348 LARGE AND SMALL CAP STOCKS IN EUROPElook at the combined effect of typical shocks occurring simultaneously on
large cap and small cap indexes. Since the unconditional correlation coeffi-
cients between the large cap and the small cap index returns are 0.62, 0.55
and 0.20 for France, Germany and United Kingdom respectively, it can be
assumed that, in all markets, shocks of the same sign occur more frequently
than shocks of different sign.
As it was mentioned in section 17.1, the volatility feedback hypothesis
is one of the theories that try to explain the asymmetric volatility phe-
nomenon. This theory relies on the existence of a positive intertemporal
relation between expected returns and conditional variances, therefore, risk
premiums are variable throughout the time. In the context of the conditional
CAPM that we are considering, the relevant measure of risk for large firms
is their variance whereas the relevant risk measure for small firms is their
covariance with large firms. Therefore, in this work, the asymmetric volatil-
ity in small firms, will be determined by their covariance with large firms.
Table 17.7 shows the incremental effect (annualized and in percentage
terms) on variances and covariances produced by a unitary shock in the large
and/or small cap indices. Results are quite similar for the three countries. In
this table, we can observe volatility and covariance asymmetry and volatility
spillovers. Volatility of both indices increase more after negative shocks
coming from any market than after positive shocks, with the exception of the
SDAX volatility. Positive and negative shocks affecting returns on the SDAX
produce the same effect on the SDAX volatility (remind that the estimated
coefficientg 22 was not significant). Covariance also increases more after
negative shocks than after positive shocks. It drops in some cases when
shocks are of opposite sign or positives. These results are consistent with the
existence of time-varying risk premiums and, therefore, with the volatility
feedback hypothesis.
If we focus on volatility spillovers, we observe that volatility spillovers
between both type of firms, large and small firms, are bidirectional. Both,
news coming from large firms and news coming from small firms affect
the other market. However, it must be highlighted that news coming
from the small cap index increase more the volatility of the large cap index
than the opposite, especially, bad news. These volatility spillovers highlight
that relevant information for portfolio management comes from the small
firms market.
17.7 Conclusion
In this chapter we have investigated volatility spillovers between large firms
and small firms in the French, German and British Stock Exchanges, tak-
ing into account volatility and covariance asymmetry. We use a conditional
CAPM with an asymmetric GARCH-in-mean covariance structure that