Actuarial Valuation Methods Insurance IFRS Seminar December 1, 2016 Bill Horbatt Session 3

Fundamental Relationships Reserve = + Present Value Future Benefits – Present Value Future Premiums Assets = Reserve “one man’s asset is another’s liability”

Asset Valuation Past Practice IFRS Phase II Accrual Basis (Amortized Book Value) IFRS Phase II Accrual Value (?) Market Value (?)

Liability Valuation No market value – except isolated situations “Replication” “Fair Value” type replacement Explicit assumptions Market based inputs Non market based inputs

Liability Methods Simplified Complex Expected Claims (e.g. Loss Ratio) Unearned Premium Complex Gross premium valuation with no gain at issue

Unearned Premium Earned in proportion to risk Simplified: pro rata Acceptable under IFRS for short duration (1 year) contracts

UPR with DAC Liability = UPR Asset = DAC Both earned in proportion to risk

Expected Claim (loss ratio) Reserve = Loss Ratio * Earned Premium Claim Reserve = Loss Ratio * Earned Premium – Paid Claims Acceptable under IFRS Phase II

t+1Vx = (1+i)[NLP + (1- qx+t) tVx] - qx+t Net Premium Valuation t+1Vx = (1+i)[NLP + (1- qx+t) tVx] - qx+t Not acceptable under IFRS Phase II Implicit assumptions No lapses Locked in assumptions Not current assumptions Options & guarantees not valued

Gross Premium Valuation t+1Rx = (1+it)[VP + (1- qx+t - lt)tRx] – qx+t + Et Where l = lapse and E = expense Acceptable in some cases for IFRS Requires a Risk Margin May require a residual Service Margin to eliminate gain at issue Requires current assumptions

Risk Margin Examples Cost of Capital (CoC): add R * tCx term R = cost rate (e.g. 6%) tCx = capital at time “t” Conditional Tail Expectation (CTE) Average of worst scenario values Explicit Margins (e.g. qx+t = 110% expected)

“Residual” Service Margin IFRS requires No gain at issue Service Margin = Premium – Initial Reserve Amortized as services performed

Example (10 year level term) Premium Expense Commission Benefits Cash Flow 1 502 (112) (452) (141) (203) 2 416 (9) (42) (172) 193 3 357 (8) (36) (195) 118 4 319 (7) (32) (208) 72 5 290 (29) (215) 39 6 264 (6) (13) (218) 27 7 243 (12) (221) 8 224 (11) (223) (15) 9 208 (5) (10) (227) (35) 10 100 (3) (122) (30)

Basic Reserve Year Cash Flow 1 (203) 2 193 3 118 4 72 5 39 6 27 7 8 1 (203) 2 193 3 118 4 72 5 39 6 27 7 8 (15) 9 (35) 10 (30) PVFCF 170 373 180 61 (10) (50) (76) (80) (65) (30) - Profit 170

Risk Margin Year Cash Flow 1 (203) 2 193 3 118 4 72 5 39 6 27 7 8 (15) 1 (203) 2 193 3 118 4 72 5 39 6 27 7 8 (15) 9 (35) 10 (30) Risk Margin Adj Cash Flow (22) (225) (19) 175 (16) 102 (15) 57 (14) 26 (13) 14 (12) (8) (11) (26) (10) (45) (0) (30) PVFCF 39 264 89 (13) (69) (95) (109) (101) (75) (30) - Profit 39 22 19 16 15 14 13 12 11 10

Residual Margin Year Adj Cash Flow 1 (225) 2 175 3 102 4 57 5 26 6 14 1 (225) 2 175 3 102 4 57 5 26 6 14 7 (8) 8 (26) 9 (45) 10 (30) Residual CF w/ RM (7) (231) (6) 169 (5) 97 (4) 53 22 10 (3) (11) (29) (47) (1) (32) PVFCF - 231 62 (35) (87) (109) (119) (108) (79) (32) Profit 29 24 21 19 18 16 15 14 13 1

Probability Weighted Cash Flows (Mean) Most Important Significant financial market impact Long tail distributions Less Important Law of large numbers applies

Stochastic Reserves Stochastic (Multiple Scenarios) most appropriate if financial markets influence benefit payments Examples Minimum interest gurantees GMxB

Stochastic Assumptions May not be material for non financial assumptions, e.g. mortality (subject to law of large numbers) Dynamic policyholder behavior May (or may not) be appropriate

Close Form Solutions Embedded Derivatives Black Sholes

Unbundling Account value + Reserve Reserve based upon cash flows not reflected in account value (e.g. additional death benefits, surrender charges, etc.)

Similar to EGP under US GAAP Revenues Unbundling Similar to EGP under US GAAP Revenues Fees Surrender charges Investment spread Expenses Benefits

Thank You