No 3/2005 Insurers’ cost of capital and economic …4 Swiss Re, sigma No 3/2005 The size of the...

sigmaNo 3/2005 Insurers’ cost of capital and

economic value creation:principles and practical implications

3 Summary

5 Introduction

9 Cost of capital in theory

14 Cost of capital and value creation in practice

22 Estimating the cost of capital

39 Appendix I: Variables used in the empirical analysis

41 Appendix II: Regression results

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3Swiss Re, sigma No 3/2005

Summary

The focus of this sigma is on insurers’ cost of equity capital.

The cost of capital is a key parameter for steering a company. This sigmadiscusses cost of capital issues in an insurance context by investigating fouraspects in particular: the theory of the cost of capital applied to insurance companies, methods that are commonly adopted to derive cost of capital estimates, the size of cost of capital for insurers, and factors determining value creation in insurance.

Cost of capital theory applied to insurance companies

Determinants of insurers’ cost of capital For all enterprises, the cost of capital is directly related to the size and type of risks assumed. Insurers in particular are primarily involved in underwriting insur-ance policies and investing in capital markets, therefore assuming insurance and financial market risks. Insurers’ cost of capital should therefore reflect their exposure to both types of risks.

Methods commonly adopted to derive cost of capital estimates

This sigma explores the appropriatenessof two models for estimating insurers’cost of capital.

Two methods for evaluating the cost of capital are reviewed in detail: the Capital Asset Pricing Model (CAPM) and the Market Consistent Pricing Model (MCPM).

CAPM is the most commonly used model for cost of capital estimates, both for its computational simplicity and the fact that it requires only publicly available information. However, experience suggests caution in applying cost of capital estimates based on CAPM for decision making in insurance. This is due primar-ily to two reasons: beta estimates have been proven unstable, and splitting the overall cost of capital down to individual lines of business, which is essential for company steering, is difficult.

MCPM is an alternative methodology, primarily suited to internal use by insur-ers. It explicitly takes key drivers of insurers’ capital costs into account by distin-guishing between the cost of capital for insurance and for investment activities separately. By isolating these two parts, MCPM also has the advantage of help-ing insurers focus on the more problematic areas, such as estimating the cost of capital of the pure insurance part of the business.

Swiss Re, sigma No 3/20054

The size of the cost of capital of insurers

Cost of capital for the US non life sectoris in the range of 7–8%. The comparablefigure 20 years ago would have beentwice as high.

Cost of capital estimates for the US non-life industry, derived by applying the CAPM and the MCPM methods, range between 7–8%. These estimates are based on an equity risk premium of 4%, a risk-free interest rate of 3% on one-year Treasury bonds and the current average industry composition of invest-ment assets. The comparable figure for the cost of capital in the 80s would have been in the range of 15%. The reason for this decline is that both risk-free inter-est rates and the equity risk premium – which are at the basis of any cost of capital calculation – are much lower today than in the past.

Empirical analyses on a sample of 27 comparable US P & C companies for the period 1993 to 2002 indicate that, in general, cost of capital estimates derived from CAPM are much more volatile through time and from company to com-pany than are equivalent estimates derived using the MCPM method. In this study, estimates of cost of capital for the company sample range from 5.1% to over 11% using CAPM and from 7.4% to around 10% under MCPM. The study used historical market values of beta, interest rates and asset and liability struc-tures of companies for these estimates.

Factors determining value creation in insurance

Investors discriminate by quality ofearnings, rewarding insurers with bestunderwriting practices, top line growthand scale of operations vs those whofocus on investment returns.

In order to test whether the cost of capital theory holds true in reality, this sigma presents the results of an empirical analysis on adjusted statutory accounting and market capitalisation data for the company sample mentioned above.Evidence was found that: The companies with the highest economic price/book ratios achieved a

combination of high underwriting profit margins, premium growth, and scale of operations. These three variables together explain two thirds of the varia-tions in price/book ratios.

Differences in investment strategy were found to have a neutral effect on the price/book ratio. Due to data limitations, it was not possible to test whether investment strategies targeting higher returns without increasing financial market risk exposure create value.

The empirical evidence supports the validity, on average and over time, of the assumptions underlying the MCPM method, and therefore its suitability for the estimation of capital costs for insurance companies.

Further research needed

Despite the fact that data mining and regressions were conducted with great care, it has to be stressed that the empirical results on value creation are based on a limited sample of US companies and therefore should be considered asindicative only. Further research on the topic with other data sources is needed.

Summary


Cost of capital and economic value

Shareholder value is created only whenthe return generated on capital investedexceeds the cost of capital.

When investors provide capital to companies, they naturally require or expecta return on that investment. This is the cost to a company of using shareholder capital. It is a well-known corporate finance concept that a company or a project creates value for its shareholders (or, in equivalent terms, economic profit) only to the extent that the returns generated by the company exceed investor require-ments.

In this report, the cost of capital is thecost of equity capital.

The scope of the analysis in this study is confined to the cost of equity capital.¹ The problem with equity capital is that there is no contractual arrangement be-tween the company and its equity investors on what is an adequate remunera-tion for the equity they provide.²

Corporate finance theory suggests that the cost of capital for a company can be determined by considering the returns earned from alternative uses of that capi-tal. This is the so-called opportunity cost of investing.³ Corporate finance also clarifies what these opportunity costs are under various circumstances:

The cost of capital is the return investorsexpect to earn on alternative projects witha comparable risk.

Companies with no capital constraints. In this situation, the relevant cost of capital is the return investors could achieve on capital markets by investing in projects with a comparable risk. In other words, the cost of capital equals shareholders’ expected returns. The riskier a project/company is, the higher the return investors will require and, thus, the higher will be its cost of capital.

Companies with capital constraints. There may be situations where there are attractive projects, but the existing capital in the company falls short of what would be needed to carry out all projects with a positive economic value. Two such scenarios can be depicted: – Companies raising capital in order to be able to exploit all opportunities.

As raising capital causes additional costs (see textbox: “Cost of raising equity capital”), the opportunity cost of capital to be applied is higher. – Companies having to choose between alternative investments, given the current amount of capital available. There may be times when the company is not able to raise capital at all. In this case, it will be the return of the least profitable project⁴ which has to be taken as the opportunity cost of capital. Clearly, the cost of capital under these circumstances may be substantially higher than under unconstrained conditions.

Introduction

¹ For a company that uses other capital sources besides equity (eg debt), the overall cost of capital is calculated as a weighted average cost of equity and debt capital, where the weights depend on the company’s targeted capital structure. The cost of debt and equity are respectively derived from market yields on the company’s long-term debt and the firm’s cost of equity capital.² For simplicity, from here onwards, cost of capital will be used as an abbreviation for cost of equity capital.³ See E.F. Brigham and P.R. Daves, “Intermediate Management”, 8th edition, 2004.⁴ In particular, it is the risk-adjusted return that is used as a benchmark to place a value on alternative investment opportunities.


Cost of raising equity capital

The marginal cost of capital exceeds theaverage cost of capital, due to transaction and signalling costs.

When companies need additional equity, the cost of capital is usually higher than in a situation in which no extra capital is needed. There are several reasons for this: Transaction costs. An insurer issuing shares must pay investment-banking

fees⁵. Another, less quantifiable, cost is the legal requirement to disclose pub-licly sensitive information in its registration statement.

Signalling costs. Investors may wonder why the insurer has decided to issue shares at this particular time. Perhaps the company feels its stock is richly val-ued or foresees problems down the road. These concerns can result in new share issues being underpriced, which leads to dilution costs for the firms ini-tial owners.The effectiveness of communication, equity capital market condi-tions at time of issue and past track record will influence the size of the dis-count at which the issuing firm offers its shares.⁶

The implication of transaction and signalling costs is that the marginal cost of additional capital exceeds the average cost of capital.

The cost of capital estimates presented later in this study refer to the situation of companies operating without capital constraints. Therefore, it is the return that existing shareholders demand.

Target setting and cost of capital

Profitability targets normally exceedthe cost of capital benchmark.

A remark on the relationship between cost of capital and target setting is useful at this point. When comparing profit targets with cost of capital estimates forinsurance companies, one often observes that most companies set their ROE targets well above their cost of capital figures, usually by 10% or more. Why is this the case? The chart below explains why ROE targets exceed the cost of capital both in unconstrained and constrained capital situations.⁷ A first answer to this question is that, in the absence of capital constraints,

maximising economic value means that each business has to earn at least its cost of capital at the margin. Setting the average company-wide ROE target higher than the firm’s cost of capital may therefore simply reflect the fact that the company has some business whose margins substantially exceed theaverage cost of capital threshold (case A in Figure 1).

A second motivation has to do with value maximisation under capital con-straint. In this situation, projects that are economically profitable have to be rejected because the company does not have enough resources to invest.⁸

Introduction

⁵ Fees for raising additional equity are usually in the range of 2.5–3.5% of the value of the transaction. However, this may differ according to the jurisdiction, the size of the offering, and the size of the placing syndicate.⁶ Over the last decade, insurers have become increasingly familiar with alternative financing sources. A full spectrum of capital instruments, ranging between senior debt and straight equity is now available, specifically addressing the issue of maximising the cost-benefit payout through various layers of capital.⁷ For simplicity’s sake, in Figure 1 the marginal cost of capital is set constant, and therefore it is equal to the firm’s average cost of capital.⁸ Alternatively, the company could raise additional capital when it has attractive opportunities to pursue. This is likely to come at higher cost (cfr. “Cost of raising equity capital” text box).


