An Empirical Map of Enterprise Risk Space for ... - ERM Symposium

(e) corr(ξi, εj) = 0 for all i,j 6
(f) [Initially] corr(ξi, ξj) = 0 for all i,j, i ≠ j. I.e., the initial extracted factors are uncorrelated
(orthogonal).
Results of Factor Analysis within the Risk Clusters and ERM Clusters -- Creation of the Risk
and ERM Tools Maps
We look to the first few factors to determine the meaning of the cluster. The first few factors are
usually responsible for a substantial proportion of the variability of the cluster variables (denoted
by the eigenvalue). And the meaning of a factor can be gleaned from the variables with highest
factor loadings. For those clusters with high eigenvalues (high variance explained by each
factor), Table 3 shows the loadings for the most significant factors in each of the of these risk
clusters. We also provide our interpretation of the resultant themes of the clusters.
Table 3 - Risk Space - Factor Loadings for the Clusters with High Variance Explained by
the Factors (Eigenvalues) and their Themes
Cluster 1
Factor Number Eigenvalue
1 9.696722
2 3.746450
3 2.679885
Theme
Variable Factor1 Low Liquidity – Asset risk
LAtotal 0.876416
LAInvestedAssets 0.841905
LpBond2Private 0.818397
LpBprivate 0.818267
LWtotal 0.753522
LpBond1Private 0.737044
LpBond3Private 0.715046
Variable Factor2 Life product risks
LpAPolicyLoans 0.523196
5 This is a natural assumption: If two ε‘s could be correlated, then part of their effects would be in common to their
two X-variables and not unique to their separate X-variables.
6 This is a natural assumption: If a common factor correlates with another unique factor, then that other unique
factor is not unique to its X-variable, but also shares in the explanation of the X-variable of the common factor. And
if a common factor correlates with its own unique factor, then that unique factor necessarily correlates with another
X-variable (because the common part is, after all, in common to the X-variables), and so is also not unique.
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