Advances in Risk Management

HELENA CHULIÁ AND HIPÒLIT TORRÓ 345

otherwise. Using these misspecification indicators, the robust conditional
moment test of Wooldridge (1990) is applied.
Table 17.6 shows the result of the robust conditional moment test. Panels
(A), (C) and (E) display the test result when unconditional moment estimates
are used. It can be seen that asymmetries are very important, especially in the
beta coefficient. Panels (B), (D) and (F) offer the test result when conditional
moment estimates are used. After this, no asymmetric pattern remains in
the conditional covariance specification. This is an important result because
it means that the GARCH specification is gathering all the possible asymme-
tries in the conditional covariance matrix. This result also guarantees that
the analysis of volatility contagion carried out later will be reliable.
Special attention is required for the beta coefficient (following
Wooldridge, 1990, a consistent estimator of the beta coefficient is built using
the continuous function property on consistent estimators; see Hamilton,
1994: 182). Last column in Table 17.6 shows that the unconditional beta
estimate has a significant error specification but the conditional beta esti-
mates within the used model are insensitive to sign and size asymmetries
in unexpected shock returns. As beta coefficients are market risk sensitivity
measures, it is important to use a conditional model in order to avoid error
specification on estimating the beta coefficients.

17.6 Volatility spillovers

In this section, volatility spillovers between large and small firms are quan-
tified. We differentiate between positive and negative shocks, but we also

Table 17.6Robust conditional moment tests

Robust Conditional Moment Test in the French Market

Panel (A): applied on original returns

υ12,t=r1,tr2,t−σ 12 υ1,t=r^2 1,t−σ^21 υ2,t=r^2 2,t−σ^22 υbetat=r1,tr2,t/r^2 1,t

−σ 12 /σ^21

I(r1,t− 1 <0) 52.57695∗∗∗ 1.68619 0.94676 317.99998∗∗∗
I(r2,t− 1 <0) 44.80857∗∗∗ 4.31226∗∗ 0.59401 317.08568∗∗∗
I(r1,t− 1 <0;r2,t− 1 <0) 24.47034∗∗∗ 3.44086∗ 1.55390 230.99999∗∗∗
I(r1,t− 1 <0;r2,t− 1 >0) 64.00011∗∗∗ 7.41064∗∗∗ 0.84142 87.94500∗∗∗
I(r1,t− 1 >0;r2,t− 1 <0) 30.81728∗∗∗ 0.87521 3.92127∗∗ 87.03500∗∗∗
I(r1,t− 1 >0;r2,t− 1 >0) 163.14585∗∗∗ 20.95558∗∗∗ 0.31124 305.02800∗∗∗
r^2 1,t− 1 I(r1,t− 1 <0) 1.13863 4.87991∗∗ 5.12130∗∗ 67.88843∗∗∗
r^2 1,t− 1 I(r2,t− 1 <0) 1.43294 6.23543∗∗ 5.38658∗∗ 72.96868∗∗∗
r^2 2,t− 1 I(r1,t− 1 <0) 2.56038 6.59357∗∗ 6.08929∗∗ 29.55023∗∗∗
r^2 2,t− 1 I(r2,t− 1 <0) 2.69359 6.74448∗∗∗ 5.88425∗∗ 27.93598∗∗∗

Continued