A Survey of Capital Allocation Metrics
CAPITAL ALLoCATIoN IS A DISCIPLINE without consen-
sus. Some believe in sticking strictly to allocating the cost of capital,
while others believe in allocating capital itself. Meanwhile, the meth-
ods for allocating capital (and its attendant costs) vary, ranging from
the simplest—standard deviation—through the increasingly complex
covariance, co-excess tail value at risk (co-xTvaR) and shared-asset
approaches. The exercise becomes one of managing trade-offs, as risk
managers balance the simplicity of effort against the potential benefits
of capital optimization.
There are two broad approaches to
allocating capital: marginal and proportional. The former involves starting
with a portfolio of risks, imposing an
incremental change (e.g., an increase or
decrease to a segment) and measuring
the impact of the change on risk and reward metrics. The proportional method
also starts with a portfolio of risks, but it
then assesses the contributions of individual segments to overall portfolio risk
metric without modifying the portfolio.
Marginal methods tend to be used for
strategic decision-making, such as reinsurance purchasing and acquisitions.
They can be used for capital allocation,
but theoretical issues (including order
dependence) require post-process adjustments such as off-balancing. The
proportional methods, on the other
hand, tend to be used for true allocations, pricing and planning.
Based on the most common goals for
capital allocation, I’ll focus on proportional approaches to capital allocation.
The complexity and inconsistencies
of marginal metrics outweigh their
benefits.
To understand the differences in proportional capital allocation methods, it
helps to have a reference point. Consider
a simple hypothetical insurer that writes
auto, general liability, workers’ compensation and property business. The loss
distributions are a bit exaggerated to
highlight some of the differences among
metrics. A profile of the company’s business is shown in Figure 1.
The company has a 30 percent expense ratio. Current accident-year
losses and changes in reserve estimates are assumed to be positively
correlated within and across lines, with
correlations ranging from 0 percent to
50 percent. The expected profit is approximately $55 million on surplus of
$350 million, for an expected pre-tax return on surplus of just under 16 percent.
