March 23rd, 2010

Corporate Decision Making Using Economic Capital Models: Part II: Identifying Capital Needs

Posted at 10:00 AM ET

Susan E. Witcraft, Managing Director

Capital needs can be defined from a number of different perspectives:

• Regulatory: which focuses on the probability of insolvency;
• Rating agency: which focuses on both the probability of insolvency and the ability to continue with the current rating; and
• Going concern: which focuses on the ability to continue to implement current plans.

The perspective determines the types of metrics that will be used to establish the level of capital required.

Many regulators require or plan to require insurers (1) to have a 1-in-200 probability of becoming insolvent in a calendar year. In those situations, the negative of value-at-risk (VaR) at the 99.5 percent probability level for one calendar year of change in net worth will determine the capital requirement.

Rating agencies similarly look at the probability of becoming insolvent, though the threshold used varies among agencies. Many such agencies are interested in not only the probability of insolvency but also the amount. As such, their focus is on the tail value-at-risk (TVaR), which is the average amount of loss across a stated set of scenarios, or the expected policyholder deficit (EPD), which is the average amount of insolvency given that there is one.

Value-at-risk, TVaR and EPD can be estimated from an economic capital model. Figure 19.3 shows the economic capital needed to meet the probabilities of default associated with various Standard & Poor’s ratings.

Fig. 19.3


The probability distribution of the change in net worth is used to determine the amount of capital needed to ensure that the probability of insolvency is less than that corresponding to each Standard & Poor’s rating. For example, at a Standard & Poor’s rating of A, the approximate probability of default is 0.15 percent. For this insurer, the change in net worth at the 0.15th percentile is USD480 million, so the capital needed to limit the probability of default to less than that of an A-rated instrument is USD480 million. The chart shows that this company has a net worth of about USD1 billion, so it has much more capital than is needed by this metric. If this metric is the only one used for evaluating capital adequacy, the company might consider stockholder or policyholder dividends, taking on more risk in its investment portfolio, reducing its use of reinsurance or writing more business through indigenous growth or acquisition.

For ongoing business management, many companies look at metrics that reflect their abilities to continue with business as planned. For example, companies might want at least a 70 percent chance that their BCAR will stay above the minimum threshold for an A rating or a 90 percent chance that the loss of net worth over some stated time period will be no more than 5 percent. Again, with the results of an economic capital model, the amount of net worth needed to meet these objectives can be estimated.

Figure 19.4 shows the capital needed to ensure that impairments of different levels happen less frequently than selected return times. To determine the amount of capital needed for a 90 percent chance that the change in net worth will be worse than a 20 percent loss, the change in net worth at the 90th percentile (USD80 million) is determined. For this amount to be no more than 5 percent of net worth, the insurer must have five times that amount in net worth or USD400 million.

Fig. 19.4


Figure 19.5 uses BCAR and selected return times to determine required capital. Figure 19.5 shows the net worth needed to keep BCAR above the minimum threshold for each rating at selected return times. The shades of black and gray correspond to return times, as shown in the figure’s key.

Fig. 19.5


The capital needed to support an A- rating exceeds the company’s net worth about once every 10 years, whereas the capital needed to support an A++ almost always exceeds the company’s net worth. As such, this company is unlikely to attain an A++ rating, but will generally have enough capital to meet the minimum requirement for an A- rating from A.M. Best.

If, for example, the company stated one of its risk tolerance requirements to be no more than a 50 percent chance that its BCAR would fall below the minimum requirement for an A rating, it would either need to increase its net worth or reduce its risk. The economic capital model can be used to identify the best choice among options such as a capital contribution, a reduction in writings, purchase of more reinsurance, a move towards greater diversification in the business written or a move to less risky assets.

Another important use of analysis of capital requirements is capitalisation of groups in totality and by company. An economic capital analysis can be instrumental in understanding and quantifying the impact of diversification effects across companies within a group. The capital allocation techniques discussed later in this chapter can also provide indications as to whether specific companies within the group are over- or under-capitalized and whether capital contributions or dividend distributions may be appropriate.

(1) “Insurers” will be used and will be assumed to include reinsurers as all concepts discussed apply to both types of entity.

(2) Net worth will be used to represent capital as measured under an accounting paradigm. Depending on the context and jurisdiction, it is sometimes referred to as economic capital, policyholder surplus, net assets or net worth, among others.   

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.  To the extent that you discuss such statements with your clients, be sure to advise your clients that all such matters should be reviewed with their own qualified advisors in these areas.

Click here to read Part I: Introduction and Quantifying Corporate Risk >>

Click here to view additional material on Solvency II >>

Click here to view additional material on modeling >>

Click here to view additional material on ERM >>

Excerpted from Susan Witcraft’s contribution to “The Solvency II Handbook,” which brings together highly regarded practitioners and academics working in the Solvency II area to provide a practical guide for implementing internal models - the focus of Pillar I and the area demanding greater attention in preparing Solvency II.

Click here to view the table of contents of The Solvency II Handbook >>

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