multi-year enterprise risk management based on … · multi-year enterprise risk management based...

Multi-year Enterprise Risk Management

based on Internal Models

Dr. Dorothea Diers,

ASTIN – Madrid 2011

• Introduction: Increasing challenges on management strategy

• Model approach for measuring multi-year risk capital

• Development of multi-year risk capital

• Management strategies

• Conclusion and outlook

Overview

Negative developments on the capital markets

Resulting: completely altered risk situation for insurance industry

Increase of natural catastrophes

Resulting: Increase of claims and reinsurance premiums

This led to a substantial decrease in economic capital

resources in insurance industry.

Requirement for a higher level of transparency of the risk

situation from management, regulators (Solvency II for

European Union member countries),rating agencies, …

Increasing challenges on management strategy

Paradigm shift to modern management techniques

such as value and risk based management.

In this context a suitable structure in insurance portfolio

together with an adequate asset allocation has become a

major task for management. It is directed towards maximum

return in relation to the risk taken for capital invested.

This requires a strategic management which should

follow a multi-year view.

Paradigm shift in insurance industry (1/2)

Return =

Premium

Profit / Loss

(statut. balance sheet)

Classical Turnover

Orientation

• Profit Premium-Ratio

• ...

Risk Capital

Expected

Economic Result

Value and Risk Oriented

• Return on Risk Adj.

Capital (RoRAC)

• EVA (Economic Value Added) = Expected

economic result beyond capital costs

Solvency II

Paradigm shift in insurance industry (2/2)






Overview

Internal models can be used as a base for strategic

decisions in value and risk based management.

Multi-year view in internal models

Using an internal risk model the individual risk situation of the

insurer can be modelled more exactly than using the standard

formula form Solvency II, which is often not adequate (->QIS 5).

Moreover the standard formula has only a one-year view and cannot

create a multi-year view.

If an insurer wants to use the internal model for solvency purposes, it

has to be accepted by the national supervisor. So with our findings

we want to give an idea of an internal model which can be accepted

by the supervisor and which could pass the “use test”.

rvereinigung).

Underwriting Risks

+ Brutto -Beiträge+ Earned Premiums (gross)

„Echte“ Kosten- Costs

Premium and Cat

Risks

(gross / net)

ReserveRisks

Investment Risks

EnterpriseRisks

Operational Risks

= ökonomisches

Ergebnis für das - Result from Operational Risks

+/- RV-Ergebnis+/ - Reinsurance Result

= Anfalljahres -

Ergebnis (netto)+/- Claims Development

Result (Net)

= Net Insurance Result

+/- Ergebnisfunktion

Aktiv (Marktwerte)+/- Investment Result

- Brutto -

Endschadenaufwand- Ultimate Losses (gross)

= Economic Result before Taxes

Random variable of economical results

modelled stochastically

Pt

Ut

Ct

Nt

DevRest

EcResLiabt

EcResAst

Ot

EcRest

For modeling the economic results we use different approaches:

Statistical methods for modeling large and

attritional claims of future accident years

Results of meteorological models as a base

for fitting distributions of catastrophe

claims (earthquakes, storm, flood, hail)

Stochastic reserving methods

Re-reserving for modeling the one-year uncertainty

Approaches for modeling dependency structures

Simulation techniques

etc.

Dichte

In Mio. €

Rückstellungen netto

Rückstellungen brutto

Best Estimate brutto: 116 Mio. €, Stdabw. = 18Best Estimate netto: 82 Mio. €, Stdabw. = 10

Stochastic Modeling in Internal Models

Management rules and management strategies in multi-year models:

Different rules in different scenarios are needed

Management rules: Increase of reinsurance premiums in

simulations/scenarios with preceding years of high claim losses

Management strategies in simulations with high claim losses, in order to

improve results and to avoid negative excess capital. This can be the case for

example after scenarios with natural catastrophes or with negative

developments at the capital markets. Possible strategies could be:

- Stop expansion in building

- Introduction of deductibles in building (to limit the effect of storm events)

- Higher reinsurance protection

- Change in asset allocation (lower risk profile)

Multi-year models

Defining multi-year risk capital helps management to

answer the essential question in order to decide for the

“best” strategy:

How many years of catastrophe events or adverse capital

market developments can the company withstand at a certain

confidence level without needing external capital resources?

