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Research Report Conclusions

Opening of the Reinsurance Market, Demand for Reinsurance and

Impacts on the Insurance Market1 (revised version)

Lauro Vieira de Faria*

Executive Summary:

The aim of this study is to discover to how much Brazils reinsurance and insurance marketswould be affected were the reinsurance market opened up and the monopoly of the Institutode Resseguros do Brasil (IRB) brought to an end. We have studied the issue of reinsuranceboth theoretically and empirically in order to shed light on the issue.

We find that at corporate level, the demand for reinsurance should be seen as a function of acompanys taxation, ownership structure, leverage, credit rating and size, as well as itsconcentration in certain businesses, its tail (lag between a premium payment and a claim), thecorrelation between the return on investments and claims costs and the profitability of itsassets. As concerns the domestic demand for reinsurance, the other factors to be added tothis list are the scale of the market, the countrys financial development and existence oflocal compulsory reinsurance companies, uncompetitive markets and restrictions on foreigncompanies.

An empirical study of the situation in Brazil shows that overall the national demand for

reinsurance has behaved as forecast by economic theory. The price of reinsurance, thecoefficient of insurance penetration and the concentration in the areas of life, health andauto insurance have had a significant negative impact on the demand for reinsurance. Thesame applies to the following factors: market share, rate of return on investments andconcentration in housing insurance. One exception to the theoretical rule was the companysize variable, which was found to have a positive impact. Ambiguous findings were obtainedfor taxation and leverage, while it would seem that foreign capital, geographicalconcentration and ownership structure/banks play no part in explaining the reinsurancedemand.

We also noted that reinsurance can be viewed as a kind of additional capital (or additionalsolvency margin) for the insurance market, and therefore one of its factors of production.An estimate of an insurance supply equation with this characteristic produced the resultpredicted theoretically in terms of the positive influence of reinsurance (and coinsurance) ondirect insurance.

(*) Economist1I should like to thank Ren de Oliveira Garcia Jr. and Cludio Contador for their inspiration, encouragement andassistance, Annibal Vasconcellos for her efficiency in collecting, clarifying and forwarding data, and the IRB and

Funenseg libraries for the literature they made available. I also thank Robert Bittar and Renato Campos MartinsF, President and Managing Director of Funenseg, respectively, for their support of this research. Without them,it would not have been possible. Naturally, any errors there may be in the text are the sole responsibility of theauthor.

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By using these equations, a mathematical model was defined that could project the demandfor reinsurance and the supply of insurance between 2005 and 2007 within an openreinsurance market. The projection exercise was designed with two basic hypotheses at itscore: that opening the market would cause reinsurance prices to fall sharply and the IRBs

relative net equity to rise sharply. The latter is taken as an indicator of the institutescapacity to supply ancillary services to insurance companies. This model demonstrates someundeniably positive impacts of opening up this market, which can be summarized as a morethan 200% leap in demand for reinsurance over three years and an increase of some 40% indirect insurance revenues in the same period.

I. Introduction:

One of the key measures in modernizing the insurance market is the opening up of thereinsurance market. As is widely known, although Constitutional Amendment No. 13 of 1996

put an end to the IRBs legal monopoly in this business, Brazils reinsurance market haschanged little in practical terms since then2.

If the IRB could be praised for keeping the reinsurance activities performed in othercountries inside Brazil and thus strengthening the countrys insurance companies by spreadingthe risk involved in auto reinsurance, there seems to be a consensus that the current modelcan no longer meet the needs of an expanded market. It would keep domestic prices higherthan they would be under free competition and would curb the supply of new insuranceproducts because there would be no corresponding reinsurance on offer. It would restrictcompetition, assuring the survival of less efficient companies reliant upon high cessions to

the IRB, and it would prevent efficiency gains via improved risk pricing, greater access oflocal insurance companies to collateral services and greater speed in contracting andprocessing reinsurance. And it would block the entry of the foreign capital the country needsfor its development. In a nutshell, maintaining the status quo would mean missing out onopportunities that could benefit not just the insurance market but the entire economy3.

Today, most countries have put their faith in open reinsurance markets, the sole exceptionsbeing Brazil, Cuba and Costa Rica. Clearly, membership of such a meager clan is a cause forconcern of itself. Evidence of the problems created by the IRB monopoly can be seen in thealleged low penetration of reinsurance in Brazil. In 2003, this industrys revenuesrepresented 7.5% of the direct insurance market, while in the largest markets in the region(Argentina, Chile, Colombia and Mexico), the rate varied between 18% and 33% (Bopp, 2005).However, the risk profile of these countries is rather different from Brazils, as they aremore badly affected by natural disasters, which especially require reinsurance, as well asother factors. Compared with the rest of the world, Brazils reinsurance penetration rate is

2 Law 9932 of 1999 regulated the privatization of the IRB and withdrew its prerogatives in the areas ofinspection and setting industry standards. However, as no real change happened, the institute was granted backsome of its rights in a natural reaction to the absence of any concrete steps to sell it.3

There are also arguments against opening up reinsurance, such as the theses that without the IRB, there wouldbe denationalization, since local insurance companies would not manage to compete with their overseas rivals,there would be a marked capital flight and greater price volatility, since the IRB effectively buffers the pricevariations during the international reinsurance cycle (Bopp, 2005).

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higher than the international average of 6.7%, while its 0.53% share in the world reinsurancemarket surpasses the market share of the countrys direct insurance industry, which is0.47%. Based on these figures, there are those who would argue that opening up thereinsurance market would have a negligible impact (Galiza, 1998).

To the current date, the discussion of this issue from an economic standpoint has beenpursued without any great recourse to theoretical and/or empirical considerations. Thisstudy intends to break the mold. It is divided into six sections: section II discusses theinternational literature on reinsurance from both a theoretical and empirical perspective; thethird section gives a summary of the history of the reinsurance market in Brazil; the fourthlooks into qualitative and quantitative aspects of the national demand for reinsurance; sectionV discusses analogous issues of the relationship between reinsurance and direct insuranceoutput; the sixth section looks into the quantitative impact of opening up the reinsurancemarket with a view to predicting its impact on both the insurance and reinsurance markets;and the final section presents the conclusions of the study.

II. Reinsurance in the international economics literature

Reinsurance is the insurance of insurance companies equity risks that arise from any excessrisk in their portfolios, allowing them to sell off the part of the risk that exceeds theirretention capacity. The first reinsurance took the form of facultative contracts betweeninsurers, the best known of whom met at Edward Lloyds coffee house in London the 1680s.By their very nature, facultative contracts can be complicated and costly. This is why themarket developed what came to be known as treaties, by which the greater risks wereautomatically reinsured either jointly or individually. As insurance companies dragged their

feet about sharing information with each other for these coinsurance treaties and incompetitive market conditions, a new development came about: the advent of reinsurers, aspecial group of insurers specialized in supplying reinsurance, who operated according to theprinciple of uberrima fides, or utmost good faith.

II.a. Karl Borchs Model

Formally speaking, the seminal paper on the reinsurance market was written in the early1960s by Norwegian actuary and economist, Karl Borch. He devises a reinsurance marketwhich operates along the lines of a barter economy, where risk-averse companies withportfolios subject to losses can maximize the expected utility of their income. In order to doso, they exchange their portfolios on the market, and in so doing they end up with differentportfolios from those they initially had, implying a certain degree of reinsurance (Borch,1990).

This author proves that under the conditions of the model, the optimal set of barters isequivalent to setting up a coinsurance pool, into which all companies put their initial portfoliosand agree on a rule for sharing the claims payments for losses incurred by the pool. This ruledepends on just a few variables: i) the statistical (probabilistic) properties of the risk of the

individual portfolios; ii) the statistical ratios between a portfolios risk and the market risk,i.e. the risk of the pool of portfolios; iii) the prevailing attitude towards risk on the part of

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the companies, and consequently the market; and iv) the total assets held by the insurancecompanies.

The definitive design of a coinsurance pool depends on pinpointing the utility function of eachcompanys income, and therefore of the market. Borch demonstrates that if these utility

functions are HARA

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, there is a linear risk-sharing rule once a coinsurance pool has been setup, which means the optimal situation is obtained by signing quota share (proportional)reinsurance contracts. Other types of utility function produce different results, such aswhen the pools risk sharing rules involve stop-loss reinsurance contracts (Borch, 1990,p.220).

The reinsurance market model described above anticipates some features of the capitalasset pricing model (CAPM). If the optimal arrangement of the coinsurance pool is a quota-share treaty, as in the case mentioned above, where each insurer ends up with a risk portfoliothat is proportional to the markets risk portfolio, this is the equivalent of the CAPM

proposal which states that under the models ideal conditions, each investor has a proportionof the market share portfolio. In the insurance market, the implication is that after anoptimal coinsurance pool is set up, all the risk portfolios (net of reinsurance) are perfectlycorrelated amongst themselves.

