228 CORRELATION BREAKDOWNS IN ASSET MANAGEMENT0,2500,2500,2000,2000,1500,1500,1000,1000,0500,0500,000
50 99 148 197 246 295 344 393 442 491 540Number of observations 558 daily changesNo. of observations
Daily correlation change1Figure 12.3Distribution function of jumps JPY–USD, 2003–05The correlation statistics show that historical data with skewness is near
zero, while the kurtosis shows a value far from 3 in the case of the correla-
tion between the Euro and the US market (1.83). In the other two cases the
values are, respectively, 3.79 and 3.04. In the case of volatility, skewness is
always far from symmetry, while kurtosis is closer to 3 (correspondingly,
3.03, 3.46 and 2.76 for the three markets considered). Afterwards we com-
puted the absolute value of correlation jumps. The resulting time series are
divided into two groups: the first is the complete time series of 558 obser-
vations; the second is that characterized by the 10 percent highest changes
(56 observations).
12.3 Correlation jumps and volatility behavior
Firstly, we studied the behavior of correlation jumps in the equity indexes, as
explained by the volatility changes observed in the originating markets. The
methodology follows the idea that it could be possible to explain correlation
changes through volatility differences. The model estimated is
ρA,Bt=α+β·σAt+γ·σBt+εt (12.1)whereρA,Btis the daily correlation difference computed at timetbetween
the two generic markets, A and B;σAtis the market A daily volatility
difference at timet; andσBtis the market B daily volatility difference at
timet.