This document is incomplete without the accompanying discussion; it is confidential and intended solely for the information and benefit of the immediate recipient thereof. Strategy Capita l Value Risk Using Dynamic Financial Analysis to Support Capital Allocation & Profit Measurement Capital Allocation and Profitability March 9/10, 2000 Manuel Almagro, FCAS, MAAA Principal Tillinghast - Towers Perrin

Capital can be allocated to business segment using the “expected policyholder deficit” measure Expected policyholder deficit (EPD) = Expected (liabilities in excess of assets) In this simple example, there is a 10% chance that losses will be $6,000; an 80% chance that losses will be $10,000; and a 10% chance that losses will be $14,000 Assets are only $13,000, so there is a 10% chance of ruin, in which case the available $13,000 will be paid, leaving a deficit of $1,000 Thus, at the funding ratio of 130%, the EPD ratio is 1% (both percentages are with respect to the expected losses of $10,000) 2

3 While the EPD illustration on the previous page is highly simplistic, the concepts readily generalize to more “real-world” situations The illustration is intended only to show the conceptual essence of the insurance transaction  Policyholders and shareholders each contribute assets towards the funding of the liabilities  Policyholders contribute premiums based on expected loss costs and compensation for risk, based on market pricing  Shareholders contribute capital for the balance, to achieve the target overall funding ratio necessary to offer policyholders adequate security  Claims “happen”, and the assets are distributed  Claims are paid, up to the available assets  Shareholders receive the residual assets, if any, as their return The split of assets between policyholder-supplied funds (premium) and shareholder-supplied funds (capital) is not necessary to the approach  The premium would reflect the expected losses of 10,000, plus a market determined return for risk-taking  Ignoring the return for risk, the premium would be 10,000 and the 130% funding ratio is equivalent to a 3.33:1 premium-to-surplus ratio

There are well-constructed theoretical arguments for the use of expected policyholder deficit in capital allocation The EPD concept is taken from Risk-Based Capital development work (see Butsic’s paper in the 1994 Journal of Risk and Insurance) EPD is different from ruin probability, because it takes into account the severity, as well as the frequency of ruinous scenarios  EPD takes the policyholder perspective – it recognizes that capital is there to provide security, and that the perceived level of security relates both to the potential frequency and severity of non-performance  Allocation on this basis is “fair" to policyholders — since they all have equal access to the entire base of capital, they are all receiving the same level of security – allocating capital based on EPD “charges them” equitably for the capital needed to create that level of security The EPD is financially equivalent to the expected value of the shareholders’ option to “put" the company to the regulators if the liabilities exceed the available assets  In such instances the liabilities in excess of the assets would have to be paid by the Guaranty Funds – thus, EPD is also theoretically equivalent to the expected Guaranty Fund assessment 4

To illustrate the use of EPD in capital allocation, consider a two line example As a starting point, each line has the same funding ratio of 130% Each line also has the same 10% ruin probability Because their risk profiles are different, the lines currently have different EPD ratio’s Product AAssetsProbabilityLiabilitiesPaymentDeficit Scenario 113, %6,000 0 Scenario 213, %10,000 0 Scenario 313, %14,00013,0001,000 Expected13, %10,0009, %1.0% Product BAssetsProbabilityLiabilitiesPaymentDeficit Scenario 113, %6,000 0 Scenario 213, %9,250 0 Scenario 313, %20,00013,0007,000 Expected13, %10,0009, %7.0% 5

If the two lines are independent, a company writing both lines would have an overall risk profile reflecting their convolution At the current funding ratio of 130%, the combined lines have an expected deficit ratio of 2.0%; and the probability of ruin is 9% If the company’s risk-capital constraint allowed only a 1% chance of ruin, additional assets of $4,000 would be required 6

The first step is to determine the required overall capital that satisfies all risk-capital constraints A funding ratio of 150% is required to reduce the probability of ruin to the threshold level of 1% After this risk-capital constraint is met, the overall EPD ratio is.20% 7

Having determined the overall level of required capital, the second step is to allocate the capital to business segment The total assets of $30,000 are allocated such that the EPD ratio is the same for each product Since Product B has larger potential losses, it has a higher funding ratio While the overall EPD ratio is.2%, the line EPD ratios are both 2.0% 8

