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Actuarial Guideline 43Actuarial Guideline 43Kansas City Actuaries Club Kansas City Actuaries Club -- June 24, 2009June 24, 2009
John Froehle, FSA, MAAA
Consulting Actuary, Actuarial Resources Corporation
AG 43: Implementation Issues AG 43: Implementation Issues and Preliminary Resultsand Preliminary Results
Here are the topics for the first half of this presentation.
� Timing and Scope for AG 43
� Stochastic Modeling with Comparison to C-3 PII
� Standard Scenario with Comparison to C-3 PII
� Hedging and CDHS
� Alternative Methodology
� Actuarial Certification and Memorandum
Here are the topics for the for the second half of this presentation.
� Case Study: AG 43 Variable Annuity Reserves
� Products (VA One, VA Two, VA Three) : Specs, In-Force
� Stochastic Model: Assumptions and Scenarios
� Results: Stochastic CTE, Standard Scenario Amount
� Time permitting, Stochastic Scenario Requirements and Alternatives
Short Break
Timing and Scope of New Requirements
December 30, 2009
December 30, 2009
AG 34 and AG 39 Become Ineffective for Statutory Reserves
Tax Reserves Pre - 2009
Tax Reserves Pre - 2009
Requirements in effect when contract issued-----------------------------e.g. AG 34 / AG 39
December 31, 2009
December 31, 2009
AG 43 effective for all business issued on or after Jan. 1, 1981--------------------------------Note: RBC applies to same bus as AG 43 regardless of when issued
Tax Reserves
2009 Issues
Tax Reserves
2009 Issues
Tax Reserves currently unknown – January 2008 Treasury Notice 2008-18 looked favorably on Standard Scenario
FutureFuture
AG 43 as Poster Child for PBR Eventually added to Valuation Manual as VM-21
Stochastic Modeling with Stochastic Modeling with Comparison to CComparison to C--3 PII3 PII
General Stochastic Modeling Requirements
� Stochastic scenarios� Company-generated or Academy Pre-packaged� Sufficient number of scenarios: no material impact from using more of them� Meet Calibration Criteria
� Integrated ALM model� Model Assets, Dynamic Re/Disinvestment� Sufficient projection period: no material impact from extension
� Prudent Estimate assumptions
� Starting Assets� Best Guess of reserve you are computing but no strict requirement� Model all SA assets, all hedge assets, GA assets can be negative
� Projection of “accumulated deficiencies” … working reserve - assets
� Working Reserve: CSV or PV of income payments
Summary Comparison of AG43 and C-3 Phase II
Actuarial Guideline XLIII
Before Tax
CTE 70
No SS Aggregation
Revenue Sharing Limited1
New CDHS recognition 2
123
45
New assumption disclosure3
New assumption guidance4
67
C-3 Phase II
After Tax
CTE 90
SS Aggregation Permitted
Prudent Revenue Sharing
Original CDHS recognition
123
45
Original disclosure
Original guidance
67
(1) See section (E) of Appendix 1, (2) See SectionA7.3 of Appendix 7, (3) See section A9.7 of Appendix 9, (4) See Section A9.2-9.3 of Appendix 9
Additional Differences from C-3 Phase 2
� Role of Reinsurance�C-3 PII TAR computed net of reinsurance�AG 43 Reserves computed both gross and net
� Discount Rates: PV Accumulated Deficiencies�C-3 PII TAR:
• Forward rates if not using an integrated model• Otherwise, forward rates or “the rates generated by that model” (after-tax 1YT)
�AG 43 Reserves:• “the same interest rates at which positive cash flows are invested” which are• (a) forward rates, (b) C-3 Phase I 200 scenarios, or (c) stochastic model “rates
developed for this purpose”
� Integrated Model: GA Assets and Interest-Rate Risk�C-3 PII TAR: Appendix 6 alternatives for i-rate risk including C-3 PI factors�AG 43 Reserves: Full ALM model, GA asset modeling appears required
Standard Scenario with Comparison Standard Scenario with Comparison to Cto C--3 PII3 PII
A3.2 – “Basic Reserve” and “Basic Adjusted Reserve”
�Basic Reserve �apply “statutory…valuation requirements … prior to adoption” of AG 43
“ignoring any guaranteed death …or living benefits in excess of account values”
� “assume a return on separate account assets based on the year of issue statutory valuation rate less appropriate asset based charges, including charges for any guaranteed death … or living benefits”
� A3.2)C): “no less than the Cash Surrender Value”
�Basic Adjusted Reserve (BAR)� To this will be added the MAX PV negative accumulated net revenue. It’s
like the Basic Reserve but …• “… free partial withdrawal provisions shall be disregarded when
determining surrender charges” and A3.2)C) shall not apply
• No CSV floor here.
