Actuarial Guideline 43 · PDF fileActuarial Guideline 43 Kansas City Actuaries Club - June 24,...

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Actuarial Guideline 43 Actuarial Guideline 43 Kansas City Actuaries Club Kansas City Actuaries Club - June 24, 2009 June 24, 2009 John Froehle, FSA, MAAA Consulting Actuary, Actuarial Resources Corporation AG 43: Implementation Issues AG 43: Implementation Issues and Preliminary Results and 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

Transcript of Actuarial Guideline 43 · PDF fileActuarial Guideline 43 Kansas City Actuaries Club - June 24,...

Page 1: Actuarial Guideline 43 · PDF fileActuarial Guideline 43 Kansas City Actuaries Club - June 24, 2009 John Froehle, FSA, MAAA Consulting Actuary, Actuarial Resources Corporation AG 43

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

Page 2: Actuarial Guideline 43 · PDF fileActuarial Guideline 43 Kansas City Actuaries Club - June 24, 2009 John Froehle, FSA, MAAA Consulting Actuary, Actuarial Resources Corporation AG 43

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

Page 3: Actuarial Guideline 43 · PDF fileActuarial Guideline 43 Kansas City Actuaries Club - June 24, 2009 John Froehle, FSA, MAAA Consulting Actuary, Actuarial Resources Corporation AG 43

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

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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

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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

Page 6: Actuarial Guideline 43 · PDF fileActuarial Guideline 43 Kansas City Actuaries Club - June 24, 2009 John Froehle, FSA, MAAA Consulting Actuary, Actuarial Resources Corporation AG 43

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

Page 7: Actuarial Guideline 43 · PDF fileActuarial Guideline 43 Kansas City Actuaries Club - June 24, 2009 John Froehle, FSA, MAAA Consulting Actuary, Actuarial Resources Corporation AG 43

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

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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

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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

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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

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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)

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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

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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

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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

Page 15: Actuarial Guideline 43 · PDF fileActuarial Guideline 43 Kansas City Actuaries Club - June 24, 2009 John Froehle, FSA, MAAA Consulting Actuary, Actuarial Resources Corporation AG 43

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:

Page 16: Actuarial Guideline 43 · PDF fileActuarial Guideline 43 Kansas City Actuaries Club - June 24, 2009 John Froehle, FSA, MAAA Consulting Actuary, Actuarial Resources Corporation AG 43

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

Page 17: Actuarial Guideline 43 · PDF fileActuarial Guideline 43 Kansas City Actuaries Club - June 24, 2009 John Froehle, FSA, MAAA Consulting Actuary, Actuarial Resources Corporation AG 43

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

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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.

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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.

Page 20: Actuarial Guideline 43 · PDF fileActuarial Guideline 43 Kansas City Actuaries Club - June 24, 2009 John Froehle, FSA, MAAA Consulting Actuary, Actuarial Resources Corporation AG 43

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.”

Page 21: Actuarial Guideline 43 · PDF fileActuarial Guideline 43 Kansas City Actuaries Club - June 24, 2009 John Froehle, FSA, MAAA Consulting Actuary, Actuarial Resources Corporation AG 43

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?

Page 22: Actuarial Guideline 43 · PDF fileActuarial Guideline 43 Kansas City Actuaries Club - June 24, 2009 John Froehle, FSA, MAAA Consulting Actuary, Actuarial Resources Corporation AG 43

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

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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

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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.

Page 25: Actuarial Guideline 43 · PDF fileActuarial Guideline 43 Kansas City Actuaries Club - June 24, 2009 John Froehle, FSA, MAAA Consulting Actuary, Actuarial Resources Corporation AG 43

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%

Page 26: Actuarial Guideline 43 · PDF fileActuarial Guideline 43 Kansas City Actuaries Club - June 24, 2009 John Froehle, FSA, MAAA Consulting Actuary, Actuarial Resources Corporation AG 43

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.

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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*

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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)

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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