It therefore follows that the target (average) return on equity for the company will be above both the cost of capital benchmark⁹ and the average profitabil-ity target in an unconstrained capital situation (case B in Figure 1).

There is also another reason for profitability targets being above the cost of capital benchmark, which has to do with accounting and economic dimen-sions. In the case of insurance companies, the accounting equity figure, which is sometimes used as a reference for the profitability target, normally underestimates the economic measure of equity on which cost of capital is calculated.¹⁰ Therefore the discrepancy between accounting-based targets and economic measures of value creation is largely artificial.

Figure 1ROE and cost of capital

Ret

urn

Cos

t of c

apita

l

Return – case B(average)

Return – case A(average)

Return(marginal)

Equity capitalB A

Cost of capital (average and marginal)

Source: Swiss Re Economic Research&Consulting

Economic value added

Cost of capital

A: Economic value under no capital constraintB: Unexploited business opportunities under capital constraints (gray area)

%

One more reason why managers usually set target returns in excess of cost of capital has to do with the company’s ability to retain its independence. In practice, a company that consistently achieves economic returns well above its cost of capital and whose investors acknowledge this and expect it to be the case in the future, will have a market value exceeding its book value. On the other hand, companies that do not succeed in earning returns in excess of their capital costs will have market values below their book values. History shows that the management of these latter companies runs a high risk of be-ing replaced or of seeing their companies being taken over.¹¹

⁹ Operating under capital constraints severely restricts a company’s growth potential. That is why companies normally set joint profitability and growth targets.¹⁰ For a definition of economic capital, see footnote 26.¹¹ Setting profitability targets independently of a company’s business potential and cost of capital may lead to sub-optimal business decisions. The most intuitive example is that of a company that uses an incorrectly low cost of capital estimate to define its profitability target. The company will end up ac- cepting business that does not cover the true cost of capital, and over time this mistake will manifest itself in a lower share price. On the other hand, consistently setting excessively high targets can be detrimental, too. Firstly, profitability comes at the expense of growth. Secondly, the management may venture into riskier activities in order to meet its declared targets. Higher profit targets that drive the company into riskier businesses will not pay off in a higher share price, as shareholders then demand a higher cost of capital.


Cost of capital and business steering

Using the right estimate of the cost ofcapital is crucial for business steering.

Business steering with the goal of maximising the economic value of the com-pany requires the management to pursue those ventures that achieve the high-est economic profits per unit of capital invested. The main revenues and costs that have to be taken into account in this process are:

Premiums + Investment income – Claims, other costs and taxes – Capital costs = Economic Profit

Capital costs are included in this calculation to reflect the fact that capital is allo-cated to “absorb” the riskiness embedded in the venture. Capital costs are cal-culated as the product of the amount of capital supporting the venture and its cost of capital. Both the cost of capital used and the amount of capital support-ing the venture affect the profitability of the business being analysed. As this publication focuses on the cost of capital, the issue of determing the capital needs for a certain business is a separate topic not dealt with in this sigma.

As the cost of capital may vary with the risk profile of different ventures, using the right estimate of the cost of capital is crucial for business steering.

Based on traditional measures of risk, the higher the volatility of economic profits, the higher the riskiness of the venture, the higher the associated cost of capital.

Furthermore, the overall profitability of the firm is positively affected by the diver-sification benefits between various insurance lines and, more generally, between investment and underwriting risks. The latter occurs because insurance andinvestment risk are largely, albeit not always, uncorrelated.

The outline of this sigma

Outline of this sigma The structure of this sigma is as follows: the next section, entitled “Cost of capi-tal in theory”, deals with the question of how to approach conceptually the issue of the cost of capital in insurance. The following chapter, “Cost of capital and value creation in practice”, offers some empirical evidence on the validity of the theory and on how value is created in insurance. Finally, the last section reviews the most frequently used methods of capital cost estimation, focusing in par-ticular on the Capital Asset Pricing Model (CAPM) and the Market ConsistentPricing Model (MCPM). It examines their suitability for insurance management decisions and, based on the empirical application of these two methods, it pro-vides concrete cost of capital estimates both for the US non-life sector and for a limited sample of US P & C companies.

Introduction


This section of the report reviews the economic theory of the cost of capital for an insurance company.¹²

In theory, the total return to shareholdersreflects the risks embedded in investingand underwriting.

In theory, the total return required by shareholders depends on the level and types of risks undertaken by the insurer. Underwriting and investment are the core activities of an insurer; they expose the company’s capital to insurance and financial market risks. Therefore, the cost of capital for an insurance company can be analysed by examining each of these sources of risk separately.¹³ Theinstrument used to separate the two cost of capital components is the replicat-ing portfolio.

Using replicating portfolios to value insurance liabilities¹⁴

Reclassification of insurance companies’ balance sheets and income statementsin market-consistent terms

As cost of capital is an economic parameter, the value of assets and liabilities on an insurer’s balance sheet has to be expressed in economic terms. This means that a market-consistent valuation of assets and liabilities is chosen as a basis for deriving cost of capital estimates.¹⁵ For those items that are liquidly traded, the market price can be taken as a reference for their economic value. This is usually the case for the financial assets held in insurers’ investment portfolios. However, insurers’ balance sheets also contain a large number of non-traded items, for which no liquid market exists. The most relevant examples are insur-ance liabilities, but also reinsurance receivables.

Replicating portfolios are used in insurance to simplify the determination ofthe value of insurance liabilities.¹⁶ The replicating, or hedge, portfolio for a non-traded liability is defined as the portfolio of traded market instruments whose cash flows match as closely as possible the corresponding cash flows of theliability being replicated (Figure 2).

Cost of capital in theory

¹² As is the case for nearly all theories of corporate finance, this theory is based upon the assumption that markets price the shares of insurance companies such that no arbitrage opportunities arise or, in other words, that the markets operate efficiently. However, markets are not completely efficient. There arearbitrage opportunities, even in liquidly traded markets. The next chapter examines how markets value insurance companies in practice and discusses how well the efficient-market assumptions hold up inreality.

¹³ This separation is artificial, as in real life companies operate in an integrated fashion. For example, in-vestment decisions usually take into account the duration and volatility of the insurance business portfo-lio. However, this breakdown is necessary to ensure correct calculation and allocation of cost of capital.

¹⁴ See Swiss Re Technical Publishing, “The Economics of Insurance”, 2001, for more information on this subject and examples of calculations.

¹⁵ Strictly speaking, a full economic balance sheet would also include items such as default option andliquidity value of the company.

¹⁶ Replicating portfolios are routinely used in finance to find market-consistent values for cashflows that are not actively traded. If non-traded assets were not priced consistently with traded cashflows, then in-vestors would arbitrage the difference by purchasing the cheaper cashflow and selling the more expen-sive one. This principle is known as the no-arbitrage principle.


Figure 2Replicating portfolio technique appliedto insurance liabilities

First year

Claims

Second year Third year

Expenses

Tax payments

Cash flows

Replicating portfolio

In the case of those insurance liabilities whose cash flows do not depend onfinancial market risks, the best approximation is achieved by matching the ex-pected cash flows of the liability with those from a bundle of zero coupon bonds. For example, a claim payment of USD 100 expected 3 years from nowis matched with a 3-year zero coupon bond with a maturity value of USD 100.

In practice, the replication of insurance liabilities is a challenging process. Infla-tion risk, duration mismatch and embedded financial options all add complexity to the analysis.

If the cash flows of the liability that is being replicated depend on financial mar-ket variables, then that liability is matched with financial market instruments whose cash flows also depend on financial market variables. For example, infla-tion-sensitive casualty liabilities may be matched with inflation-indexed bonds; similarly a Guaranteed Minimum Death Benefit (GMDB) embedded in a life con-tract is normally matched with a put option on the relevant stock market index.

Cost of capital measured as the sum of investment andinsurance cost of capital

The balance sheet of an insurer can be segmented into an investment balance

sheet and an insurance balance sheet with the use of replicating portfolios (Fig-ure 3).¹⁷ The insurance balance sheet shows the replicating portfolio as an asset and the investment balance sheet shows the replicating portfolio as a liability.

Figure 3Breakdown of an insurancebalance sheet

Liabilities Liabilities

EconomicNet Worth

Replicatingportfolio

Replicatingportfolio

EconomicNet Worth

Assets Assets= +

+=

Insurance company Investment operations Insurance operations

Cost of capital Investment cost of capital Insurance cost of capital


¹⁷ Figure 3 shows a simplified view of an insurers’ balance sheet where all assets are traded financialmarket assets and all liabilities are non-traded insurance liabilities.


The breakdown of an insurer’s balance sheet is instrumental to identifying thecost of capital components.

The investment balance sheet is exposed only to traded financial market risks, as, by construction, it only contains traded market instruments. In contrast, the in-surance balance sheet does not contain any traded financial market risk. This is because the replicating portfolio was constructed so as to hedge out any traded risk embedded in the insurance liabilities.¹⁸

Cost of capital drivers can be derived for each of these two components of aninsurer’s balance sheet, as described below. The details on how to estimate the investment cost of capital and the insurance cost of capital are presented in the section “Estimating the cost of capital”.

Investment cost of capital

Under this framework, the estimate of the investment cost of capital is straight-forward. Shareholders of insurance companies provide risk capital that is in-vested on their behalf in financial assets. Shareholders could have taken those same investment positions on their own or by investing in a leveraged invest-ment fund with the same asset allocation. The return that they would haveotherwise achieved by investing in a leveraged fund is the opportunity cost of investing in an insurance company.

