ACLI-EBC-CLHIA Interim Proposal _J_ June Final.PDF

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2 ACLI-EBC-CLHIA ACLI EBC / CLHIA CTE 3

3 ACLI-EBC-CLHIA 3 CTE CTE CTE60 CTE 1) CTE(60) CTE(80) CTE(90) 2) 100 3) 8) 3 Mercer Oliver Wyman Actuarial Consulting

4 ACLI-EBC-CLHIA 4 Limited 4 10, ,000 10,000 3

5 ACLI-EBC-CLHIA ( ) : :

6 ACLI-EBC-CLHIA 6 = + = = = CTE(60)CTE(80) = Max[CTE(60),0] = 40 = Max[CTE(80),0] = 20 : CTE(60) CTE(80) CTE 6. CTE(90) CTE90

7 ACLI-EBC-CLHIA 7 (a) (b) (c) (d) : 8. ( ) CTE(90) CTE(60) 3 =.. : ,000 CTE(60) 9.

8 ACLI-EBC-CLHIA 8 : : : : 13. 3

9 ACLI-EBC-CLHIA 1 2.0% 2 2.0% 3 2.0% 4 2.5% 5 3.0% 6 4.0% 7 5.0% % % : = Max [50%, * (ITM% - 10%)] ITM% > 10% = 100% ITM% = GMB/AV 1 : = Min [150%, * (ITM% + 10%)] ITM% < -10% = 100% 9

10 ACLI-EBC-CLHIA : : 15 CTE CTE 2

11 ACLI-EBC-CLHIA 11 3 Mercer Oliver Wyman Actuarial Consulting Limited RSNL2 ( ) 7 : TOPIX MSCI ( 10 ); ( 10 ); ( 10 ); ( ) ( ) ( ) : ( ) ( )

12 ACLI-EBC-CLHIA RSNL2 ( ) ( ) RSLN2 Cox-Ingersoll-Ross 1 P 1: Table 1: Asset Classes for Scenario Modeling Asset Class Market Proxies Historic Period Notes Scenario File Japan LT Interest Rates Japan 10-yr Government Bond Yields (1) JGB_10y.csv U.S. LT Interest Rates U.S. 10-year Treasury Yields (1) UST_10y.csv Japan Equity TOPIX Total Return Index (3) TOPIX.csv Japan Fixed Income Nomura BPI (2) NOMURA.csv Foreign Equity MSCI Kokusai ex Japan $LOCAL (3) KOKUSAI.csv Foreign Government Bond U.S. Intermediate Government $US (2) USITGVT.csv Foreign Corporate Bond U.S. Long-Term Corporate Bonds $US (2) USLTCORP.csv 12

13 ACLI-EBC-CLHIA Foreign Fixed Income 65% USITGVT + 35% USLTCORP USBOND.csv the Mersenne Twister RSNL2 (57.24% 1 ) RSNL2 (TOPIX) ( ) (1) P Cox-Ingersoll-Ross ( CIR ) ( 1 ) i t = α i t 1+ ατ + σ i t 1 Zt ( 1 ) i = α i + ατ + σ i Z t t 1 t 1 t i t t i 10 Z t Z t ( ) ( ) αα, ττ, CIR 2 2 r = Cox-Ingersoll-Ross Table 2: Model Parameters for Cox-Ingersoll-Ross Interest Rate Processes α τ σ Starting Rate 13

14 ACLI-EBC-CLHIA 10-year JGB Yields % % 10-year UST Yields % % (2) ( ) ( ) ( ) ( ) r = β i + κ β i i + σ i Z t 0 t 1 t t 1 t 1 Z 3 γ 3 ( ) Table 3: Model Parameters for Fixed Income (Bond Fund) Returns β 0 κ β 1 σ γ NOMURA USITGVT USLTCORP (3) ( ) ψ ER [ k] r ψ = = σk TOPIX K σ k ( ) [ E R k ] r 3.345% CIR 10 RSNL2( ) RSLN TOPIX ( ) π = = 0.5 ( ) 4 RSLN2 5 Schwartz-Bayes Criterion[ ] (µ) (σ) ( )ρ12 ρ21 14