II.b. Criticisms of Borchs model

Many criticisms have been made of Borchs model. Garven & Lamm-Tennant (2002) criticizedthe models emphasis on the issue of risk management to the detriment of the function ofreinsurance in the management of decisions concerning capital, especially those related to

the likelihood of insolvency. Additionally, though the model works for privately ownedinsurance companies, it is unable to take into account the complexity of larger insurers with alarge proportion of shares traded on the market, which need to sign explicit and implicitcontracts with their different stakeholders, such as their shareholders, managers, insureds,regulators and tax authorities. In these cases, postulating an unequivocal utility function ofincome for a given company, as Borch does, would mean that it would have to be stated whomthis function would serve in terms of well-being, how this result was reached, and what kindsof risk it was hoped to reduce or eliminate through means of reinsurance operations.

A more difficult criticism to rebut was formulated by the proponents of the CAPM model 5.As they see it, unlike CAPM, Borchs model does not give the capital markets a role indetermining the maximizing actions of insurance companies or their owners. Under theconditions set by CAPM, insurance companies shareholders must be seen as diversifiedinvestors who hold shares in an insurance company as part of a broad-based share portfolio.The possibility of diversification through the financial markets implies that theseshareholders would be less concerned with unsystematic risk, which could be eliminated bydiversifying their portfolios, than with the systematic risk of the market portfolio as awhole, which cannot be eliminated. Under such conditions, the CAPM model indicates that the

4 Hyperbolic absolute risk aversion, whose quadratic utility functions, like , where x is

income, are special cases.

2/)( 2bxaxxu =

5 CAPM was developed independently by Sharpe (1964), Lintner (1965) and Mossin (1966).

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return an investor would receive for holding shares in an insurance company or being theircontroller could be given by the risk-free interest rate plus a part (risk premium, equivalentof the loading of the insurance market) related exclusively to the systematic risk. Therefore,the maximizing decisions taken by investors in these companies could be described bymodeling reinsurance decisions based on the expected utility of the income, which does not

differentiate between systematic and non-systematic risk, as in the Borch model (for moreon this see Cummins, 1990).

However incredible it may seem, in the ideal world of the CAPM, both insurance andreinsurance are irrelevant for the shareholders of the company that cedes the risk. Thehypotheses of CAPM, it should be added, are as follows: flawless capital markets in thatthere are no transaction costs and agents cannot interfere in prices; investors are riskaverse and can take out and cede unlimited loans at a risk-free rate; and there arehomogeneous expectations concerning the joint density function of the share returns.

It has been demonstrated (Cummins, 1976 and Main, 1982 and 1983) that investors wouldhold an optimally diversified part of the market portfolio, which would protect them entirelyagainst any pure (unsystematic) risk of the company they have invested in. In other words, bydiversifying, they would be able to insure themselves without any cost of risk, so that if thecompany they invested in were to contract insurance or reinsurance to cover unsystematicrisks, this would not raise the market value of its shares. Further, if the company were totake out insurance or reinsurance policies against systematic risks those which arecorrelated to the market as a whole this would bring them no benefit whatever. This isbecause the insurance companies that sell these policies, also basing their pricing on theCAPM, would charge premiums whose loading would exactly offset the taking on of this

additional systematic risk. In the end, the companys market value would not be enhancedbecause the gain it would obtain by taking out the policies against systematic risks would beentirely offset by the higher premiums they would have to pay to the insurance companiesfor them to take on these risks. Basically, this was how the paradoxical conclusion wasreached that it is irrelevant to a companys shareholders whether that company is insured orreinsured or not.

II.c. Demand for reinsurance beyond the CAPM6

Obviously, a conclusion so far removed from reality could only have been reached because ofthe unreal hypotheses assumed by the CAPM model. The next logical step, then, was toresearch to what extent adopting less restrictive hypotheses would yield the result found inpractice: that reinsurance is indeed a factor which adds value to insurance companies.

One way would be to model the insurance market in a less simplified way. This was done byDoherty & Tinic (1981), who included not just insurers and reinsurers in their referencescenario, but also insureds. Their model assumes that the insurance market is perfectlycompetitive, that insureds are neutral towards an insurance companys risk of bankruptcy,that no transaction costs are associated to the purchase of reinsurance or share

6 This section is based extensively on Garven & Lamm-Tennant (2002, 2003), Carneiro & Sherris (2005) andMayers & Smith (1990).

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transactions, and that contracts between a companys stakeholders are complied with at nocost. This led them to the same conclusion as Cummins & Main above, that a companys shareswill not gain value if they acquire reinsurance because when an insurance company rids itselfof a risk, its gain is exactly offset by the excess premium charged by the reinsurer when itshoulders this risk. However, when some flexibility is introduced into the hypotheses, and

insureds demand is no longer elastic As concerns an insurance companys risk of bankruptcyand that they are not perfectly diversified, what Doherty & Tinic show is that an insurancecompanys value can be enhanced when it contracts reinsurance. This is because reinsuranceallows an insurance company under the threat of bankruptcy to charge higher premiums thanit would charge if it had no reinsurance, thereby guaranteeing its shareholders theirexpected return.

Along similar lines, Mayers & Smith (1982, 1990) established that insurance and reinsuranceare important for public companies (including insurance companies) not because of their riskaversion but because of market flaws, such as taxes, transaction costs (including agency

costs7

), costs relating to the expectation of bankruptcy, etc. Blazenko (1986) chose toinvestigate the hypothesis of perfectly competitive direct insurance markets by introducingthe possibility of insurable risks not being completely diversifiable. By so doing, he provedthat reinsurance may add value to insurance companies in that it provides the market withadditional capacity to spread risks. The influence of transaction costs was explored by Froot,Scharfstein & Stein (1993), who discussed their impact on investment decisions broughtabout by price differences between domestic and foreign financing, the former of which isknown to be cheaper than the latter because of its lower transaction and agency costs. Theyproved that risk management strategies, of which reinsurance is one, are an effective toolfor assuring companies liquidity and thereby enhancing their value.

Below, we set out a more detailed description of the effects of the aforementioned marketflaws on demand for reinsurance.

i) Taxes

If, as is the case in most countries, the marginal corporate income tax rate is an increasingfunction of earnings before tax, then net profit tends to be a concave function of grossprofit8. This being the case, the mathematical expectation of net earnings is lower than thenet earnings associated to the mathematical expectation of gross earnings. By acquiringreinsurance, the volatility of gross profit can be reduced and in theory a fine-tuned resultcan be achieved that is half way between the extreme probabilistic situations in which acompany pays low taxes if it books a loss but much higher taxes when it is profitable. Thus,provided the reinsurance is of a moderate cost, it will allow companies to plan the grossearnings they intend to book, which will put them in the tax bracket that will provide them again relative to the situation in which the risk was retained. This effect was first mentionedby Mayers & Smith (1982, 1990).

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An agency relationship is defined as a contract in which one person (principal) uses another person (agent) toperform some service in their name, which involves delegating authority. It is understood that the principal almostalways incurs costs to assure the faithful compliance of the agent in this type of contract.8 At least at certain intervals of the function that links one variable to the other.

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Reinsurance is also a tool for setting tax shields between companies. Garven & Louberg(1996) demonstrated this feature of reinsurance in a market equilibrium model in which theinsurance market seeks to minimize the aggregate value of its tax burden. In so doing, theyfound that reinsurance was an efficient means of allocating tax benefits for those companiesthat most needed them. They then extended model to investigate the international insurance

trade, leading to the prediction that the differences between different countries tax rateswould eventually create tax clientele, whereby the insurance companies in countries withlower taxes would provide reinsurance for insurance companies in countries with higher taxes.Internationally, then, the mean retention rates would be inversely proportional to the meantax rates. A tentative empirical study into this was carried out by Outreville (1996) in astudy into imported reinsurance (external retrocession) involving 42 developing nations.

ii) Expected bankruptcy costs

When an insurance company goes bankrupt this means it has failed to meet its obligations toits insureds and lenders. Bankruptcy costs can be described, then, as a kind of agency cost,

and can be high. In the US these costs have been estimated at an average of between 11%and 17% of a companys value up to three years before its bankruptcy (Altman, 1984). Thissaid, the protection provided by reinsurance or hedge mechanisms to reduce expectedbankruptcy costs may enhance a companys value (Smith & Stulz, 1985). Nonetheless, itshould be noted that this protection tends to be related to a companys size, with smallercompanies turning to these techniques more often than large public corporations (Warner,1977).

iii) Adverse Selection

Adverse selection takes place when an insurance company is unable to sift good risk from

bad risk because of an asymmetry of information, which obviously makes it difficult for itto price policies. In the realm of theoretical economics, this was first discussed byRothschild & Stiglitz (1976), who showed that an insurers optimal option restricts the rangeof policies available. To simplify, they show that if there were only two policies on offer, onewith a low premium and a high minimum claim and the other with no minimum claim amount buta high premium, it would be possible to induce the good risk by buying the cheap policy andthe bad risk by buying the expensive one. If we transpose this to the reinsurance market, theadverse selection problem explains the long-term implicit contracts between insurers andreinsurers as a means of reinforcing their mutual trust, thereby getting round the problemof information asymmetry, especially concerning risks that occur less frequently and involvehigher sums, such as industrial property risks. This effect was demonstrated by Jean-Baptiste & Santomero (2000), who showed that these implicit contracts allow new, significantinformation to be factored into the pricing of coverage, that insurers obtain a more efficientamount of reinsurance and at lower prices.

