Insurance and Interconnectedness in the Financial Services Industry

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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 12
are considered significant (Tabachnick and Fidell, 1996.) 26 Using this criterion, we find the factor loadings on the overall sample in Panel B of Table 1 indicate that each financial service portfolio loads similarly on the first principal component with the exception for hedge funds, which loads less on the first component, yet more heavily on the second component. Brokers load heavily on the third component in all periods while FHCs load on the fourth component in all but one of the time periods. Insurers are notably sensitive to both the third and fourth principal components. In other words, insurers are affected by the same factors that affect other financial service firms, but there are other factors that affect insurers that do not affect brokers, banks, FHCs, and hedge funds. Interpreting the components The observation that there are factors that affect the returns on financial service firms is interesting, but not helpful in understanding the drivers of returns. Our understanding of asset pricing leads us to believe that the first and most important factor in explaining returns is the return on the market. This is consistent with what we observe in terms of the proportion of variation explained and the factor loadings. Correlating the return on the S&P500 index with the principal components provides supporting evidence: Returns on the S&P 500 p-‐value for test of correlation Correlation Ho: ρ= 0 PCA1 0.8812 0.0000 PCA2 0.0867 0.2174 PCA3 -‐0.1321 0.0597 PCA4 0.0901 0.1999 A stronger correlation, and consistent with evidence by Semaan and Drake (2012), is the correlation between PCA1 and the mean of the pair-‐wise correlation of the portfolio returns, 0.9599, which is different from zero at the one percent level for PCA1. We calculate the mean of the pair-‐wise correlations by first calculating 24-‐month rolling correlations of portfolio returns for each pair of portfolios (e.g., brokers and banks); hence, we are able to calculate correlation means from December 1996 through December 2010. The mean of the correlations is similar to the overall mean model for asset pricing discussed by Elton and Gruber (1973) 26 In section 13.6.5, Interpretation of Factors. Loadings greater than 0.71 are equivalent to 50% of the variance overlapping; 0.63 equals 40% overlap; 0.55 equals 30%; 0.45 equals 20% and 0.32 is equivalent to 10% of the variance overlapping (Comrey and Lee, 1992.) 13
Page 1 and 2: Insurance and Interconnectedness in
Page 3 and 4: Insurance and Interconnectedness in
Page 5 and 6: elationships with banks and expansi
Page 7 and 8: Life insurers **************** Inse
Page 9 and 10: Financial guarantee insurers Financ
Page 11 and 12: • Within the insurance industry,
Page 13: ! !
Page 17 and 18: We graph the first two principal co
Page 19 and 20: directionality is reversed in the c
Page 21 and 22: REFERENCES Acharya, Viral V., Lasse
Page 23 and 24: TABLE 1 Principal Components Analys
Page 25 and 26: Table 2, Panel B, continued Eigenve
Page 27 and 28: TABLE 3, CONTINUED PANEL E PROPERTY
Page 29 and 30: TABLE 4, CONTINUED PANEL E PROPERTY
Page 31 and 32: FIGURE 2 Proportion of insurance as
Page 33 and 34: FIGURE 4 Principal components analy
Page 35: FIGURE 6 Variation explained by pri

Insurance and Interconnectedness in the Financial Services Industry

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