Reinsurance

PAK Study Manual Enterprise Risk Management (ERM) Exam

Spring 2015 Edition

Extreme Value Theory

Solvency II

Strategic Risk Management

Coherence Risk Measure

Operational Risk

Copula

VaR

KRD

Principles-Based Reserves and Capital

Stress Testing Economic Capital

CTE

Risk Aggregation

Tail Dependency

PAK Study Manual for ERM Spring 2015

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1. Summary (ERM Core + ERM Extension) The PAK Study Manual covers the entire Enterprise Risk Management (ERM) syllabus (The ERM extension is included). Not only does it give you the detailed explanations on conceptual, calculation, and exam materials, but it also fills in the gaps among the topics that are not covered in the source readings. It helps you better understand and master the confusing logics and difficult materials.

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PAK STUDY MANUAL PACKAGE

Economic Capital Modeling Practical Considerations

PAK Study Manual

Economic Capital is the amount of capital that is needed to cover unexpected losses at a certain risk tolerance level

Credit: Economic Capital Modeling: Practical Considerations p.4 (by Milliman)

PAK Study Manual

Income StatementYear-End 20X0 20X1 20X2 20X3 20X4 20X5 20X6 20X7 20X8 20X9(+) Premium Income 247.2 282.6 320.5 361.2 405.1 452.6 504.1 560.1 621.1 687.6(+) Investment Income 60.5 71.8 85.0 99.9 116.7 135.4 156.1 179.0 204.4 232.3(=) Total income 307.7 354.4 405.5 461.1 521.8 588.0 660.2 739.1 825.5 919.9

(–) Death Benefits 23.0 26.7 31.2 36.4 42.4 49.7 59.0 69.9 81.5 93.6(–) Annuity, Surrender, and Other Benefits 43.1 52.0 62.0 73.2 85.6 99.5 114.9 131.9 150.7 171.5(–) Premium Taxes 4.9 5.7 6.4 7.2 8.1 9.1 10.1 11.2 12.4 13.8(–) Reserve Increase (Changes in Stat Res) 155.5 180.3 205.2 232.2 258.2 287.9 319.4 353.1 389.7 429.3(–) Other Expense 8.5 12.9 14.3 15.9 17.6 19.5 21.5 23.8 26.3 29.0(–) Commission 51.2 55.5 62.1 69.2 76.9 85.0 93.7 103.1 113.6 125.0(=) Total Benefits and Expenses 286.2 333.1 381.2 434.1 488.8 550.7 618.6 693.0 774.2 862.2

PAK(+) Statutory Profit on Existing and New Business 21.5 21.3 24.3 27.0 33.0 37.3 41.6 46.1 51.3 57.7(–) Unallocated Expense 5.5 1.8 1.1 0.3 0.0 0.0 0.0 0.0 0.0 0.0(+) Interest on Capital 3.3 3.6 4.3 5.0 5.7 6.6 7.5 8.6 9.7 11.0(=) Total Pre-Tax Earnings 19.3 23.1 27.5 31.7 38.7 43.9 49.1 54.7 61.0 68.7

(–) Federal Income Tax 8.6 10.9 13.0 15.7 18.6 20.7 23.0 25.5 28.3 31.6(=) After-Tax Earnings (Net Income) 10.7 12.3 14.4 16.0 20.2 23.2 26.1 29.2 32.7 37.1

PV(Net Income) = 100

PAK Study Manual

Income StatementYear-End 20X0 20X1 20X2 20X3 20X4 20X5 20X6 20X7 20X8 20X9(+) Premium Income 247.2 282.6 320.5 361.2 405.1 452.6 504.1 560.1 621.1 687.6(+) Investment Income 60.5 71.8 85.0 99.9 116.7 135.4 156.1 179.0 204.4 232.3(=) Total income 307.7 354.4 405.5 461.1 521.8 588.0 660.2 739.1 825.5 919.9

