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Using Dynamic Financial Analysis

to Structure Reinsurance

Session: Using DFA to Optimize the Value of Reinsurance

2001 CAS Special Interest Seminar on Dynamic Financial Analysis, June 6-8, 2001, Boston

Reto Angliker, Martin Melchior and Markus Stricker, Swiss Re

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Underlying Data Set: DFA Insurance Company

• This case study for the DFA Insurance Company is based on the data available on the CAS web-site

• The DFA Insurance Company is a fictional insurance company with two lines of business:

• Property: Gross written premium: 1.29 Bio USD (short tail business)

• Casualty: Gross written premium: 1.26 Bio USD (long tail business)

(for the payout patterns see appendix)

• Each line of business has only non-proportional reinsurance: Working excess of loss with one layer and an infinite number of reinstatements

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DFA Model

We have selected a relatively simple DFA model for this case study.

• The level of detail of the data provided for the DFA Insurance Company is not enough to initialize a sophisticated DFA model. Hence, by analyzing with a sophisticated DFA model, we would have to introduce additional assumptions which may divert the focus away from our primary objective. Consequently, we work with a simple DFA model to produce the following case studies.

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Result for the Base Scenario• The key figures such as underwriting result, annual result, underwriting cash flow,

GAAP RoE and solvency ratio are stable.

• Due to the conservative asset allocation (71% Bonds, 11% Equities, 11% Cash), the main contribution of the volatility of the annual results stems from insurance business and not from investments.

• Due to claims inflation (assuming 3% on average) the reserves for outstanding claims payments and total claims paid increase.

• The book value of the investments increases although any earning is paid out to the shareholders. This stems from the increase of reserves and premium due to claims inflation.

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DFA Insurance Company: Case Study 1

• The set-up: We study the effect of two different reinsurance programs with an equal amount of risk transfer, i.e. the programs have the same volatility of the net-loss ratio and the same technical result distribution.

• The two reinsurance programs as of beginning of 2001:Most of the risk transfer ceded to reinsurance stems from property business.Most of the risk transfer ceded to reinsurance stems from casualty business.

• Pricing assumptions:The net present value (based on a fixed interest rate used for pricing) of the gross insurance business and the reinsurance business is chosen to be equal to zero.

Underwriting Result

-500,000

-400,000

-300,000

-200,000

-100,000

0

100,000

200,000

2000 2001 2002 2003 2004 2005

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Outstanding Claims Provisions DFA Insurance Company

• Yellow: More casualty (long-tail) business is retained, thus more reserves for outstanding claims are built up.

• Magenta: More property (short-tail) business is retained such that the reserves for outstanding claims are not equally large.

Outstanding Claims Provisions

2,000,000

2,500,000

3,000,000

3,500,000

2000 2001 2002 2003 2004 2005

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Time Limited Effects DFA Insurance Company

• For a transitional period the two different reinsurance programs have a significant effect on net claims paid and underwriting cash flows.

• On long term average, retaining more casualty business leads to slightly lower underwriting cash flows. This is caused by the pricing assumptions.

Net Claims Paid

1,300,000

1,550,000

1,800,000

2000 2001 2002 2003 2004 2005

Underwriting Cash Flow

-200,000

-100,000

0

100,000

200,000

2000 2001 2002 2003 2004 2005

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Other Key Figures DFA Insurance Company

The two different reinsurance programs have only marginal effects on the following key figures:

• annual result

• surplus

• solvency ratio

• GAAP RoE

GAAP RoE

-10.0%

0.0%

10.0%

20.0%

2000 2001 2002 2003 2004 2005

Solvency

50.0%

60.0%

70.0%

80.0%

90.0%

2000 2001 2002 2003 2004 2005

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Case Study 1: Conclusion

• Reinsurance programs with an equal amount of risk transfer can still have a significantly different impact on the total reserves and claims payments of an insurance company.

• When switching between such reinsurance programs, the effect on underwriting cash flows and change in reserves usually is time limited. After a transition period these effects almost vanish, depending on the assumed pricing.

Question: How can one exploit these effects to create value?

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DFA Insurance Company: Case study 2

• We consider the same reinsurance structures as in case study 1,ie, more reinsurance on property versus more on casualty such that the risk transfer is the same.

• We attempt to exploit the effects created by the change in reinsurance by applying a more aggressive asset mix as of 1st January 2001.

• The more aggressive asset mix is:

– 51% bonds (71%)

– 31% equity (11%)

– 11% cash

– 7% other investments

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Investments DFA Insurance Company

• Since the new asset mix encompasses a larger proportion of equity, the volatility and the average growth rate of the investments (book value) is much higher.

• The same qualitative effects appear under both asset allocation strategies: When more business is retained in the long tail LoB, more reserves have to be held, and hence the volume of investments increases.

Investments - aggressive asset allocation

4,500,000

5,000,000

5,500,000

6,000,000

6,500,000

7,000,000

2000 2001 2002 2003 2004 2005

Investments - conservative asset allocation

4,500,000

5,000,000

5,500,000

6,000,000

6,500,000

7,000,000

2000 2001 2002 2003 2004 2005

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Investment Income + Realized Gains DFA Insurance Company

• A slightly higher investment income is achieved if more casualty business is retained since the investment volume is larger.

• Since dividend yields in our framework are chosen to be smaller than the yields from fixed income securities, the investment income drops after implementing the more aggressive asset allocation strategy.

• The drop becomes only visible in 2002, since in 2001 - when the new asset mix is implemented - the realized gains from the sale of the bonds offset the smaller yield due to the new asset mix.

