Development of Risk and (Market) Valuation Models:From Measurement to Management

Farid KabbajFarid KabbajInge ZeilstraInge Zeilstra

>> 18 September 2003AFIR Colloquium 2003 Maastricht

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Introduction

Development of Risk and (Market) Valuation Models Farid Kabbaj, Inge Zeilstra

Introduce concepts using an example product. Risk/ Return, Risk Based Capital, Multi Party Flow Analysis

Extensions to these concepts Dynamic Management Decisions, Projected Realistic Balance Sheets

Analysing results Sensitivities, Analysis of Change

Conclusions

fkabbaj@bw-deloitte.com

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Example Product Description

Regular Premium Endowment Product

Reserve = 800 mln.

Profit sharing = 80% (investment return – VRI – 0,5%)

Valuation Rate of Interest (VRI) = 4%

Strategy Equity Fixed Income

1 0% 100%

2 2.5% 97.5%

3 5.0% 95.0%

4 7.5% 92.5%

5 10.0% 90.0%

6 12.5% 87.5%

5% Solvency Margin

Free Assets (including SM) = 45 mln.

New business not included

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Risk v Return

50, 1

50, 2

50, 3

50, 4

50, 550, 6

22,000,000

22,500,000

23,000,000

23,500,000

24,000,000

24,500,000

25,000,000

25,500,000

26,000,000

26,500,000

27,000,000

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

Mean Value : Surplus < req solvency margin

Mea

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Risk/ Return Measures

Within the 5th percentile for risk of ruin, strategy 3 (5% equity) seems the preferred option (over a 20 year horizon) as this gives the highest average free assets.

We are maximising equity exposure under a constraint (risk of ruin).

Classic ALM technique. The development of the average free assets is compared to the associated risk of ruin.

example productexample product

Strategy 2 (2,5% equity) would be preferred when the objective is minimisation of risk.

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Risk Based Capital

Definition: Capital required to ensure that the company is not impaired, over a certain period of time (1 yr), to a certain level of probability (99%).

Conceptually comparable to Value at Risk and Economic Capital

“Locked-in Capital” – can’t be used to fund business growth

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Risk Based Capital

1 year time horizon, 99% confidence interval RBC required to protect 100% solvency No new business

New business strain can have a huge impact

Based on this information alone, Strategy 1 seems optimal.

Strategy 1 Strategy 2 Strategy 3 Strategy 4 Strategy 5 Strategy 6

Risk Based Capital 18.7 19.6 20.7 21.9 23.0 24.2

example productexample product

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Multi Party Flow Analysis

A possible split of stakeholders: Policyholders, paying a premium and receiving

benefits.

Shareholders, providing capital injections/ receiving dividends.

Government, tax is paid by the shareholders and policyholders.

Expense receivers, costs are made to run the company like wages and rent.

etc.

Which choice is best from a commercial point of view? Might impact new business volumes, lapse rates, pricing decisions, etc

These decisions have an impact on the cash inflow. The pie can get bigger!

In the Multi Party Flow Analysis the value of the company is attributed to various stakeholders like a pie being sliced.

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Multi Party Flow Analysis

FV Liabilities ~ Policyholder Value + Expenses > Traditional Reserve Margins in traditional valuation are not sufficient (in this example). For example, the best

estimate expenses are bigger than the expense loadings.

Shareholder value is negative! (in this example)

Strategy 1 Strategy 2 Strategy 3 Strategy 4 Strategy 5 Strategy 6Policyholder Value 811 811 812 814 817 820Gross Shareholder Value -19 -19 -20 -22 -25 -28Expenses 31 31 31 31 31 31Opening Fund Value 823 823 823 823 823 823

example productexample product

Shareholder value decreases when the equity backing ratio increases The greater volatility of equity causes the investment return to fall below the guarantee (the

VRI = 4%) more often.

The dynamic effect on sales and lapses has not been taken into account (minor impact).

Value of expenses constant Linked to inflation only

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Dynamic Interactions

Investment strategy For example Constant Proportion Portfolio Insurance (CPPI)

New business volumes, lapse rates Based on assumptions regarding profit sharing rates relative to the market,

financial strength, etc

Other – expenses, profit sharing strategy, pricing, indexation

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Run Time Issues

Calculations previously very difficult due to run time issues Previously, 50 simulations in 10 hours was considered acceptable

Standard run now very fast - 5,000 simulations in 1 hour 1,000 liability segments (grouped)

20 year projection period

2.6 GHZ PC Pentium IV

Intel Compiler

Run time decreases linearly when using multiple PCs Acceptable run times for large companies

For development work a smaller number of scenarios is used250 Simulations in 3 minutes – a huge number of strategies can be investigated

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Two Dimensional Matrix

Horizontal axis - from deterministic to dynamic stochastic modelling

Vertical axis - understanding and measurement of risk and return

No fixed categorisation

Gives good insight in the way models are heading

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Projected Realistic Balance Sheets

FSA (UK regulator) – Realistic Balance Sheet Companies to file a balance sheet on IFRS basis using a stochastic approach.

Projecting forward requires a combination of stochastic techniques with Black–Scholes and/ or interpolation formulae to place a fair value on embedded options.

PVK (NL regulator) – Continuïteitstoets (Long Term Solvency Test)

The PVK stated that a projected realistic balance sheet approach will be required but so far a discussion paper has not been released.

Solvency II

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Analysis of Change

AoC for Embedded Value AoC for Risk Based Capitalillustrativeillustrative illustrativeillustrative

Important tool for “Back Testing” results

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Sensitivities

Even more important in a stochastic model than in an EV model. Greater complexity requires more sensitivities to get a grip on the results Helps to capture the drivers of Risk Based Capital 50+ sensitivities to the base run is not exceptional in the development stage Run times are essential

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Management Strategies and Solutions some examples

Traffic Light Approach Different strategy for green/ amber/ red

situations

Management actions tested before needed

Enhanced dynamic decisions

Dynamic Asset Strategy (e.g. CPPI) Risk exposure dependent on buffer available

Gives satisfying results but needs to followed in practice – strict guidelines

We see many companies using stochastic techniques in product design.

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Conclusions

Multiple risk measures are needed to get an understanding of the risk/ return profile of the company.

An integrated model is preferable

Consistency

Regulatory pressures – projected realistic balance sheets

Dynamic management decisions implemented in the model

Greater complexity increases the need for digging into results

Run times are essential

Development of Risk and (Market) Valuation Models:From Measurement to Management

Farid KabbajFarid KabbajInge ZeilstraInge Zeilstra

>> 18th September 2003AFIR Colloquium 2003 Maastricht