gathered and systematically categorized according to various criteria such as year published, journal, sample universe, and underlying methodology. Thereby, the potential of a publication bias in existing literature and several study-specific parameters that may be able to explain the diverse empirical findings are analyzed. The figure shows the number of positive and negative observations.

The mixed results are driven by different proxies for idiosyncratic volatility.
The study finds that there is indeed a statistically significant publication bias towards negative results in the dataset. By looking at the differences between the reported coefficients and the study-specific parameters that may cause variation in the empirical findings, Dr. Seidens reveals that the main driver for the diverse empirical results is the proxy of idiosyncratic volatility itself. Empirical results based on unconditional volatility are mostly negative, while empirical results based on conditional volatility are mostly positive (this in line with the underlying theory regarding imperfect markets). The impact of other parameters such as underlying market or methodological differences seem to be weaker.

Overall, the meta-analysis supports the observation in the previous literature, as that the relation between idiosyncratic volatility and expected returns is heavily dependent on the respective proxy of idiosyncratic volatility. This is in line with the findings of other researchers, who assume that the diverse empirical results are due to the use of different proxies of idiosyncratic risk.

Please refer to the original paper for further details:

Seidens, S. (2018). A Review of the Cross-Section of Volatility and Expected Returns. Working Paper.