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Published on April 13, 2008

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Insurance and Finance Convergence and Divergence:  Insurance and Finance Convergence and Divergence Presented by Michel M. Dacorogna First Bonzenfreies Colloquium on Market Dynamics and Quantitative Economics, Alessandria, Italy, Sept. 9-10,2004 Outline of the Talk:  Outline of the Talk Institutional framework Products Valuation methods Conclusions Banks and Insurances as Risk Bearers:  Banks and Insurances as Risk Bearers Banks have traditionally been taking credit risks on their books in their wholesale lending operations, but also market risks through their securities trading operations. Insurances and reinsurances have been taking most other kinds of risks: mortality and interest rate risks for life insurance, natural disasters, liability, accident risks for the non-life insurances. The traditional providers of risk management solutions are the investment banks and the reinsurers. Recently, banks by securitizing most of their credit risks are moving away from their traditional risk bearing function. Banks and Insurances as Risk Bearers(II):  Banks and Insurances as Risk Bearers(II) For banks the risk assumption on the balance sheet is only a small part of their activity; the main activities are intermediation and other services. The investment bank is a sort of broker (financial intermediary) to access the financial markets. It is taking little risk itself except when trading securities for its own account. While the reinsurer provides its own capital and balance sheet to carry the risk. He is a sort of risk warehouse and risk appears on both sides (asset and liability) of their balance sheet. That is why capital to asset ratio is substantially higher in non-life insurances, somewhat smaller for life insurances, but still higher than for banks. Drivers of Convergence:  Drivers of Convergence Trend towards enterprise risk management (capital leverage, diversification, regulatory and accounting arbitrage). Deregulation: US repealing of the Glass-Stegall Act leading to increased competition. Changing risk landscape: growth in insurance risks (particularly property values in natural catastrophe areas but also new diseases, legal changes …). Limited insurance capacity and imperfections of the insurance markets: price cycles, lack of transparency … The “Allfinanz” idea: one shop for all financial needs of the customer. Limits of Convergence:  Limits of Convergence Complexity of the solutions: the risk models are not easy to grasp. Different distribution channels: brokers for insurances versus branch offices for banks. Regulatory, accounting and tax issues. Limits of the providers: credit risk and capacity. Differences in the time horizons: short-term in banks and longer terms in insurances. Value added: basis risk, transaction costs, liquidity, conservatism. Moral hazard and adverse selection. high entry costs Banks Have Been Quite Resilient During the Latest Financial Crisis:  Banks Have Been Quite Resilient During the Latest Financial Crisis Banks have performed far better over the past two years than during the recession of 1990-91 and after previous periods of great stock market weakness. In the US there were 205 bank failures in 1989, 160 in 1990 and 109 in 1991*. There were only 7 in 2000, 4 in 2001 and 11 in 2002, and only 2 so far this year*. The US Bank capital has increased by 12.8% in 2001*. Many factors can explain this resilience, but definitely the consequent implementation of risk management has played an important role. *Source Financial Times June 18,2003 Insurances Much Less:  Insurances Much Less No doubt that we are facing challenging times. The Insurance Industry Lags Behind in Terms of Risk Management:  The Insurance Industry Lags Behind in Terms of Risk Management More volatile business cycles, unprecedented corporate failures, regional economic crises and international terrorism make it even more important to understand risks. The solvency rules still rely on premium instead of risk based capital. Profit from insurances have lagged behind other industries and naturally the insurance shares are also under-performing the market. To regain profitability, insurances must concentrate on understanding risks and their interactions using the new tools developed by risk management. Falling Assets Hit Insurances:  Falling Assets Hit Insurances Insurers have been hit harder by falling equity returns than by underwriting losses since the September 11, 2001 attacks on the US, according to a study commissioned by Chicago-based broking, consulting and underwriting group Aon Corp. The report found that falls in insurers' investment portfolios coupled with extra reserving to cover liability exposures had left many in a profoundly weakened financial position. Commenting in the light of the study's findings, Aon chief executive Dennis Mahoney noted that the stock-market slump was "now undoubtedly the most significant factor influencing the future of the insurance industry, as insurers strive to maintain solvency levels and balance their assets and liabilities“. Consequences:  Consequences Profound disillusion about convergence opportunities. Divestitures from banks in insurances: Citigroup and Travellers. Divestitures from insurances in financial services: Zurich Financial Services sold all its banking operations. The alternative risk transfer (ART) activities between reinsurers and investment banks have diminished substantially. Nevertheless, there are needs to continue to work together to provide better protection against risks. Products:  Products The products can be roughly grouped into two major categories: Alternative Risk Transfer: products that evolved from the traditional insurance-reinsurance contractual model: finite risk, contingent capital, multi-year multi-line products (MMP), multi-trigger products (MTP) . Insurance-linked derivative products on so-called exotic