Advances in Risk Management

HELENA CHULIÁ AND HIPÒLIT TORRÓ 335

Table 17.1 Continued

Q(20) 42.6930 [0.002] 165.3912 [0.003]

Q^2 (20) 196.426 [0.000] 162.9281 [0.000]

A(20) 252.419 [0.000] 216.6783 [0.000]

Notes: Data frequency is weekly. Mean test tests the null hypothesis of means equal-

ity and itsp-value are displayed as [.]. Levene statistic tests the null hypothesis of

variances equality and itsp-value is displayed as [.]. Skewness refers to series skew-

ness coefficient. The asymptotic distribution of the skewness coefficient under the null

hypothesis isN(0,6/T), whereTis the sample size. The null hypothesis tested is whether

that coefficient is equal to zero. Kurtosis refers to the series kurtosis coefficient. The null

hypothesis tested is whether that coefficient is equal to zero. The asymptotic distribu-

tion of the kurtosis coefficient under the null hypothesis isN(0,24/T), whereTis the

sample size. Normality refers to the Bera-Jarque statistic test. This statistic tests the nor-

mality or non-normality of the series. The Bera-Jarque statistic is calculated as follows,

T[S^2 /6+(K−3)^2 /24], whereSis the skewness coefficient andKis the kurtosis coef-

ficient. Under the null hypothesis of normal distribution, the Bera-Jarque statistic has

an asymptoticχ^2 (2) distribution. Q(20) and Q^2 (20) are Ljung-Box tests for twentieth-

order serial correlation in the returns and squared returns. A(20) is Engle (1982) test

for twentieth-order ARCH. Thep-values of these tests are displayed as[.]

in variance between the large cap and small cap indices. Secondly, there are
not significant differences in means, although for many years, like 2000, the
return was quite different indicating that both markets could be offering dif-
ferent sensitivities to risk factors. Large firms depend on global risk factors,
however, risk factors that affect small firms are located basically in their own
economy. Thirdly, in all countries the correlation between both indices has
dropped. We can interpret this last fact as a segmentation of both markets.
Therefore, diversification strategies would be gaining an important role in
portfolio management. These results point out that it is important to study
more accurately the covariance dynamic between both financial time series.

17.4 Results

This section presents the model estimates. With theADC model it is possible
to quantify volatility spillovers and contrast the volatility feedback effect.
In order to estimate the model in equations (17.1) and (17.2), a conditional
normal distribution for the innovation vector is assumed and the quasi-
maximum likelihood method is applied. Bollerslev and Wooldridge (1992)
show that the standard errors calculated by this method are robust even
when the normality assumption is violated. Panel (A) of Table 17.3 displays
the quasi-maximum likelihood estimates of the CAPM-ADC model for the
three countries. Panel (B) displays the Wald test for the restrictions imposed
on the ADC model to obtain the encompassed models.
The results for the three countries are quite similar, and three facts can
be highlighted from the estimation. Firstly, the price of risk (Y) is positive