Insurance Risk Study - Aon

Size and Correlation
Insurers of different sizes face different levels of
correlation across their portfolios. For small insurers,
the process risk in each line of business may keep the
correlation observed between lines relatively low. In
contrast, large insurers are exposed primarily to the
systemic risk in each line, but correlation in systemic
risk will drive observed correlations across the portfolio.
The U.S. correlation coefficients published earlier in
the Study represent an average level of correlation for
companies with premium volume above a threshold
Workers Compensation vs. Other Liability — Occurrence Commercial Auto vs. Other Liability — Occurrence
Correlation Above Threshold
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
10 100 1,000 10,000
Size Threshold, $M
Correlation
Risk Study Coefficient
Correlation Above Threshold
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
Aon Benfield
of $100 million. We selected this threshold as
representative of the size of a typical product division
within a medium to large insurance company. The
observed level of correlation varies within this threshold,
as shown below for several pairs of lines. Companies
with volume exceeding $100 million will observe an
increasing level of correlation between lines. For
example, between workers compensation and other
liability occurrence, the correlation at $100 million is
63 percent, at $500 million it is 72 percent, and at
$1 billion it is 80 percent.
0
10 100 1,000 10,000
Size Threshold, $M
Correlation
The table below shows the measured correlation coefficients at different premium thresholds between U.S.
Schedule P lines. In each case, both premium amounts exceed the threshold.
Risk Study Coefficient
Line of Business Correlation by Premium Size Threshold
Line A Line B $25M $50M $100M $250M $500M $1,000M
Homeowners Private Passenger Auto 10% 11% 8% 17% 33% 33%
Commercial Multi Peril Commercial Auto 33% 37% 53% 55% 73% 58%
Commercial Multi Peril Workers Compensation 27% 31% 42% 48% 48% 59%
Commercial Multi Peril Other Liability — Occ 22% 27% 48% 46% 53% 53%
Commercial Auto Workers Compensation 49% 60% 63% 71% 73% 85%
Commercial Auto Other Liability — Occ 51% 54% 67% 78% 82% 78%
Workers Compensation Other Liability — Occ 44% 51% 63% 67% 72% 80%
Other Liability — Occ Other Liability — CM 45% 50% 57% 55% 59% 65%
Medical PL — CM Other Liability — CM 65% 72% 72% 64% 68% n/a
Medical PL — CM Workers Compensation 47% 72% 71% 73% 77% n/a
The larger the company, the more important correlation becomes for the company. Regulators and rating agencies
scrutinize correlation assumptions in their evaluations of capital adequacy. Aon Benfield Analytics can help
companies understand the sensitivity of their model results to correlation assumptions and guide them during the
rating agency review process.
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