Parallel between insurers and investment funds

By issuing insurance policies, insurers enter into an agreement with their policy-holders, whereby the insurers receive a premium today in exchange for the pay-ment to the policyholders, at some point in the future, of a financial compensa-tion, if a pre-specified uncertain event occurs. The funds raised by selling insur-ance policies are then invested in financial assets, while the promise of future compensation gives rise to an insurance liability.

The investment part of the balance sheet of an insurance company therefore looks very much like that of a leveraged investment fund, which typically raises debt through capital markets and invests the proceeds in liquidly traded finan-cial assets.

Comparable risks The risks to which the leveraged fund is exposed are essentially financial market risks. Its performance is typically measured against a market benchmark. In eco-nomic terms, the market benchmark represents the fund’s cost of capital from the point of view of the investors in the fund. It is the opportunity cost of invest-ing in the fund. Investment funds create value for their investors only when their performance meets or exceeds that of the relevant benchmark.

¹⁸ This means, for example, that if interest rates go up, the economic value (discounted value) of liabilities goes down. However, the value of the replicating portfolio constructed out of fixed income instruments will also go down. If the replicating portfolio was constructed correctly, the change in market value of the replicating portfolio should exactly offset the change in the economic value of the liability.


An important point here is that the investment cost of capital for the insurer’sinvestment arm depends on the riskiness of the investment portfolio selected.

Investors in a listed fund expect a lower return if the fund is invested in Treasury bonds, rather than in stocks. Similarly, shareholders of insurance companies will adjust their required return, or cost of capital, as a function of the investment risk assumed.

Figure 4 below highlights the main risk components underlying the cost of capi-tal of the investment operations.

Figure 4Risk spreads relevant for theinvestment cost of capital


Financial investments oninsurers’ balance sheets

Expected return in excess ofrisk-free rate

Shares Equity risk premium

Government bonds Sovereign default riskpremium

Corporate bonds Credit spread (adjusted fordefault rate)

Real estate Illiquidity premium +occupancy risk premium

Private equity Equity risk premium(adjusted for leverage) +illiquidity premium

Funds of funds Equity risk premium +illiquidity premium

On a final note, all else being equal, one would expect the total cost of capital for an insurance company to be at least as much as the cost of capital for aninvestment fund taking the same investment positions.

Furthermore, if the investment cost of capital is any different for an insurer than for an investment fund with the same investment positions, that means thatarbitrage opportunities exist. These potential arbitrage opportunities are dis-cussed in the next chapter.

Insurance cost of capital

In addition to the investment risks of a leveraged investment fund, insurers also take insurance risks, which give rise to additional costs known as frictional capi-tal costs.¹⁹


¹⁹ Although financial theory predicts that in a frictionless world markets would not charge for diversifiable risks, in practice markets operate with frictions that result in significant costs for taking diversifiable in-surance risk.


Frictional capital costs capture the opportunity costs shareholders incur when in-vesting capital via an insurance company rather than directly in financial markets.

There are three sources of frictional capital costs in insurance, as depicted in

Figure 5 below.

Figure 5Drivers of frictional capital costs

Frictional capital costDriver

Cost of financial distressFranchise value, capitaladequacy

Agency, uncertainty costsTransparency, reputations,incentives

Illiquidity cost related toregulatory and rating capital

Regulatory and rating environment(restrictions on capital)


Costs of financial distress This component arises due to potential direct and indirect costs of financial dis-

tress. Selling insurance introduces the risk that an insurer will experience finan-cial distress.²⁰ Financial distress can be costly due to both direct costs – such as the dead-weight costs of needing to raise fresh capital, legal fees and lost value from distressed sales – and indirect costs – primarily loss of reputation and as-sociated franchise value.

Agency costs The second component of frictional capital costs is agency costs. When share-

holders invest via an insurance company, they entrust their capital to manage-ment, who take investment and underwriting decisions on their behalf. Share-holders expect management to act in their best interests, but (differently from an investment fund) this is difficult to control due to an intrinsic lack of transpar-ency. As a result, shareholders require an additional return to compensate themfor the possibility that management may not always act strictly in their bestinterests.²¹

Cost of illiquidity due to regulatory restrictions on capital Insurers operate in a regulated environment which requires them to hold mini-

mum levels of capital to support blocks of business. As capital is locked in, itbecomes illiquid. It can only be physically accessed by selling or securitising the underlying business, which generally gives rise to additional costs due to the lack of a liquid market for insurance liabilities. Therefore, the capital illiquidityintroduced by insurance regulation is a friction shareholders have to be com-pensated for.

²⁰ An aggressive investment strategy may also increase the risk of financial distress.²¹ Agency costs arise whenever the owners of a company are not its managers, independently of the

industry being analysed. However, they are relevant in this context as insurers are compared toleveraged investment funds, which have no agency costs, as their sources of performance are rather transparent.


As discussed in the previous section, the cost of capital for an insurance com-pany depends on its investment and insurance risk portfolios. In this chapterthe theory of cost of capital is tested for its validity in practice.

Given the limited size of the sample, the results presented below cannot be re-garded as representative of the whole US P & C sector nor can they be extended to other insurance markets. It would be interesting to enlarge the analysis to cover a broader group of companies and different geographic markets.

The sample

The empirical analysis focuses on a set of 27 traded US P & C companies.²² These companies were chosen because US P & C statutory filings provide enough infor-mation to construct economic balance sheets and income statements, including replicating portfolios and a split of income into investment and insurance income. The sample was limited to companies that had ten years of statutory filings (1993–2002)²³ and whose net assets declared in statutory filings (adjusted to a GAAP basis) covered between 80% and 120% of their GAAP net assets.²⁴

Economic price/book ratios as indicators of value creation

When a company earns a return that is higher than the cost of its tangible capi-tal (economic net worth), it is said to earn an excess return. If investors expect a company to earn an excess return, they will be willing to pay more for the com-pany than just the value of its economic net worth. This is reflected in a highratio of market capitalisation to economic net worth, called an economic price/book ratio in this publication. Companies that do not earn their cost of capital, on the other hand, have market values which fall short of the value of their eco-nomic net worth.

In this chapter, we examine the relationship of investment strategies, underwriting

and company size to economic price/book ratios.

Cost of capital and value creation in practice

²² Limited data availability for other markets prevented the study from having a broader geographic scope.²³ The Onesource database (which is the source used for companies‘ statutory filing) does not offer data

before 1993. This conditioned the length of the data series.²⁴ The objective was to exclude those companies that had other significant businesses not captured under

US non-life statutory filings (eg life, foreign business). Only for the companies that met these criteria could the adjusted statutory data then be meaningfully compared with their market valuations.


Value creation through investment operations

The hypothesis According to the theory, companies that take less financial market risk will have

a lower investment cost of capital than companies that follow riskier investment strategies.²⁵ Therefore, the extra return generated by taking financial market risk does not create shareholder value. This also means that the price/book ratio will not be affected by the investment strategy.

On the other hand, value could be created by actively managing investmentsand identifying market mispricing opportunities. This is because extra returns areaccrued without taking extra market risk.

Do investors require equity-likereturns from insurers?

One widely held view is that investors expect an “equity-like” return from insur-ance shares. Insurers need to take some financial market risk if they wish to meet these expectations. In other words, given two insurers that generate the same total return but follow different investment strategies (one investing in shares and the other in government bonds), the one that takes less investment risk is not fully compensated for the “higher quality” of its earnings with a lower cost of capital. If this opinion were true in reality, then insurers that take morefinancial market risk should display higher price/book ratios. Conversely, insur-ers that do not take on enough investment risk may experience depressed share prices and soon become takeover candidates.

Given the insurers’ dramatic move out of shares after the burst of the stock-market bubble and the staggering insurance loss related to 9/11, the impact of investment strategy on cost of capital is of great current relevance.

The following section tests the relationship of the investment strategy and in-vestment return to the share valuation of insurers. However, due to data limita-tions, it was not possible to test whether investment strategies targeting higher returns without increasing market risk exposure really create value.

²⁵ For simplicity’s sake, the effect of frictions, such as taxation, are ignored in this analysis.


The empirical analysisInvestment strategy has a neutraleffect on value creation.

The first test uses the percentage of Economic Net Worth²⁶ invested in shares as a proxy for the market risk taken by insurance companies. This parameter isplotted against economic price/book ratios²⁷ for a sample of 27 companies.The values on both axes are averages over the 1993–2002 period²⁸. As the chart shows (Figure 6), the sample covers a wide range of strategies, fromnearly no share investment up to nearly 80% of economic net worth investedin shares. Consistently with the theory, no relationship between investment in shares and economic price/book ratios is observed.

The empirical evidence supports the theoretical view that investing in shares does not lead to a higher price/book ratio.

Figure 6Economic price/book ratio versusequity gearing

Econ

omic

pric

e/bo

ok ra

tio

0% 10% 20% 30% 40% 50% 60% 70% 80%

0%

50%

100%

150%

200%

250%

300%

350%

400%

y = –0.32 × +1.51R² = 0.01

Stock investments / Economic net worth

Sources: Statutory filings derived from Onesource, DataStream, Swiss Re Economic Research & Consulting own calculations

Note: The graph above contains 27 scatter points; each point represents the 10-year average value of the

selected variables for each company included in the sample. A linear regression line is added, together with relevant regression parameters. Unless otherwise stated, the same format is applied to all scatter graphs in this study.