Definition of Standard Scenario Reserve
AG 43, section A3.3: Standard Scenario Reserve is
� Basic Reserve for contracts w/o guaranteed benefits (i.e. use existing CARVM reserves)
� On a seriatim basis, Max{ CV, a+b-c} wherea) Basic Adjusted Reserve
b) Max{0,GPV of –Accumulated Net Revenue (ANR)}:
� Starting at 0 and using Discount Rate as accumulation rate
� Adding in Prescribed Margins
� Subtracting direct contract benefits in excess of AVs less individual reinsurance recoveries plus reinsurance premiums
c) Allocation of approved hedges and aggregate reinsurance� But limited to the GPV of -ANR
OR
Comparison of AG 43 & C-3 PII Standard Scenario Components
Item AG XLIII C-3 PII
Accumulated Net Revenue
Before Tax w. PV at DR
After Taxw. PV at DR (1- tax rate)
Discount Rate (DR) Pre-Tax SVL Rate(s) 10-Yr CMT + 50 bps(3% � DR � 9%)
Basic Adjusted Reserve CARVM w/o free withdrawals & w/o CSV Floor
Working Reserve: CSV or PV Income Payments
Revenue Sharing Guaranteed included Not included
Mortality Rates
70% of 1994 VA MGDB thru age 85, increase 1% per
year to age 115
80% of 1994 VA MGDB thru age 95, increase
1% per year to age 115
Surrender Charge PeriodLengthy Calculation to
Determine “Surrender Charge Amortization Period”
Not as well defined
AG 43 & C-3 PII Standard Scenario Margins
Max{�GMDB explicit charges, 20 bps AV}
Guaranteed Net Revenue Sharing
40 bps Fixed AV40 bps Fixed AV
Min{65 bps AV, 50% of charges over those in SC
period} +
50% of charges (excl GNRS) over those in SC period (excl
GNRS) +
Additional Margins After Surrender
Charge Amortization Period
Max{ �GMxB explicit charges, 20 bps AV}
Max{�GMLB explicit charges, 20 bps AV}
10 bps AV +20 bps AV +
Margins During Surrender Charge
Amortization Period*
C-3 PIIAG XLIIIItem
* C-3 PII refers to Surrender Charge Period whereas AG 43 defines a Surrender Charge Amortization Period
AG 43 & C-3 PII Standard Scenario Drops & Returns
Drops & Returns Compared: AG 43 / RBC
ClassesProjection Periods
Initial Year 1 Years 2 – 5 Year 6+
Equity Class ������ ���� � ��� �� ���� ���� ����
Bond Class � ��� � ��� ����� ������ ����� � �����
Balanced Class ����� ����� � ��� ����� � �� �� ���� � �� ��
Fixed Accounts and General
Account� ���
Max{ �� �������
guar rate} �
current rate
Max{ �� �������
guar rate} �
current rate
Max{ �� �������
guar rate} �
current rate
AG 43 & C-3 PII Standard Scenario Benefit Election Rates
Overriding Rule: Election of any VAGLB prohibited if another VAGLB has larger current value
75% or contract minimum
50% or contract minimum
25% or contract minimum
Withdrawals do reduce other ITM benefits
100%75% or contract minimum
50% or contract minimum
Withdrawals do not reduce other ITM benefits
60 < x+t-150 � x+t-1 � 60x+t-1 < 50
Guaranteed Minimum
Withdrawal Benefit
���� � �������� � ���
At Last Election Date
ITM Any Time After Waiting PeriodGuaranteed Minimum
Accumulation Benefit
������� � ������ � ����� � ���
20% � ITM10% � ITM < 20%
ITM < 10%At Last Election
Date
Prior to Last Election DateGuaranteed
Living Benefits other than GMWB
Contractholder Election Rates Compared: AG 43 / RBC
AG 43 & C-3 PII Standard Scenario Lapse Assumptions
��������Any Other Guaranteed
Living Benefits ITM
�� � ���� � ���� � ���� � ��Any Guaranteed Minimum Accumulation Benefit ITM
20% � ITM10% � ITM< 20%ITM < 10%Rates that Vary by In-The-Moneyness
�����All Guaranteed Living Benefits OTM
�����Death Benefit Only Contracts
After Surrender Charge PeriodDuring Surrender Charge PeriodCategory
Lapse Assumptions Compared: AG 43 / RBC
ITM:
• AG 43: ITM = 100% * ((Current Value of the guaranteed living benefit /Account Value) - 1)
• C-3 PII: ITM = Max {1 – (Account Value/ Value of Guaranteed Benefit at time of exercise of benefit), 0},
where the maximum is determined over all future possible benefit payout start dates
Alternative MethodologyAlternative Methodology
Alternative Methodology
AG 43 Appendix 4 A4.1.A) “The Conditional Tail Expectation Amount determined using the Alternative Methodology for a group of contracts with GMDBs shall be determined as the sum of amounts obtained by applying factors to each contract inforce as of a valuation date and adding this to the contract’s Cash Surrender Value.”
C-3 PII Modeling Methodology “A company may choose to develop capital requirements for Variable Annuity contracts with no VAGLBs, by using the Alternative Method, as defined in Appendix 8 of this report instead of using scenario testing if it hasn’t used scenario testing for this purpose in previous years.“
From the 2008 RBC instructions
AG 43 Appendix 3 A3.1.A) “A Standard Scenario Reserve shall be determined for each of the contracts falling under the scope of the Guideline by applying section A3.3). This includes those contracts to which the Alternative Methodology is applied.”
Hedging and CDHS Hedging and CDHS
Modeling of Hedges
InstrumentsCurrently Held Costs and benefits shall be included
Positions Expectedto be Held
� Costs and benefits shall be included if CDHS� Hedging Strategy meets requirements of Appendix 7
Strategy Changes To the extent hedging strategies change over time, document and include effective date of change.