iv) Agency Costs: Shareholders versus Managers

Company executives are generally assumed to be less diversified that shareholders becausethey often have a high degree of investment in the firm for which they work. This inducesthem to reduce the companys risk exposure below levels that might be of interest to its

shareholders. In a model that admits three different compensation schemes for executives,Doherty (2000) showed that i) those companies that offer compensation based on shareownership are very likely to hire hedge schemes, one of which is reinsurance; ii) the

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executives from those companies which compensate them in the form of fixed salaries havesimilar behavior to the first group, but on a smaller scale; and iii) those companies that offertheir executives stock option schemes are unlikely to contract this kind of protection9. Thisfinding was confirmed empirically by Tufano (1996) in a study into the risk managementpractices of gold mining companies, which found that those mining companies that provided

their employees with shares in the company took out more protection against risk than thosethat adopted stock options.

v) Agency Costs: Shareholders versus Loan Creditors

Under certain circumstances, it may make sense for a shareholder to restrict borrowing,even when this will benefit the company tax-wise and the capital markets can be assumed tobe perfectly competitive. Myers (1977) proved this when he showed that there exist statesof nature where a lucrative yet risky investment product partially financed by equity is nottaken forward because the gains are mainly appropriated by the loaners and newshareholders to the detriment of older shareholders. This sets up a conflict between these

agents which could spark off a state of underinvestment. Mayers & Smith (1987) and Garven& MacMinn (1993) showed that the problem of underinvestment can be eradicated byincluding insurance coverage in the contract for the loan taken out to make the projectfeasible.

Jensen & Meckling (1976) argue otherwise, saying that under certain circumstances ashareholder may expropriate the lender by changing their risk decisions. They devised asequential situation in which the controller first promises to choose a low risk investmentproject, then takes out a debt, actually chooses the high risk project, and ends up selling hisshares on the market at a profit. Obviously, lenders avoid this kind of situation by

incorporating the likelihood of the high risk project being chosen into the price of their loan.The loan cost thus augmented is an agency cost which the economics literature refers to as aproblem of asset substitution. Leland (1998) showed that this problem can be eradicated ifonce the debt has been taken out, the controller voluntarily engages in hedges which, thoughthey benefit the lender, are advantageous for the company if the tax deductions the greaterleverage permits exceed the income transferred to the lender.

vi) Optimal risk sharing

As mentioned above, Borchs model draws no distinction between small, private insurancecompanies and large, public insurance corporations, which must sign implicit and explicitcontracts with a variety of stakeholders. While the latter companies can have diversifiedportfolios which will rid them of unsystematic risk, the former have trouble so doing.Therefore, small, privately owned insurance companies will probably take out reinsurance forthe same reason that individuals take out insurance: risk aversion. As a consequence, thedemand for reinsurance should vary with companies size and ownership structure, withgreater demand being found amongst small companies with a limited capacity to diversify.Mayers & Smith (1990) found, for instance, that associations like Lloyds, where contractsare provided by individual underwriters, use more reinsurance than large, public insurance

9 This is because the option introduces an asymmetry between the gain when the price of the share rises and the(small) loss when it falls, so that the scheme induces executives to demand volatility.

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companies. The same applies to the subsidiaries and insurers of conglomerates, which requiremore reinsurance than their competitors.

vii) Efficiency gains in the supply of services

Apart from their main product, reinsurance companies also offer a number of ancillary

services developed to take advantage of their corporate edge in dealing with low probabilityevents and the global and wide-ranging nature of their activities. These include informationabout the best way to price policies, new product design, and consultancy about the entirelifecycle of a policy. These services add value to the companies that offer them by enhancingtheir efficiency. They are probably mostly hired by smaller insurers and those that are moregeographically dispersed or that provide a greater variety of business lines (Mayers & Smith,1990).

To sum up, the actuary models of the reinsurance market (pre -CAPM) tend to emphasize thesupply and demand of risk transfers in a barter market where the insurers risk aversion is

the key factor at play. Financial models, for their part, emphasize the influence of the supplyand demand of shares in the capital markets on the maximization decisions taken byinsurance companies owners and/or shareholders. Thus, if for small companies the demandfor reinsurance may be attributed to their owners risk aversion, for large companies with ahigh number of shares traded on the market, the demand is a function of tax benefits andmarket flaws such as agency costs, adverse selection and other factors.

II.d. Demand for Reinsurance Empirical Tests

In Table 1 below, we present a summary of the findings of four empirical studies into the

demand for reinsurance10. They are: Mayers & Smith (1990), Garven & Lamm-Tennant (2003),Carneiro & Sherris (1990) and Outreville (1996). The left-hand column shows the variables 11that these authors use to determine the reinsurance demand. S(+), S(-) and NS stand for apositive and (statistically) significant relationship, a negative, significant relationship and aninsignificant relationship, respectively. Blank fields mean that the variable was not tested bythat author. As can be seen, none of the studies tested all the variables put forward and onlyGarven & Lamm-Tennant based their empirical test on a previously developed microeconomicmodel.

As for the statistical methodologies employed, Mayers & Smiths work is based on a cross-section regression analysis of 1,276 American insurance companies operating in the corefields (property and casualty) in 1981. Garven & Lamm-Tennant use a panel regression analysis(combining cross-section and temporal series data) of 176 American insurance companiesfrom the same business between 1980 and 1987. Carneiro & Sherris do the same for 98Australian insurance companies from 1996 to 2001. In these three works, the dependentvariable is the proportion of premiums ceded per company. Outreville, for his part, tests thefactors that influence the premium retention rate in domestic markets in a cross-sectionregression analysis of 42 developing nations in 1988 and 1989.

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There are more empirical studies into the demand for insurance by companies outside the insurance market. Thefindings of these studies are not included as they do not cover the issue of reinsurance.11 Some are proxy variables, i.e. they are used to substitute other relevant variables. Others are dummies, i.e.binary variables, in general, whose values can only be 0 or 1.

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TABLE 1:

Lag between Loss Report/Claim Settlement (tail)

Mayers;Smith(1990)

Garven;Tennant(2003)

Carneiro; Sherris(2005)

Outreville (1994)

Tax rating (taxes/premiums) NSTax Deduction Margin (tax shields) NS

Ownership Structure/Control (dummies) S(+) NS NS

Leverage S(+) S(+)

Credit Rating S(-)

Size S(-) S(-) NS

Concentration on Business Lines S(-) S(-)

Geographical Concentration S(-) S(-)

Time Indicator(dummies) NS NS

Volatility of Assets S(+)

Lag betw. event and payment of claims (tail) S(+)Correlation betw. investment return/loss ratio S(-)

Rate of return on investments NS

Scale variable (premium/GDP) S(-)

Financial Development [(M2-M1)/M1] S(-)

Uncompetitive Market (dummy) S(-)

Market restricted to National Cos. (dummy) S(+)

Existence of compulsory local reinsurer(dummy) NS

Looking at the cross-section and panel regression analyses of companies, only two variablesappear in all three works: ownership structure and company size, and the findings for theseare not consistent. In the studies by Mayers & Smith and Garven & Lamm-Tennant, acompanys size measured as its total assets has a significant negative influence on thedemand for reinsurance, but in Carneiro & Sherriss work, this is not significant. Theownership structure variable only has a significant positive impact in Mayers & Smiths work,while it is not significant for the other two. The variables investigated in any two of thepapers are leverage, concentration in business lines, geographical concentration and time.Both the papers that investigate leverage find it has a positive, significant influence ondemand for reinsurance, while the business concentration and geographical concentration

have a significant negative influence. The time indicator is not significant. The influence ofsome other variables are investigated in individual papers: average tax rate, margin for taxdeductions, credit rating, asset volatility, tail, ratio between the return on investments andthe cost of losses, and the rate of return on investments. The tax variables and return oninvestments are not significant but the others have significant effects, predicted by thetheory, i.e. the demand for reinsurance rises the greater the asset volatility is, the longerthe tail is, and the lower the credit rating and correlation between returns/cost of lossevents are12.

12 Curiously, Mayers & Smith, who were the first to discuss the potential effect of taxation on the demand forreinsurance, chose not to explicitly test this variable in the empirical part of their work.

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As mentioned above, Outreville studied the factors that affect the premium retentioncapacity in different countries. If we look at this another way, we can note the influence ofthese factors on the demand for foreign reinsurance, i.e. on part of the domestic demand forreinsurance. He notes that this demand seems high (low retention) in most developing nations,and puts this down to the fragmentation and small size of these domestic markets, which are

often split between low value coverage such as auto insurance and high value high riskcoverage, like industrial property insurance. In such a context, when the concentrationincreases, imposing a degree of monopoly on domestic markets, this may reduce the demandfor imported reinsurance as insurance portfolios grow in size and diversity.

