Adding time diversification to risk diversification

Adding time diversificationto risk diversificationPresented by Michel M. Dacorogna

Moscow, Russia, April 23-24,2008

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Economy of Risk in InsuranceMichel M. DacorognaApril 23-24, 2008

Important disclaimerAlthough all reasonable care has been taken to ensure the facts stated herein are accurate and that the opinions contained herein are fair and reasonable, this document is selective in nature and is intended to provide an introduction to, and overview of, the business of Converium. Where any information and statistics are quoted from any external source, such information or statistics should not be interpreted as having been adopted or endorsed by Converium as being accurate. Neither Converium nor any of its directors, officers, employees and advisors nor any other person shall have any liability whatsoever for loss howsoever arising, directly or indirectly, from any use of this presentation.

The content of this document should not be seen in isolation but should be read and understood in the context of any other material or explanations given in conjunction with the subject matter.

This document contains forward-looking statements as defined in the US Private Securities Litigation Reform Act of 1995. It contains forward-looking statements and information relating to the Company's financial condition, results of operations, business, strategy and plans, based on currently available information. These statements are often, but not always, made through the use of words or phrases such as 'expects', 'should continue', 'believes', 'anticipates', 'estimated' and 'intends'. The specific forward-looking statements cover, among other matters, the reinsurance market, the outcome of insurance regulatory reviews, the Company's operating results, the rating environment and the prospect for improving results, the amount of capital required and impact of our capital improvement measures and our reserve position. Such statements are inherently subject to certain risks and uncertainties. Actual future results and trends could differ materially from those set forth in such statements due to various factors. Such factors include general economic conditions, including in particular economic conditions; the frequency, severity and development of insured loss events arising out of catastrophes; as well as man-made disasters; the outcome of our regular quarterly reserve reviews, our ability to raise capital and the success of our capital improvement measures, the ability to exclude and to reinsure the risk of loss from terrorism; fluctuations in interest rates; returns on and fluctuations in the value of fixed income investments, equity investments and properties; fluctuations in foreign currency exchange rates; rating agency actions; the effect on us and the insurance industry as a result of the investigations being carried out by US and international regulatory authorities including the US Securities and Exchange Commission and New York’s Attorney General; changes in laws and regulations and general competitive factors, and other risks and uncertainties, including those detailed in the Company's filings with the US Securities and Exchange Commission and the SWX Swiss Exchange. The Company does not assume any obligation to update any forward-looking statements, whether as a result of new information, future events or otherwise.

Please further note that the Company has made it a policy not to provide any quarterly or annual earnings guidance and it will not update any past outlook for full year earnings. It will however provide investors with perspective on its value drivers, its strategic initiatives and those factors critical to understanding its business and operating environment.

This document does not constitute, or form a part of, an offer, or solicitation of an offer, or invitation to subscribe for or purchase any securities of the Company. Any securities to be offered as part of a capital raising will not be registered under the US securities laws and may not be offered or sold in the United States absent registration or an applicable exemption from the registration requirements of the US securities laws.

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Agenda

1Bank and insurance as risk bearer and the challenges ahead

2 The example of natural catastrophes reserving

3 An investors’ perspective on catastrophe risks

4 Conclusion and perspective

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Changing Risk LandscapePeak risks are growing due to:

Demographic changes: concentration of population in hazardous areas, movements of populations favors the spread of diseases (AIDS, SARS, …)

Social & political changes: better leaving standards, more demanding people (e.g. liability), changing of legal systems, terrorism, political instabilities in oil rich regions, …

New technologies could bring along new risks: nanotechnology, cellular phones, new drugs (VIOXX) …

New financial products (especially in life insurance and credit)

More demanding & more attentive stakeholders: policyholders concerned with financial stability, regulators revisit insurances, better informed investors (Return on Equity ROE).