Derivative Use State statutes, laws and regulations still govern use of derivative instruments
Clearly Defined Hedging Strategy
�Risks being hedged
�Objectives
�Risks not being hedged
�Financial instruments being used
�Trading rules and permitted tolerances
�Metric(s) for measuring effectiveness
�Criteria used
�Frequency of measurement
�Conditions hedging will not take place
�Persons responsible for implementing
Appendix 7 Modeling of hedges
� Hedging strategy effectively implemented for at least three months
� Recognize all risks including basis risk and gap risk
� Recognize associated costs, imperfections in hedges
� Hedging Certification: responsibilities of actuary and financial officer
� Hedging Documentation: strategy, current positions, methods, procedures, assumptions, supplementary analyses
AG 43 CTE Amount
Where:
CTE Amount (best efforts) = hedged
CTE Amount (adjusted) = no dynamic hedging
E represents an effectiveness factor
E no greater than 70% (30% if hedge cash flows not modeled directly or not 12 months experience to justify E)
CTE Amount (Reported) = E x CTE Amount (best efforts)
+ (1 – E) x CTE Amount (adjusted)
C3 Phase 2 TAR Reported
Where:
TAR (best efforts) = hedged results
TAR (adjusted) = recalculated TAR adjusting for uncertainty of effectiveness (compensate for potential overstatement of impact)
E => error factor representing level of sophistication (minimum of .05)
TAR (Reported) = TAR (best efforts)
+ E x Max{0, TAR (adjusted) – TAR (best efforts)}
Value of Approved Hedges for Standard Scenario Amount
� Approved hedge�Asset held on valuation date�Used as hedge for contracts included in AG43�Comply with statutes, laws & regulations of domiciliary state or jurisdiction
� Discounted value of pre-tax cash flows less statement value on valuation date (PV using 1-yr CMT)�Cash flow for hedges expiring within a year, based on holding to expiry,
otherwise liquidation value one year from valuation date. (Consistent with assumed returns of standard scenario, Black-Scholes pricing, risk-free rate of 5 year CMT.)
� Allocation to contract
CDHS Modeling QuestionsCDHS Modeling Questions
Liability Greeks and their calculation?
Asset Greeks and their calculation?
“Stochastic-on-Stochastic”Modeling?
“Market Consistent”Scenarios?
Speed Issues / Frequency of Dynamic Rebalancing / # of Inner Simulations?
Greek Estimation Techniques?
Model “inside” or “outside” the ALM model?
Dynamic Rebalancing?
Actuarial Certification and Actuarial Certification and MemorandumMemorandum
Certification and Memorandum
“Actuarial Certification of the work done to determine the Aggregate Reserve shall be required. “ (1)
“An actuarial memorandum shall be constructed documenting the methodology and assumptions upon which the Aggregate Reserve is determined.” (1)
(1) AG 43: section A.2.3
Appendix 8: Certification Requirements
Certification is 6 required paragraphs on identity, scope, reliance, calculation certification, assumptions certification, surplus adequacy non-opinion statement
Memorandum is 5 large sections on description of method, alternative method employed, alternative factors employed, stochastic modeling, and standard scenario.
Case Study: AG 43 Variable Annuity ReservesCase Study: AG 43 Variable Annuity Reserves
Case Study Product Descriptions
Assumption VA ONE VA TWO VA THREE
Durational PremiumFree Withdrawal
3%
4% Rollup or Annual Ratchet15 Basis Points for either
None ROP at Year 10 None
None 25 Basis Points NA4% ROLL, Age 60 or 10-Year WP
50 Basis PointsGMIB Income A2000 & 100% Imprvqx & Int 1.50%
Ann. Ratchet w life payout75 Basis Points
M&EFund Mgmt FeeRev Sharing
1.5%
Surr Chg Pct & Base
7% decling 1% / yearAccount Value
10% of Account Value
125 Basis Points75 Basis Points50 Basis Points
No charge
NoneGMWB Type & Charge None
None
Fixed AV Guar & Cred IntGMDB Type & Charge
GMAB Type & Charge
GMIB Type & Charge None
Portfolio Yield less 2.25% less rider chargesReturn of Premium
7% declining 1% / year
Case Study Business In Force
Issue Average Contract Account CashProduct Year Iss. Age Count Value Variable Fixed ValueVA-One 1996 57 145 6,414,289 5,672,198 742,090 6,414,289
1997 62 105 6,995,682 5,785,785 1,209,897 6,995,682 1998 60 166 7,796,665 5,705,458 2,091,207 7,796,665 1999 62 70 4,434,925 4,145,394 289,531 4,434,925 2000 65 35 1,880,721 1,871,743 8,978 1,880,721 2001 69 27 1,380,206 1,265,796 114,410 1,380,206 2002 59 41 2,412,559 2,206,763 205,796 2,390,846 2003 53 34 1,405,743 993,647 412,095 1,380,439 2004 66 44 2,279,211 2,122,710 156,501 2,217,672
Subtotals: 61 667 35,000,000 29,769,493 5,230,507 34,891,445 VA-Two 2004 60 72 3,357,902 3,020,235 337,667 3,267,238