Outrevilles findings were consistent with the hypotheses he formulated. He found that thesize of domestic markets measured by their premium/GDP ratio, the development of theirfinancial systems as measured by the ratio between quasi currency and currency, and theextent to which the domestic insurance market was monopolized all had a significant negativeimpact on demand for imported reinsurance, while the existence of barriers blocking the

entry of foreign firms raised this demand. Outreville also tested the effect of compulsoryreinsurance schemes in domestic markets on the demand for imported reinsurance, but theresult was not significant.

Thus, on a theoretical plane, it seems quite clear that for small insurance companies, theirmain motivation for taking out reinsurance is their risk aversion, while for large companies,factors relating to volatility and capital structure, tax costs, agency costs, adverse selection,bankruptcy costs, etc. have a greater weight. The empirical papers mentioned above confirmthe importance of most of these motivations, with the exception of the paper by Carneiro &Sherris, which only finds companies leverage to be a significant factor.

Meanwhile, as for applying these works to a study of the Brazilian scenario, there are clearlytwo shortcomings. None of them measures the influence on the demand for reinsurance ofthe reinsurance price (premium) or the efficiency gains achieved via access to ancillaryservices, of which the supply of new products is particularly relevant13. Interestingly, in thediscussions about whether to open up reinsurance in Brazil, it is precisely these two variablesthat have been mentioned over and again as the most important, the latter more than theformer, in that it is hoped that a in future competitive reinsurance market, reinsurancepremiums will be reduced and new products supplied, both resulting in a greater volume ofbusiness for reinsurers and insurers alike14. Also, none of the papers explicitly models impact

13 Mayers & Smith mention this factor as part of the set of ancillary services that are important to reinsurance,but they do not measure its direct influence on the demand for reinsurance.14 For more on this, see Bopp (2005), Morante & Sheppard (2000), Botti (2005) and Poon-Affat (1999). Theomission of the efficiency gains via ancillary services variable could be inevitable in view of the difficulty ofobtaining statistical data. But the complete disregard for the reinsurance price in studies into its demand as wellas the price of substitute or complementary products seems particularly odd. In empirical cross-section studiesof companies, the absence of this variable assumes the hypothesis that all companies pay the same reinsurancerates or that their behavior does not vary with the price. The first assumption could have an element of truth,but not the second. In analyses involving time variations, a disregard for the price variable violates the existence

of reinsurance cycles, during which premiums can double in value. The same can be said for cross-section analysesof countries, given the differences between the countries based on their market structure, degree ofdevelopment, risk profile, etc. In Brazil, where reinsurance is supplied by a monopolistic state-owned company, andwhere prices can be expected to vary considerably in a competitive environment, any demand estimate cannot,

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a reinsurance monopoly would have on the insurance market, though Outreville seeks tomeasure the effect of this variable on determining the premium retention rate on a nationallevel.

III. Overview of the Reinsurance Market in Brazil15

Until 1939, reinsurance in Brazil was done almost exclusively abroad either directly orindirectly via foreign companies operating in the country. The creation of the IRB, a state-owned company with a monopoly over reinsurance, coinsurance and retrocession operationshad a dual purpose. Firstly, and in line with the nationalist ideology prevailing at the time, itwas designed to strengthen the nations insurance companies by maximizing their retentionrates and secondly, given the chronic shortage of capital, it was to keep reinsurancepremiums previously passed on to other countries inside Brazil.

In 1966, Decree/Law 73 granted the IRB the following legal powers: to inspect all compulsory

and facultative reinsurance in Brazil and abroad; to organize and administrate consortia; toliquidate losses, to distribute the unretained part of insurance amongst the insurancecompanies; to place the excess risk on the domestic market abroad, and to take out anyreinsurance (retrocession) of interest to the country. With time, it was also given the job ofsoftening the impacts of external underwriting cycles on the internal insurance market16. Inthis case, the institute acts as a price buffer, so that when there is a hard market (strongforeign market), price hikes are not passed on in full or immediately to the cedants, and whenthe inverse occurs, the same is true for price cuts.

Operationally, it is the IRBs job to set technical limits for each insurance business, which

are added to the underwriting limits, solvency margins and minimum capital established by thenational regulatory agencies, Susep and CNSP. In insurance companies, any risk over andabove the technical limit must be transferred to another company via coinsurance and/orreinsurance (retrocession in the case of the IRB). Once the IRB accepts a reinsuranceoperation, it can choose to retain this additional risk if the sum is within its technical limit, itcan retrocede it to the domestic market if the sum exceeds its technical limit but is withinthe retention capacity of Brazilian insurance companies, which is calculated as the sum oftheir technical limits plus the IRBs technical limit, or it can retrocede it to the foreignmarket if the sum exceeds the domestic markets retention capacity.

Until 2000, retrocession was automatic and the IRB was paid a percentage commission. Theoperation was performed by means of quotas that were determined each year based on thenet assets of each insurance company, the volume of reinsurance ceded and the result ofceded insurance operations. Insurance companies had to accept at least 50% of what theywere offered, the remaining amount being placed with other insurance companies that were

then, fail to consider the effect of the reinsurance price as well as potentially the price of substitute orcomplementary hedging schemes, like coinsurance, for instance.15 This section is partly based on Andrade (2001), Azevedo (1997), Bidino (1998), Bopp (2005), Castro (2003),

Castro (2004), Castro & Duarte (2002), Forbes (2004), IAIS (2004), Souza (2001) and Morante (2000).16 This applies more to large-scale industrial and transport risks. Risks in the auto, life and health businesses(more than 70% of the local market) follow the external reinsurance market in a less marked way and are moredependent upon domestic factors.

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willing to take on risks beyond their retrocession quotas. Meanwhile, coinsurance has workedas an alternative to this monopoly for its simplicity and speed, given that this kind ofoperation is normally more expensive than reinsurance17. Reinsurance contracts on theinternational market are signed based on the excess of all the insurance companies and theIRB, i.e. foreign reinsurance companies insure the Brazilian market as a whole 18. Therefore,

the IRB has wide-ranging normative and economic functions within the insurance market. Asit sets plans and rates, it also defines the minimum level for insurance diversification andprices in the domestic market, since insurance companies must offer policies whoseconditions and prices are in line with the IRB requirements. One might say that the market ispriced by the IRB.

As this is a market whose supply is dominated by a monopoly, any analysis naturally turns itsattention to the monopoly-holder. Graph 1 below shows the development of the reinsurancepremiums issued by the IRB since 1970 and the countrys gross and net demand forreinsurance, all as percentages of the insurance premiums issued. The data derive from the

balance sheets annexed to the IRBs annual reports19

. I define gross reinsurance demand asthe difference between the total premiums issued by the IRB and the premiums relating torisks from abroad, while net demand is taken as gross demand minus internal retrocession. Ascan be seen, between 1970 and 1994 the reinsurance market shrank relative to the directinsurance market, though it has stabilized and seen some growth since then. The total ofreinsurance premiums fell from an average of 28.1% of insurance premiums in the 1970s tojust 5.4% between 1994 and 2000, rising to 7.2% between 2001 and 2004. A similar trendcan be seen for the gross and net demand for reinsurance, which dropped from 27% and12.5%, respectively, in the 1970s to 7.2% apiece between 2001 and 2004. The recoveryduring the last four years can be linked to two factors: a) the shift of premiums previously

allotted to coinsurance consortia to reinsurance as foreign insurance companies which do notuse coinsurance account for an increasing market share; and b) the strong growth of incomein sectors of the economy that particularly require reinsurance, such as oil and gas,electricity and agricultural exports.

17 This is why it is hoped that the end of the IRB will also bring about the end of the coinsurance pools, because itis unlikely that an insurance company will seek out a competitor to share or facilitate reinsuring policies.18

In larger scale operations, insurers normally deal directly with foreign reinsurers, and it is the IRBs job toapprove these deals, taking on part or all of the risk and/or changing the retrocessionaire.19 The way balance sheets and account plans are presented changed significantly during the period analyzed, whichcould make it difficult to make the historical series compatible.

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Graph 1: Premiums Issued by the IRB and Gross and Net Demand for Reinsurance

There was a convergence between total reinsurance premiums and the corresponding grossdemand as of 1996, when the IRB practically stopped accepting risks from abroad. In the1970s, the governments export drive led to the development of a policy of reciprocitydesigned to set up an exchange with Brazilian insurers, and encouraged the IRB and insurancecompanies to take on risks from abroad. In the IRBs case, such business peaked at 8.4% ofreinsurance premiums issued (in 1980s), since which time it has dropped sharply. Meanwhile,there was a convergence between gross demand and net demand for reinsurance as of mid2000, when the automatic internal retrocession scheme ceased, which had been part of the

denationalization thrust started in 1996 when the legal monopoly enjoyed by IRB was broughtto an end. Until June 2000, the IRB and the market had a retrocession consortium whichmaximized the domestic markets retention capacity. When new legislation (Law 9932/00,later suspended) put an end to such operations, the domestic market became more dependentupon the foreign market. Measured as a percentage of all reinsurance premiums, externalretrocessions saw sturdy growth from the late 1980s onward, rising from 12.9% in the 1980sto 38.2% between 1994 and 2004.