underlyings: weather derivatives, credit default swaps, credit enhancements, CAT Bonds … The major success of the collaboration between banks and insurances is the securitization of insurance natural disasters exposure: the CAT Bonds. On the retail side: life & pension contracts with embedded investment components (unit linked products). Simplified Structure of a CAT Bond:  Simplified Structure of a CAT Bond Insurance Investors Reinsurance Special Purpose Vehicle Collateral Account Insurance Insurance Insurance Insurance Swap Counterparty Development of the CAT Bond Market* :  Development of the CAT Bond Market* * Source Swiss Re Capital Markets February 2004 The numbers include two issues from non natural catastrophe bonds: golden goals (FIFA) and vita (life) deals CAT Bond and Structured Finance:  CAT Bond and Structured Finance Although big in absolute terms, the market is still small compared to the general structured finance market. For instance, new issues in 2001 of corporate bonds in the US represented more than 75 billion USD. Mortgage Backed Securities (MBS) new issues (private and commercial) in the US represented a volume of more than 230 billion USD in 2001 compared to 0.8 billion for the CAT Bonds. The success of securitization for financial products should encourage the insurance market to continue in this direction. The reinsurance premiums are around 200 billion USD for the whole world while the US bond market alone represents about 2000 billion. Skills and Competences:  Skills and Competences Re/Insurers Origination Risk Engineering U/W and Selection Pricing Portfolio Management/ALM Claims Management and Services Bankers Structuring U/W: Pricing Structure Distribution (access to the financial markets) Regulatory / Compliance Expertise Points of Contact:  Points of Contact One of the most fruitful parts of the convergence between the finance world and the insurance world is the exchange of approaches when it comes to evaluating risks. Banks have learned from insurance to cope with extreme events. The example of the ETH (Swiss Federal Institute of Technology) in Zurich is a good illustration. Insurance mathematicians specialized in extreme value theory have made their marks in the field of finance. Insurance learned from banks to account and price financial risk on the basis of an evaluation of risk-based capital. To illustrate this point, we shall discuss the pricing methodology used at Converium. Correctly Pricing Risk Is Crucial:  Correctly Pricing Risk Is Crucial Joseph Brandon CEO of GenRE about the reinsurance industry problems: "I don't think the industry has a denominator problem with the amount of capital. I think there is a numerator problem, which is what is the profitability of the industry.” In his 2001 letter to shareholders, Warren Buffet wrote about GenRE: “The company violated three basic rules of insurance underwriting: accept only risks that can be properly evaluated and be profitable, limit the amount you can lose in a single event or related events and avoid business involving moral risk - policyholders who are less than ethical and honourable. What is the Correct Price ?:  What is the Correct Price ? The risk is to have a claim that far exceeds the expected loss. Thus risk is an unexpected loss. In order to quantify the risks, we need to choose a confidence threshold at which the company wants to operate (1 over 100 year event). Pricing the risk at the expected loss plus costs means running the risk of losing more. Thus the need to put up capital for covering this risk (Risk Based Capital). Providing capital has a cost – investors want a return on investment. The Price of Assuming Risk:  The Price of Assuming Risk Insurance companies have learned from banks to measure their profitability on the capital at risk (RAROC and RORAC). For running a profitable insurance company, the premium for assuming a risk must include three elements: The expected loss to be paid back, The cost of capital (also called risk loading) for covering unexpected losses, The internal costs for writing the policy. All these elements constitute the price of an insurance policy or a reinsurance treaty. From Risk Loading to Cost of Capital:  From Risk Loading to Cost of Capital The traditional approach to pricing in insurance was to load the expected loss by the uncertainty of the outcome through a factor times the standard deviation or more generally: Where L are the losses, r is a risk measure (like s, s2 or Value-at-Risk), k the risk loading factor and m the costs. This approach is not compatible with premiums that depend on the losses, which is very common in reinsurance (reinstatements). It also completely neglects the payout patterns of the losses, the portfolio effect and the cost of capital or target profitability. From Pricing the Losses to Pricing the Profits:  From Pricing the Losses to Pricing the Profits Moreover the traditional approach with certain risk measures (standard deviation, VaR) is not always additive. Introducing some basic finance idea we should price the profit to be expected rather than the loss. Let X be a reinsurance treaty with a profit P for the reinsurer: We can now simply introduce the time value of money by computing the Net Present Value (NPV) of P discounting it to today. P = Premium-Losses-Expenses Some Alternative Pricing Principles:  Some Alternative Pricing Principles We now use X=NPV(P) as the variable to compute the premium. Distorted Probability: Denneberg in 1988 and Wang independently in 1995 proposed to find a distortion function G:[0,1][0,1] increasing, surjective and concave such that: They then define the technical premium as the one for which X satisfies the above equation. Such a principle is additive. Applying this methodology one can derive the risk neutral probability that is used in finance for pricing derivatives. Slide24:  Coming up with a Quotation Introducing Diversification and Discounting:  Introducing Diversification and Discounting The simple