2005 63 62 4,019,081 3,365,621 653,460 3,874,394 2006 59 100 4,601,204 3,349,553 1,251,651 4,394,150 2007 62 35 2,217,462 1,541,583 675,879 2,097,719 2008 65 15 804,351 656,537 147,814 753,677
Subtotals: 61 284 15,000,000 11,933,528 3,066,472 14,387,179 VA-Three 2007 55 1 37,929 37,929 - 35,881
2008 58 719 49,962,071 46,030,739 3,931,332 46,814,460 Subtotals: 58 720 50,000,000 46,068,668 3,931,332 46,850,341
59 1,671 100,000,000 87,771,689 12,228,311 96,128,965 Grand Totals:
Account Value Distribution of Funds
VA - One VA - Two VA - Three
Money Market Funds
US Government Bond Funds
Corporate Bond Funds
Fixed Income Funds
Balanced Funds
US Large Cap Equity Funds
International Equity Funds
US Small Cap Equity Funds
Aggressive Equity Funds
Fixed Account
Death Benefits In-The-Money
28%
29%
29%
30%
30%
2007 2008 T otal :
I s s u e Y e a r
V A- T hr ee GM DB I T M P er cent
0%
5%
10%
15%
20%
2004 2005 2006 2007 2008 Total :
I ssue Y ear
VA - Two GM DB ITM P e r c e nt
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%
1996 1997 1998 1999 2000 2001 2002 2003 2004 Total:Issue Year
VA-One GMDB ITM Percent
Issue Year Account Value GMDB Value ITM
Percent
1996 6,414,289 4,708,687 0%1997 6,995,682 6,464,159 2%1998 7,796,665 8,256,005 13%1999 4,434,925 6,017,788 37%2000 1,880,721 2,740,603 46%2001 1,380,206 1,707,020 24%2002 2,412,559 2,491,028 6%2003 1,405,743 1,396,050 4%2004 2,279,211 2,794,947 23%Total: 35,000,000 36,576,287 13%
2004 3,357,902 3,801,093 14%
2005 4,019,081 4,723,180 18%2006 4,601,204 5,270,586 15%2007 2,217,462 2,534,123 14%2008 804,351 803,720 0%Total: 15,000,000 17,132,702 15%
2007 37,929 49,243 30%
2008 49,962,071 64,390,729 29%
Total: 50,000,000 64,439,972 29%Grand Total 100,000,000 118,148,961 21%
VA-One ROP GMDB In-The-Moneyness
VA-Two ROP GMDB In-The-Moneyness
VA-Three Ratchet / Rollup GMDB ITM
Living Benefits In-The-Money
0.0%
2.0%
4.0%
6.0%8.0%
10.0%
12.0%
14.0%
2004 2005 2006 2007 2008 Tot al
I ssue Ye a r
VA-Tw o GMAB ITM Percent
Issue Year
Account Value
GMAB Value
ITM Percent
2004 1,265,648 1,279,816 2.0%2005 1,745,106 1,819,045 4.9%2006 3,314,841 3,661,604 10.7%2007 2,049,714 2,310,398 12.7%2008 804,351 803,722 0.0%Total 9,179,660 9,874,585 7.9%
VA-Two GMAB In-The-Moneyness
0%
5%
10%
15%
20%
25%
30%
2007 2008 Total:Issue Year
VA-Three GMIB ITM Percent
0%
2%
4%
6%
8%
10%
12%
2008 Total:Issue Year
VA-Three GMWB ITM Percent
Issue Year Account Value
GMIB Value ITM Percent
2007 37,929 49,243 30%2008 11,353,049 12,910,199 14%Total: 11,390,979 12,959,442 14%
VA-Three GMIB In-The-Moneyness
Issue Year Account Value
GMIB Value ITM Percent
2008 13,739,022 15,258,321 11%Total: 13,739,022 15,258,321 11%
VA-Three GMWB In-The-Moneyness
Case Study Reserves Prior To AG 43
Issue Total Statutory Basic Basic AdjPlan Year Reserves Variable Fixed AG 34 AG 39 Reserve Reserve
VA_ONE 1996 6,414,289 5,672,198 742,090 - - 6,414,289 6,361,297 1997 6,995,688 5,785,785 1,209,897 6 - 6,995,682 6,945,673 1998 7,811,439 5,705,458 2,091,207 14,775 - 7,796,665 7,739,032 1999 4,507,790 4,145,394 289,531 72,866 - 4,434,925 4,425,560 2000 1,919,866 1,871,743 8,978 39,145 - 1,880,721 1,859,160 2001 1,383,674 1,265,795 114,410 3,468 - 1,380,206 1,368,876 2002 2,399,201 2,193,208 204,674 1,318 - 2,397,883 2,397,367 2003 1,388,182 980,591 407,102 489 - 1,387,693 1,386,697 2004 2,245,558 2,073,649 152,909 19,001 - 2,226,557 2,223,678
Subtotal 35,065,688 29,693,821 5,220,799 151,068 - 34,914,620 34,707,341 VA_TWO 2004 3,306,828 2,948,280 329,562 17,745 11,241 3,277,842 3,272,594
2005 3,953,280 3,263,560 636,446 40,751 12,523 3,900,006 3,894,096 2006 4,490,913 3,220,725 1,210,804 47,000 12,385 4,431,529 4,423,537 2007 2,177,897 1,476,946 650,618 44,565 5,766 2,127,565 2,124,187 2008 762,888 619,822 140,029 686 2,352 759,850 758,461
Subtotal 14,691,806 11,529,333 2,967,459 150,747 44,267 14,496,791 14,472,875 VA_THREE 2007 35,902 35,881 - - 21 35,881 35,021
2008 47,451,938 43,375,800 3,718,033 357,936 169 47,093,833 46,739,274 Subtotal 47,487,840 43,411,681 3,718,033 357,936 190 47,129,714 46,774,295 Total 97,245,334 84,634,835 11,906,291 659,752 44,457 96,541,126 95,954,511
AG 33 Reserve
Modeling AssumptionsModeling Assumptions
Add-On Payments: 0% Partial Surrenders: 0%
Base* Surrender Rates:
Mortality: A2000
Maintenance Expense: annual $60 per contract w/ 3% inflation
Commissions: 25 bps through contract year 7, 50 bps thereafter
* before GLB multiplier
Contract Year: 1-5 6-7 8 9 10 11+
Surrender Rate: 3% 5% 25% 15% 10% 5%
Start GA Assets: Non-Callable Bonds
GA Investment Strategy: Reinvestment at 5YT + 50 bp’s, Proportional Disinvestment
Corporate Borrowing at reinvestment rate if/when GA assets go negative
Run Model on first 1,000 Academy pre-packaged scenarios
Dynamic Living Benefit AssumptionsDynamic Living Benefit Assumptions
(1) Subject to waiting period and age limits.
