Volatility amongst firms in the Dow Jones Eurostoxx50 Index

Abstract

This article presents a study of asset price volatility, correlation trends and market risk premia. Recent evidence shows an increase in firm-level volatility and a decline of the correlation among stock returns in the US (Campbell et al ., 2001). We find that, in relation to the Euro-area stock markets, both aggregate firm-level volatility and average stock market correlation are trended upwards. This article estimates the time series of market and idiosyncratic volatilities for the firms composing the index Dow Jones Eurostoxx50 for the 1992–2001 period following the volatility decomposition method of Campbell et al . (2001) Monthly time series of market and firm-level volatility are obtained using within monthly daily returns relative to the market return. This article also investigates the time series properties of the volatility series, in particular whether there are trends and whether there is a risk-return trade-off. The main findings are the following. There is a positive trend in both market and firm level volatility and consequently, average correlation among firms has increased. This contrasts with the US evidence in Campbell et al . (2001) of a strong positive trend in firm-level volatility, no trend in market volatility and consequently, a decrease in the average correlation. There is a statistical significant market risk-return trade-off and that firm-level volatility has no predictive power for subsequent market returns.

Acknowledgement

The authors wish to thank the two anonymous referees for their critical comments and useful suggestions which have helped the clarity and brevity of this article. Xuan Vinh Vo also wishes to thank the Australian Research Council for financial support wides the project “Risk Management for Bonds, Currencies and Commodities”, Project number RM02853.

Notes

¹ See for a review Campbell et al . (2001).

² According to Campbell et al . (2001) there has been a ‘noticeable increase in firm-level volatility relative to market volatility’.

³ Lagged volatility measures will be used as proxy variables for conditional/expected volatility, relying on the usual persistence of volatility time series, as suggested by Goyal and Santa-Clara (2003).

⁴ Probably under the influence of the earlier State-preference Theory, asset pricing is mainly related to the risk of common, undiversifiable variations of aggregate wealth in the economy.

⁵ Unfortunately, it is not possible to solve analytically the Black and Scholes (1973) differential equation for σ. Implied volatility must therefore be calculated by searching with an iterative procedure for the value that, given all other parameters, the appropriate boundary conditions and the option price, satisfies the Black and Scholes (1973) differential equation. A formal iterative procedure would be the Newton–Raphson method, which is designed to solve any equation of the form f(x) = 0. It start with a guess of the solution x = x ₀ and then produces successively better estimates x = x ₀, x = x ₁, … , x = x_n of the true solution using the formula x = x_{i +1} = x_i  − f (x_i )/f′(x_i ).

⁶ With specified adjustments for liquidity and to make sure that holdings are not double-counted.

⁷ As in Campbell et al . (2001) we experimented also with time-varying means, but the result is almost identical.

⁸ When lagged values of the dependent variable are included among the regressors the standard Durbin–Watson test is no longer valid. We can use instead Durbin's h-statistic. Under the null of nonauto-correlated error terms it is asymptotically distributed as a standardized normal variable. Its 5% critical value is therefore 1.96.

⁹ Exponential generalized auto-regressive conditional heteroscedasticity models were introduced by Nelson (1991).

¹⁰ We have chosen not to use the 1-day Euribor rate because of the sudden oscillation that often occur to this rate due to contingent causes related to the liquidity of the inter-bank market. We believe that the 1-week rate is relatively immune from these oscillations and therefore provides a good proxy for the risk-free rate. The data source is Bloomberg.

¹¹ On this, see also Goyal and Santa-Clara (2003), who regress market return on lagged total variance and lagged market variance. They use lagged variance as a proxy for conditional total variance on the basis of the usual persistence of variance time series. Their regression aims at testing the ICAPM claim that market variance is the only priced risk factor.