²⁶ In this study, the Economic Net Worth (ENW) is defined as the market-consistent value of assets less the market-consistent value of liabilities. It is the economic equivalent of the accounting tangible equity used as a base for calculating the ROE. Details on the calculation of the ENW are given in the Appendix I.

²⁷ In this study, the economic price/book ratio is defined as market capitalisation divided by economic net worth.

²⁸ Given the limited data set available, it was not possible to produce a more sophisticated regression analysis on individual years. Averages were therefore used, although this means that some information may be lost.


Using replicating portfolios to allocate investment income

The replicating portfolio can also be used to split up the economic income of the company into investment income and underwriting income. To make the split, it is necessary to allocate some measure of investment income to the in-surance function of the company.²⁹ The part allocated to the underwriting func-tion is the actual investment return on the replicating portfolio, as this is careful-ly matched to the characteristics of the insurance liabilities themselves. More-over, the return on the replicating portfolio equals the actual investment return the company would receive if it chose to minimize its investment risk. Any return the company receives as a result of taking investment risks then accrues to the investment operations of the company.

Separating the return generated by taking insurance risks from the returns gen-

erated by taking investment risks allows investment and underwriting decisions to be evaluated in isolation. This avoids unprofitable underwriting being com-pensated by higher returns from engaging in riskier investment activities.

Has the insurance industry been ableto generate excess returns throughinvesting?

The second test uses historical average investment return as a proxy for insur-ers’ ability to drive price/book ratios through investing (see Figure 7). Invest-ment return is calculated as the actual mark to market return on investments less the return on the replicating portfolio and so will include returns from all types of investment, not just shares. Again, figures are ten-year averages and there is no apparent relationship.

Figure 7Economic price/book ratio versusinvestment return on economicnet worth

Econ

omic

pric

e/bo

ok ra

tio y = –5.95 × +1.83R² = 0.04

0% 5% 10% 15%

0%

50%

100%

150%

200%

250%

300%

350%

400%

Investment return on economic net worth


²⁹ Through the sale of insurance policies, the company collects funds that are invested by the asset man-agement arm in financial markets. Asset management needs to pay the underwriting business for the use of those funds, by allocating of some investment income to the insurance function of the company.


The above result is more general than that of the first test, as it looks at all invest-ment-risk-taking activities. The empirical evidence presented above indicates that it is difficult in practice for insurers to earn excess returns through invest-ment strategies simply involving more market risk. Certainly, there are a fewinsurers out there that can consistently beat the market. The empirical analysis, however, cannot verify this.

On the other hand, the analysis indicates that taking investment risk does not hurt share valuations either. In addition, there are strong liquidity and tax argu-ments for why insurers should be investing in corporate bonds and shares.³⁰

Furthermore, riskier investment strategies are expected to generate higher

investment income and ROE (all else being equal). Therefore, insurers can choose their investment portfolio based on their financial market risk appetite, which is affected not only by the company‘s own risk tolerance overall, but also by restrictions imposed by solvency, rating and financial analysts‘ requirements.

However, insurers should not expect taking more investment risk to compensate for poor underwriting profitability, as the analysis in the next section indicates.

Value creation through insurance operations

The hypothesisUnderwriting profitability and premium growth are drivers of value creation.

Can insurers earn excess returns in insurance markets? If insurers are able to generate extra profits through underwriting, then this should pay off in a price for insurance shares which exceeds their book value. Furthermore, financialtheory suggests that the better the prospects of growth, the higher the market valuation. This section examines the relationship between underwriting varia-bles (underwriting profitability and volatility, premium growth and company size) and share price valuation.

The empirical analysis To test this hypothesis, the study used average historical underwriting return³¹

combined with average historical premium growth as a proxy for profitable growth in underwriting. Again, this was plotted against average price/bookratios (the value creation proxy in this study) for the selected sample. Figure 8below shows the result of this regression: historically, companies with a higher underwriting profitability combined with top line growth have a higher price/book ratio. This variable is a better predictor of price/book ratios than either profitability or growth alone, indicating that investors will pay a large premium for companies that can simultaneously achieve profitability and growth. On the other hand, investors are not willing to pay for growth if it comes at the expense of profitability (see Appendix II for more detail on the regressions).


³⁰ See “The Economics of Insurance”, cited in footnote 14, for a discussion.³¹ Underwriting ROE is obtained by dividing the economic underwriting income by the economic net worth.


Figure 810-year average economic price/book ratio vs underwriting ROE * premium growth

Econ

omic

pric

e/bo

ok ra

tio

y = 88.26 × +1.21R² = 0.59

U nderwriting R0E *premium growth

0%

50%

100%

150%

200%

250%

300%

350%

400%

–1.0% 0.0% 1.0% 2.0% 3.0%


Underwriting volatility and value creation Another test of underwriting performance measured whether the volatility of underwriting results (a proxy for insurance riskiness) decreases the price/book ratio. This is a plausible assumption since it is indeed the uncertainty of insur-ance cash flows that gives rise to the frictional capital costs of insurance opera-tions (see chapter on “Cost of capital in theory”). Figure 9 below depicts theaverage price/book ratios over the 10-year sample period versus the historical average volatility of underwriting results. Coherently with the theoretical tenet, the regression line slopes downward. As underwriting volatility increases, so does the cost of capital, which in turn has a negative impact on the price/book ratio (all else being equal).

However, the empirical evidence suggests that this impact is rather small. Two considerations can help explain this result: The fact that the insurance cost of capital is only a small part of the total cost

of capital. Therefore the impact of changes in this component on market capi-talisation is limited.

The range of underwriting result volatility for the companies included in the sample is rather narrow. If the relationship to market capitalisation is not per-fectly linear (for example, it is shaped like a concave curve so that the price/book ratio decreases faster, the higher the volatility), this would also explain the inelastic reaction of the price/book ratio to changes in underwriting vola-tility.


Figure 910-year average economic price/book ratio vs volatility of underwriting result

Econ

omic

pric

e/bo

ok ra

tio

y = –2.25 × +1.60R² = 0.03

Standard deviation of underwriting ROE

0% 5% 10% 15% 20% 25%

0%

50%

100%

150%

200%

250%

300%

350%

400%


There are various reasons why some companies have a lower underwritingvolatility than others. Better risk diversification, risk selection and use of reinsur-ance or alternative risk transfer techniques are the most obvious ones.

Other determinants of value creation for insurers

The impact of size on value creation There is wide empirical evidence that share price performance is affected by the size of the issuer (the so-called size effect).³² In this study, size was tested forits impact on value creation, again expressed as economic price/book ratio.Figure 10 below shows a plot of size (proxied by market capitalisation) versus economic price/book ratio. The regression is significant from a statistical point of view.


³² See G. Lelekadis, I. Davidson, J. Smith, “Does Firm Size Predict Stock Returns? Evidence from the London Stock Exchange”. EFMA 2004 Basel Meetings Paper, for recent general evidence of this phenomenon.


Figure 1010-year average economic price/bookratio vs logarithmic transformationof market capitalisation

Econ

omic

pric

e/bo

ok ra

tio

y = 0.1633Ln(x) + 0.2837R² = 0.1861

Size (Market capitalisation in USD millions on logarithmic scale)

0%

50%

100%

150%

200%

250%

300%

350%

400%

10 100 1000 10 000 100 000


This empirical result suggests that investors may seek the comfort of investing in larger companies, as the latter may be better positioned to secure their long-term profitability. It may also be interpreted as the evidence that economies of scale are important in the insurance industry.

Conclusions

The results of these analyses indicate that three factors – underwriting profitabil-ity, growth, and size – together explain two thirds of the variability in economic price/book ratios for the sample (see Appendix II).


It is essential to understand the methodolo-gies used for estimating the cost of capital.

Despite the difficulties and uncertainties involved in estimating the cost of capi-tal, many decisions companies need to take depend on it. As a result, themethod a company chooses to estimate its capital costs and the way it incorpo-rates these estimates into its decision-making process are extremely important.

What is required for this purpose is a methodology that serves the following

needs: to provide a global cost of capital estimate. This allows companies to check if

their overall achieved profitability meets shareholders’ expectations. to allocate capital costs to individual risky activities. This will help understand

where and how value is created within the company.

Cost of capital and business potential realisation

The cost of capital is most useful inevaluating business activities.

In order to take the cost of capital into account in decision-making within the firm, a company needs to know the cost of capital for individual transactions. For example, what is the required return on a life contract with a minimumreturn guarantee versus one without such a guarantee? What is the requiredreturn on a property cover with natural catastrophe exposure? It is inappropriate to use the firm’s average cost of capital to analyse individual transactions. This practice would inevitably favour riskier ventures and penalise less risky ones. This not only leads to inaccurate internal performance comparisons, it may also have external consequences. Businesses whose allocated capital costs fall short of the actual risk involved may experience adverse selection problems. Con-versely, businesses to which the cost of capital is over-charged may not be com-petitively priced, and may fail to achieve their full profit and growth potential.

Only cost of capital methods that reflect the risk profile of each line of business and measure it in a market-consistent way can provide unbiased guidance for pricing and strategic decisions. They also have the great advantage of aligning business objectives, enhancing internal transparency and facilitating compara-bility within the firm.

Methodologies most commonly adopted

The cost of capital for a company canbe estimated internally or externally.

