Magazine article Risk Management

# Calculating the Value of Insurance

Magazine article Risk Management

# Calculating the Value of Insurance

## Article excerpt

What is the value of insurance world of skyrocketing premiums? Along with rates, the value equation is shifting. To capture this value, risk managers are using sophisticated financial tools to test insurance designs across a wide range of loss scenarios. These tools have come from advancements in statistical and computing technology. But other conceptual innovations, such as the notion of economic capital, are allowing insights into the foundations of risk management.

By using economic capital to estimate value, risk managers can identify opportunities where the value proposition of insurance still holds, even in today's hard market.

The concept of economic capital is rooted in investment banking, where it arose as a means of measuring performance. The manager of a trading unit needed to distinguish between deals that offer the opportunity to profit and deals without the potential. The manage also needed to be able to identify (and reward) high-performance traders. In a trading operation, where risks are taken only with the expectation of generated returns, the goal to maximize return while taking the least amount of risk could be achieved through risk-adjusted performance measurement. Risk adjusted return on capital (RAROC) thus became a vital management metric, with economic capital as its key risk-sensitive input.

Return on capital (ROC) can be adjusted for risk to become RAROC in a number of ways. The risk adjustment can be affect the numerator or denominator (or both) of the ROC ratio. Risk adjusted return (RAR) implies an adjustment to the numerator, while risk adjusted capital (RAC) implies an adjustment to the denominator. The corresponding ratios can be distinguised as RORAC and RAROC. If a ratio is constructed with adjustments to both the numerator and denominator, it is risk adjusted return on risk adjusted capital with the clumsy acronym RARORAC. In common usage, these measures are seldom distinguised from the another and are generically referred to as RAROC.

Utilizing economic capital to adjust for risk has become fairy standard. By this approach, each investment has both a safe an a risky component. The risky component implies exposed capital beyond the investment's nominal cost. The additional exposed capital is economic in nature and is referred to as economic capital. If the expected return is constant, increasing risk results in lower RAROC. With this tool, good investments, i.e., those that make efficient use of economic capital, can be distinguished from bad investments.

For example, an investment of \$1.00 growing to \$1.20 over the course of one year has a return of 20 percent. Consider two such investments, each expected to earn an identical 20 percent, but where investment A is very conservative and low risk, while investment B is highly speculative and high risk.

Risk implies the use of capital. If the low-risk investment uses \$0.25 in economic capital and the high-risk investment utilizes \$1.50 in economic capital, on a risk-adjusted basis the two investments can be compared as follows:

[RAROC.sub.A]

= 0.20/(1.00+0.25)

= 16%

[RAROC.sub.B]

= 0.20/(1.00+1.50)

= 8%

Economic capital figures, as functions of the risk of each investment, facilitate the comparison. If two investments are expected to earn the same amount, but one carries more risk than the other, then all rise being the same, the one with less risk is preferred.

Economic capital is not like book capital that is tracked by accountants and shows up on financial statements. It is a calculated amount that is scaled to unexpected outcomes, in particular unexpected negative outcomes. By virtue of its construction, economic capital is a number that facilitates comparisons on a risk-adjusted basis. Therein lies the utility of the concept of economic capital in the insurance context. …

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