FiguRE 6: Cost of Capital by Line Using Shared-Asset Approach
Policy type Cost of Capital (thousands) Allocation
Auto 660 8.5%
General Liability 740 9.5%
Workers’ Compensation 970 12.5%
Property 5,410 69.5%
FiguRE 7: Allocation Percentages
Allocation Based on:
Co-xtVaR
(expected
income)
Co-xtVaR
(zero
income)
20.0% 15.7%
22.2% 18.0%
28.9% 23.6%
Policy type
Auto
General Liability
Workers’
Compensation
Property
Standard
Deviation
13.4%
14.2%
20.1%
Covariance
7.4%
8.2%
10.5%
Shared
Asset
8.5%
9.5%
12.5%
52.2%
73.9%
28.9%
42.7%
69.5%
expected income as the threshold and
the same cost of capital. (There is also a
metric, weighted co-x TVaR, which will
produce equivalent results to the shared
asset approach with the same weights.
As is inferred by its name, weighted co-x TVaR is a weighted average instead
of an unweighted average of the values
used in the co-x TVaR calculation.)
The shared asset approach has similar advantages and disadvantages as
co-x TVaR. Additional benefits to this approach are ( 1) its avoidance of directly
allocating capital to line, which recognizes that all surplus is available to all
lines, and ( 2) the ability for the user to
specify greater preference for smaller
surplus losses than larger ones.
when moving from standard deviation
to covariance. Recall that covariance
considers these correlations whereas
standard deviation does not. (There is
a rarely used metric called co-standard
deviation—the square root of the covariance—that would produce coherent
allocations.)
The use of the one-sided co-xTVaR metrics leads to very different
allocations when compared to the two-sided covariance metric. (Although
rarely used, one-sided metrics that are
not conditional on the overall result include semi-variance and semi-standard
deviation. These metrics are calculated
in the same manner as variance and
standard deviation with the exception
that only values less than the mean for
the statistic being calculated—rather
than for the total—are included.)
When the co-x TVaR threshold is
expected income, smaller deviations
from the mean are relatively more important and surplus is allocated fairly
evenly among business segments. As
the metric focuses on increasingly severe metrics, such as co-x TVaR with
a zero income threshold and then the
shared asset approach, which gives even
greater weight to adverse results, the allocation to property increases again as
property catastrophe losses (a segment
of the property model) are the primary
drivers of severe adverse results for this
company.
Insurers have choices in evaluating
how to allocate capital and its cost. The
ultimate goal is to strike a balance between feasibility (based on management
acceptance and effort) and capital optimization. Eventually, most companies
are likely to migrate toward contribution
methods, along the lines of co-x TVaR
and the shared-asset approach, with
thresholds varying with the specific
questions being reviewed and specific
corporate risk tolerances.
Resource
Mango, Donald F. “Insurance Capital as a
Shared Asset,” ASTIN Bulletin International
Actuarial, 2005: 35: 2, 471-486, http://www.
casact.org/library/astin/vol35no2/471.pdf.
Comparing metrics
A comparison of the percentages of
capital or the cost of capital allocated to
each line using each of the proportional
methods is shown in Figure 7. As you can
see, there are significant differences in
allocation percentages among the different metrics.
The high correlation between property and total results leads to an increase
in the allocation percentage for property
SUSAN WITCRAFT is a fellow of the
Casualty Actuarial Society and a member
of Contingencies’ Editorial Advisory
board. She is managing director for
Guy Carpenter INSTRAT. Guy Carpenter
& Co. LLC provides this material for
general information only. Guy Carpenter
& Co. LLC makes no representations
or warranties, express or implied. The
information is not intended to be taken
as advice with respect to any individual
situation and cannot be relied upon as
such.
