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by Donald F. Mango Enterprise Risk Analysis for Property & Liability Insurance Companies, a newly published book from leading global risk and reinsurance specialist Guy Carpenter, provides a comprehensive and practical guide to enterprise risk management (ERM) for insurance executives, risk managers, actuaries, academics and others. It covers both traditional ERM topics like loss distribution modeling and loss reserve models, as well as emerging solutions such as timeline simulation and linking risk management and capital optimization. The following article is adapted from Enterprise Risk Analysis for Property & Liability Insurance Companies.
Evolution of corporate decision making under uncertainty Simulation modeling is widely used in all forms of corporate and organizational decision making under uncertainty. A science has developed around this topic and is known as decision analysis, which involves the three-step evolutionary process illustrated in exhibit 1. 1. Deterministic Project Analysis: Using a single deterministic forecast for project cash flows, an objective function such as present value or internal rate of return is produced. Sensitivities to critical variables may be shown. Uncertainty (along with other intangibles) is handled judgmentally (i.e., intuitively) by decision makers. 2. Risk Analysis: Forecasts of distributions of critical variables are fed into a Monte Carlo simulation engine to produce a distribution of present value of cash flows. Risk judgment is still applied intuitively. 3. Certainty Equivalent: Certainty equivalent is an extension of risk analysis that quantifies the intuitive risk judgment by means of a corporate risk preference or utility function. The utility function does not replace judgment but simply formalizes the judgment so it can be consistently applied. Best practice in actuarial risk modeling has evolved to step 2, the risk analysis stage. Indeed, that is what actuaries call DFA. There is not yet consensus that the next evolutionary leap from step 2 to step 3 is proper or even meaningful. The debate centers on the role of corporate risk preference in an efficient market/modern portfolio theory world. An attempt to summarize the debate might go as follows:
Within such a theoretical framework, there is no apparent place for the step 3 certainty equivalent approach, with its mathematical formulation of corporate risk preferences. Managers should care only about the wealth, risk preferences and other investment opportunities of the firm’s owners. Absent a real-time survey system, the best proxy for this information is the record of stock prices – both their own stock and other comparable stocks. Firm managers and equity analysts perform these (admittedly complex) analyses in an attempt to discern the probable impact of major firm decisions on the stock price. While this theory is appealing and has many advocates, it is short on practical advice for use in risk management decision making within the firm itself. For example:
Decision making with an internal risk model (IRM) Now we will discuss how corporate risk management decision making might be done with an internal risk model (IRM), a DFA model of the organization itself. Exhibit 2 shows the major elements in the process. Elements 5a and 5b will be our focus here. We will begin with corporate risk tolerance. Element 5a: Corporate risk tolerance We seek a mechanism that: 1. Takes an aggregate loss distribution, with many sources of risk (e.g., lines of business); 2. Assesses (quantifies) the impact of the possible aggregate loss outcomes on the corporation; 3. Assigns a cost to each amount of impact; and 4. Attributes the cost back to the risk sources.
Alternatively, the translation of impact into cost requires a risk preference function of some form, either implicitly taken from an outside source (e.g., the capital markets), or explicitly derived from firm management attitudes. The key point is that any selected method implies some type of translation from impact to cost. Some questions facing practitioners include: Should the choice be yours or someone else’s (i.e., adopted by default)? Should it be implicit or explicit? If a firm would like to develop its own explicit risk preferences, there are methods available. It’s possible to identify the parameters of a normative corporate risk policy using a series of experiments involving indifference. One of the outputs of such a process is the transparent, objective, mathematical expression of the corporation’s acceptable risk-reward tradeoffs. Such a function can improve cost-benefit analyses by quantifying, for example, the minimum decrease in risk (measured by any number of possible metrics) sufficient to justify a certain mitigation cost. Without such a function, cost-benefit analysis (CBA) decisions will still be made; however, the criteria will be inconsistent and opaque, driven in large part by the individual decision makers’ intuitions and preferences. Mr. Walls’ innovation is the notion that in order to select one of the efficient frontier portfolios, the firm must be able to answer the following questions:
The first question requires an answer to the firm’s risk tolerance. The answer will indicate the riskiest portfolio choice that is tolerable. The second question requires the firm to express its risk preferences. The answer will allow the firm to select among available returns for given risk levels. Once the first two answers are known, the third question can be answered. Mr. Walls shows how, by using a corporate utility function, “decision makers can incorporate their firm’s financial risk propensity into their choices among alternative portfolios.” Of particular importance is the idea that modern portfolio theory presents a set of choices among possible portfolios. Which of those portfolios to choose is still a firm-specific decision, requiring explicit expression of firm risk preferences. Element 5b: Cost of capital allocated Capital allocation is among the most significant open questions in actuarial science. While a thorough treatment is well beyond the scope of this article, there appears to be general agreement that what is really allocated is the cost of risk capital as opposed to capital itself. This is in contrast to the capital allocations that occur in manufacturers. Those allocations involve actual cash transfers of retained earnings and the investment of that capital in the operation of the business – in salaries, materials, power, marketing, etc. Risk capital allocations, on the other hand, are completely theoretical. When an insurer writes an automobile policy, no risk capital is transferred to that policy. Perhaps by an unfortunate turn of history, the same manufacturing capital language was used to describe risk capital. This reinforced the adoption of capital decision analysis techniques based on manufacturing analogies, such as internal rate of return. Risk capital for financial intermediaries provides a buffer that secures a certain counterparty status for the firm in total. In this regard, risk capital is a measure of the firm’s total risk-bearing capacity. Because of the portfolio phenomena of diversification and accumulation, however, this capacity is solely an aggregate measure, only having meaning for the portfolio in total. In the case of a generic firm, the “portfolio” is the accumulation of risk exposures from all sources – operational, credit, market, etc. Because the elements of portfolios may have nonlinear interdependence, the impact of any one element on the portfolio can also be nonlinear. This makes a linear, proportional allocation of a total amount back to individual elements quite complicated. There are many possible ways this problem can be solved, each having its own compromises and limitations. Many researchers continue to allocate risk capital but use it as an interim step in assigning the cost of that risk capital to portfolio elements. The cost is the product of a riskadjusted capital amount and a hurdle rate. Since the capital is risk adjusted, this goes by the acronym RORAC (Return on Risk-Adjusted Capital).
Given cost of risk capital, with no allocated capital amount, a good candidate decision variable is economic value added (EVA®)2. The formula for EVA is: EVA = NPV Return – Cost of Capital EVA is typically expressed as an amount. An activity with a positive EVA is said to “add value,” while one with a negative EVA “destroys value.” Element 5c: Cost-benefit analysis (CBA) for mitigation Once the corporate risk tolerance and capital cost allocation are completed, the CBA is straightforward. For example, under the EVA approach, any mitigation effort resulting in a positive incremental EVA is worth doing. Under capital allocation, any mitigation project where benefit (reduced capital cost) exceeds costs should be undertaken. Risk management in an organization with multiple business units and risk sources involves analysis of a complex, multidimensional space. Effective decision making in that space will be challenging, based solely on a single risk metric. Statistical theory would recommend a suite of decision metrics that are (as much as possible) distinct and independent, reflecting different dimensions of the space, and responsive to different dynamics. However, corporate realities often mandate that a compromise be struck in the interest of parsimony. Corporations must make decisions, and effective decision making often simplifies complex situations as much as possible, but no more so. 1 Journal of Petroleum Science and Energy 44 (2004) pp. 55-56 Donald F. Mango is a managing director in the Instrat® unit at Guy Carpenter. He focuses on analysis and advice for clients and has extensive experience in and knowledge of enterprise risk management. Mr. Mango can be reached at . |
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Neither external (market) nor internal (company) perspectives appear sufficient on their own. However,
there may be a perspective from which both approaches
are seen as complementary parts of a single whole.
Shareholders want market value maximized. Market value
consist of book value (the recorded value of held assets)
plus franchise value (the present value of future earnings
growth). Risk management aims to both facilitate future
earnings growth and prevent loss of future earnings
– that is, to protect franchise value. So it appears that
shareholders and managers may be aligned in this regard.
Both want risk management in place to protect the
franchise value. Therefore, both camps should support
an internal corporate risk policy to help the firm make its
risk management decisions in a more objective, consistent,
repeatable and transparent manner. This provides some
degree of support for the evolution to step 3.
Corporate risk tolerance is needed in steps 2 and 3.
The impact (effect) of a loss depends on the organization’s
size, financial resources, and ability and willingness to
tolerate volatility. We will call this combination of factors
the corporation’s risk tolerance.
Others have tried to address this by taking a fundamentally
different tack. They define risk capital for a financial
intermediary as the amount needed to guarantee the
performance of that intermediary’s contractual obligations
at the default-free level. Under this framework, the notion
of return on risk capital has no meaning, since they have
bypassed the two-step RORAC process and leapt straight
to a cost. In extending this approach to insurance, we’ve
spurred a fundamental innovation – the recognition and
treatment of the entire pool of risk capital as a shared asset
or common pool resource.
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