Cost of capital estimates are available from a variety of sources.³³ The methods applied vary depending on whether the cost of capital estimates are for an in-dustry, a company, or a specific business area of a company. The data available also condition the methodology adopted. The proliferation of estimation tech-niques and publications on this subject has accelerated as companies look for more sophisticated ways to estimate capital costs.

Estimating the cost of capital

³³ Financial analysts calculate the cost of capital when valuing companies. Companies – particularly large ones – estimate their own capital costs as an aid to quantitatively assessing business decisions. Cost of capital estimates are also available from academics and consultants. Ibbotson Associates and Barra, for example, produce cost of capital estimates for industries and individual companies using a variety of methods.


There are several methodologies forevaluating the cost of capital.

Although many methodologies have been used over time to determine insurers’ cost of capital, most are variations on a handful of core approaches: the historical average of stock market excess returns; the historical average of accounting returns on equity; the discount rate required to equate the stock market value of a company to

the expected future cashflows it will generate (the discounted cash flow mod-el is used in application to both historical and forward-looking parameters);

the “sum of the parts” approach used by some financial analysts, which de-rives the cost of capital from a weighted average of capital costs for various businesses;

the Capital Asset Pricing Model (CAPM) and related linear multi-factor models; and

the Market Consistent Pricing Model (MCPM).

The following table provides an overview of the key features of the cost of capi-tal methods mentioned above.³⁴

Table 1Methods for total cost of capital estimates

Method Data used to derive the cost of capital estimate Cost of capital estimate Share price Interest rate Investment Industry Growth structure environment/ potential business mixHistorical average Yes Yes No No No Risk-free rate + equity risk premium (esti-of stock market (ex post) (ex post) mated through historical series of stock returns market excess returns)Historical average No No No No No Historical average accounting returns ad-of adjusted justed to an economic basis (eg adjusted ROE)accounting returns as a proxy for investors’ expected returnDiscounted Yes Yes No No Yes Discount rate implicitly required for cash flow model consensus earnings estimates to match the current share price of a given stock Sum of the parts Yes No Yes Yes No Fundamental risk coefficients applied to risk- based capital allocated by line of business CAPM Yes Yes No No No Risk-free rate + β * equity risk premium (one factor) (ex post) (ex post) (sensitivity of the company’s stock return to that of the overall market) CAPM Yes Yes No No No Risk-free rate + β₁ * equity risk premium + β₂(Fama-French (ex post) (ex post) * financial distress factor + β₃ * size factor3 factors) MCPM Yes Yes Yes Yes Yes Investment cost of capital (1) + (ex post) (ex post) (ex post) insurance cost of capital (2)

(1) risk-free rate + investment risk premium(*) (2) frictional capital costs

(*) For example: equity risk premium * equity gearing + credit risk premium * bond leverage

Source: Swiss Re Economic Research & Consulting

³⁴ See Shannon P. Pratt, “Cost of Capital: Estimation and Applications”, 2nd edition, 2002, for a fuller expla-nation of these other methods of evaluating the cost of capital.


In this study, only the CAPM and MCPMmodels will be reviewed extensively.

This study takes a close look at CAPM and MCPM because the former is the most widely used model, while the latter is best suited to meeting an insurance company’s internal business steering needs. MCPM is more appropriate for in-surers because it takes into account the insurance companies’ dual use of capi-tal for underwriting and investing and allows for explicit allocation of capital costs between these two activities.

All models involve a trade-off betweenusability and correctness.

Both the CAPM and the MCPM models assume that financial markets are effi-cient. This assumption may be too strong to hold true in reality every time. How-ever, no model can perfectly replicate reality – a balance must be found be-tween usability and correctness. Indeed, all cost of capital estimation method-ologies mentioned in this report are just tools to assist management in taking decisions, and therefore the choice between one or another depends on their respective usefulness.

The next two chapters describe the main assumptions and features of CAPM and MCPM in more detail and present estimates of the cost of capital for the US P & C industry based upon these models.

For the reader’s convenience, there follows a summary of the main parameters used in this sigma for the derivation of cost of capital estimates, under boththe CAPM and the MCPM models. Parameters which are specific to one or the other method are addressed in the section dedicated to that method.

Derivation of the parameters used in this sigma

The risk-free rateThe risk-free rate is taken as 3.0%. The risk-free rate is usually set equal to some short-term rate on T-bills in the US

(or other short-term government bond elsewhere), but some practitioners prefer to match it to the expected duration of the investment being analysed (typically, 3 to 5 years, but occasionally 10 years). Furthermore, its historical level has changed tremendously over the last three decades, as Table 2 illustrates.

Table 2Risk-free rate ranges,January 1976 to May 2005

Max (Aug 1981) Min (June 2003) Average Median Last (May 2005) 16.72% 1.01% 6.73% 6.13% 3.33%

Source: www.economy.com, based on US Federal Reserve data. Interest Rates: 1-Year Constant Maturity Securities, (% P.A.), monthly returns.

In this report, the risk-free rate used as reference for the cost of capital estimate is the one-year rate, estimated to be 3%. When estimating historical cost ofcapital values, as is the case for the selected company sample (see the section “Comparison of CAPM- and MCPM-based estimates for the company sample” at the end of this chapter), actual historical interest rates were used. The aver-age yearly risk-free rate between 1993 and 2002 was 4.67%.



The equity risk premiumThe equity risk premium is taken as 4.0%. The equity risk premium is the extra return generated by the stock market over

the risk-free rate.³⁵ The equity risk premium has been at the centre of a long – and as yet unresolved — debate among practitioners and academics. Estimates of the equity risk premium vary depending on whether it is backward-looking or forward-looking, whether it is computed using arithmetic mean returns or geo-metric mean (compound) returns, and as a function of the risk-free rate and of the index adopted to represent the market portfolio. However, no matter how it is empirically derived, there is abundant evidence that the equity risk premium has declined over the last 50 years.³⁶ For this study, the equity risk premium is assumed to be 4%.

The Capital Asset Pricing Model (CAPM)

CAPM is the most widely used modelfor cost of capital estimates.

CAPM is by far the most widely used model of capital cost in insurance andother industries. It allows for a quick comparison across companies and indus-tries and represents a good first approximation of capital costs.³⁷

CAPM takes diversification into account. The basic idea underlying CAPM is that the risk posed by any individual stock does not matter to an investor. The risk that matters is the combined risk of the investor’s entire portfolio. The return that an investor demands for any individual stock then depends on that stock’s contribution to the total risk of the investor’s whole portfolio. If a single stock contributes significantly to the investor’s overall risk, the investor should demand a high return from that investment. On theother hand, if a risk diversifies with the other risks on the investors’ portfolio and so does not add to the investor’s total risk on the margin, that risky investment is no more costly for the investor than a risk-free investment. Similarly, if adding an investment to the portfolio reduces the total risk of the portfolio, this investment is actually better than a risk-free investment and the investor can be satisfied with a return that is even less than the return on a risk-free investment.

Beta measures the contribution ofa single stock to the total risk of the“market portfolio”.

If all investors hold the same “market portfolio” of investments, the contribution of any individual stock to the risk in the portfolio can be measured by that stock’s beta, which captures the relationship between the return on that stock and the market return. A company whose shares move up and down propor-tionally with the market will have a beta of 1.0. If, however, the company’s shares tend to react to market developments more strongly than the overall mar-ket, its beta will be higher than 1.0. For example, if a stock’s beta is 1.3, a 10% rise in the market overall would be expected to be accompanied by a 13% rise in the value of that stock. Similarly, a company with a beta less than 1.0 tends to exhibit less pronounced reactions to developments that affect the entire market.

³⁵ This is generally estimated through a geometric difference, as indicated in the formula: ERP = where rm stands for market return and rf for risk-free rate.³⁶ See Swiss Re Economic Research & Consulting insights,“The US equity risk premium:

framing reasonable expectations”, July 2004.³⁷ There are variants on CAPM in common use. See, for example, Rosenberg, Barr and Andrew Rudd,

“The Corporate Uses of Beta,” in Chase Financial Quarterly, Vol 1, No 4, Summer 1982, available atwww.barra.com/research

1+rm

1+rƒ–1


The mathematical formula for estimating beta is:

Beta of stock i = βi = covariance (market return, stock i return)/variance (market return)

Although theoretically beta could assume any value, it is rarely negative, usually lying between 0.0 and 2.0.

Under CAPM, the cost of capital is therisk-free rate plus beta times the equityrisk premium.

Under CAPM, the cost of capital (or the return expected by investors in the com-pany’s shares) can be expressed through a linear relationship to three compo-nents: the risk-free rate (rf); the difference between the expected overall market return and the risk-free

rate, also known as “equity risk premium” (rm – rf); and the beta of the company’s stock return relative to that of the overall market.

The mathematical formula used to calculate the cost of capital for the company is:

Cost of capital = rf + (rm – rf) β

Forward-looking parameters and ratesare preferable for the beta and equityrisk premium.

In theory, forward-looking parameters and rates are preferable for beta and the equity risk premium. But because these cannot be directly observed, they have to be estimated. Normally, past market returns and individual share returns are used to estimate the company’s beta. The equity risk premium is also usually de-rived ex-post by comparing the historical market return to the risk-free rate, im-plying that the past is a good indicator of future developments. Some work has been done on estimating forward-looking parameters.³⁸

The use of backward-looking estimates of the cost of capital may present a problem when applying CAPM internally. Betas are estimated using historical share price volatility, and so decisions that change the risk profile of the com-pany going forward are not reflected in the estimate of the cost of capital. Thisis typically the case when a company undergoes material business restructuring or is involved in an M & A transaction.

