APRA’s GI Capital Requirements:Prescribed Method v Internal Model

Christian Sutherland-Wong

Actuarial StudiesFaculty of Commerce and Economics

University of NSWEmail: c.s-wong@student.unsw.edu.au

Actuarial Studies Symposium, UNSW 14th November, 2003

Purpose of Study

APRA recently introduced two methods to calculate MCR Prescribed Method Internal Model Based (IMB) Method

Aim is to analyse the implications for two key stakeholders Insurers APRA

Contents

Background

Data & Methodology Internal Model

Results Implications

Further Work

Background

APRA recently updated their GI Prudential Standards

External Developments Basel II IAA Insurer Solvency Working Party NAIC, FSA, Canada

Calculating the MCR Prescribed Method IMB Method

Data & Methodology

Data Sources APRA’s June 2002 GI statistics Tillinghast and Trowbridge Risk Margins Allianz, Promina, IAG

Methodology Model Insurer

5 Business Lines – Domestic Motor, Household, Fire & ISR, Public Liability and CTP

Large, mature portfolio – 10% market share Industry Investment Mix

6000 simulations Compare capital requirements

Data & Methodology (cont’d)

Methodology Scenario Analysis

Different Volatility Assumptions

Riskier Investment Portfolio

Short Tail only and Long Tail only

Smaller business size

Internal Model Prophet DFA model used

Economic Model – The Smith Model (TSM)

Insurance Model

3 Claims Processes Attritional Claims, Large Claims, Catastrophe Claims

Superimposed Inflation – Two state Model Reinsurance – Individual XoL and Catastrophe XoL

EconomicModel

InsuranceModel

DFASimulation

DFAOutput Inflation

Internal Model (cont’d)

Assumptions

Expected Claims (incl. expenses and reins. costs) Set to provide a 15% after-tax return on capital

(capital = 1.5x Prescribed MCR)

Claims Volatility – Tillinghast report

Reinsurance – Maximum Event Retention (MER) set to $15M

Results

MCR calculated under IMB Method >

MCR calculated under Prescribed Method

Minimum Capital Requirement (MCR) Original Scenario $'000 IMB Method Prophet MCR 309,396 + Adjustment for Credit Risk 28,705 TOTAL 338,101 Prescribed Method TOTAL 233,323 Std Error IMB 10,912 Probability 0.000 H0: IMB Method MCR = Prescribed Method MCR

HA: IMB Method MCR ≠ Prescribed Method MCR

Results (cont’d)

Distribution of Capital Requirements

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.016

0.018

0.020

Capital Required (t=0)

Pro

b.

99.5th Percentile ± 2 Standard Errors

Results (cont’d)

IMB v Prescribed: Short & Long Tail split

Small difference between IMB and Prescribed Method

IMB v Prescribed Capital Allocations

0%

10%

20%

30%

40%

50%

60%

70%

80%

Short Tail Long Tail

% A

lloca

ted

IMB

Prescribed

Results (cont’d)

IMB v Prescribed: Business line split

Significant differences by business line Household > Motor under IMB Method CTP > Public Liability under IMB Method

Short Tail Allocations

Motor

Motor

Home

Home

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

IMB Method Prescribed Method

% O

f Sho

rt T

ail A

lloca

ted

Long Tail Allocations

CTPCTP

PublicLiability

PublicLiability

0%

20%

40%

60%

80%

100%

IMB Method Prescribed Method

% L

ong

Tai

l Allo

cate

d

Results (cont’d)

Scenario Results

H0: IMB Method MCR = Prescribed Method MCR

HA: IMB Method MCR ≠ Prescribed Method MCR

Comparisons for All Scenarios

Original Scenario

Trow- bridge CVs

80% Equities

Short Tail Only

Long Tail Only

Small Insurer

$'000 $'000 $'000 $'000 $'000 $'000 IMB Prophet 309,396 94,586 370,414 209,196 228,828 139,951 Method Credit Risk 28,705 28,705 28,705 10,745 12,513 5,577 TOTAL 338,101 123,291 399,119 219,941 241,341 145,528 Investment Risk 36,391 36,391 85,366 9,157 22,656 9,098 Prescribed Credit Risk 28,705 28,705 28,705 10,745 12,513 5,577 Method OSC Liability 91,290 88,237 91,290 7,890 80,999 28,808 Premium Liability 61,641 59,415 61,641 30,885 23,789 15,876 Concentration Risk 15,000 15,000 15,000 15,000 0 15,000 TOTAL 233,027 227,749 282,001 73,677 139,956 74,359 Std Error IMB 10,912 3,469 13,517 5,221 9,056 5,413 Probability 0.000 0.000 0.000 0.000 0.000 0.000

Results (cont’d)

Scenario Results

Trowbridge scenario: IMB << Prescribed

Riskier Asset Mix: Greater increase under IMB ($61.0M v $49.0M)

Other scenarios: MCR as % of Original

43%

71%65%

60%

32% 32%

0%10%20%30%40%50%60%70%80%90%

100%

Origina

l Sce

nario

Short

Tail O

nly

Long

Tail

Only

Small

Insu

rer

Scenario

% o

f O

rigin

al

IMB

Prescribed

Implications

Dependence on outcome on volatility assumptions Insurers will choose different methods depending on

volatility assumed Need for greater agreement in the industry

Prescribed Method not necessarily conservative Even if we believe Trowbridge report, the Tillinghast

CVs will be representative of some insurers APRA may need to address business line capital

charges Increase CVs for household or CTP Include diversification discounts, concentration charges or

charges by business size

Implications (cont’d)

Inadequacy of investment risk charge Increase charges for risky asset classes (equities) Include diversification discounts or concentration

charges

Lack of an incentive to use the internal model Lower MCR under Prescribed Method “Black-box” stigma Trust in method from financial analysts

Further Work

Results in this study are preliminary and highly dependent on assumption that the MCR calculated by the internal model reflects the actual MCR

Further research: Consensus on CVs Different dependence models eg Copulas Different internal model calibrations