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New Risks are Multiplying with Varying Severity and Likelihood

The 26 Core Global Risks: Likelihood with Severity by Economic Loss

Likelihood

below 1%

250

bil

lio

n –

tril

lio

n

S

ev

eri

ty (

in U

S$

)

1-5% 5-10% 10-20% above 20%

Mo

re t

han

1 t

rill

ion

50-2

50 b

illi

on

10-5

0 b

illi

on

2-10

bil

lio

n

NatCat:

NatCat:

Infectious disease, developing world

Collapse of NPT

Loss of freshwater

International terrorism

NatCat:Extreme inland

flooding

Emergence of nanotechnology risks

Failed & failing states

Fiscal crisis in advanced economies

Food insecurity Extreme climate change related weather

Retrenchment from globalization (emerging)

Major fall in US$

Heatwaves & droughts

Middle East instability

Liability regimes

Interstate & civil wars

Earthquake

Cyclone

Transnational crime and corruption

CII breakdown Chronic disease, developed world

Pandemic

Slowing Chinese economy (6%) Oil and gas price spike

Retrenchment from globalization (developed) Asset price collapse

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Urban population concentratesin riskiest areas

Source : Sherbinin, Shiller & Pulsipher (2007)

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Number of Terrorist Attacks is Rising Dramatically

Source: MIPT terrorism knowledge base

Number of international (since 1968) and domestic (since 1998) incidents

INC

IDE

NT

S

0

1000

2000

3000

4000

5000

1968

1970

1972

1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

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Issues in Risk Management

Society is asking more and more financial markets and insurances to be the main providers of risk mitigating solutions as far as the financial impact of risk is concerned.

However, the finance service industry and particularly insurers are faced with two major issues in risk management:

1. New regulation: Basel II (banks) and Solvency II (European insurers)

2. New accounting rules: IFRS

Academic research should help the industry facing them by providing better tools and models.

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Challenge for theFinancial Service Industry

Both questions challenge the industry and the academic world in terms of the methods used to model for instance operational risk

or in the insurance industry to account for the reserves.

Often the rules applied to insurers are derived from those applied to banks because the latter have already been in place for a few years and have been quite successful.

After all they are both risk bearers. Aren’t they?

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Banks and Insurers 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.

Insurers and reinsurers have been taking most other kinds of risks: mortality and interest rate risks for life insurers, natural disasters, liability and accident risks for non-life insurers.

The traditional providers of risk management solutions are investment banks and reinsurers.

Recently, banks by securitizing most of their credit risks are moving away from their traditional risk bearing function.

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Banks and Insurances as Risk Bearers (continued)

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 except when trading securities for its own account.

The reinsurer on the other hand provides its own capital and balance sheet to carry the risk. It is a sort of risk warehouse and risk appears on both sides (asset and liability) of its balance sheet.

That is why capital-to-asset ratio is substantially higher for non-life insurers, somewhat smaller for life insurers, but still higher than for banks.

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Regulators and Accountants

Regulators want insurers to develop internal models for risk-based capital (RBC) (first and second pillar of Solvency II).

Accountant standard setters want insurers to mark-to-market their assets (IAS 39) and eventually their liabilities.

Most of those rules are inspired by the bank regulations and accounting.

The purpose is to protect the policyholders (regulators) and to bring more transparency in the value creation of the industry (accountants).

Is the industry ready for these challenges?

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Challenges and Questions Ahead

First of all, the insurance industry needs still to adopt a common language and disseminate best practices to build models.

Are we able to model the complexity of the business and the risks to a good level of accuracy? Do we have the methods and data in place?

Is the requirement for transparency (Pillar III of Solvency II and IFRS) going too far and introducing artificial volatility?

Is the principle of conservatism in accounting still followed: “anticipate no profit but anticipate all losses”, when using probabilities or NPVs in balance sheets?

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More Questions and Challenges

Are we insuring verifiability and limiting the amount of discretion that managers may exert in deciding what the “right” numbers are: marking-to-market the liabilities might open Pandora’s box , because there is no financial market for insurance liabilities?