The CAPM-specific parameter: beta

The beta is dependent upon the time period of estimation and the market return index utilized. Figure 11 uses two years of data for each beta estimate, but there is no rule on the right timeframe for the beta estimate; in practice, two- andfive-year betas are the most common. Usually, a broad market index such as the S & P 500 is used.


³⁸ See Rosenberg, cited in footnote 37.


Figure 11Two-year rolling beta estimates for the US P & C sector vs DataStream whole marketindex and whole market excluding TMT

–0.5

0.0

0.5

1.0

1.5

2.0

DS Insurance index vs DS Total mkt index (excl. TMT)DS Insurance index vs DS Total mkt index

200

320

02

2001

200

019

99

199

819

9719

96

199

519

94

1993

1992

1991

199

019

89

198

819

8719

86

198

519

84

198

319

8219

8119

80

1979

1978

1977

Sources: DataStream market indices, Swiss Re Economic Research & Consulting own calculations

The estimated value of the P & C sector’s beta between 1999 and 2002 varies dramatically depending on the index used (in this case, the DataStream US total market index or the DataStream US total market index, excluding the Technology, Media and Telecommunication (TMT) sector). These years were characterised by a disconnect between the TMT sector and the rest of the market, causing the beta of the insurance sector relative to the whole market to decrease to zero.On the other hand, the beta estimated with the market index excluding the TMT sector increased over the same period.

The beta is taken as 1.03. For the purpose of calculating the cost of capital for US P & C insurers, this study takes the long-term beta estimate of 1.03, based on the market index excluding the TMT sector.

CAPM-based estimates of the cost of capital for the insurance sector

As Figure 12 below shows, the cost of capital for the P & C insurance sector in the US has been declining over the last 25 years. The downward trend is due to the decline in all components of the CAPM model over this period — the equity risk premium, beta and the risk-free rate. (Although the equity risk premium has been trending downwards, for the purposes of this figure it is assumed to be constant).


Figure 12Estimates of cost of capital for the USP & C sector based on CAPM approach

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

20%

Cost of capital (excl. TMT)Risk-free + equity risk premiumRisk-free

20

03

20

02

20

01

20

00

19

99

19

98

19

97

19

96

19

95

19

94

19

93

19

92

19

91

19

90

19

89

19

88

19

87

19

86

19

85

19

84

19

83

19

82

19

81

19

80

19

79

19

78

19

77

Sources: DataStream market indices, www.economy.com, Swiss Re Economic Research & Consulting own calculations. Cost of capital estimated based on rolling 2-year beta and fixed equity risk premium of 4%.

Based on the parameter estimates suggested above (“Derivation of the parame-ters used in this sigma” textbox), this study derives a CAPM-based estimate of cost of capital for the US P & C industry of 7%.³⁹

The challenge of applying CAPM for business steering

CAPM does not explicitly makeallowance for underwriting risk.

When using cost of capital estimates derived by the CAPM method for business steering, insurers encounter a number of difficulties.

First of all, the instability of company beta estimates (as highlighted in the text-box “The CAPM-specific parameter: beta”) represents one of the key problems associated with the CAPM method. Which value of beta should be used in-stead? As sector betas tend to be more stable than company ones, some insur-ers opt for industry-wide parameters. However, the risk of this approach lies in the fact that not all companies have an insurance and investment risk exposure identical to the industry average.

Attempts to adapt CAPM to insurance com-panies have been less than satisfactory.

Secondly, being a model of the cost of capital for the entire firm, CAPM does not help insurers solve the problem of how to allocate their total cost of capital toindividual transactions so as to reflect the associated cost of capital in pricing.


³⁹ The economic price/book ratio for the US P & C industry is 1.2, based on historical average. This sug-gests that the industry has been able to accumulate some franchise value over time. The industry has to earn on average an economic ROE of at least 8.4% if it wishes to maintain the current level of fran-chise value.


Line-of-business betas One approach followed by the industry to bypass this limitation is to estimate betas by line of business. This involves estimating betas for groups of insurance companies that specialise in particular lines (eg marine, credit, or accident and health) and applying these beta estimates to the individual lines within a multi-line company. However, there are severe limitations to this approach. The firstis the fact that there is a relatively small number of listed companies operatingin only one line of business (monoliners), so this approach can at best provide beta estimates for a handful of lines of business. Another limit refers to factors such as investment strategy and market capitalisation that affect a multiline company’s cost of capital but are not reflected in the line-of-business betas esti-mated in this way.⁴⁰

The limitations of CAPM severely hamper its usefulness for business steering purposes: its ample scope for errors may lead to wrong decisions, which ulti-mately have a negative impact on the economic value of the company.

The Market Consistent Pricing Model (MCPM)

The Market Consistent Pricing Model (MCPM) was developed to address the shortcomings experienced when trying to apply CAPM for the company’s inter-nal purposes. As the name implies, MCPM is based upon market-consistentvaluations of an insurer’s assets and liabilities. It widely follows the theory pre-sented in the chapter “Cost of capital in theory”.

The key to implementing MCPM is the adoption of replicating portfolios. The cost of capital for the insurance company can be identified by estimating the ex-pected return on the relevant benchmark for the investment operations and then adding the additional margin that investors require as compensation for taking additional insurance risks.

Estimating the investment cost of capital

The compound risk premium is theweighted average of the risk premiumsfor the various asset classes.

The cost of capital of the investment operations (or the expected return frominvestment activity on economic net worth) can be estimated as the risk-free rate earned on non-risky investments plus a compound risk premium:

Investment cost of capital = risk-free rate + compound financial risk premium

The compound risk premium is calculated as a weighted average of the risk pre-miums estimated for various classes of risky assets. Each asset class in which the company invests is exposed to some form of financial market risk. The po-tential impact of this exposure on the company’s economic net worth can be captured through leverage ratios. For instance, in the case of stock investments, the equity gearing is defined as the ratio of the market value of these invest-ments to the company‘s ENW.

⁴⁰ For those interested in beta applied to divisional cost of capital estimates see J.D. Cummins andR.D. Phillips, “Estimating the cost of equity capital for property- liability insurers”, 2003, available atfic.wharton.upenn.edu/fic/papers/03/p0331.html


If a company restricts its risky investments to stocks and corporate bonds, the compound risk premium is:

Compound financial risk premium =(equity risk premium) * (equity gearing) + (credit risk premium) * (bond leverage)

The credit risk premium

The default-adjusted credit risk premiumis taken as 0.5%.

The credit risk premium is the extra return generated by bonds over the risk-free rate. This premium reflects the fact that corporate bonds are exposed, inter alia, to the risk of default: if the issuer gets into trouble, it may not be able to service its obligations under the bond terms. Different corporate bonds present different risk levels, depending on the issuer characteristics and the terms of the specific bond.⁴¹ In this study, the credit risk premium is assumed to be 0.5%, which is the historical average credit spread between 1990–2003 for investment-grade bonds in the US market, adjusted for the experienced default rate.⁴²

The cost of capital of investment operations is 5.6%.

Based on the parameters detailed above (“Derivation of the parameters used in this sigma” textbox), this study estimates that the average cost of capital of in-vestment operations for the US P & C insurance industry is equal to 5.6%. These estimates are based upon excess returns and leverage ratios for the various as-set classes as of 2002:

Investment cost of capital = 3% + (4% * 37% ) + (0.5% * 219%) = 5.6%

Estimating the insurance cost of capital

Measuring the insurance cost of capitalby component is not feasible.

It is not possible to measure the various components of the insurance capital cost separately. There is no estimate of frictional capital costs for insurers (or for any other industry for that matter), since such costs cannot be directly observed. One way to overcome these limitations is to estimate all frictional capital costs jointly and indirectly. Three approaches are followed in this study to arrive at an estimate of insurance cost of capital in the aggregate: analysis of historical underwriting returns, market price of insurance risk as represented by insurance-linked securities

(ILS), and independent research on the percentage of premium devoted to underwriting

risk.


⁴¹ For more information on corporate bonds and default risk, see E.F. Brigham and P.R. Daves, “Intermedi-ate Financial Management”, 8th edition, 2004, Chapter 4.

⁴² Market value weighted excess returns on Lehman US Credit Indices were used.


Historical underwriting returnsInsurance operation capital costs canbe estimated jointly, and are about 2%.

Economists usually estimate the cost of capital based upon historical average returns, under the assumption that on average investors get the returns that they require.⁴³ Figure 13 below shows the actual economic income generated by the insurance operations of the US P & C insurance industry between 1976 and 2002. It is expressed as a percentage of the aggregated economic net worth of US P & C companies, based on statutory data. This was the only data source available for the US P & C industry, and only for the last quarter of a century.

As discussed in the section “Cost of capital and value creation in practice”, the economic income from insurance operations includes an allocated investment income based upon the return on the replicating portfolio.

Figure 13Historical economic underwritingincome of US P & C industry in %of economic net worth

–10%

–5%

0%

5%

10%

15%

20%

Economic underwriting income

200

220

0120

00

199

919

98

1997

199

619

95

199

419

9319

9219

9119

90

198

919

88

1987

198

619

85

198

419

83

1982

1981

198

019

7919

7819

7719

7619

75

% o

f Eco

nom

ic n

et w

orth

Sources: AM Best Statutory filings (aggregates), Swiss Re Economic Research & Consulting own calcula-tions. See Appendix I for variables, definition and calculation.