How much risk capital the company will need to be able to

survive the next five years – taking five future underwriting

years into account – without external capital supply?

Multi-year risk capital

Defining multi-year results

-2000

-1800

-1600

-1400

-1200

-1000

-800

-600

-400

-200

0

200

400

2011 2012 2013 2014 2015

incremental cumulative

Results (per simulation):

Incremental vs. cumulative

-1000

-500

0

500

1000

1500

2000

2500

2011 2012 2013 2014 2015Risk

capital

Risk

capital


Results (per simulation):

Incremental vs. cumulative

incremental cumulative

Definition of multi-year risk capital

Per simulation and per year t we define cumulative losses

Cum. Loss (1) = Loss (1) = -EcRes (1)

Cum. Loss (t) = Cum. Loss (t-1) + Loss (t), 1≤ t ≤ n.

We define the maximum over the years:

MaxLoss = Max Cum. Loss (t)

MaxLoss represents the maximum of the amount that needs to be covered over the

years for each simulation.

The selected risk measure, ρ, can now be applied to the MaxLoss: Ω → IR in order

to determine the risk-capital requirement.


1≤t≤n

Definition of multi-year risk capital

This amount needs to be provided at t=0 in the simulation

path to allow the insurance company to cover all losses

incurred over the entire period simulated (n years) without

external capital supply in this simulation path.







Overview

Risk Capital (multi-year view)

In Million €

291372

412 437 450

Risk Cap.1 year

Risk Cap.2 years

Risk Cap.3 years

Multi-year risk capital (company)

Risk Cap.4 years

Risk Cap.5 years

+28%

+55%

+14% +9% +4%

Exam

ple-Data from

Sim

ulation Study

We use TVaR 99.8% for quantifying one-year and multi-year risk capital.






Overview

In practice management has to decide which strategy might

improve the risk (and return) situation of a company if not

enough (multi-year) risk capital is available: Lowering risk via

change of the asset allocation, lowering risk via introduction

of deductibles, extending reinsurance cover, or any suitable

combination of these strategies. In this context the

appropriate use of diversification effects plays an important

role.

Management strategies

In the paper we studied the effects of different management

strategies with regard to the realisation of the best of a given set of

possible strategies for the risk and return situation of the company.

We analysed the effects of

- reinsurance structures,

- introduction of different amounts of deductibles,

- growth in special LoBs,

- change of asset allocation,

- different dependency structures,

- different capital allocation methods.


Return: Expected Results

Return and risk situation as a base for value- and risk-based management

Risk: Risk Capital

0

These lob create a negative return. Here management should think about strategies to improve the return situation.

Management has to think about

strategies so that risk capital requirement decreases (e.g. deductibles, reinsurance). If the insurance has enough economic

capital to cover risk capital requirement, no change in strategy is necessary if the return

position is adequate.


We also analysed the effects of introduction of deductibles in storm, which leads to a significant reduction in risk capital.

SB 500

Risk Capital in Storm

(TVaR 99.8%)

Without Ded.

Ded.€ 250

Ded.€ 500

Ded.€ 1.000

Lo

ss R

ed

uctio

n f

rom

De

du

ctib

les

Deductibles in €

Fire Storm

Management strategies (Introduction of deductibles)

Economical results of the company

Economical results in storm


Economical results in storm Economical results in storm


Economical results in storm


Actual Strategy New Strategy (after deductibles and

reinsurance)

Economical results in storm Economical results in storm

Economical results of the company Economical results of the company

The effects of strategies (example data)

The effects of strategies (here: introduction of deductibles and reinsurance)

can be shown in the percentile graph (reduction of risk, but also reduction of

expected return).

Brutto

Netto

RV

Risk Capital

291

Gross Reinsurance Net

201

90

Simulated results (actual vs. new strategy)

New Strategy

The effects of strategies

Actual Strategy

-250

-200

-150

-100

-50

50

-300

-350

The strategies and their impact need to be analysed at company level, where high

diversification effects have a positive effect on total risk capital and economic value

added (EVA).