Investment Income + Realized Gains (more aggressive asset allocation)

200,000

300,000

400,000

500,000

2000 2001 2002 2003 2004 2005

Investment Income+Realized Gains

200,000

300,000

400,000

500,000

2000 2001 2002 2003 2004 2005

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Revaluation Reserves DFA Insurance Company

• The change in unrealized capital gains is excluded from the statutory income statement and contributes to the revaluation reserve.

Because we assume a low turn-over of the portfolio, the major contribution to the income statement comes from investment income cash flow.

• Revaluation reserves and its volatility increases dramatically under the more aggressive asset mix

Revaluation Reserves - agressive asset allocation

-100,000

400,000

900,000

1,400,000

1,900,000

2000 2001 2002 2003 2004 2005

Revaluation Reserves - conservative asset allocation

-100,000

400,000

900,000

1,400,000

1,900,000

2000 2001 2002 2003 2004 2005

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RoE and Solvency DFA Insurance Company

• The more aggressive asset mix affects income marginally, but increases revaluation reserves and surplus significantly

• Consequently the solvency ratio is increased and return on equity is lowered by the more aggressive asset allocation strategy. The volatility of solvency ratio and RoE is largely increased.

GAAP RoE

5.00%

6.00%

7.00%

8.00%

9.00%

2000 2001 2002 2003 2004 2005

Solvency

60.00%

70.00%

80.00%

90.00%

100.00%

2000 2001 2002 2003 2004 2005

Aggressive asset strategy, more casualty retained

Aggressive asset strategy, more property retained

Conservative asset strategy, more casualty retained

Conservative asset strategy, more property retained

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Case Study 2: Conclusion

• A more aggressive asset mix affects merely the balance sheet and only marginally the income statement, as long as the capital gains are not realized, consequently profitability (RoE) and solvency ratios are affected by a more aggressive asset strategy.

• The change in investment income due to a different asset allocation kicks in only with a time delay of at least one year due to realized gains associated with the reallocation.

• Qualitatively, this picture results under both reinsurance programs.

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Appendix: Representation of the Data Set• The loss ratio of each line of business is the sum of a log-normally distributed ground

up loss ratio and a ratio for large losses (Compound Poisson-Pareto Process). The ratios are stated as percentage of the gross earned premium income.

• The mean and the standard deviation of the individual gross loss ratios is given as:

• The non-proportional reinsurance program applies only to the compound Poisson-Pareto-Processes

LoB. Property Casualty

loss ratio ground up large loss ground up large loss

mean 20.20% 48% 22.50% 48%

std. dev. 7.10% 2.22% 6.90% 2.22%

LoB. Property Casualty

loss ratio ground up large loss ground up large loss

Deductible na. 0.05% na. 0.05%

Cover na. 5.00% na. 5.00%

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Appendix: Payout Patterns for Property & Casualty

• Property represents insurance business with short tail loss development whereas Casualty represents insurance business with long tail loss development.

• The claims development payout pattern (lag factors) have been determined as follows:

Property: Lagfactors

20%

40%

60%

80%

100%

Loss Development Year

Casualty: Lagfactors

20%

40%

60%

80%

100%

1 3 5 7 9 11 13 15 17 19

Loss Development Year

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Appendix: Presentation of the Simulation Outputs

• We work with the 5%, 20%, 50%, 80% and 95% percentiles

• percentiles can give an intuition for the shape of the distribution of the key figures

Technical Result

-500,000

-400,000

-300,000

-200,000

-100,000

0

100,000

200,000

2000 2001 2002 2003 2004 2005

60% of the sample data fall within this range

90% of the sample data fall within this range

5%

95%

80%

20%

50%

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Output: Technical & Annual Result DFA Insurance Company

• The technical result is rather stable. The little “bump” in year 2002 is mainly due to inflation which affects premiums and claims after different time lags and which has no influence on the expenses.

• The main proportion of the volatility of the annual results stems from insurance and not from investments

• The volatility of the annual result - which is reported after tax - is smaller than the volatility of the technical result, which is reported before tax.

Technical Result

-500,000

-400,000

-300,000

-200,000

-100,000

0

100,000

200,000

2000 2001 2002 2003 2004 2005

Annual Result

-200,000

-100,000

0

100,000

200,000

300,000

400,000

500,000

2000 2001 2002 2003 2004 2005

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Investments

4,000,000

4,500,000

5,000,000

5,500,000

6,000,000

6,500,000

2000 2001 2002 2003 2004 2005

Output: Investments & Claims Provisions DFA Insurance Company

• The book value of total assets is about 5.3 Bio. USD

• 71% Bonds

• 11% Equity

• 7% Other investment

• 11% Cash

• It is assumed that this asset mix is also the target asset mix for future years

• Due to claims inflation the reserves for outstanding claims payments increase accordingly

Outstanding Claims Provisions

1,900,000

2,100,000

2,300,000

2,500,0002,700,000

2,900,000

3,100,000

3,300,000

3,500,000

2000 2001 2002 2003 2004 2005

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Output: Cash Flow DFA Insurance Company

• The technical cash flow is rather stable and the median (50% percentile) lies in the positive area

• Total payments for claims increase due to claims inflation

Technical Cash Flow

-250,000

-150,000

-50,000

50,000

150,000

250,000

2000 2001 2002 2003 2004 2005

Claims Payments

1,000,000

1,200,000

1,400,000

1,600,000

1,800,000

2,000,000

2000 2001 2002 2003 2004 2005

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GAAP RoE

-10.0%

-5.0%

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

1999 2000 2001 2002 2003 2004 2005

Output: GAAP ROE & Solvency DFA Insurance Company

• The median of the return on equity distribution is rather stable at about 8% - slightly increasing

• Solvency is rather stable, however a slight downward trend is visible

Solvency

0.0%10.0%20.0%30.0%40.0%50.0%60.0%70.0%80.0%90.0%

1999 2000 2001 2002 2003 2004 2005