Despite their obvious similarities, have we really considered the major differences between banking and insurance?

In insurance reserving is crucial and very difficult. Insufficient reserves account for two third of insurance insolvencies.

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The Example of CAT Reserving

Reserving for natural catastrophes (CAT Reserving) is a good example of the problems that face the insurance industry in applying the new accounting rules

US-GAAP and the new IFRS rules do not allow to carry over reserves for future business. If no loss has occurred during the year then the reserves must be released: equalization reserves are not allowed anymore

Two main arguments speak for the introduction of those rules:

1. It is in the interest of shareholders to diminish the amount of free cash flows at the disposal of managers for fear of misuse.

2. Moreover, the tax authorities want to avoid artificial reserve increases that diminish tax payment.

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Agenda





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Premiums and Claims

We have seen that insurance premiums are computed on the basis of the expected loss:

Premium = Expected Loss + Cost of Capital + Expenses

It is in the nature of CAT business that most of the time the claims will be much below expectation

Once in a while though, a catastrophe will occur with claims much above expectation and the yearly premiums would not suffice to cover the liabilities

To survive such situations, insurance companies have learned to diversify their risks

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Mitigating Catastrophic Risks

Diversification is usually thought in terms of geography and of type of risks.

For instance a reinsurance company would reinsure European windstorm and Japanese earthquakes as well as American

hurricanes.

Given this type of risk, geographical diversification will not suffice to avoid large fluctuations in the results, as we have seen

recently.

Uncertainty in the results is penalized by investors. They will require higher reward for their investments.

This will, in turn, increase the cost of insurance policies.

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Time Diversification HelpsTraditionally, insurers have built equalization reserves to dampen the effects of natural catastrophes on their balance sheet.

This is nothing else than diversifying the risk over time.

Some countries particularly exposed to catastrophic risks like Japan even require their insurance companies to hold equalization reserves.

The idea is simple: the years without natural disaster are used to build up reserves for the years where such a catastrophe occurs.

Since the probability of occurrence is low, it is possible on average to build substantial reserves before large claims happen.

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Capital or Reserves, That is the Question !

The argument against equalization reserves is that capital is here to be used when the premiums do not cover the claims.

If not actively invested, analysts would argue that capital should be given back to shareholders and again raised only when it is needed.

Unfortunately, if an insurance company tries to tap the market when it is known to have several hundred million dollars of

claims to pay, it finds:

That there is less cash available from the market; and

That the cash that can be found is much more expensive than keeping it on the balance sheet.

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Time Diversification is also Goodfor Long-Term Investors

Clearly, it is to the benefit of the policyholders to keep an extra cushion.

Is it also true for shareholders?

For short-term investors: the chances of getting high returns is bigger, if reserves are released at the end of the year.

For long-term investors: the volatility incurred by an insurer that releases its CAT reserves every year is high, thus the Sharpe Ratio of the investment will be lower.

The extra-cash kept in the reserves differs from the capital:

1. it is not rewarded at the cost of capital and

2. no new risk is written against it.

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Agenda





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An Illustrative ExampleIn a simple example we illustrate the view of a long-term investor:

We consider two companies that write only CAT risk against an initial capital of 100,000 USD.

One company follows US-GAAP and the other one is allowed to keep equalization reserves (time diversification).

We compute the yearly return on equity (ROE), Ri, which an investor would make by investing in such companies (all profits are paid as dividends) over a long period (10 to 30 years).

We also compute the Sharpe Ratio, S, for both investments assuming a risk free rate (R0) of 3% and computing:

0

0

[ ]

( )i

i

E R RS

R R

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Business Cycles and Cost of Capital

We introduce business cycles by assuming softening of the market if the previous loss ratio is below 60%. The price is then reduced by 20% for the next year.

