Does idiosyncratic risk matter? Evidence from European stock markets

Abstract

This article examines if idiosyncratic risk can forecast stock returns for 10 European markets. We found little evidence to suggest that idiosyncratic volatility, equally or value weighted, can predict future stock market returns. However, we found that idiosyncratic risk measured as the equally weighted average variance of all stocks can significantly predict future size and value premia.

Notes

¹ Verbeek (2004, page 343) notes that ‘because panel data sets are typically larger than cross-sectional or time series data sets and explanatory variables vary over two dimensions (individuals and time) rather than one, estimators based on panel data are quite often more accurate than from other sources. Even with identical sample sizes, the use of a panel data set will often yield more efficient estimators than a series of independent cross-sections (where different units are sampled in each period’).

² For more information about the construction of the idiosyncratic risk measures, see Goyal and Santa-Clara (2003), Bali et al . (2005) among others.

³ The number of stocks covered by Datastream was variable during the study period. The first number in the parentheses below shows the number of stocks per country covered in 1988 and the second the number of stocks in August 2005: Belgium (85, 192), Denmark (157, 275), France (158, 1188), Germany (462, 1122), Italy (135, 353), Netherlands (141, 274), Spain (62, 205), Sweden (90, 485), Switzerland (158, 353) and United Kingdom (1492, 3628).

⁴ The average value premium shown in Table 1 is quite similar to the average return difference between the high and low Book-to-Market portfolios for the 10 European markets calculated by K. French and provided in his homepage: http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/. The reported average value premium by K. French for the period 1988:01 to 2004:12 for the UK, Germany and France are 0.19%, 0.63% and 0.28%, respectively, which are quite close to those in Table 1. The sample runs from January 1988 to December 2004. Results for the other countries are available upon request.

⁵ There is evidence that the size anomaly is not stable over time. Dimson and Marsh (1999) and Horowitz et al . (2000) argue that the size premium might be now negative.

⁶ Campbell et al . (2001) reported that idiosyncratic risk in the US market rose dramatically during the last decade, while market volatility remained constant. Following the work of Campbell et al . (2001), we test for a deterministic trend in idiosyncratic volatility by computing the PS-statistic described by Vogelsang (1998) and the implied 90% confidence interval for the trend coefficient. According to Vogelsang's (1998) statistic, the increase of idiosyncratic risk that has been reported in US cannot be verified to European countries. The detailed results are available upon request.

⁷ The equally weighted asset specific risk and the market volatility graphs are available from the authors upon request.

⁸ The finding that idiosyncratic volatility is persistent for several months is at odds with evidence from estimates of volatility based on Garch models. According to Christoffersen et al . (1998), a shock to volatility estimated using a Garch model decays at a horizon of about 10 days (see also the evidence on the persistence of idiosyncratic volatility of various asset classes in the US market in Richards (1999)).

⁹ The existing evidence on the inter-temporal relationship between market returns and market volatility is conflicting. Some authors find a significant positive relation (see Harvey, 1989; Turner et al ., 1989; Scruggs, 1998) while others find that market returns are insignificantly or negatively related with market volatility (see French et al ., 1987; Campbell, 1987; Glosten et al ., 1993; Whitelaw, 1994; Goyal and Santa-Clara, 2003).

¹⁰ In all cases we perform a panel-based unit root tests that have higher power than unit root tests based on individual time series. Specifically, we perform the Levin et al . (2002), Breitung (2000) tests and in all cases we reject the null hypothesis of unit root.

¹¹ For more information on the SUR method, see Chan et al . (1991) and Elsewarapu (1997) among others.

¹² Liew and Vassalou (2000) provide evidence consistent with the hypothesis of Fama (1996) that SMB and HML act as state variables in the context of Merton's (1973) inter-temporal capital asset pricing model. They find that SMB and HML can forecast GDP growth in several countries.

¹³ According to the ICAPM as discussed in Fama (1996), the dynamics of market portfolio returns can be modelled as: , where () is the sensitivity of the market return to the SMB (HML) portfolio. The orthogonal market portfolio is defined as .