Graph 2 shows how retained premiums and internal and external retrocessions have fared,measured as a percentage of direct insurance premiums. As can be seen, internal

retrocessions suffered a marked relative decline throughout the period, dropping from 20%in 1970 to negligible values since 2001. The current state of affairs is, then, a far cry fromthat of the early 1970s, when the policy of maximizing retention led the IRB to retrocedealmost all the reinsurance premiums it ceded to the domestic market. As for externalretrocessions, there is a milder relative decline, with this variable slipping from 3.6% of alldirect insurance premiums on average in the 1970s to 1.8% in the 1990s. Since 2000, thispercentage has recovered to 3.4%.

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Graph 2: IRB Retained Premiums and Internal and External Retrocessions

Graph 3 shows the quotients of the retained losses and the administrative and brokerageexpenses over retained premiums. These quotients are, then, approximations of the betterknown terms, loss rate and expense ratio and the sum of both is roughly the same as thecombined index20. As can be seen in the graph, from 1970 to 1987 the IRBs reinsuranceoperations tended to be profitable. Actually, in this period the sum of the aforementionedquotients was 69 on average. Generally speaking, from 1988 to 2000 the opposite was thecase: the index in question rose to 124, with its peak of 214 coming in 1989. From 2000 to2004 the institute again started to book underwriting profits expressed as an average sumof quotients of 77. The source of these changes quotients of the retained losses andadministrative and brokerage expenses over retained premiums can be seen in the samegraph. The loss ratio was low and moderate until the early 1990s, when it started to rise untilthe end of the decade, peaking at 85% in 1999 then declining sharply afterwards to previouslevels. The expense ratio evolved differently. From 1970 to 1987 it was stable and low, likethe other indicator, with an average of 34. From 1988 to 1994 it climbed sharply to 88,reaching its maximum level of 165 in 1989. From then on, the average fell to 28, much thesame as in the 1970s.

20 We have used retained premiums rather than claims because of the changes in accounting practices between1970 and 2004, which made it difficult to identify the real variation of reserves, and because of the instability of

the impacts on revenues/expenses caused by the losses incurred in foreign operations, and exchange rateadjustments. This said, as the reinsurance market was in relative decline throughout most of the period inquestion, it is likely that more reserves were used up than built up, so the factor used has probably given theindicator an overall upward bias.

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Graph 3: Indicators of Loss and Expense Ratios and of the Combined Index

Graph 4 shows the two components of the expense quotient: administrative expenses andbrokerage expenses over retained premiums. It can be seen that the first ratio isdeterminant of the (total) expense ratio in view of the fact that the latter ratio was steadyuntil 1995 (average: 13) before falling to 8 between 1996 and 2002. This discussion showsthat the period in which underwriting losses were incurred (1988 to 2000) can be split intotwo parts. In the first, there was a predominantly negative effect caused by increasedadministrative expenses (basically between 1988 and 1994), while in the second period (1995

to 2000) the overriding effect was brought about by increased Losses derived from Claims21

.

Graph 4: Indicators of Total Expense, Administrative and Commercialization Ratios

21

The sharp rise in administrative expenses between 1986 and 1994 is related to the runaway inflation during theperiod, and maybe the 1990-92 voluntary retirement plan and its ramifications. Interestingly, there is a reverse

trend for the losses derived from claims and administrative expenses indicators between 1995 and 2000,indicating a national policy to offset losses in one case with gains in the other.

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Overall, the IRB has booked profits, as can be seen in Graph 5. From 1970 to 2004, theprofitability of its net equity was 22.8%. However, this period can be split into three clearphases. The first goes until 1976, when the mean rate was 59.1%; the second, from 1977 to1994, was marked by a drop of this variable to 7.2%; and in the third, running until 2004, it

picked up to reach 20.4%. It is worth noting the contribution of net equity and financialrevenues to the IRBs overall income. These figures, along with the percentage of retainedpremiums, stayed high throughout the entire period, with a mean of 88.1%. They grewexponentially until the mid 1980s (with a peak of 417% in 1985) and then fell in a similarmanner thereafter. It is obviously these revenues that are behind the IRBs overallprofitability during the periods in which there was a negative underwriting margin.

If we look at the businesses with the most reinsurance, there has been little change since1970. The IRBs turnover has been concentrated in traditional areas, such as property risks,followed by fire and transport, all of which involve high value policies. From 2003 to 2004,

the fire insurance business brought in the greatest revenues, with 53% of retainedpremiums, followed by transport, with 24%, financial, with 12%, government, with 5%,personal insurance, with 7%, and foreign risks, with 1%. The personal insurance business istraditionally less reinsured, so the steady growth of this lines share of the overall businessas of the mid 1980s, with more savings-type coverage than life assurance, is what mostlyunderpins the drop-off in demand for reinsurance relative to insurance premiums. Anotherfactor is the decline in the relative share of the fire insurance business in the wholeinsurance market. While the natural disaster business has seen strong growth internationally,it has seen little change in Brazil because of its geography.

Graph 5: Profitability of the PL and Ratio of Financial Revenues/Retained Premiums

Finally, the IRB must be viewed from the perspective of the global reinsurance market. It isactually very small alongside its counterparts in the globalized marketplace, whose main

jurisdictions are in the Bermudas, France, Germany, Japan, the UK and the US. According tothe International Association of Insurance Supervisors, in 2003 the world reinsurancemarket had a turnover of US$149.5 billion in gross premiums, of which US$117.8 billion was

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not from life insurance (79% of the total) and US$31.7 billion was (21%) 22. In the same year,the Brazilian reinsurance market moved just US$ 996 million in gross premiums. The foreignmarket is considered competitive because it contains enough buyers and sellers for there tobe price competition, there is free entry, and there is a considerable supply of venturecapital, etc. The proof of the competitive nature of this market is the squeeze on profits it

suffers periodically when there are unexpected losses. The industry operates with astandard price lag in function of losses which gives rise to its underwriting cycle. However,economies of scale and expertise in offering supplementary services and technologicaltraining are factors which could give larger companies a competitive edge.

In the 1990s, the opening up of the markets, both domestic and foreign, along with thestabilization of the currency had a profound effect on the insurance market. Notsurprisingly, the IRBs monopoly had to be reviewed. When the IRBs monopoly was ended onpaper and there was talk of its privatization, some 20 foreign reinsurance companies set upoffices in Brazil, encouraged by the example of Chile, whose market expanded sharply after

reinsurance was opened up. Ten years on and little has changed, so much so that some ofthese offices have been closed. In other words, the fears of those against opening up themarket have held sway, namely: 1) the obligation to raise underwriting standards andaccountability; 2) the need for greater efficiency to compete on an international level; 3) theend of fronting, which allows some insurers to operate as brokers of most of the risks theyunderwrite, and 4) the fear of bankruptcy because of insufficient financial backing andtechnical know-how to take out contracts with large international reinsurance companies.

IV. Demand for Reinsurance in Brazil:

We initially attempted to estimate the aggregate demand for reinsurance in the Brazilianmarket by conducting a temporal series study upon annual data between 1970 and 2004.Next, these findings were further investigated by means of cross-section analysis (percompany) and panel analysis for the years 2001-2004.

As concerns the time series analysis, the explicative variables had to undergo someadaptations we had to deal with total sums or annual market mean values. Some variableshad to be discarded due to the absolute lack of data concerning a given period, such as taxrates, ownership structure, credit rating, the tail, and the correlation between inversionreturn and claim costs. Other variables became meaningless, like geographic concentration orthe effect of compulsory local reinsurance. Some gaps in the data had to be filled in bymeans of interpolation and the use of proxies.

In addition, because until the early 1990s IRB refunded the domestic market a significantpercentage of the reinsurance premiums, the dependent variable was faced with twopossibilities: a) a gross demand for reinsurance, given the ratio between reinsurancepremiums issued by IRB (as concerns Brazilian risks) and total premiums issued by theBrazilian market; and b) a net demand for reinsurance derived from the quotient betweenreinsurance premiums issued by IRB (domestic risks), net amounts of internal retrocessions,

22 Swiss Res estimate for the size of the global market in the same year was US$175.5 billion in gross premiums,of which US$146.0 billion was not for the life business and US$29.5 billion was.

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and total premiums issued by the Brazilian market. We chose the latter, for it seems to moreappropriately express the monopoly and reinsurance role eventually played by IRB, by eithershouldering part of the reinsurance risks or by placing the surplus of the collected amountsin the external market. The retrocessions pool managed by IRB does not seem to fullyconstitute a market demand, once its constitution and objectives, in terms of the currency

exchange economy and the feasibility of minor insurers, goes beyond the mere economicplane. Therefore, the percentage of reinsurance premiums refunded to domestic market wasconsidered to be external to the actual demand for reinsurance.