example before does not elaborate on two facts: The insurer should price against his portfolio, The payout patterns of the losses count: when does the insurer pay the loss. We need to introduce here more complicated notions of capital allocation and discounting. Allocating capital against the portfolio requires to know the dependence between lines of business and to use a risk measure that accounts for diversification (sub-additive). Some Conventions:  Some Conventions For the sake of simplicity, we always assume sufficient differentiability, e.g. Each random variable is assumed to have a density. Empirical distributions can be approximated by smooth distributions (for our purpose, as good as we wish). For a random variable S, we denote by FS the cumulative distribution function of S. We use as our basic variable the NPV of the profit of a treaty X: X represents the random variable while X is the full treaty. X = NPV(Premium-Losses-Expenses) What Is an Appropriate Amount of Profit?:  What Is an Appropriate Amount of Profit? Clearly the expectation of X, E(X) should be positive. It should also cover the cost of capital to be paid back to the investors. It should cover the expenses of the operation. It should include a safety loading as seen before: The higher the risk the higher the loading, and the higher the dependence with the portfolio the higher the loading. The Portfolio Viewpoint:  The Portfolio Viewpoint Let us consider the following portfolio Z: where Xi are the different risks. The portfolio Z is supported by a Risk Based Capital K. An allocation of capital Ki to Xi requires a technical premium such that where ti is the duration of the risk Xi and h is the profit target. Capital Allocation: Euler Principle:  Capital Allocation: Euler Principle We allocate capital to a subportfolio S (e.g., treaty, Line of Business) in Z according to the Euler principle: Assume all ti=1. Then, roughly speaking, this is the only allocation principle satisfying the following property (D. Tasche, 1999): If ES ≥ hKS then slightly increasing the share of S, increases the portfolio’s RoRBC and vice versa. Steering the portfolio through pricing. Tasche’s result:  Tasche’s result Theorem (D. Tasche, 1999). Under the above assumptions and some mild differentiability assumptions we have: Thus we allocate capital to a line of business according to its contribution to the bad performance of the whole portfolio. In order to use this principle in practise, we need a sound portfolio model! To this end, we need a sound model to describe dependencies. We use here copulas, CX,Y . Allocation of Capital to a Treaty:  Allocation of Capital to a Treaty C. Hummel (2002) showed that suppose we are given a treaty S of Z and the copula CS,Z between S and Z. Then: with We call HS the Diversification Function of S in Z. The distorted probability depends on the diversification of S within Z. Note that we do not need to know FZ to calculate KS.. Interpretation:  Interpretation Consequently, the technical premium should insure a profit X for treaty X that satisfies This is equivalent to (C. Hummel 2002): Compare this to Denneberg and Wang’s premium principle: In our setup, the distorted probabilities differ from treaty to treaty and are determined from the diversification of the treaty in the reinsurer’s portfolio. Using the Traditional Method for Pricing:  Using the Traditional Method for Pricing Using the standard deviation loading makes all these programs lie on a straight line since they present very similar risk characteristics. Risk Rate on Line Active Portfolio-Management: An Example:  Active Portfolio-Management: An Example The capital allocation taking into account the diversification effects within the portfolio results in different loading for similar risks. Active Portfolio-Management: An Example (II):  Active Portfolio-Management: An Example (II) Diversification or risk accumulation are favoured respectively penalized in the price. As a result, the pricing mechanism implicitly optimizes the portfolio. Conclusion:  Conclusion The institutional framework offers little convergence or synergies between banks and insurance. In the long run, we do not see a big future in these financial conglomerates. On the product side: many failures (insurance derivatives), but also some successes. In particular: credit derivatives, cat bonds and other securitization products. Valuation methodology: quite some successful convergence. The ability to valuate products is crucial for their acceptance on both the supply and the demand side. Outlook:  Outlook The integration of risk management, however, will demand more and more solutions that will imply a strong cooperation between insurances and banks. The lack of capacity requires also that the financial markets bear some of the risks instead of the reinsurers. The brightest future for convergence – in the short run – is certainly in the methodologies to evaluate and price risks, since this is instrumental for the acceptance of new products. But nobody really knows … References:  References H. Bühlmann, An Economic Premium Principle, Astin Bulletin 11 (1980), 52-60. M. Denault, Coherent Allocation of Risk Capital, Ecole des H.E.C Montreal, Sept. 1999, revised Jan. 2001, www.risklab.ch/Papers.html#Denault1999 . D. Denneberg, Verzerrte Wahrscheinlichkeiten in der Versicherungsmathematik, quantilsabhängige Prämienprinzipien, Universität Bremen, 1989. C. Hummel, Capital Allocation in the Presence of Tail Dependencies, May 2002, Presentation at the Eurandom Workshop on Reinsurance Eindhoven, The Netherlands. D. Tasche, Risk contributions and performance measurement, Zentrum Mathematik (SCA), TU München, Jun. 1999, revised Feb. 2000, www-m4.mathematik.tu-muenchen.de/m4/pers/tasche/ D. Tasche, Conditional Expectation as Quantile Derivative, Nov. 2000, --- “ ---. S. Wang, Premium Calculation by Transforming the Layer Premium Density, Astin Bulletin 26 (1996), 71-92.

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