The hardening of the market is modeled by a price increase of 200% if the previous loss ratio has reached 150%.

The cost of raising new capital is put at 5% of the sum raised, which corresponds to the usual investment bank fees. We

neglect other costs due to distress.

The company is allowed to keep equalization reserves up to an amount equivalent to the expected loss minus the paid losses. The cumulated reserves are not allowed to exceed the

VaR(1%), i.e. 100,000 USD.

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Performance Comparison in aSimple Deterministic Model

Sharpe Ratio ROE Sharpe Ratio ROE

No Cycle Recapitalization 0.57 15.00% 1.26 15.00%

Recapitalization with costs (5%) 0.53 14.70% 1.25 14.90%

No recapitalization 0.46 13.23% 1.27 14.90%

Cycle Recapitalization 0.39 13.32% 0.63 13.32%

Recapitalization with costs (5%) 0.37 12.90% 0.61 13.20%

Recapitalization with costs (5%) and taxes (25%) 0.15 4.90% 0.30 5.70%

Recapitalization with costs (5%), taxes (25%) and interest (3%) 0.14 4.91% 0.29 5.89%

No recapitalization 0.17 5.79% 0.60 12.30%

No recapitalization with taxes (25%) -0.03 -0.88% 0.28 5.10%

No recapitalization with taxes (25%) and interest (3%) -0.05 -1.68% 0.25 4.78%

US-GAAP Time DiversificationModels

In all cases, the time diversification company presents better Sharpe Ratios and most of the time better ROEs over 10 years (large loss 7th year).

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The Stochastic Models

We model the risk with a lognormal distribution:

The parameters are chosen so that the Value-at-Risk (VaR) at the 1% level always equals 100,000 USD, assuming that this is the risk-based capital (RBC).

We vary the coefficient of variation allowing for various tails to the distribution but keeping the same VaR.

The premium is computed according to the technical price: Expected Loss + 15% of the RBC + Expenses

Expenses are taken to be 5% of the expected loss.

2

2(ln )

21( )

2

x

f x ex

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The Stochastic Model (Fréchet Distribution)

We use also a fat-tailed distribution, the Fréchet distribution:

We compute the expectation:

And the expected shortfall:

Where (a,z) is the incomplete gamma function:

,

0, 0

( )exp , 0s

s

x

x xx

,

11sE s

,

1(1 )1

; (1 , ln )1sES r s rr

1

0

1

0

za x

a x

x e dx

x e dx

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Influence of the Parameters of the Distributionon the Expected Shortfall

Lognormal distribution

For all parameters the VaR at 99% is 100’000

Fréchet distribution

For all parameters the VaR at 99% is 100’000

CoV Expectation ESF10 6'787 192'3461 20'388 135'788

0.1 79'686 104'2880.01 97'705 100'430

Alpha Expectation ESF1.1 16'041 1'104'6131.3 11'465 434'6961.5 12'476 300'7551.9 16'607 211'490

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Buildup of the Reserves Over Time

For Lognormal Ditributions

0

20'000

40'000

60'000

80'000

100'000

0 5 10 15 20 25 30

Years

Ex

pe

cte

d A

mo

un

t o

f R

es

erv

es

CoV=10

Cov=1

CoV=0.1

CoV=0.01

We use 10,000 simulations over 30 years

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Buildup of the Reserves Over Time (II)

For Fréchet Ditributions

0

20'000

40'000

60'000

80'000

100'000

0 5 10 15 20 25 30

Years

Ex

pe

cte

d A

mo

un

t o

f R

es

erv

es

alpha=1.1

alpha=1.3

alpha=1.5

alpha=1.9

The CAT reserves’ buildup behavior is complex and depends on the fatness of the tails of the distribution (limit 100,000 USD).

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Simulation Results

We simulate 10,000 times a period of 30 years and look at the results for two corporate finance metric the Sharpe ratio of the shareholder investment and the call option based on Merton’s model.

