Property / Casualty Aspects of ERM Frank Sommerfeld EMB Köln (Cologne), Germany

Agenda Cash-Flows in P&C insurance Liquidity risk Risk Matching Example Risk-Matching Summary

Cash-Flows in P&C insurance

Liquidity risk

Risk Matching

Example Risk-Matching

Summary

Cashflows in P &C insurance The expected CF in a calendar year is the sum of the diagonal. Assuming a constant ultimate per origin year it is 26%. No new accident year would implicate no new business no renewals no unearned premium A new accident year does pay out 74% and does reserve the other 26%  the expected reserves remain unchanged.  the expected cash-flow balance is 0 Additionally the cash-flow is highly volatile Matching strategies (Duration, cash-flow,..) don’t make sense  unrealistic

The expected CF in a calendar year is the sum of the diagonal. Assuming a constant ultimate per origin year it is 26%.

No new accident year would implicate

no new business

no renewals

no unearned premium

A new accident year does pay out 74% and does reserve the other 26%  the expected reserves remain unchanged.  the expected cash-flow balance is 0

Additionally the cash-flow is highly volatile

Matching strategies (Duration, cash-flow,..) don’t make sense

Example - Volatility of cash flows at „going concern“ Expectation close to zero and very volatile

Duration of cash flows at „going concern” You will not match this duration!

Cash flow P&C Cash flows of P&C insurance are totally different to the cash flow of life insurance: Considerably more volatility Large claims Catastrophe claims Adverse run-off The expected cash flow is usually small A liquidity risk is not arising form a mismatch in duration but rather due to the volatility How can liquidity risk be assessed? How can the liquidity risk be managed?

Cash flows of P&C insurance are totally different to the cash flow of life insurance:

Considerably more volatility

Large claims

Catastrophe claims

Adverse run-off

The expected cash flow is usually small

A liquidity risk is not arising form a mismatch in duration but rather due to the volatility

How can liquidity risk be assessed?

How can the liquidity risk be managed?

Agenda Cash-Flows in P&C insurance Liquidity risk Risk Matching Example Risk-Matching Summary

Cash-Flows in P&C insurance

Liquidity risk

Risk Matching

Example Risk-Matching

Summary

Example of the liquidity risk on the basis of three paths Liquidity gap arises from one extreme negative u/w cash flow or from two medium negative cash flows.

Example - Volatility of cash flows at „going concern“ The ERM models we will not run with 3, but e.g. 100,000 simulations. The results will be measured in probabilities

Example liquidity risk

Strategies on managing liquiditiy risks The liquidity risk is an asset/liability matching risk  market value of fungible assets <  payment obligations The liquidity risk can arise out of Decreasing market values Insufficient fungibility Increasing payment obligations The liquidity risk is a timing problem and due to this fact it can not be capitalized Strategies to decrease the risk can be set at the asset and the liabilites side Asset side Matching of the asset cash flow can not lead to the target Market values: Investments in less volatile assets Fungibility: Investments in more liquid markets Liabilities side Arrangements of the reinsurance contracts Implementation of „Cash-Calls“ The handling of liquidity risks defines a constraint but does not determine a whole strategy

The liquidity risk is an asset/liability matching risk

 market value of fungible assets <  payment obligations

The liquidity risk can arise out of

Decreasing market values

Insufficient fungibility

Increasing payment obligations

The liquidity risk is a timing problem and due to this fact it can not be capitalized

Strategies to decrease the risk can be set at the asset and the liabilites side

Asset side

Matching of the asset cash flow can not lead to the target

Market values: Investments in less volatile assets

Fungibility: Investments in more liquid markets

Liabilities side

Arrangements of the reinsurance contracts

Implementation of „Cash-Calls“

The handling of liquidity risks defines a constraint but does not determine a whole strategy

Agenda Cash-Flows in P&C insurance Liquidity risk Risk Matching Example Risk-Matching Summary

Cash-Flows in P&C insurance

Liquidity risk

Risk Matching

Example Risk-Matching

Summary

Risk Matching The insurer is exposed to underwriting and market risks The ERM models calculates both profit profiles The risk capital can be calculated from the profit profiles VAR TVAR …

The insurer is exposed to underwriting and market risks

The ERM models calculates both profit profiles

The risk capital can be calculated from the profit profiles

VAR

TVAR

…

Risk Matching The asset and liability risks have a only a small dependency There is a strong diversification effect between both sides Bad results on the one side are often balanced by good ones on the other side This diversification effect can be measured In this example the worst case scenarios are caused by the liability side Total result < - 400