In the example portfolio presented in the case study the introduction of deductibles

in storm line of business led to growing diversification effects in insurance results

(between storm and the other lines of business). The same holds for special types

of reinsurance contracts. The effects of these strategies always depend on the

portfolio structure.

Lowering multi-year risk capital and growing diversification effects offer the

possibility of extending in lines of business where the return exceeds the capital

costs and which show a high diversification towards the other lines of business in

the portfolio.


I. Methods

II. Time horizon

III. Risk Tolerance

IV. Required return

Management has to

define:

„Optimisation“ of reinsurance

3

Comparison to risk limit,management requirements,

decision for a strategy or definition of new strategies if

necessary

6

5

Simulation of the selected strategies for the company

Iterative process(repetition with

different strategies to

find the “optimal“

strategy)

Simulation of theactual strategy

(results, risk capital) andcomparison with

managementrequirements

1

4

„Optimisation“ of asset allocation

2„Optimisation“ of liabilities (gross)

Iterative management process

The iterative management process should consider the following restrictions:

Management requirements concerning the results in the

statutory balance sheets (intended investment or technical results,

annual surplus, etc.)

Regulatory restrictions (actually for European countries:

Solvency I and analyses of worse scenarios; in the future:

Solvency II)

Iterative management process with conditions






Overview

With our multi-year model we can compare the effects of different

management strategies. These results will influence various

company processes such as risk limitation, development of

insurance products, pricing, reinsurance, asset management,

marketing.

In this context future product development will be oriented

towards goals such as required risk capital and use of

diversification potential. Instruments such as deductibles for

policyholders in storm insurance aimed towards reducing risk capital

requirement are gaining in importance. In this context adequate

capital allocation methods are needed.

Conclusion and outlook

In addition to practitioners, regulators will also benefit from these

results. Since the “use test” will play an important role for the

approval of internal models, regulators will check if the internal model

is used as a base for management decisions in enterprise risk

management and in the ORSA process, whereby both should be

based on a time horizon of several years.

Conclusion and Outlook

Future Research

• Extend the simulation model in various directions

• Capital allocation in multi-year context

• Use the concept for strategic management on a group level

Conclusion and Outlook

Thank you very much

for your attention!

• CEIOPS: Own Risk and Solvency Assessment (ORSA). Issues Paper,

http://www.gcactuaries.org/documents/ceiops_issues_paper_orsa.pdf (2008)

• Diers, D. (2007): Interne Unternehmensmodelle in der Schaden- und Unfallversicherung – Entwicklung eines

stochastischen internen Modells für die wert- und risikoorientierte Unternehmenssteuerung und für die Anwendung im

Rahmen von Solvency II. ifa-Verlag, www.ifa-ulm.de (2007)

• Diers, D. (2011): Management Strategies in Multi-year Enterprise Risk Management, Geneva Papers on Risk and

Insurance, 36(1), 107–125

• Elderfield, M. (2008): Solvency II: Setting the Pace for Regulatory Change. Geneva Papers on Risk and Insurance 34,

35-41

• Eling, M., Toplek, D. (2009a): Modeling and Management of Nonlinear Dependencies: Copulas in Dynamic Financial

Analysis. Journal of Risk and Insurance, 76(3), 651–681

• Eling, M., Toplek, D. (2009b): Risk and return of reinsurance contracts under copula models. European Journal of

Finance, 15(7), 751-775

• England, P., Verrall, R. (2006): Predictive Distributions of Outstanding Liabilities in General Insurance. Annals of

Actuarial Science: 1, 221-270

• Mack, T.: Distribution-free Calculation of the Standard Error of Chain Ladder Reserve Estimates. ASTIN Bulletin 23,

214-225 (1993)

• Merz, M., and Wüthrich, M. V. (2008): Modeling the claims development result for solvency purposesl, Casualty

Actuarial Society E-Forum, 542-568.

• Salzmann, R., Wüthrich, M.V. (2010): Cost-of-capital margin for a general insurance runoff. Astin Bulletin 40/2, 415-

451.

References

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