We see that the company can on average build up sufficient equalization reserves if the tails are sufficiently fat.

The fatter the tails the faster the equalization reserves buildup for both stochastic processes.

We see that with both investment metrics the US-GAAP company is valued lower than the company allowed to keep reserves over time.

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Comparison of Sharpe Ratios

Lognormal Fréchet

Cov Alpha

10 73.2% 1.1 82.3%

1 96.3% 1.3 76.3%

0.1 97.7% 1.5 82.5%

0.01 100.0% 1.9 89.5%

In general, the Sharpe ratio for time diversified companies is better than for US-GAAP companies.

The percentages are influenced by what happens at the beginning of the experiment. If the company is bankrupted after one or two years the US-GAAP company is better off.

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The Merton Model Appliedto CAT Reserving

The Merton model views the share as a call option on the assets of a company.

In this case, we value the call options using the NPV of the cash flows over 30 years of both the time diversified company and the US-GAAP company.

We discount the cash flows with a risk free rate at 3%.

The result is that the option for the time diversified company has a higher value than the one of the US-GAAP company, in line with our Sharpe ratio results.

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Costs and Benefits of Setting up Cat Reserves

The economics literature discusses two types of cost that could play a role in the determination of the optimal amount of cat reserves:

1. “Agency Costs of Free Cash Flows” (Jensen, AER, 1986) Instead of paying out free cash flows to shareholders, managers might use “free money” to engage to investment activities that (unverifiably) are not in the best interest of shareholders (e. g. negative NPV “empire building”, unduly diversify operations).

2. “Costs of Financial Distress” (e. g. Warner, JoF, 1977) Companies in distress face constraints on operating and investment decisions (imposed by regulators, creditors, nervous shareholders) that may prevent even good investment decisions.

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Tradeoffs between Agency & Distress Costs in Cat Insurance

Higher cat reserves potentially accentuate the agency problem of free cash flows:

More cat reserves increase the amount of “free money” available for empire building.

Higher cat reserves potentially mitigate the financial distress costs:

More cat reserves diminish the likelihood of the firm running into a distress situation.

An Open Question:

How does the new cat risk modeling technology affect the optimal amount of cat reserves that insurers should set?

The answer…

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Consequence of CAT Modeling

The new catastrophe modeling technology has been standardized and made the measurement of catastrophic risk exposure more transparent :

This diminishes the potential for the abusive setting or using of catastrophe reserves (for empire building, for engaging in or hiding negative NPV projects, for tax evasion etc).

The existence of standard cat modeling tools and the application of financial

valuation over the long-term reinforce the argument for allowing cat reserves

– even from a shareholder’s view

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Agenda





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Conclusion

It is dangerous to simply apply rules designed for banks on insurance risks.

To mitigate risks insurers need all the diversification they can get including time diversification.

New technology allows for more transparency without abandoning some old prudent habits (equalization reserves).

The integration of risk management, however, will demand more and more solutions that should imply a strong cooperation

between insurances, banks and academics.

The lack of capacity requires also that financial markets bear some of the risks instead of the reinsurers.

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Outlook

There are three important axis of development for research in risk management:

1. Develop the stochastic models to truly multi-period models where time plays a key role.

2. Apply financial valuation methods to risks: this will accelerate the transfer of risks to financial markets and thus open up new investment opportunities.

3. Fully integrate the concepts of fat-tails and non-linear dependence in the pricing of risks.

Progress in this field can only help us coping with the growing risks and offer further economically sound risk management solutions.

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Looking for New Risk Transfer Avenues

Insurance Risks

Insurance /Reinsurance

(Re)Insurance Balance sheets

CapitalMarket Risks

Investment /Hedging

Capital Markets

“Securitization”:Insurance-linked securities (CatEPut, Surplus Notes)

Securitization, CAT bonds, longevity bonds, etc.

Documents

Adding time diversification to risk diversification