Advances in Risk Management

HELENA CHULIÁ AND HIPÒLIT TORRÓ 329

Which effect, leverage effect or volatility feedback effect, is the main
determinant of asymmetric volatility, remains an open question. Those stud-
ies that focus their analysis on the leverage hypothesis (Christie, 1982 and
Schwert, 1989) show that this effect is too small to explain the full asym-
metry. On the other hand, authors like Braunet al. (1995), Bekaert and Wu
(2000) and Wu (2001) find clear evidence in favor of the volatility feedback
effect as the main cause of the asymmetric behavior.
Our main contributions to the research in this field are threefold. Firstly,
we analyse volatility spillovers between large and small firms in the French,
German and British stockmarkets since the existing empirical studies have
focused in the American, Japanese and Australian equity markets. In order
to do so, a conditional CAPM with an asymmetric multivariate GARCH-in-
mean covariance structure is used. Results show that there exist bidirectional
volatility spillovers between both types of companies. Secondly, we explore
the volatility feedback hypothesis as a possible explanation of asymmetric
volatility in stock returns, finding significant evidence for this hypothesis.
Finally, the study uncovers that conditional beta coefficient estimates within
the used model are insensitive to sign and size asymmetries in the unex-
pected shock returns but unconditional beta estimates have a significant
specification error.
The remainder of the chapter is organized as follows. Section 17.2 for-
mulates the empirical model, while section 17.3 presents the data. Section
17.4 discusses the empirical results; section 17.5 shows an analysis of asym-
metries; section 17.6 analyses volatility spillovers between large and small
firms; and section 17.7 summarizes the results.

17.2 The econometric framework

Following Bekaert and Wu (2000), in the present study a conditional ver-
sion of the CAPM is used to examine the interaction between means and
variances. In the assumed version of the conditional CAPM, excess returns
of the large cap index is proportional to its conditional variance and excess
returns of the small cap index is proportional to the conditional covariance
between the small cap and the large cap index returns, being the proportion
(constant) the same in both cases: the price of risk. Therefore, the conditional
mean equations are defined as:

r1,t−r

f

t−1,t=Yσ

2

1,t+ε1,t

r2,t−r

f

t−1,t=Yσ12,t+ε2,t

(17.1)

wherer1,tandr2,trefer to the large and small stock indexes respectively,Y

is the price of risk andr
f
t−1,tis the risk-free interest rate known at timet−1.