Such adjustments led us to initially estimate a regression formula that comprehended all thepossible explicative variables, as follows:

PASSPLIRDAIRDESFINJUROSRCOMPET

TAMPENTVIDAKESTALVMERPRESSDRSS

+++++

+++++++=

.(1)

Some explanations about these variables are supplied below:a) DSSR: net demand for reinsurance, that is, the quotient between reinsurance premiumsissued by IRB (domestic risks), net amounts of internal retrocessions (DRSSL), and totalpremiums issued by the Brazilian market 23 (PREM). The sources used were the annual reportsand, in some cases, IRB annual balance sheets and Funensegs and Suseps databases.

b) PRESS: average reinsurance price index, an approximation of the ratio between theretained reinsurance premiums, net commissions, and the sum of retained claims with variableprovisions. The numerator reflects IRBs operating turnover and the denominator is anestimate of its total sum. Therefore, a proxy of the reinsurance average price correspondsto dividing the reinsurance turnover by the reinsurance sum measured likewise. This approachwas used in foreign studies about the supply of life insurance and generates a product proxywith adequate stability over time24. We consider such concept applicable to the Brazilianreinsurance market, once the non-existence of catastrophic risks and its monopoly conditionlead to similar stability characteristics25. From the theoretical standpoint, we expect theimpact of such variable to be negative upon the demand for reinsurance. Our source of datais the same as the previous case. Unfortunately, given the lack of historical data, it was notpossible to include coinsurance price in the equation, as coinsurance became a significantsubstitute for reinsurance in the mid 1980s.

c) ALVMER: average market leverage, defined as the quotient between the insurers retainedpremiums and their own net equity (PL). Retained premiums are issued after the IRB hasdeducted the internal retrocessions. Coinsurance premiums were not considered because they

23 In the historic series, for some years, the direct premiums were reported rather than the issued premiums, thedifference being accounted for discounts, cancellations and refunds. Additionally, such premiums include,eventually, those granted in social security operations of the VGBL type, that is, life insurance is reported in latusensus.24 We have also used the profitability of the net capital as a proxy of the reinsurance price. The regressions

showed a negative sign which was, nonetheless, not meaningful,25 The ideal procedure would be to use the estimates about retained claims or, in the lack of that, to reach anapproximation by statistical treatment of the series of observed claims, which demand a long historic series. Thelack of either condition prevented us from doing so.

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are annulled in the aggregate market value given the fact that the coinsurance accepted byan insurance company corresponds to the coinsurance underwritten by another. We expectthe effect of this variable to be positive as leverage gets higher, which means more risk andbigger demand for reinsurance.

d) KEST: foreign companies share in the overall insurance market turnover. The reason forincluding this variable is the claim that such companies, whose market share has increasedconsiderably since 1996 because of the opening-up of legislation, are historically moredemanding of reinsurance than Brazilian companies. The expected effect is, therefore,positive.

e) VIDA: the share of life, health, and auto premiums in total premiums. We all know that thefocus on such business lines, such as the ones aforementioned that involve less risk, reducesthe demand for reinsurance. The expected impact is, therefore, to be negative.

f) PENT: coefficient of domestic market penetration, defined as the ratio between issuedpremiums and GDP. That is a scale variable and theoretically, the effect upon the demandfor reinsurance should be negative, as more mature markets tend to endure higher retentionrates.

g) TAM: insurers average company size, measured by dividing the quotient of premiums andGDP (PENT) by the number of insurance companies (NE). Our sources are Consultec,Funenseg, and Susep. Foreign studies that we analyzed measure company size as per theirtotal assets. In Brazil, this datum series for the market as a whole between 1970 and 2004 isincomplete, so we had to use the volume of premiums issued by each company as per the GDP.

As concerns company size, this seemed to be a better approximation than each companysmean aggregate net equity. As in the previous variable, we expect the impact of TAM to benegative, as bigger companies have higher retention rates.

h) COMPET: binary variable that seeks to capture structural changes implemented as of the1990s - the abrupt fall in inflation rates and, by means of changes in regulation, a morecompetitive insurance market and overall economy of the country. This variable is assumed tobe 0 (zero) between 1970 and 1990 and 1 (one) as of then. If tighter competition implies inmore market concentration, the expected demand for reinsurance is lower; if there is lesscompetition, the expected demand should be higher. In other words, little can be assumed inthis case.

i) JUROSR: actual interest rates for overnight transactions hedged on federal bonds. Thisvariable has been included as a proxy of the return rate of the insurers inversions.Therefore, in theory, the higher this rate the bigger the profit generation capability theinsurers will have, and the lower the demand for reinsurance. The sources for this variableare ANDIMA, IBGE and IPEADATA.

j) DESFIN: financial development, measured as the quasi-currency ratio in the GDP. The

concept of quasi-currency was approximated by the difference between M4 and M1 monetaryaggregates (means of payments). Positive effects are expected, as the busier and more

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complete the financial market, the bigger the supply of risk prevention instruments, as is thecase of reinsurance. BCB and IBGE were our sources for this variable.

l) DAIR: IRB administrative expenses such as the percentage of reinsurance premiums. Byincluding this variable we aimed to approximate the impact of efficiency gains via

supplementary services offered by the reinsurer. We acknowledge IRBs cuts in personnel inthe last year and naturally, this affects the supply of the supplementary servicesaforementioned, as the ability to capture and transfer technology. Thus, this variable isexpected to have a negative effect upon the demand for reinsurance. The sources for thisvariable are IRB annual reports.

m) PLIR: IRBs net equity as a ratio of the insurers aggregate net equity. This variable servesthe same purposes as the previous one, now comparing the evolution of IRBs equity againstthe insurers equity. Theoretically, the lower the ratio, the less able will IRB be to supply thesupplementary services requested by the insurers.

n) PASS: IRBs required liabilities as a ratio of its net equity. Overseas and in the case of bigreinsurers, such variable is over 10 (ten). As concerns IRB, this ratio is lower and has been ona falling trend since the 1970s, when it reached 5 (five) and then dropped to the current 2(two). IRBs low leverage, on one hand, guarantees its solvency; on the other hand, it preventsthe supply capability at the hardest times of the economic cycle, when financial revenues arecritical for the companys profitability. Therefore, PASS aims to address IRBs occasionalinsufficient supply and in particular, issues related to efficiency gains via supplementaryservices supplied by big reinsurers to the insurance market. This variable is expected tohave a positive effect upon the demand for reinsurance.

The regression that refers to equation (1) showed five variables (KEST, JUROSR, DESFIN,DAIR e PLIR) that are statistically meaningless (indifferent of zero) and so have beenexcluded from the following regression26. Based on the currently available data, this seems tobe the most appropriate regression to explain the o object of this study within the focusupon the time series. The estimated equation is the following:

PASSCOMPETTAMPENT

VIDAALVMERDALVMERPRESSDPRESSDRSS

+++

++++++= )()((227)

26 The regression that refers to equation (1) is shown in Annex I.27 D in equation (2) represents the first difference, that is, D(PRSS) = PRSS - PRSS(-1).

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Table 2 below shows the descriptive statistics of these variables:

TABLE 2: Descriptive Statistics Temporal Series

Sample: 1970 2004

DRSS PRSS ALVMER PENT TAM VIDA PASS COMPETMean 9.69 1.42 1.67 1.42 0.01 51.63 2.64 0.4Median 9.95 1.33 1.79 1.04 0.01 47.05 2.3 0.0Maximum 17.42 2.53 2.73 2.55 0.02 76.00 5.5 1.0Minimum 4.28 0.52 0,66 0.83 0.0 29.40 1.7 0.0Std. Dev. 3.94 0.52 0,56 0.59 0,0 18.41 0,88 0.5Skewness 0.24 0.43 -0.19 0.65 0.59 0.12 1.64 0.41Kurtosis 1.91 2.67 2.2 1.77 2.91 1.27 5.37 1.17

Jarque-Bera 2.06 1.25 1.14 4.68 2.04 4.82 23.94 5.87Probability 0.36 0.54 0.56 0.1 0.36 0.09 0 0.05

Observations 35 35 35 35 35 35 35 35

As central trends of the domestic insurance market we can identify low leverage, littlereinsurance practice, operations mostly concentrated on life, health and auto insurance, andlow penetration coefficient. PRSS and PASS variables are indicators whose absolute valueonly makes sense when compared to other markets (we shall recap on this point below). Theresulting platykurtic distribution is, in general, right-skewed and within normality.