15 ACLI-EBC-CLHIA (MSIC ) MLE RSLN2 [ ] 4RSLN2 ( ) Table 4: RSLN2 Parameters (Monthly) Equity Markets µ1 σ1 ρ12 µ2 σ2 ρ21 π1 π2 TOPIX KOKUSAI MLE KOKUSAI Schwartz-Bayes Criterion Table 5: Values for the Log Likelihood Function and Schwartz-Bayes Criterion Regime-Switching Lognormal Lognormal Log Likelihood SBC Log Likelihood SBC TOPIX KOKUSAI MLE KOKUSAI ( ) 6 Table 6: Correlation Matrix for Integrated Scenario Model TOPIX KOKUSAI JGB_10 UST_10 NOMURA USITGVT USLTCORP TOPIX KOKUSAI JGB_ UST_ NOMURA USITGVT USLTCORP

16 ACLI-EBC-CLHIA 7A 10,000 7B 7A Table 7A: Historic Correlations Based on Monthly Log Returns TOPIX KOKUSAI NOMURA USITGVT USLTCORP TOPIX KOKUSAI NOMURA USITGVT USLTCORP B Table 7B: Sample Scenario Correlations for the Monthly Log Returns TOPIX KOKUSAI NOMURA USITGVT USLTCORP TOPIX KOKUSAI NOMURA USITGVT USLTCORP ,000 (Drift) (Volatility) (Skew) (Mean) 20 Stdev1 ( ) 8 Table 8: Sample Investment Return Statistics Drift Volatility Skew Mean Stdev1 Japan Bond 2.58% 2.93% % Foreign Government Bond 5.72% 4.80% % Foreign Corporate Bond 5.89% 7.69% % Foreign Equity 5.62% 14.81% % Japan Equity 6.61% 17.40% %

17 ACLI-EBC-CLHIA ( ) ( 2.5%, 5%, 10%, 90%, 95% 97.5%) 9 TOPIX )RSLN2 MLE 10,000 [ ] ( RSLN2 TSX ( )) [ ] ( RSLN2 SP500 ( )) Table 9: Sample Percentiles for Accumulation Factors 2.5% 5% 10% 90% 95% 97.5% Calibration Points: Japan Equity (RSLN2 Fit to TOPIX TR ) One Year Five Year Ten Year Calibration Points: CIA Task Canadian Equity (RSLN2 Fit to TSX TR ) One Year Five Year Ten Year Calibration Points: AAA LCAS U.S. Equity (RSLN2 Fit to S&P500 TR ) One Year Five Year Ten Year Japan Bond One Year Five Year Ten Year Foreign Government Bond One Year Five Year Ten Year Foreign Corporate Bond One Year Five Year Ten Year Foreign Equity One Year Five Year Ten Year Japan Equity 17

18 ACLI-EBC-CLHIA One Year Five Year Ten Year RSLN2 RSLN MSCI ( E[R] = ( ), V = ( ), s = ) $LOCAL MLE: E[R] = 11.55%, V = 14.70%, s = $US MLE: E[R] = 11.64%, V = 14.80%, s = YEN MLE: E[R] = 8.13%, V = 17.56%, s = '$LOCAL MODEL'( ) ( ) $LOCAL MODEL: E[R] = 7.67%, V = 14.77%, s = ( % ) 17.56% RSLN2 1 RSLN % 8.48 ( 8.13% 7.67% ) 82%

19 ACLI-EBC-CLHIA 19 * * * [] P Q Q Q P [] The Mersenne Twister [] [] ( ) [] SBC RSLN2. [] ( ) ( ). [] ( ) RBC ( )

20 ACLI-EBC-CLHIA

21 ACLI-EBC-CLHIA 21