The asset and liability risks have a only a small dependency

There is a strong diversification effect between both sides

Bad results on the one side are often balanced by good ones on the other side

This diversification effect can be measured

In this example the worst case scenarios are caused by the liability side

Risk Matching „ Stand alone“ adds both risk capitals which were calculated separately „ Diversified“ determines the risk capital on the aggregated risk profile Sub-additivity RK(A+B) ≤ RK(A)+RK(B) With capital allocation methods (here TVAR) the diversified capital can be allocated back How can you find the optimal diversification? Net of RI Gross of RI Liabilities dominates the total Risk capital is allocated more equally

„ Stand alone“ adds both risk capitals which were calculated separately

„ Diversified“ determines the risk capital on the aggregated risk profile

Sub-additivity RK(A+B) ≤ RK(A)+RK(B)

With capital allocation methods (here TVAR) the diversified capital can be allocated back

How can you find the optimal diversification?

Risk Matching To compare different risk strategies a comparison of the risk capitals is insufficient The (expected) return has to be compared against to calculate the performance/efficiency of the capital Economic Value Added (EVA™) = return – cost of capital * risk capital Return On Risk Adjusted Capital (RORAC) = return / risk capital Other constraints have to be considered additionally Business policy Accounts … Higher risk capital Higher expected return A B C D Risk liabilities (Reinsurance) Risk Asset (SAA)

To compare different risk strategies a comparison of the risk capitals is insufficient

The (expected) return has to be compared against to calculate the performance/efficiency of the capital

Economic Value Added (EVA™) = return – cost of capital * risk capital

Return On Risk Adjusted Capital (RORAC) = return / risk capital

Other constraints have to be considered additionally

Business policy

Accounts

…

Agenda Cash-Flows in P&C insurance Liquidity risk Risk Matching Example Risk-Matching Summary

Cash-Flows in P&C insurance

Liquidity risk

Risk Matching

Example Risk-Matching

Summary

Risk Matching – simplified example Asset risk FI and equity Managing via equity share Liabilities risk Stochastic gross result NatCat exposed Managing via reinsurance

Asset risk

FI and equity

Managing via equity share

Liabilities risk

Stochastic gross result

NatCat exposed

Managing via reinsurance

Risk Matching – simplified example From 15 % equity the risk capital increases faster than the expected return 13,9%

Risk Matching – simplified example For lower equity exposure the asset risk is overlain by the u/w risk. There is a large diversification potential on the asset side. 32,2%

Risk Matching – simplified example The diversification potential for the asset side decreases if the risk is mitigated on the liability side. 25,7%

Risk Matching – simplified example If the risk on the liabilities side is decreased even more the risk on the asset side has to be reduced as well. 14,7%

Risk Matching – simplified example 16,1%

Agenda Cash-Flows in P&C insurance Liquidity risk Risk Matching Example Risk-Matching Summary

Cash-Flows in P&C insurance

Liquidity risk

Risk Matching

Example Risk-Matching

Summary

Risk Matching - Summary Use the diversification potentials between risks Between asset and liabilities Within the asset side between the asset classes Within the liabilities side between the lines of business The whole balance between several risk operators is important A balanced influence on the overall result Dependent on the risk aversion In practice: Optimum at given risk capital Changes in the risk strategy have always consequences in all areas Holistic ERM should be integrated in the company BUT: No blind trust in the models Techniques are helpful to support decisions but not to replace them Understanding the effects is essential – no Black-Box! ERM must be lived – clear communication within the whole company is necessary

Use the diversification potentials between risks

Between asset and liabilities

Within the asset side between the asset classes

Within the liabilities side between the lines of business

The whole balance between several risk operators is important

A balanced influence on the overall result

Dependent on the risk aversion

In practice: Optimum at given risk capital

Changes in the risk strategy have always consequences in all areas

Holistic ERM should be integrated in the company

BUT: No blind trust in the models

Techniques are helpful to support decisions but not to replace them

Understanding the effects is essential – no Black-Box!

ERM must be lived – clear communication within the whole company is necessary

Your contact for questions Frank Sommerfeld EMB Tel.: +49 (0)221 35 66 26 41 [email_address] emb.com