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

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

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

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

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

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

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

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

9. 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

10. 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

11. 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)

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

13. 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)

14. Basic Reserve Year Cash Flow 1 (203) 2 193 3 118 4 72 5 39 6 27 7 81
(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

15. 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

16. Residual Margin Year Adj Cash Flow 1 (225) 2 175 3 102 4 57 5 26 6 141
(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

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

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

19. 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

20. Close Form Solutions
Embedded Derivatives
Black Sholes

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

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

23. Thank You