Surrender Rates Multiplier
(effective pre-election point)
ITM = Benefit Base / AV Surrender Rate
Multiplier>= <
0 1 75%
1 1.2 50%
1.2 1.4 25%
1.4 0% GMIB Election Rate(1)
ITM = GMIB Pymt / AV Pymt(2) GMIB Monthly Election Rate>= <
0 1 0%
1 1.2 5% / 12
1.2 1.4 15% / 12
1.4 � 25% / 12
(2) “AV Pymt” is AV-based modal payment at current payout rates.
GMWB Election Rate (1)
If ITM � 1.05 then 100% , else zero.
Scenario AssumptionsScenario Assumptions
The model was run for 50 years. The pre-packaged scenarios were “extended” from 30 years to 50 years using:
1.Stochastic Log Volatility Equity Return Model, C-3 PI i-rates model, AAA bond returns model and mixed funds model.
2. Mersenne Twister pseudo random numbers.
3. Correlation through Choleski Decomposition.
“Length of Projections. Projections of Accumulated Deficiencies shall be run for as many future years as needed so that no materially greater reserve value would result from longer projection periods.” AG43
The effect of “extension” on Case Study AG 43 results.
Aggregate CTE(70) Results
20 Year Projection 97,027,677
30 Year Projection 97,169,481
40 Year Projection 97,180,192
50 Year Projection* 97,196,676
*This “extension” testing was done before a small change to model which caused final, “reported” 50-year results to change.
Stochastic Model Results (in millions)Stochastic Model Results (in millions)
96.5247.1114.5034.9196.52Starting Model Assets
96.13 46.85 14.39 34.89 96.13 Cash Surrender Value
100.00 50.00 15.00 35.00 100.00 Account Value
97.6448.11 14.60 34.93 97.18(CTE70)
97.25 47.49 14.69 35.0797.25Pre-AG43 Reserve
100.4%101.3%99.3%99.5%99.9%Ratio AG43 / Pre-AG43
96.13 46.85 14.39 34.89 96.13 Median Scenario Result
96.58 47.23 14.45 34.90 96.44 Mean Scenario Result
Non-AGG SUM
VA THREE
VA TWO
VA ONEAGGREGATEAG 43 Reserve
Statistic (1,000 scenarios)
100.57 50.69 14.87 35.00 99.11 (CTE90)
2.92 2.59 0.27 0.07 1.93 “RBC”*
96.13 46.85 14.39 34.89 96.13 Median Scenario Result
96.59 47.25 14.44 34.90 96.43 Mean Scenario Result
Non-AGG SUM
VA THREE
VA TWO
VA ONEAGGREGATEC-3 PII TAR
Statistic (1,000 scenarios)
* actual RBC under PBA takes into account the standard scenario (ignored here) for both the reserve and C-3 PII TAR calculations.
Standard Scenario Results (in millions Standard Scenario Results (in millions (4)(4)))
96.13 (3)46.8514.47 34.89Results IF calculation performed in Aggregate
97.49 47.61 14.60 35.28 AG 43 Rsv (1) = MAX(CSV, BAR +MAX(PV Neg ANR (2)))
1.36 0.76 0.13 0.39 Effect of “Seriatim” AG 43 Std Scen Requirement
95.99 46.81 14.47 34.71 Basic Adjusted Reserve (BAR)
96.13 46.85 14.39 34.89 Cash Surrender Value (CSV)100.00 50.00 15.00 35.00 Account Value
TotalVA THREEVA TWOVA ONE
1: The AG 43 Reserve is determined seriatim.
2: “PV Neg ANR” is Present Value of Negative Accumulated Net Revenue
3: The “Total” In this “aggregate test” is not the sum of parts but the reserve calculation performed in aggregate.
4. The standard scenario was run for the same 50 years as the stochastic model.
Reported Results (in millions)Reported Results (in millions)
1: The “Total” for the stochastic results is not the sum of parts but the reserve calculation performed in aggregate.
97.49Reported: Std. Scen. + Max(0, Stoch. - Std. Scen.)