The results of the regression are presented in Table 3 below and regressions show anadequate explanation power. R shows a mean 90% and the low probability of F-statisticindicates the relevance of the set of explicative variables. Both the 1.93 Durbin Watson Test(DW) and the Breusch Godfrey Test statistics indicate the absence of serial correlation in

the residues. The regression did not show any signs of heteroscedasticity, according toWhites test. The coefficients of the explicative variables are statistically different fromzero, with probabilities lower than 94%, as per the respective standard errors, except forthe first difference in leverage. The coefficients show the expected signs: negative signs forreinsurance price (PRSS) and for penetration coefficient (PENT), and positive signs formarket leverage (ALVMER), the share of life, health, and auto premiums in total premiums(VIDA), and IRBs required liabilities as a ratio of its net equity (PASS). The COMPETvariable had a positive coefficient, thus showing that the more competitive environment ofthe 1990s fostered an increased demand for reinsurance. The initial differences between thePRESS and ALVMER variables aimed to account for time dynamic effects. Both global and

steady-state cases show the impacts as expected according to theory, the former withnegative while the latter positive.

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TABLE 3: Demand for Reinsurance Temporal Series

Dependent Variable: DRSSMethod: Least SquaresSample(adjusted): 1971 2004Included observations: 34 after adjusting endpoints

Variable Coefficient Std. Error t-Statistic Prob.

C 14.38 2.28 6.30 0.PRSS -1.89 0.81 -2.34 0.D(PRSS) 1.65 0.62 2.67 0.

000301

ALVMER 1.88 0.72 2.61 0.D(ALVMER) -0.45 1.14 -0.39 0.PENT -11.98 2.66 -4.51 0.TAM 1270.44 228.67 5.56 0.VIDA -0.15 0.05 -2.90 0.PASS 0.82 0.42 1.96 0.

COMPET 3.93 1.70 2.31 0.R-squared 0.90 Mean dependent var 9.81

027000000106

03

Adjusted R-squared 0.87 S.D. dependent var 3.94S.E. of regression 1.44 Akaike info criterion 3.81Sum squared resid 49.72 Schwarz criterion 4.26Log likelihood -54.70 F-statistic 24.

Durbin-Watson stat 1.93 Prob(F-statistic) 0.Breusch-Godfrey Serial Correlation LM Test (n lags=01)

F-statistic 0.03 Probability 0.86Obs*R-squared 0.04 Probability 0.83

77

00

The variable company size shows a significant and positive sign in the regression, thus theopposite of what was expected, indicating that ceteris paribus, Brazilian insurancecompanies growth led to a higher demand for reinsurance. That was not predicted by theory,but is to be considered a possibility if such growth is not supported by changes in theinsurers ownership structure. We should remember that the connection between demand forreinsurance and the insurers company size is established by ownership structure: within thecontext of the CAPM model, bigger insurers are usually open-capital companies and operateactively in the capital markets; as a consequence, they have more access to assetdiversification mechanisms that reduce exposure to unsystematic risks and thus, their need

for reinsurance. If companies grow but keep stable ownership structures, theaforementioned effect may not occur. It should be noted that in the empirical studyconducted by Carneiro and Sherris (2005) for the Australian reinsurance market, suchvariable was not significant. Until recently, in Brazil, the insurers growth was not followed bysignificant changes in ownership structure due to little market competition. This is possiblythe reason for the positive sign that was found. This estimate was carried in time seriesthrough a multivariate regression. Next, we conducted estimates for demand through cross-section regression and/or panel data regression at corporate level in order to verify theprevious findings. Such approach undoubtedly requires several adaptations.

Firstly, we must specify which companies will be the set object of the statistical study. Mostforeign empirical studies focused on elementary insurance companies (property/casualty),either because such companies allow for a less heterogeneous sample of the insurance market

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or because these companies are considered to operate in a significantly different way fromthose that specialize in insurance plans for individuals. That also explains the fact that inseveral countries, they have to be legally constituted one way or another. In Brazil, althoughthis legal distinction has been recently established, in practice, the difference between thetwo sets of insurance companies is still too little to justify a single study focused on both

sets.

Another problem to be solved regards the groups of insurers. Data collected by SUSEPbetween 2001 and 2004 reveal that 118 insurance companies operate in Brazil. However,several of them belong to banking or insurance conglomerates so that part of a given insurersdemand for reinsurance may be addressed by another company that belongs to the sameconglomerate. It thus makes sense to focus upon company conglomerates rather thanindividual insurers. Searching the Internet sites of the referred conglomerates, we wereable to collect several balance data and to study a set of 61 groups of insurance companiesand individual insurers between 2001 and 2004. Seeking homogeneity, we chose to keep the

same set of companies along all these years so that groups of companies or individual insurersmentioned as concerns one specific type of data are not excluded from the sample. This setof companies for the year 2001 is presented in Annex II. Finally, instead of time seriesanalysis, the cross-section focus did not take into account those figures that refer to healthinsurance, as these refer to data per company that pertains to SUSEP database.

Having defined the set of companies, the next step was to establish the equation to estimatethe demand for reinsurance and, therefore, the variables to be considered. Our startingpoint was Garven and Lamm-Tennant (2003), aforementioned, who studied a set of 176American insurers that operated in elementary insurance between 1980-1987. We shall start

our analysis upon cross-section regression, moving on to panel data regression. This, theequation of the estimated demand for reinsurance for 2001-2004, through cross-sectionanalysis, in the following:

1.......... dbanckestgeoinvtaxvidahhtamalvdrs ++++++++++= (3)

The Greek letters represent the parameters to be estimated. The abbreviations, in thespecific order and per company, refer to the demand for reinsurance, leverage, company size,market share, concentration in life and auto business, rates, inversion revenues, geographic

concentration, and mean foreign capital. The variable banc is a dummy that aims to verifythe influence of the factor belongs to a banking conglomerate upon the demand forreinsurance. Therefore, this variable takes up the value of 1 if the group or individualinsurer is a banking institution and 0 if otherwise. The variable d1 is another dummyassigned value 1 if the group or individual insurer specializes in home insurance and 0 ifotherwise. Except for the latter variable, included in the equation to allow for betterregression line adjustment, the reason for considering the other variables are the same asfor the focus on time series.

The demand for reinsurance at corporate level and at a given year (drs) was defined as the

quotient of the paid reinsurance premiums, net accepted retrocessions, over direct insurancepremiums. Leverage (alv) was defined as the quotient of direct premiums over net equity.Company size (tam) was attributed by the natural logarithm of total assets. A given companys

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market share (hh) was based on its direct premiums and was attributed by the respectiveHirshmann-Herfindah indexl28. The concentration in life and auto business (va) was set by theshare in the premiums issued for these types of insurance in total premiums. Tax rating (tax)was established as income tax and social welfare taxes expenses as the percentage of directpremiums. The inversion return rate (inv) was set as the sum of net financial revenues plus

equity as a percentage of total assets. Geographic concentration (geo

) was based on a giveninsurers or a group of companies operation in different states of Brazil. Therefore, forinstance, a given company operating in the states of So Paulo and Rio de Janeiro but notoperating in the rest of the country was assigned a mean value equal to the share of thesestates total GDP in the countrys GNP. Foreign capital share (kest) was set by the number ofshares held by this shareholder against the total shares issued by a group or an individualinsurer. The source of primary data is SUSEP. A number of potentially important variableswere not considered, like tax shields, credit rating, asset volatility and the correlationinversion returns/claims costs, given the lack of respective data.

Focusing on cross-section analysis has both pros and cons when compared to time seriesanalysis. One of the obvious advantages was studying the reaction at corporate level. Thisway, variables such as a companys market share, its geographic concentration, tax rating, andownership structure effects like those captured by the dummy banccan only be investigatedthrough cross-section analysis (or panel analysis, which integrates both foci). Analogously,the variable inversion return rate - which is approximated by real interest rates in timeseries analysis - can be more accurate in cross-section regression analysis. On the otherhand, a major disadvantage was not being able to include the variable reinsurance price inthe regression. In fact, at corporate level, the indicator used for this variable in time seriesanalysis the ratio between retained reinsurance premiums, net commissions, and the sum of

retained claims with the variable on the provisions showed little reliability, given itsinstability. For the same reasons, it was not possible to consider the variable coinsuranceprice, which is a substitute product for reinsurance. The regression did not comprise theratio between IRBs required liability/net equity which, in the time series analysis,approximated the variable efficiency gains via supplementary services, for absolute lack ofdata at corporate level.

Table 4 below shows the main descriptive statistics of the aforementioned variables in theperiod 2001-2004.

28 This index, better known as HH, is defined as the square sum of the percentage market share of a givencompany.

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TABLE 4: Descriptive Statistics of the Variables Under InvestigationSample: 2001 2004

DRS ALV TAM VIDA HH TAX INV GEO KEST BANC D1

Mean 130.05 257.7 52.09 73.54 1537,14 14.05 79,2 74.02 41.93 0.18 0.07Median 52 235.5 51 83 7.5 9 77 100 31 0 0

Maximum 836 1754 76 100 57065 222 232 100 100 1 1Minimum -30 22 32 0 0 -360 -50 7 0 0 0Std. Dev. 188.87 186.68 8.36 27.34 6793.42 46.18 41.02 31.26 44.29 0.39 0.25Skewness 2,16 2.98 0.48 -0,98 6.44 -1,48 0,3 -0.78 0.32 1.66 3.51Kurtosis 7.12 20.41 3.02 2.95 46.56 23,01 3.86 2.17 1.32 3.77 13.32

Jarque-Bera 361.99 3442.27 9.33 38.9 20973.75 4160,59 11.02 31.78 33.03 118.42 1583.83Probability 0 0 0.01 0 0 0 0 0 0 0 0

Observations 244 244 244 244 244 244 244 244 244 244 244Cross sections 61 61 61 61 61 61 61 61 61 61 61

As the table shows, also in terms of central trends, the set of insurers under study may bedescribed as companies that make little use of reinsurance, operate with low leverage, focus

more on life and auto business both in terms of size and market share - operate in most ofthose states of Brazil that have significant GDP, collect little amounts of taxes, get goodinversion return rates over assets, show a significant foreign capital share as well as a lowshare of banks and companies that focus on home insurance. Distribution is, in general, right-skewed leptokurtic and not within characteristics of normality.