Over the observed period, the average income generated by the insurance op-erations of US P & C companies amounted to 2.6% of ENW. The value range for this estimate, though, is 16.4% to –9.4%. This wide interval reflects the difficul-ties of estimating the cost of capital of insurance operations based on historical performance.

⁴³ Based on rational expectation hypothesis.


Interpreting historical underwriting returns

The long-term historical average (from 1976 to 2002) of underwriting profit-ability is 2.57% (see Figure 13 above).

Recently, however, there has been a strong downward trend in underwriting profitability. In particular, between 1983 and 2002, the average underwriting profitability of the industry was –0.9%.⁴⁴

There are a number of factors to explain this low-to-negative underwriting profit-ability: The low returns may be due to a series of adverse shocks to the industry con-

centrated over the chosen observation period. A case in point is the liability crisis in the US. It has been estimated that the liability crisis had produced an additional strain on the industry of about 2 percentage points in terms of combined ratio⁴⁵ as of 2002.

Reduced level of regulation of the insurance industry today, compared to the 70’s and early 80’s, has led to a gradual decline in underwriting margins, squeezing out any abnormal profits the industry might have earned in the past. Even in those lines that are still regulated, there is some evidence that the methodologies employed to determine the regulatory rate have led to lower margins for insurers.

The industry may have been overcapitalised in the 1980s and 1990s, leading to unprofitable underwriting practices.

Since 2002, insurance companies have undertaken many of the necessary steps to address shareholders’ expectations of better returns in the future, as the re-cent hard market testifies. This has led to a very positive underwriting profitability in the recent past, which is not captured by the historical analysis presented in this study.

Market pricing of insurance risk through ILS An alternative approach to estimating the insurance cost of capital looks at the

market spreads on a new asset class, denominated insurance-linked securities (ILS).⁴⁶

Figure 14 below depicts the development of market spreads over the last four years for a selection of ILS issues. Risk spreads have been declining and cur-rently stand in the range of 100 to 200bps over risk-free rate.


⁴⁴ It should be noted that, since the underwriting profitability figures quoted above are expressed on an economic basis, they are not affected by changes in interest rates. Thus, the downward trend cannot be ascribed to a similar development in interest rates over the observation period.

⁴⁵ This estimate has been derived through the following ratio:

Cumulative reserve strengthening + adverse claim development over observation periodCumulative US P&C premium volume over observation period

Number of years included in the observation period

⁴⁶ See Swiss Re Technical Publishing, “Insurance Linked Securities”, 2003, for more details on this kind of instrument and its market structure.


Figure 14Spread development on selectedinsurance-linked securities

Lehman BB

Jun01

Sept01

Dec01

Mar02

Jun02

Sept02

Dec02

Mar03

Jun03

Sept03

Dec03

Mar04

Jun04

Sept04

Mar05

Dec04

Jun05

Post-11 September:Spreads widen acrossmarkets

July 2002WorldCom files largestbankruptcy ever

Moody’s report released:Most severe period of creditstress since the Depression

100

200

300

400

500

600

700

800

900

Euro WindUS WindMulti-perilJapan EQ

Mid

-mar

ket s

prea

d ov

er L

IBO

R (b

p)

Source: Swiss Re Financial Products

The idea underlying this approach is that one could take the market spread of ILS as a reference for the pure insurance risk, and therefore for the insurance cost of capital. However, there are reasons why such a comparison is not pre-cise, and these can be grouped as follows: Reasons for higher insurance cost of capital of companies vs ILS spread:

– Agency costs. Index-based ILS are structured to minimise agency costs, whereas investing through insurance companies always involves some amount of agency cost.

– Scope of risk exposure. Investors in an insurance company are exposed to the full range of insurance risks underwritten. ILS, by contrast, transfer only selected risk to investors. By “slicing” insurance risk via ILS, investors get exactly their preferred risk and are therefore satisfied with a lower return than if they were exposed to the entire risk portfolio.

– Cost of financial distress. ILS have no franchise value to put at risk. This isin fact the case for most insurance companies. Furthermore, ILS carry no credit risk, as capital is invested in AAA bonds, while insurers do.

Reasons for higher ILS spread vs insurance cost of capital of companies: – The role of the insurer as intermediary. Investors are more comfortable

taking insurance risk indirectly by investing in insurance companies. Thisis due to the fact that insurers have been investing in models for pricing and managing risk on behalf of their shareholders for many years. Theyare therefore more advanced on the learning curve. However, a dedicated class of insurance-linked securities investors is emerging to fill this role.As a result, spreads on ILS have been falling significantly over the last five years.


Independent research on percentage of premium devoted to underwriting risk Independent research focused on fair premium rates in the US has estimated

that the percentage of the premium that is required to compensate for under-writing risk stands at about 1%.⁴⁷ This can be translated into an insurance cost of capital estimate by assuming that, for each dollar of premium underwritten, 50 cents of capital must be put aside (ie a 50% solvency ratio, which reflects the average for the US P & C sector). Then a 1% margin on premium translates into a 2% expected return on capital.

Based on the approaches used in this study, preliminary estimates of insurance cost of capital place it in the 2% range.

Total cost of capital under MCPM

The MCPM method indicates an average cost of capital of about 7.6%.

Combining the two components of the MCPM method, the investment and in-surance cost of capital, results in a total cost of capital estimate of 7.6% (5.6% + 2%), which refers to the economic tangible capital.

Figure 15 depicts the development of the cost of capital for the entire US P & C industry⁴⁸ over the last ten years, based on the MCPM approach. These esti-mates reflect a varying investment mix as well as prevailing risk-free rates. The estimated cost of capital reached a low of just above 7% in 2002 due to lowinterest rates and the shift by the industry out of shares.

Figure 15Estimates of cost of capital for the USP & C sector based on the MCPM approach, using a variable risk-free rate and variable leverage ratios

1%

3%

5%

7%

9%

11%

13%

Total cost of capital (including underwriting risk premium)Risk-free + financial market risk spreadRisk-free rate

2002200120001999199819971996199519941993


⁴⁷ See: Richard Derrig, “The use of investment income in Massachusetts private passenger automobile and workers’ compensation ratemaking”, 1983, reprinted in Cummins, Harrington, “Fair rate of return in property-liability insurance”, 1987, pp 119–145.

⁴⁸ Aggregate of all companies making statutory filings, as reported by AM Best Aggregates and Averages for the US P & C sector.



The cost of capital for insurershas been declining.

Similar to the results obtained based on CAPM, the MCPM method implies that the cost of capital for the insurance sector in the US has been declining over the past few years. As shown in the figure, this downward trend is due to the reduc-tion in two cost components of the MCPM method over the period observed: declining risk-free rates and a shift in investment allocation out of stocks and into bonds (which reduces the compound risk spread above risk-free, sinceequity investments demand a higher risk premium than bonds). Risk premiums on shares and bonds have also been trending downward, but these and theunderwriting cost of capital are assumed to be constant in this graph.

The challenge of using MCPM estimates for business steering

Both the MCPM and CAPM methods encounter problems in defining the insur-ance cost of capital for different insurance lines of business. The advantage of MCPM over CAPM is that the former confines the area of uncertainty to the in-surance cost of capital, while the latter provides no input on what capital cost should be allocated to the investment arm. Although promising approaches are being developed within the MCPM framework to arrive at a differentiation of in-surance cost of capital by line of business, at the moment there is still consider-able room for improvement on this subject.

Comparison of CAPM- and MCPM-based estimates for the company sample

In this final section, the study presents the results of an estimate of the cost of capital for a sample of US P & C insurers. The objective is to compare the out-comes of the MCPM and the CAPM methods and see whether and why the es-timates differ. The company sample is the same as used in the chapter “Cost of capital and value creation in practice”.

The analysis on a sample of US P & C insurers over a ten-year horizon highlights a great variance in the cost of capital estimates for individual companies based on the CAPM and MCPM methods.

Figure 16Range of cost of capital estimates,using CAPM, 27 US companies, forperiod 1992–2002

0%

5%

10%

15%

20%

25%

30%

35%

40%

10.5% andabove

9.25–10.5%8.00–9.25%6.75–8.00%6.75% andbelow

8

10

4 4

1

Source: Swiss Re Economic Research & Consulting Note: Distribution of CAPM-based cost of capital of company sample – all data based on 10-year averages.

The number above each bar chart indicates the number of companies with cost of capital estimates in-cluded in the defined range.


The variation between companies is due to the beta, which makes the lowest cost of capital more than one-half of the highest.

The distribution in Figure 16 above refers to 10-year averages of CAPM-based cost of capital estimates for the sample of companies. The highest estimate is more than twice as high as the lowest. Since the risk-free rate and the equity risk premium are the same for all companies, this variation reflects differences in company-specific betas.

A beta puzzle

As Figure 17 shows, betas vary by size of company. This implies, all else being equal, that small companies have lower capital costs than larger ones, which runs counter to historical experience.⁴⁹ The implication is that beta, and the CAPM method, may not best reflect insurers’ cost of capital.

Figure 17Averages of company betas (2-year rolling) versus averages of market capitalisation, 1993–2002

Bet

a

y = 0.1772Ln(x) + 0.4247R² = 0.609

Size (market capitalisation in USD millions)

0%

20%

40%

60%

80%

100%

120%

140%

160%

180%

10 100 1000 10 000 100 000


MCPM-based cost of capital estimates for the same companies and over the same period reveal a smaller variance, with the highest estimate exceeding the smallest by 36% (Figure 18 ). Companies are more evenly distributed amongst the five groups than in the equivalent case under CAPM, because the risk-free rate, the insurance cost of capital, and the equity and credit risk premiums are equal for all companies.⁵⁰ The only factor that varies by company is the leverage ratios used to calculate the financial market risk premium, thus capturing differ-ences in investment strategies.