0.000.500.000.00Excess of Stochastic Result over Std. Scen. Result
97.25 Pre-AG43 Reserve
97.4948.1114.6035.28MAX(Stochastic Result, Std. Scen. Result)
97.4947.61 14.6035.28Standard Scenario Result97.18 (1)48.1114.6034.93Stochastic Model Result
TotalVA THREEVA TWOVA ONE
AG 43 Section IV.A) Definition of General Reserve Methodology:“The Aggregate Reserve for contracts falling within the scope of the Guideline shall equal the Conditional Tail Expectation Amount but not less than the Standard Scenario Amount, where the Aggregate Reserve is calculated as the Standard Scenario Amount plus the excess, if any, of the Conditional Tail Expectation Amount over the Standard Scenario Amount.”
VA THREE and Scenario #425VA THREE and Scenario #425
Scenario #425 is the 99th percentile result.
AG 43 Auditing Stochastic Projections
425
983
51
165
645
663
146
476
217
350
Scen. #
55.2 #10
55.2 #9
55.4 #8
55.5 #7
55.8 #6
56.0 #5
56.8 #4
56.8 #3
58.3#2
58.7 #1
Scenario Reserve(millions)
ReserveRANK
VA THREE ResultsWorst Ten Scenarios
VA THREE: Scenario #425 Projected VA THREE: Scenario #425 Projected Excess Benefits PaidExcess Benefits Paid
AG 43 Auditing Stochastic Projections
Projected Excess Benefits Paid
Projection Period
0.0
0.0
0.0
0.0
0.0
0.4
0.6
1.2
1.4
1.2
0.8
GMdB Excess Benefits
yrs 46-50
yrs 41-45
yrs 36-40
yrs 32-35
yr 31
yrs 26-30
yrs 21-25
yrs 16-20
yrs 11-15
yrs 6-10
yrs 1-5
0.00.0
0.00.0
0.00.0
0.00.0
0.10.0
0.30.1
0.70.2
2.82.4
1.68.0
0.01.7
0.00.0
GMwB Excess Benefits
GMiB Excess Benefits
How are “excess benefits”calculated?
Why is GMiB cost the biggest of the three types?
Does the projection have dynamic living benefits elections or dynamic surrenders?
Scenario Reserve Calculation: VA THREE, Scenario #425
Projection Year-End
Accumulated Deficiency (A)
= (B) – (C)
Projected Working
Reserve (B)
Projected Assets Value
(C)
Projected Discount
Factor (D)= �(1+R*
t)-1, from 1 thru t
Present Value Accumulated Deficiency =
(A) * (D)
0 (256,182) 46,850,341 47,106,523 1.0000 (256,182)
1 (1,180,177) 37,889,279 39,069,456 0.9799 (1,156,469)
2 (1,148,821) 39,474,448 40,623,269 0.9578 (1,100,363)
3 (1,038,139) 33,075,436 34,113,575 0.9341 (969,769)
4 (870,522) 31,165,049 32,035,570 0.9103 (792,448)
5 (719,835) 30,761,917 31,481,752 0.8802 (633,577)
10 78,994 18,558,583 18,479,590 0.7892 62,339
15 6,366,307 8,417,616 2,051,309 0.7109 4,525,785
20 12,328,524 8,936,683 (3,391,840) 0.6068 7,481,512
25 16,088,406 6,295,856 (9,792,550) 0.4905 7,890,604
30 20,342,159 2,947,944 (17,394,215) 0.3951 8,037,808
31 21,390,499 2,997,081 (18,393,418) 0.3786 8,097,635
35 25,263,039 1,646,176 (23,616,862) 0.3147 7,949,389
40 29,409,920 781,076 (28,628,844) 0.2713 7,979,227
45 35,512,857 218,107 (35,294,750) 0.2246 7,977,649
50 44,096,391 31,051 (44,065,341) 0.1831 8,074,953
Starting Assets: 47,106,523 GPVAD: 8,097,635Scenario Reserve: 55,204,158 = +
“R” is discount rate = the rate at which positive cash flows are reinvested
Stochastic Scenario Stochastic Scenario Requirements and Requirements and
AlternativesAlternatives
AG 43 Scenario RequirementsAG 43 Scenario Requirements
Overview: AG 43 document Appendix 5.
Overview: The AAA pre-packaged scenarios and SLV equity statistics and fit to calibration table.
RSLN2 Empirical Test: Alternative real-world scenario sets.
In this section, we will cover:
AG 43 Appendix 5AG 43 Appendix 5
� The Appendix focuses on the S&P 500 as a proxy for returns on a broadly diversified U.S. equity fund.
� It is encouraged to establish some sort of correlation of scenario returns between different funds and to consider historic data that suggests correlation is not stationary.
� Funds with higher expected returns should have higher expected volatilities so one might establish ‘consistent’ parameters that assume a nearly constant market price of risk:
� The equity scenarios must be available in an electronic format.
σσ
� � � �−� �= = � �� �� �� �� �
XE[ ]-r [ ] rRMarket Price of Risk Y
YX
E R
AG 43 AG 43 AppendixAppendix 5 [cont.]5 [cont.]
� Gross returns for use in modeling separate accounts diversified U.S. equities must satisfy the “calibration criteria” but “need not strictly satisfy all calibration points”.
� Actuary should explain significant differences from the calibration points and should be satisfied reserves are not materially understated while being mindful of the tail that most affects the business.