(–) Death Benefits 23.0 26.7 31.2 36.4 42.4 49.7 59.0 69.9 81.5 93.6(–) Annuity, Surrender, and Other Benefits 47.4 57.2 68.2 80.5 94.2 109.5 126.4 145.1 165.8 188.7(–) Premium Taxes 4.9 5.7 6.4 7.2 8.1 9.1 10.1 11.2 12.4 13.8(–) Reserve Increase (Changes in Stat Res) 155.5 180.3 205.2 232.2 258.2 287.9 319.4 353.1 389.7 429.3(–) Other Expense 8.5 12.9 14.3 15.9 17.6 19.5 21.5 23.8 26.3 29.0(–) Commission 51.2 55.5 62.1 69.2 76.9 85.0 93.7 103.1 113.6 125.0(=) Total Benefits and Expenses 290.5 338.3 387.4 441.4 497.4 560.7 630.1 706.2 789.3 879.4

PAK(+) Statutory Profit on Existing and New Business 17.2 16.1 18.1 19.7 24.4 27.4 30.1 32.9 36.2 40.6(–) Unallocated Expense 5.5 1.8 1.1 0.3 0.0 0.0 0.0 0.0 0.0 0.0(+) Interest on Capital 3.3 3.6 4.3 5.0 5.7 6.6 7.5 8.6 9.7 11.0(=) Total Pre-Tax Earnings 15.0 17.9 21.3 24.3 30.2 33.9 37.7 41.5 46.0 51.6

(–) Federal Income Tax 7.1 9.0 10.9 13.1 15.6 17.2 19.0 20.9 23.1 25.6(=) After-Tax Earnings (Net Income) 7.9 8.9 10.4 11.2 14.6 16.7 18.7 20.6 22.9 25.9

PV(Net Income) = 90

PAK Study Manual

Difference = 100 – 90 = 10 1 Data Point

Difference100th 6099th 5898th 5597th 5296th 5095th 4994th 4893rd 4792nd 4591st 42

VaR(95%) = 50

1. Take the difference 2. Rank them 3. Calculate the VaR

TVaR(95%) = (60+58+55+52+50)/5 = 55

PAK Study Manual

VaR(95%) = Quantile – Expected Value = 60 – 10 = 50

1. Rank them 2. Take the difference 3. Calculate the VaR

Loss

Prob.

Expected Loss VaR(95%)

95th

PercentileMean Loss

Reserve Economic Capital

PV(Net Loss)100th 7099th 7898th 6597th 6296th 6095th 5994th 5893rd 5792nd 55

50

10 60

PAK Study Manual

Major Risks Total

Total Risk

Underwriting Risk

Credit Risk

Market Risk

Operational Risk

Liquidity Risk

PAK Study Manual

Risk Sources Descriptions

Market Risk The risk that market levels, interest rates, or volatility change, result in losses

Credit Risk The risk that an asset held experiences either a default or a significant fall in its credit quality

Liquidity Risk The risk that reduced liquidity constrains the ability to buy and sell assets, resulting in losses

Underwriting / Demographic Risk

The risk that actual demographic experience turns out worse than expected

Operational Risk The risk that there is a failure in the operational aspects of the business—people, process, or system

PAK Study Manual

• VaR vs. Tail VaR 1

• Stochastic Analysis vs. Stress Test 2

• Real World vs. Risk Neutral 3

• Diversification Effect 4

• Time Horizon 5

• Negative Cumulative Surplus 6

• Future New Business 7

Practical Concerns

PAK Study Manual

Economic Capital Underwriting Risk 10

Credit Risk 20

Market Risk 30

Operational Risk 40

Liquidity Risk 50

Underwriting

Risk Credit Risk Market Risk Operational

Risk Liquidity

Risk Underwriting Risk 1 0 0 0.5 0.5

Credit Risk 0 1 0.5 0 0.5

Market Risk 0 0.5 1 0 0.5

Operational Risk 0.5 0 0 1 0.5

Liquidity Risk 0.5 0.5 0.5 0.5 1

Economic capital w/o diversification = 10 + 20 + 30 + 40 + 50 = 150

Economic capital with diversification

[ ]