⁴⁹ The finance literature provides evidence from a sample of all firms (ie not only insurance companies) of just the opposite relationship. Small size is associated with high beta and high returns, even adjusting for bankruptcy risk.

⁵⁰ The risk-free rate and the equity and credit risk premiums are the same because all companies operate in the same macroeconomic environment, while the insurance cost of capital is the same by assump-tion. A more complete calculation would take differences in insurance operations into account.


Figure 18Distribution of MCPM-based cost ofcapital of company sample – all databased on 10-year averages

0%

5%

10%

15%

20%

25%

30%

9.5% and above9.0–9.5%8.5–9.0%8.0–8.5%7.4–8.0%

5

7

4 4

7


Note: Distribution of MCPM-based cost of capital of company sample – all data based on 10-year averages. The number above each bar chart indicates the number of companies with cost of capital estimates in-cluded in the indicated range.

The discrepancy in the results obtained under the two methodologies can be better seen in Figure 19, where they have been combined.

The cost of capital estimates from MCPM vary less for the same companies than the CAPM estimates.

The largest absolute difference between the cost of capital estimate for anygiven company is 3.95%, while the average absolute difference is 0.99%.

Figure 19Comparison of cost of capital estimatesfor the sample of companies based on CAPM and MCPM

CA

PM

MCPM

5% 6% 7% 8% 9% 10% 11% 12%

5%

6%

7%

8%

9%

10%

11%

12%


Finally, Figure 20 below depicts the insurance cost of capital implicit in the CAPM estimates for the selected sample of companies.


Figure 20Insurance cost of capital implicit inCAPM estimates for selected sample

0%

5%

10%

15%

20%

25%

30%

35%

4% and above3–4%2–3%1–2%0–1%<0%

9

4

8

2

3

1


Note: The number above each bar chart indicates the number of companies included in the indicated range.

This was calculated by subtracting from the CAPM total cost of capital the in-vestment cost of capital obtained under the MCPM method. The values of the insurance cost of capital implicit in CAPM vary significantly. This result supports the view already expressed in this study that CAPM is not an appropriate cost of capital method for companies that follow strategies different from the sectoraverage. Furthermore, the fact that under CAPM nine companies out of 27have negative implicit insurance cost of capital (ranging between –1.95% and–0.17%), is once again an indication that company betas are unreliable.

Conclusions and areas for further analysis

The MCPM method is more consistentfor a range of company types.

In broad quantitative terms, CAPM and MCPM provide similar results for the cost of capital of the US P & C insurance industry. However, CAPM gives unreli-able measures of the cost of capital for companies that are not typical or aver-age (eg, small companies have a cost of capital half that of large companies). The MCPM approach overcomes these problems, confines the guesswork to the insurance part of the business, and focuses management on the insurance-specific issues of taxation, regulation, investment and underwriting profitability.

This sigma study aimed to provide a theoretical and methodological background for addressing the issue of the cost of capital of insurers. Given the very broad scope of the subject, the decision was taken to focus on some key aspects and messages. This also meant that some areas of material interest to the industry had to be omitted, for instance: fine-tuning of estimates of insurance cost of capital components, analysis of the cost of capital of various insurance lines of business. allocation of tangible capital across different business lines and relationship

to cost of capital and risk.

sigma solicits more contributions on these important issues.



Table 3Background information on theempirical analysis

Data sources For industry series Aggregated statutory returns provided by AM Best (only US P & C sector) Market capitalisation data

For company series Statutory returns provided by Onesource Market capitalisation data provided by DataStream

Sample Comprises 27 “pure-play” US P & C companies The limited sample was imposed by the fact that all geo-

graphically diversified or composite insurance companies were excluded in order to be able to compare meaningfully their P & C statutory capital with their market capitalisation.

Regression variables (All 10-year averages) Value created The ratio of market capitalisation to economic net worth (dependent variable) (economic price/book ratio)

The ratio of franchise value to market value (alternative dependent variable tested, not published in the report)

Value drivers Equity gearing, defined as the ratio of market value of (explanatory variables) investments in stocks to ENW;

Size, defined as year-end market capitalisation or its natural logarithmic transformation; Economic investment return on ENW; Economic underwriting return on ENW; Premium growth; Standard deviation of underwriting return; Economic underwriting return * Premium growth

The methodology adopted to arrive at economic values

The methodology applied forthe empirical test

A number of adjustments were made to the raw statutory data (both for the in-dustry as a whole and for the companies sample) in order to obtain economi-cally consistent figures, which were used to build the variables for the ordinary least square regressions. The adjustment methodology applied can be summa-rised as follows:⁵¹

Table 4Necessary adjustments to convert statutory values into economic values

Balance sheet adjustments to convert statutory values into equivalent economic values Firstly, for each accounting year, insurance liabilities are discounted at the risk-free rates

of appropriate maturities to reflect their economic value. Items adjusted include “claims and related expenses”, “unearned premium reserves”, and potential “dividends due topolicyholders”.

Secondly, assets are adjusted (if necessary) to reflect their market values. This applies to financial assets (such as investments in stocks, bonds and other traded instruments), for which market value are available. In the case of reinsurance receivables, these are dis-counted to reflect their economic value.

The economic net worth (ENW) is thus derived as the difference between the market value of assets and liabilities in each year.

The ENW is then subtracted from the average market capitalisation of the company for the year to obtain the franchise value.

The franchise value represents the value of intangible assets of the company and can be reasonably assumed to match the present value of future economic extra profits expected by investors.

⁵¹ Also refer to “The Economics of Insurance”, cited in footnote 14, for examples of calculations.

Appendix I: Variables used in the empirical analysis


Income statement adjustments to convert statutory values into equivalent economic values Firstly, incurred losses are adjusted to reflect the discounting of claims reserves (both case

reserves and IBNRs). Secondly, the “virtual” return on the replicating portfolio is allocated to the underwriting

income. The return on the replicating portfolio is obtained by applying the risk-free yield appropriate for the duration of the liabilities to the insurance liabilities, and a one-year risk-free yield to the unearned premiums reserves.

The sum of premiums earned, adjusted losses incurred and return on the replicating port-folio is equal to the economic underwriting net income. Taxes are allocated to the under-writing operations, since they pertain to these from an economic point of view.

Finally, the investment net income is calculated by subtracting from the reported invest-ment results the return allocated to the underwriting operations.

Other net income, which is typically extraordinary in nature, has been ignored in order to derive normalised net income results.

These adjustments were made both to aggregated industry series and to com-pany-specific series in order to derive an economic measure of underwriting profitability and investment profitability.

In this study, profitability measures are calculated as the ratio of economic un-

derwriting net income and/or investment net income to ENW as of year-end.

The results presented in this paper refer to market capitalisation relative to eco-nomic net worth. The results, however, remain fundamentally unchanged when value creation is defined as a function of franchise value as a percentage of market capitalisation.


Table 5Results of the linear regressions –key statistics

All regressions using economic price/book ratio as dependent variable

Figure 6 Figure 7 No Figure Figure 9 No Figure Figure 8 Figure 10 Equity Investment Underwrit- U/w Premium Prem.growth gearing const return const ing return const volatility const growth const * U/w return const Size (*) const

Coefficient (0.32) 1.51 (5.95) 1.83 7.75 1.31 (2.25) 1.60 4.49 0.97 88.26 1.21 0.16 0.28

Standard errorof coefficient 0.61 0.27 5.88 0.45 1.91 0.09 2.51 0.27 1.62 0.18 14.88 0.08 0.07 0.47

t statistic (**) (0.53) 5.66 (1.01) 4.04 4.05 13.85 (0.90) 6.01 2.77 5.34 5.97 14.73 2.39 0.60

Not Not Not Comment significant significant Significant significant Significant Significant Significant

R2; Standarderror of Yestimates 1% 62% 4% 61% 40% 48% 3% 61% 23% 54% 59% 40% 19% 56%

F-distribution;Degrees offreedom 0.28 25 1.02 25 16.40 25 0.80 25 7.66 25 35.62 25 5.72 25

Regression sumof squares;Residual sumof squares 11% 959% 38% 932% 384% 586% 30% 940% 228% 742% 570% 400% 180% 789%

Table 6Results of the linear regressions of size, premium growthand underwriting ROE on economic price/book ratio

Size (*) Premium growth Underwriting ROE Constant

Coefficient 0.14 2.78 5.98 0.12

Standard error of coefficient 0.05 1.29 1.72 0.36

t statistic (**) 2.85 2.16 3.49 0.35

Comment Significant Significant Significant Significant

R2; Standard error of Y estimates 61% 40% #N/A #N/A

F-distribution; Degrees of freedom 12.08 23 #N/A #N/A

Regression sum of squares; Residual sum of squares 593% 376% #N/A #N/A

(*) Size is expressed as logarithm of market capitalisation.(**) For each regression, a standard two-tailed t-test with a 5% level of significance was used to test the null hypothesis that the coefficient is equal to zero.A t-statistic above the absolute value of 1.96 indicates significance with 95% confidence.


Appendix II: Regression results


Recent sigma publications

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Swiss Reinsurance CompanyEconomic Research & ConsultingMythenquai 50/60P.O. Box8022 ZurichSwitzerland

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