� The actuary shall document annualized mean and standard deviation of the scenario “wealth factors”; gross accumulated values with complete reinvestment of income and maturities, starting with a unit investment.
AG 43 Calibration CriteriaAG 43 Calibration Criteria
S&P 500 Gross Wealth Ratios at Calibration Points
Calibration Point 1 Yr 5 Yr 10 Yr 20 Yr
2.5% 0.78 0.72 0.79
5.0% 0.84 0.81 0.94 1.51
10.0% 0.90 0.94 1.16 2.10
90.0% 1.28 2.17 3.63 9.02
95.0% 1.35 2.45 4.36 11.70
97.5% 1.42 2.72 5.12
Scenario Gross Returns for quantiles < 50% may not exceed table value
…
and those for quantiles > 50% may not be less than table value.
AAA PreAAA Pre--Packaged ScenariosPackaged Scenarios
� 19 “csv” files, each with 10,000 scenarios, 360 months data.
� 10 treasury yields generated using the C-3 PI generator.
� 4 equity funds with returns generated with a Stochastic Log Volatility model (“SLV”): AGGR, INTL, SMALL, US
� 3 bond funds with returns modeled as a function of interest rates: MONEY, U.S. ITGVT, U.S. LTCORP
� 2 mixed funds: BALANCED, FIXED
� The generators were parameterized by fitting the models to 40-50 years of historical data.
� To aid in updating the pre-packaged scenarios, the AAA provides correlated random number files .
� Advantages to AAA scenarios is they are well documented and free to use, they use familiar C-3 Phase I model interest rates, SLV equity model is robust and fits calibration criteria well.
� Disadvantages include using scenarios “as is”, only 30 years in length, require manual updating to new yield curve, the SLV equity generator is complex and unavailable for user modification and parameterization.
AAA SLV Equity Returns AAA SLV Equity Returns Statistics*Statistics*
*2.4million data points: 240 months across 10,000 scenarios.
Monthly Return Correlations
US / AGGR US / INTL US / SMALL
AGGR / INTL
AGGR / SMALL
INTL / SMALL
58% 56% 77% 49% 57% 45%
Monthly Return Average
AGGR INTL SMALL US
0.91% 0.74% 0.81% 0.70%
Monthly Return Std. Devn.
AGGR INTL SMALL US
7.1% 4.9% 5.8% 4.3%
AAA US Fund Calibration AAA US Fund Calibration ResultsResults
AAA US Fund Gross Wealth Ratiosat Calibration Points
Calibration Point 1 Yr 5 Yr 10 Yr 20 Yr
2.5% 0.76 0.722 0.77
5.0% 0.82 0.81 0.92 1.41
10.0% 0.89 0.93 1.12 1.83
90.0% 1.30 2.22 3.81 10.15
95.0% 1.37 2.48 4.44 12.92
97.5% 1.44 2.72 5.17
Difference
Calibration Point 1 Yr 5 Yr 10 Yr 20 Yr
2.5% (0.02) 0.002 (0.02)
5.0% (0.02) (0.00) (0.02) (0.10)
10.0% (0.01) (0.01) (0.04) (0.27)
90.0% 0.02 0.05 0.18 1.13
95.0% 0.02 0.03 0.08 1.22
97.5% 0.02 0.00 0.05
Pass or Fail
Calibration Point 1 Yr 5 Yr 10 Yr 20 Yr
2.5% PASS FAIL PASS
5.0% PASS PASS PASS PASS
10.0% PASS PASS PASS PASS
90.0% PASS PASS PASS PASS
95.0% PASS PASS PASS PASS
97.5% PASS PASS PASS
Calibration Criteria
Calibration Point 1 Yr 5 Yr 10 Yr 20 Yr
2.5% 0.78 0.72 0.79
5.0% 0.84 0.81 0.94 1.51
10.0% 0.90 0.94 1.16 2.10
90.0% 1.28 2.17 3.63 9.02
95.0% 1.35 2.45 4.36 11.70
97.5% 1.42 2.72 5.12
RSLN2 Scenarios Generation RSLN2 Scenarios Generation TestTest
� Advantages to RSLN2: only 6 parameters, intuitive model and can be parameterized logically using historical data or through a demonstrated MLE process.
� Disadvantage to RSLN2: may be difficult to fit both left / right calibration criteria as tightly as AAA scenarios.
� “RSLN2” : Regime Switching Log-Normal with two regimes (high volatility low frequency regime, low volatility high frequency regime).
� 6 parameters for each fund: mean / std. devn for both regimes, probability for switching between regimes.
Fund
Mean Regime 1
Std. Devn. Regime 1
Mean Regime 2
Std. Devn. Regime 2
Transition Probability
1 to 2*
Transition Probability
2 to 1*
AGGR 13.63% 19.08% -15.52% 34.03% 3.92% 19.37%
INTL 12.91% 13.70% -16.24% 24.43% 3.92% 19.37%
SMALL 13.30% 15.43% -15.86% 27.52% 3.92% 19.37%
US 12.91% 11.82% -16.24% 21.08% 3.92% 19.37%
Transitions are performed independently for each fund. It would be interesting to test large, positive correlation in transitions between funds under the theory shifts in various markets effect one another.