9 When there are more than two products, with different covariances, the allocation of the benefit requires a marginal analysis To illustrate, consider a three product example in which the results for Product A are independent of the results for Products B and C, but the results for Products B and C are 100% correlated. The 1% ruin standard implies a corporate EPD of.20%. The total covariance benefit is 5,400, which is allocated based on a comparison of the marginal decrease in required assets when each product is added in to the other business For example, Products B and C require assets of 39,600. When A is added in the total requirement drops from 55,400 to 50,000, for a marginal benefit of 5,400 At EPD of.20%MarginalNet FundingRequiredCovarianceLineRequired ProductRatioAssetsBenefitAllocationAssets A 158.0% 15,8005,4003,24012,560 B 228.0% 22,8001,8001,08021,720 C 168.0% 16,8001,8001,08015,720 Total55,4009,0005,40050,000 A U B 175.0% 35,00034,280 A U C 145.0% 29,00028,280 B U C 198.0% 39,60037,440 A U B U C 166.7% 50,000

10 The illustration demonstrates a workable approach to capital allocation In summary, the capital allocation steps are as follows:  Set risk-capital constraints  Determine overall required assets and capital to meet all constraints  Translate overall required capital into implied EPD ratio  Calculate capital required by each line standing alone at constant EPD ratio  Determine overall covariance benefit across lines  Allocate covariance benefit based on marginal contribution of each line The basic approach can be extended to incorporate other risks, and more realistic scenarios  Expenses, investment income, income taxes  Multiple accounting periods, timing of cash flows  Asset uncertainty  Accounting valuation rules, affecting the timing of the recognition of revenue, expense, and profit

Once the capital is allocated to a segment using the EPD approach, performance can be judged on an ROCE basis A major benefit of the exercise is the ability to measure the returns on the capital employed by each segment, and to gauge the returns in relation to their risk Returns in this context are the notional shareholder distributions, reflecting the investment of capital into the segment, and the release of that capital back to shareholders  Returns are measured on an economic, rather than a reported basis  This approach is consistent with actuarial appraisal theory, which measures economic values in the essentially the same manner In addition to the expected results, the financial model produces a distribution of results – that distribution can be converted to a distribution of returns  Risk/return tradeoffs can be made by comparing expected ROCE to ROCE volatility  Rather than using standard deviation as the risk measure, a measure that emphasizes downside potential (below selected threshold) should be used ROCE - Return on Capital Employed, or return on allocated capital 11

12 To measure the riskiness of returns, we suggest using “Below Target Risk”, rather than standard deviation The use of standard deviation as a measure of risk has been criticized  Standard deviation is a statistical measure of dispersion from the mean, which is not necessarily the same as risk  Standard deviation gives the same weight to dispersion below the mean as dispersion above the mean - a risk-averse person would place greater weight on the downside than the upside Below Target Risk is computed in the same manner as a standard deviation, except  Deviations are measured from the “target”, which can be the mean or some other selected value reflecting the company’s “threshold for pain”  Only results below “target” are included in the calculations - deviations above the target are ignored  If the distribution is symmetric and the mean is chosen as the target, then the BTR will be one-half of the standard deviation BTR =

13 The advantage of Below Target Risk over standard deviation can be illustrated by an example These two return probability distributions have the same expected return of 13%, and the same standard deviation. The top return distribution is clearly preferable to the bottom, as it has more upside, and less downside Using a target return of 13%, the top distribution has a BTR of 23.5%; the bottom distribution has a BTR of 32.5% Using a target return of 3% (roughly equivalent to a zero real return), the top distribution has a BTR of 17.6%; the bottom distribution has a BTR of 27.7% 13% Rate of Return Probability

14 Distributions of results can be translated into distributions of returns on capital Professional Liability Return Distribution -100% -80% -60% -40% -20% 0% 20% 40% 60% 80% 100% Cumulative Probability Rate of Return EXAMPLE

15 Security Market Line 2% 6% 10% 14% 18% 0.0%4.0%8.0%12.0%16.0% Below Target Risk (Negative Real Return) Expected Return Small Cap Stock Large Cap Stock Bond Index Cash Long Bond Real Estate Homeowners Illustrative The adequacy of returns can then be judged in relation to risk Risk to investors is measured by Below Target Risk as a proxy for systematic risk Personal Automobile