Insurance and Interconnectedness in the Financial Services Industry

We provide the percentage explained and eigenvectors in Table 1, and provide the proportions
of returns explained by the principal components in Figure 4. As you can see, the first principal
component explains approximately 70% of the variability among financial institutions from 1994 to
2010. More specifically, the first principal component (PCA1) is dynamic, capturing from 60% to 80% of
return variation in the different periods. These results are consistent with those observed by Merville
and Xu (2002). In Figure 4 you can see that the explanatory power of PCA1 peaked around the Long-­‐
Term Capital Management crisis in August 1998, and subsequently decreased until it began rising again
from late-­‐2002 through mid-­‐2005. Finally, we can see in Figure 4 that throughout the financial crisis of
2007-­‐2009, the first and second principal components explains more than 80% of the return variation
and is persistent over time for each of the portfolios. Our results are consistent with those of Billio,
Getmansky, Lo and Pelizzon, who observe that the first component’s explanatory power is higher during
periods of market stress.
These results are also consistent with those of Kritzman, Li, Page and Rigobon (2010), who refer
to the variation explained by a specific number of factors as the absorption ratio. The absorption ratio,
they contend, is a measure of the fragility of a system, and hence systemic risk. Related to this is the
observation by Billio, Getmansky, Lo and Pelizzon that correlations among returns of securities increase
in periods of market stress. Our observation that two principal components explain stock returns is
consistent with other studies, including Lo and Wang (2010):
Absorption
Absorption
ratio:
Time frame
ratio: PCA1 PCA1 and PCA2
Entire period 70.84% 86.63%
1994 through 1999 75.88% 89.35%
2000 through 2004 59.88% 86.26%
2005 through 2008 73.09% 87.46%
2009 through 2010 80.49% 90.95%
We provide the factor loadings of the components in Panel B of Table 1. The factor loadings
indicate the importance of the principal component in explaining the portfolio’s returns; the higher the
loading, the more important the component. It is commonly accepted that loadings of 0.32 and above
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