Correlations
AGGR INTL SMALL US
AGGR 1.000 0.521 0.610 0.64
INTL 0.521 1.000 0.480 0.613
SMALL 0.61 0.48 1.000 0.842
US 0.64 0.613 0.842 1.000
RSLN2 Test: Model Input RSLN2 Test: Model Input ParametersParameters
*2.4million data points: 240 months across 10,000 scenarios.
Monthly Return Correlations
US / AGGR US / INTL US / SMALL
AGGR / INTL
AGGR / SMALL
INTL / SMALL
58% 56% 77% 48% 56% 44%
Monthly Return Average
AGGR INTL SMALL US
0.92% 0.76% 0.82% 0.73%
Monthly Return Std. Devn.
AGGR INTL SMALL US
6.6% 4.8% 5.3% 4.1%
RSLN2 Equity Returns RSLN2 Equity Returns Statistics*Statistics*
RSLN2 US Fund Calibration RSLN2 US Fund Calibration ResultsResults
RSLN2 US Fund Gross Wealth Ratios at Calibration Points
Calibration Point 1 Yr 5 Yr 10 Yr 20 Yr
2.5% 0.68 0.63 0.70
5.0% 0.73 0.72 0.83 1.28
10.0% 0.79 0.85 1.04 1.75
90.0% 1.27 2.20 3.99 11.77
95.0% 1.34 2.46 4.80 15.22
97.5% 1.40 2.74 5.51
Difference
Calibration Point 1 Yr 5 Yr 10 Yr 20 Yr
2.5% (0.10) (0.09) (0.09)
5.0% (0.11) (0.09) (0.11) (0.23)
10.0% (0.11) (0.09) (0.12) (0.35)
90.0% (0.01) 0.03 0.36 2.75
95.0% (0.01) 0.01 0.44 3.52
97.5% (0.02) 0.02 0.39
Pass or Fail
Calibration Point 1 Yr 5 Yr 10 Yr 20 Yr
2.5% PASS PASS PASS
5.0% PASS PASS PASS PASS
10.0% PASS PASS PASS PASS
90.0% FAIL PASS PASS PASS
95.0% FAIL PASS PASS PASS
97.5% FAIL PASS PASS
Calibration Criteria
Calibration Point 1 Yr 5 Yr 10 Yr 20 Yr
2.5% 0.78 0.72 0.79
5.0% 0.84 .81 0.94 1.51
10.0% 0.90 0.94 1.16 2.10
90.0% 1.28 2.17 3.63 9.02
95.0% 1.35 2.45 4.36 11.70
97.5% 1.42 2.72 5.12
Empirical Test Results Empirical Test Results (RSLN2 v AAA SLV)(RSLN2 v AAA SLV)
AG 43 Stochastic ALM Projection for Net Reserve
(408,019)
387,351
321,580
139,045
-
-
104,866
-
31,460
Difference
(RSLN2 – AAA)
0.22%47,967,154 47,862,289 (CTE70)
0.67%60,621,353 61,029,372 100th percentile
0.00%46,850,341 46,850,341 70th percentile
0.00%46,850,341 46,850,341 80th percentile
0.29%47,454,165 47,315,120 90th percentile
0.65%49,461,040 49,139,460 95th percentile
0.73%53,405,201 53,017,850 99th percentile
0.00%46,850,341 46,850,341 Median Scenario Result
0.07%47,185,385 47,153,926 Mean Scenario Result
% ABS DifferenceRSLN2 Equity
Scenarios
AAA Pre-Packaged
Equity Scenarios
VA THREE Product
(10,000 scenarios)
Testing RSLN2 equity scenarios to calculate CTE(70)
AG 43 Stochastic ALM Projection for Net Reserve
Empirical Results: Scenario SubEmpirical Results: Scenario Sub--SetsSets
AAA Pre-Packaged Scenarios
Scenario
Sub – Set
CTE(70)
Result
Difference
from Full Set
% ABS
Difference
1 - 1000 48,093,767 231,478 0.48%
1001 – 2000 47,885,975 23,686 0.05%
2001 – 3000 47,700,962 (161,327) 0.34%
3001 – 4000 47,993,127 130,838 0.27%
4001 – 5000 48,047,658 185,370 0.39%
5001 – 6000 47,784,274 (78,015) 0.16%
6001 – 7000 47,761,380 (100,909) 0.21%
7001 – 8000 47,800,821 (61,467) 0.13%
81001 – 9000 47,617,490 (244,798) 0.51%
9001 - 10000 47,937,433 75,144 0.16%
Full 10,000 47,862,289
Testing successive sets of 1,000 scenarios for the VA THREE product.
RSLN2 Equity Scenarios
Scenario
Sub - Set
CTE(70)
Result
Difference
from Full Set
% ABS
Difference
1 - 1000 47,917,518 (49,636) 0.10%
1001 – 2000 47,954,231 (12,924) 0.03%
2001 – 3000 47,982,804 15,650 0.03%
3001 – 4000 47,856,939 (110,215) 0.23%
4001 – 5000 48,230,600 263,446 0.55%
5001 – 6000 48,276,763 309,608 0.65%
6001 – 7000 47,783,689 (183,466) 0.38%
7001 – 8000 47,870,013 (97,141) 0.20%
81001 – 9000 47,999,405 32,251 0.07%
9001 - 10000 47,799,582 (167,573) 0.35%
Full 10,000 47,967,154