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Insurance and Interconnectedness in the Financial Services Industry

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• With<strong>in</strong> <strong>the</strong> <strong>in</strong>surance <strong>in</strong>dustry, <strong>the</strong> f<strong>in</strong>ancial guarantee <strong>in</strong>surers were most volatile,<br />

outperform<strong>in</strong>g <strong>the</strong> o<strong>the</strong>r l<strong>in</strong>es of <strong>in</strong>surance follow<strong>in</strong>g deregulation, but experienc<strong>in</strong>g <strong>the</strong><br />

greatest drop with <strong>and</strong> follow<strong>in</strong>g <strong>the</strong> f<strong>in</strong>ancial crisis (Panel B).<br />

Though we see correlation, convergence, <strong>and</strong> divergence patterns among <strong>the</strong>se return series <strong>in</strong> Figure 3,<br />

we provide more direct methods to assess <strong>the</strong> nature of <strong>the</strong>se returns, us<strong>in</strong>g pr<strong>in</strong>cipal component<br />

analysis <strong>and</strong> Granger causality.<br />

METHODOLOGY<br />

The question rema<strong>in</strong>s as to <strong>the</strong> degree of <strong>in</strong>terconnectedness of <strong>in</strong>surance companies with o<strong>the</strong>r<br />

f<strong>in</strong>ancial service companies, <strong>and</strong> whe<strong>the</strong>r <strong>the</strong> <strong>in</strong>terconnectedness differs among <strong>the</strong> different types of<br />

<strong>in</strong>surance companies. We use pr<strong>in</strong>cipal components analysis to determ<strong>in</strong>e <strong>the</strong> strength of <strong>the</strong><br />

relationship between <strong>the</strong> returns for <strong>in</strong>surance companies, <strong>and</strong> also to assess <strong>the</strong> degree of<br />

<strong>in</strong>terconnectedness among <strong>in</strong>surance companies. The results of this analysis provide <strong>in</strong>formation on<br />

whe<strong>the</strong>r <strong>in</strong>surance companies <strong>in</strong> general or by type are systemically important.<br />

Whereas pr<strong>in</strong>cipal components analysis is useful <strong>in</strong> detect<strong>in</strong>g commonality among <strong>the</strong> returns of<br />

<strong>the</strong> portfolios, <strong>the</strong>re may be a lead-­‐lag relationship <strong>in</strong> returns that would also suggest systemically<br />

important relationships. Therefore, <strong>in</strong> addition to pr<strong>in</strong>cipal components analysis, we also estimate<br />

Granger causality among <strong>the</strong> portfolio returns, focus<strong>in</strong>g on <strong>the</strong> relation between returns to <strong>in</strong>surance<br />

companies <strong>and</strong> those of o<strong>the</strong>r f<strong>in</strong>ancial services firms.<br />

PRINCIPAL COMPONENTS ANALYSIS<br />

In general terms, pr<strong>in</strong>cipal components analysis (PCA) is a nonparametric, l<strong>in</strong>ear transformation of a<br />

data matrix to a new coord<strong>in</strong>ate system. Us<strong>in</strong>g PCA, we extract a structure from a data set that is<br />

o<strong>the</strong>rwise not noticeable or obvious. PCA does this by restat<strong>in</strong>g <strong>the</strong> dataset, filter<strong>in</strong>g out noise, <strong>and</strong><br />

identify<strong>in</strong>g an orthogonal set of components that expla<strong>in</strong> <strong>the</strong> variation <strong>in</strong> <strong>the</strong> data. The result<strong>in</strong>g<br />

components – <strong>the</strong> pr<strong>in</strong>cipal components – are based on <strong>the</strong> assumptions of l<strong>in</strong>earity.<br />

The first pr<strong>in</strong>cipal component (PCA1) is <strong>the</strong> direction <strong>in</strong> which <strong>the</strong> greatest variance lies. The<br />

second component (PCA2) is <strong>the</strong> direction <strong>in</strong> which <strong>the</strong> next largest variance lies, <strong>and</strong> so on. How many<br />

components are used? It depends on <strong>the</strong> data, but <strong>the</strong>oretically <strong>the</strong>re are as many components as <strong>the</strong>re<br />

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