The results of the cross-section regressions are shown in Table 5 below29.

29

The econometrics software used was E-Views 3.1. Due to problems to export data in Excel sheets with Latinnotation (thousands separated by points and decimals by comas)to E-Views that uses English notation (thereversed use of points and commas), the variables drs, tam, taxand invwere multiplied by 10, and the variable alv,by 100.

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Table 5: Cross-Section Regressions 2001-2004

Dependent Variable: DRSMethod: Least SquaresSample(adjusted): 1 61Included observations: 61 after adjusting endpoints

Variable Coefficient t-Statistic Coefficient t-Statistic Coefficient t-Statistic Coefficient t-StatisticC 754.65 5.42 923.61 7.14 802.33 7.26 893.87 7.22ALV -0.18 -1.97 -0.16 -2.62 -0.17 -1.93 -0.12 -1.21TAM -3.00 -0.96 -3.13 -1.17 -1.46 -0.59 -3.41 -1.4VIDA -5.78 -9.35 -7.19 -11.62 -6.65 -13,84 -6.82 -13.03HH -0.01 -2.14 0.00 0.24 0.00 -0.33 0.00 -0,06TAX -0.38 -0.82 -0.21 -0.6 -0.18 -0.82 -0.55 -1.72INV 0.13 0.31 -0,3 -0.89 0.08 0.27 0.29 0.78GEO -0.02 -0.04 0.07 0.13 -0.24 -0.49 0.00 0.0KEST -0.32 -0.89 -0.32 -0.97 -0.58 -1.9 -0.85 -2.7BANC -2.35 -0.05 -8.29 -0.2 20.69 0.53 35.31 0.85D1 -204.71 -3.08 -256.75 -4.19 -259.49 -4.96 -248.92 -4.68

R-squared 0.67 0.78 0.82 0.81Adjusted R-squared 0.61 0.73 0.79 0.77S.E. of regression 110.1 99.94 88.71 95.03Sum squared resid 606091.3 499373.8 393437.41 451488.18Log likelihood -367.27 -361.37 -354.1 -358.29Durbin-Watson stat 2.25 2.09 1.77 1.77Mean dependent var 115,54 133,36 137.75 133.54S.D. dependent var 175.53 193.15 192.2 197.79Akaike info criterion 12.4 12.21 11.97 12.11Schwarz criterion 12.78 12.59 12.35 12.49F-statistic 10.25 17.41 23.17 21.00Prob(F-statistic) 0.00 0.00 0.00 0.00

2001 2002 2003 2004

Regressions show adequate explanatory power (adjusted R-squared are over60% in the four

years) and the set of variables were found significantly different from zero, as per F-statistic. Coefficients of the variable life show negative signs and are statisticallydifferent from zero, as predicted by theory and found through time series analysis. In otherwords, the higher the concentration on this insurance segment, the lower the demand forreinsurance. Coefficients of variable leverage show negative signs in the four regressions,being non-significant only in 2004. The results are, therefore, contrary to what waspredicted by theory and found in the time series regression. In fact, a priori, we shouldexpect that the higher the leverage - thus implying in higher risks - the higher the demandfor reinsurance would be. Coefficients of variable company size point to negative impactsover the demand for reinsurance, as expected by theory, but these were statisticallydifferent from zero in the four years. The variable market share, calculated by HH, wasfound negative and statistically different from zero, as expected, only in 2001; and in theother years, indifferent from zero. The variable tax rating had negative impact on thedemand for reinsurance, but only in 2004 this effect was statistically different from zero to10% of significance. Coefficients of variable foreign capital were negative in the four yearsand found significant in 2003 and 2004, thus pointing to the possibility of less demand fromforeign companies than from domestic companies30. The variable concentration on homeinsurance, assessed by the dummy d1 showed negative and significant coefficients in thefour years, thus indicating that companies that focus on this type of insurance, notedly Caixa

30 It should be noted that such result is contrary to what is sometimes claimed as reference to foreign companiesbehavior.

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Econmica Federal, show lower demand for reinsurance than the others. The variablesinversion return rate, geographic concentration and belonging to a banking conglomeratedid not show statistically different from zero coefficients in any of the four years.

Cross section analysis shed light over certain aspects not assessed by time series analysis.

The statistical problem with the latter is that the estimated coefficients are possiblycontrary to what is expected, given the non-identified heterogeneity between the severalcomponents of the data set31. Panel data studies might correct this problem, that is,regression analyses with both dimensions spatial and temporal. Combining time series andcross-section analysis can improve estimates in three aspects: a) it allows for the correctionof the statistical problem mentioned just above; b) it unveils dynamics that are otherwiserarely detected in cross-section analysis; and c) it can significantly increase the number ofobservations when we multiply the N observations in cross-section analysis by the T timeperiods. Additionally, the results and referents aforementioned for the variables leverageand company size, contrary to what was assessed through time series regression, reinforce

the argument for conducting panel data analysis.

Having said that, for panel data analysis, the estimated equation was the following:

invtaxkesthhvidatamalvdrs ........ +++++++= (4)

Again the Greek letters represent the parameters to be estimated. The signs refer, percompany, to the same variables in equation (1). As variables geo, bancand d1hypotheticallyremain the same for every company along all the years under study, they could not beincluded in equation because they lead to multicollinearity and, therefore, do not allow for

the inversion of the explicative variables matrix. This represents a disadvantage of paneldata analysis over cross-section analysis. We also attempted at a specification of equation (2)which includes as proxies of the reinsurance price and of the efficiency gains viasupplementary services the same indicators used in time series analysis. This implied thehypothesis of variable constancy for all the insurers in a given year. The estimation did notyield consistent results for reinsurance price, thus making this hypothesis unreal and so bothvariables were excluded from the regression. The results of the regression that refers toequation (4) are shown in Table 6 below.

31 Na analogous problem occurs in time series regressions, when the contrary may occur given non observedheterogeneity between diverse periods of time.

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Tab le 6 : Pane l Ana l ys i s F i xed E f fec ts (2001 2004)

Dependent V ariable: DRS Me thod: Pooled Least Squ ares (f ixed effects)Sam ple: 2001 2004 Included observations: 4 (2001 - 2004)Number of cross-sections used: 61 Total panel (balanced) observations: 244W hite Heterosked astici ty-Cons istent Standard Errors & Co variance

Variable Coeff icient t-Statistic Prob.

ALV -0 .0 79 -2 .7 8 0.0 1TAM 7.56 4.13 0.0V IDA -1.64 -3.98 0.0HH -0.0036 -3.28 0.0KEST 0.30 0.67 0.5TAX 0.08 1.63 0.11INV -0.19 -2.25 0.03

R-squared 0.97Adjuste d R-s quared 0.96

S.E. of regression 36.64F-statistic 1046.9Prob(F-statistic) 0.00Mean depende nt var 130.05S.D. dependent var 188.87Sum squared resid 236271.34Durbin-W atson stat 2.00

Cho w's po olabi li ty test 0.005501Hau sma n's test (f ixed x random effects) 18.17Hau sma n's test (pooled x f ixed effects) 215.75

Before moving on to panel data analysis, it should be questioned whether the data set can be

pooled into both dimensions spatial and temporal. We then conducted Chows poolabilitytest, whose statistics (0.0055) show that such pooling is possible. The next step is then tochoose one of the possible models for aleatory error. The most commonly used hypotheseslead to simple pooling, fixed effects and random effects models. Random effectspresupposes that sample observations be aleatory within a given population. However, this isnot a reasonable hypothesis when, as in this case, the object of study is a fixed set ofinsurance companies sampled year by year and within a specific domestic market. Thus, wechose the fixed effects model. It should be noted, however, that the statistical value ofHausmans test (18.17) to guide decisions between fixed or random effects equally justifiesboth32. An analogous test was used to help decide between fixed effects and simple pooling.

The statistics of this test (215.75) rejected the latter model. In Annex III, we present theregressions that use simple pooling and random effect models.

The regression presented in Table 3 had adequate explanatory power (R-squared adjusted to96%) and the set of variables is significantly different from zero, as per F-statistic. Whenfocusing on a four-year period (2001-2004),

faria, opening of the reinsurance

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