October 22nd, 2012

Risk Preference Function – Embedding Risk-Reward in Capital Allocation

Posted at 1:00 AM ET

mango_don_gcciDonald Mango, Head of Global Advisory
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Capital allocation decisions are among the most important decisions made by company management. Through our own research and thought leadership and our observance of best practices at clients around the world, Guy Carpenter’s Enterprise Risk Management Advisory practice has compiled a set of leading practices around capital allocation for (re)insurers.

We would like to highlight one of the practices here, the Integration of Explicit Statements of Risk Preference. The first key insight in this process is the notion that every risk metric has an implicit risk preference behind it. 

The practice can be illustrated by looking at the simplest metric: Value-at-Risk (VaR - also known as probable maximum loss (PML) or percentile), as shown in Figure 1 below.

Figure 1

impli-1

A common example of VaR is the 99.5 percentile capital metric from Solvency II. Underlying a VaR metric is a laser-focus on the change in a single percentile of the earnings downside distribution. Capital allocation decisions are multi-dimensional, making them unsuited for any single metric decision process. Many companies recognize the weaknesses of using a single VaR, and they extend their metric to Tail Value-at-Risk (TVaR) (Figure 2), the average of all VaR points beyond a certain return period threshold.

Figure 2

impli-2

TVaR is a definite improvement over VaR because of the additional stability provided by averaging over a larger portion of the tail. However, TVaR treats all scenarios in that portion of the tail equivalently, meaning, for example, the firm is indifferent between losing 10 percent of capital and losing 15 percent, or between losing 15 percent and 20 percent, and so on. Most management teams would not support this statement of their underlying risk preferences. Company leaders recognize that there are knock-on effects associated with greater and greater losses of capital, ranging from ratings watch to downgrade to loss of franchise viability. Companies are beginning to quantify these knock-on effects using what we call a “zones of impact” approach. An example is shown in Figure 3.

Figure 3

impli-3

We have found a three-zone approach to be a good starting point. Management teams can wrap their heads around the relative severity of the impact. The heights of the boxes are a visual representation of what we call a risk preference function. It is the quantification of management’s risk reward tradeoffs, and our best practice capital cost allocation approach can translate that function into capital cost allocations. This gives a company a seamless, transparent means to drive risk management from the leadership team down to the field.

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Statements concerning tax, accounting, legal or regulatory matters should be understood to be general observations based solely on our experience as reinsurance brokers and risk consultants, and may not be relied upon as tax, accounting, legal or regulatory advice, which we are not authorized to provide. All such matters should be reviewed with your own qualified advisors in these areas.

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