What is the value of insurance in today’s 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 more 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.
Measuring Risk-Adjusted Performance
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 that potential. The manager 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 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 distinguished as RORAC and RAROC. If a ratio is constructed with adjustments to both the numerator and the denominator, it is risk adjusted return on risk adjusted capital with the clumsy acronym RARORAC. In common usage, these measures are seldom distinguished from one another and are generically referred to as RAROC.
Utilizing economic capital to adjust for risk has become fairly standard. By this approach, each investment has both a safe and 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:
RAROCA = 0.20/(1.00+0.25) = 16%
RAROCB = 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 else 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.
Insurance and Value Generation
Retaining risk exposes the firm’s capital base to loss. Whether or not retained risk is specifically funded—through an accounting accrual, self-insurance fund or captive insurer—in the event of a loss the firm’s capital base must respond. (The firm’s capital base is defined in a broad economic sense, including debt and equity funding.) Whether or not a loss has actually happened, retained risk implies that the firm’s base of economic capital is working. Thus when a firm chooses to buy insurance, it is utilizing insurance industry capital in lieu of the firm’s own economic capital.
In this way, the link between insurance and value creation can be characterized by efficient use of capital, and value creation can be explicitly measured as RAROC.
Rarely is the purchase of insurance viewed as a value-generating activity. In the event of a loss, insurance is perceived as merely making a bad circumstance less bad. It is otherwise considered an undesirable expense. But insurance is the principal way by which a firm can regulate the use of its economic capital to support operational risks.
For the insurance decision maker, just as for the investment banker, the ability to discern good deals from bad deals is critical. Risk is capital, and understanding the extent to which the firm’s economic capital supports retained risk shapes the insurance purchase. If a decision to buy insurance is effectively a decision to utilize insurance industry capital in place of one’s own capital, then the converse is also true. That is, a decision to retain risk is appropriate when rewarded by an adequate economic return. As risk imposes a cost to an organization, if that cost can be reduced, then value is effectively generated. An optimal insurance design generates maximum value for the firm.
The Economic Cost of Risk
How can a risk manager act on these concepts? Modern computing tools allow us to model future outcomes, and the models allow us to estimate the effects of risk on an organization. These same models of risk can be used to allocate economic capital and to identify optimal insurance solutions.
Though actuarial science has long focused on expected value losses and long-run average losses, the costs that arise from insurable events vary from period to period and cannot be predicted with absolute certainty. The potential for losses to be higher or lower than what is expected is real uncertainty. The potential for downside risk is where economic capital plays a role. Statistical models of risk, capturing the full spectrum of probabilistic outcomes, are used to estimate not just average losses, but also the severe tail events that drive the need for economic capital.
The costs risk imposes on an organization can thus be quantified and divided into three categories:
1. Expected retained losses (and other variable expenses)
2. Premiums (and other fixed expenses)
3. Economic capital (supporting volatility)
The economic cost of risk (ECOR) is the sum of these three quantities. The first two categories account for the dollar trading inherent in the insurance transaction. The third category is typically calculated as an opportunity cost, but this by no means implies that real capital needs be segregated from the working capital of the firm.
Independent of these three variables, there is no optimal insurance decision. For example, we cannot say that a firm of a given size will have an ideal retention level. We can say, however, that a firm may have the capacity to retain a certain amount of risk before feeling unacceptable levels of financial pain. But we can determine the desirability of retaining risk only with knowledge about the underlying risk and marketplace opportunities.
Risk carries an economic cost. Focusing on a specific insurable risk, economic cost without insurance can be estimated as total expected losses plus the cost of capital. With insurance, economic cost can be estimated as the sum of the three components. The difference between the ECOR with and without insurance is an estimate of the dollar value generated for the firm through the purchase of insurance. Taking this one step further, if an investment of economic capital (the retention) yields an economic return (economic savings) we can measure the quality of this investment as RAROC.
For example, an insurable risk is estimated to have annual discounted expected losses of $1 million, with a volatility such that an additional $10 million in economic capital is required for its support. With a cost of capital of 20 percent the ECOR before insurance can be estimated as:
ECOR<no ins> = $1 million + ($10 million x 20%) = $3 million
Now suppose the firm can insure catastrophic outcomes under a policy with a large deductible. If the policy costs $700,000, and still leaves the policyholder with a hedged risk having discounted expected retained losses of $900,000, which requires capital support of an additional of $2 million, then the ECOR after insurance can be estimated as:
ECOR<ins> = $0.7 million + $0.9 million + ($2 million x 20%) = $2 million
Economic cost savings is $1 million, which is the value generated for the firm. Viewing the retention as an investment opportunity, we can estimate RAROC as economic return divided by economic capital or:
RAROC = $1 million / $2 million = 50%
Rational Dynamic Response
To maximize the value generated for the firm through the purchase of insurance, risk managers must quantify not only the average long-run expense associated with the risks involved, but also the support needed for unexpected loss provided by the firm’s economic capital. When viewed this way, insurance is surrogate capital, and the insurance decision generates value. Risk in and of itself is not necessarily bad; strategically used, insurance allows it to be taken profitably.
The reality is that as time goes on and the firm, the risks and the market change, optimal retentions will also change. Maintaining an optimal level of insurance, like maintaining an optimal capital structure, is an ongoing challenge.
In-House or Outsourced Data Analysis?
Risk managers have approached the implementation of these concepts in various ways. In the Midwest, at least two large retailers have relied on outside consultants to provide the required analyses and expertise. Outsourcing quantitative work is probably the fastest way for a risk manager to access these new methodologies; and especially when the analysis is used primarily within a risk management department to help make insurance decisions, relying on consultants may be just fine given the needs of their organizations. In some large organizations, however, not just risk management is not the only group interested in sophisticated financial analysis. Some have found that treasurers and CFOs are also interested parties. In these organizations, the discussion of insurance couched in use-of-capital terminology has resulted in a sudden and shared language that can be nothing short of revolutionary. In response, risk managers have hired permanent full-time quants to provide the analyses required given their organization’s ongoing and enhanced internal communication needs. |
Mark Ames is a principal and Alan Crowe, FCAS, MAAA, is managing director with Mercer Risk, Finance & Insurance Consulting, a division of Mercer Oliver Wyman, in Philadelphia.