0.51 0 0 0.5 0.5 100 1 0.5 0 0.5 20

10 20 30 40 50 1070 0.5 1 0 0.5 300.5 0 0 1 0.5 400.5 0.5 0.5 0.5 1 50

= =

Diversification benefit = 150 – 107 = 43

PAK Study Manual

Economic capital with diversification

Market Credit Liquidity Insurance Operational Group Aggregate

5% 1203 1173 1183 1056 1356 1215 7186

5% VaR 203 173 183 56 356 215 1186

Credit Liquidity Market Operational Insurance Group

Credit 1.00 0.30 0.40 0.20 0.25 0.10

Liquidity 0.30 1.00 0.50 0.25 0.10 1.00

Market 0.40 0.50 1.00 0.10 0.10 0.50

Operational 0.20 0.25 0.10 1.00 0.10 0.50

Insurance 0.25 0.10 0.10 0.10 1.00 0.40

Group 0.10 1.00 0.50 0.50 0.40 1.00

[ ]

0.51 0.3 0.4 0.2 0.25 0.1 173

0.3 1 0.5 0.25 0.1 1 1830.4 0.5 1 0.1 0.1 0.5 203

173 183 203 356 56 215 8160.2 0.25 0.1 1 0.1 0.5 3560.25 0.1 0.1 0.1 1 0.4 560.1 1 0.5 0.5 0.4 1 215

= =

PAK Study Manual

• Determine the appropriate level of capital needed 1

• Understand the capital requirements 2

• Measure performance based on capital usage 3

• Assess the return on capital 4 • Understand how well

capitalized companies are 5

Benefits

PAK Study Manual

Economic Capital Modeling

Key points • Define economic capital • Understand how it is calculated • Know the aggregation calculation • Describe the practical concerns • List the benefits

PAK Study Manual

Practice Questions

© PAK Study Manual 1 SOA ERM Exam

ERM-106-12: Economic Capital Modeling: Practical Considerations Q1: You are given these two definitions: A. The capital that is required to support a business with a certain probability of default B. The capital that is the excess of the value of the company’s assets over the value of its liabilities on a realistic or market-consistent basis Recognize which types of economic capital they are. Data for Q2-Q6 Credit Market Operational Economic Capital 100 200 50

Credit Market Operational Credit 1 0.8 0.3 Market 0.8 1 0.2 Operational 0.3 0.2 1

Q2: Calculate the aggregated (total) economic capital without diversification benefit. Q3: Calculate the aggregated (total) economic capital with diversification benefit. Q4: Calculate the amount of diversification benefit. Q5: Describe what will happen on your aggregated economic capital if the correlation between market risk and operational risk increases. Q6: Describe what will happen on your aggregated economic capital if the correlations among the risks become zero.

Practice Questions

© PAK Study Manual 2 SOA ERM Exam

ERM-106-12: Economic Capital Modeling: Practical Considerations S1: A Required Economic Capital and B Available Economic Capital

S2: Total EC (without diversification) = 100 + 200 + 50 = 350

S3: 0.5

1 0.8 0.3 100100 200 50 0.8 1 0.2 200

0.3 0.2 1 50

0.5100

100 1 200 0.8 50 0.3, 100 0.8 200 1 50 0.2, 100 0.3 200 0.2 50 1 20050

× + × + × × + × + × × + × + ×

298.75=

S4: Diversification benefit = 350 – 298.75 = 51.25

S5: If the correlation between market risk and operational risk increases, the total economic capital calculated based on the correlation matrix will increase. This will decrease the diversification benefit.

S6: If the correlations among risks become zero, the total economic capital = (1002 + 2002 + 502)0.5

= 229.13. The total economic capital decreases and the diversification benefit increases.