new developments in mortality risk pooling · pooling, so that the risk aversion adjustments only...

Session 132 L - New Developments in Mortality Risk Pooling

Moderator:

Deborah A. Tully, FSA, EA, FCA, MAAA

Presenter: Rowland Davis, FSA

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SOA Annual Meeting: October 17, 2017

Session 132: New Developments in Mortality Risk Pooling

Presenter: Rowland Davis, FSA

Moderator: Deborah Tully, FSA

Overview

Three key questions- What is the value of mortality risk pooling?- Why do retirees usually choose non-pooled options?- What are the best ways to build product packages that include pooling?

Agenda- Traditional economic analysis- Insights from behavioral economics- Analysis of real-world options- Proposal for a collective risk-sharing payout plan

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Traditional Economic Analysis

Based on life-cycle utility framework- Posits a rational desire to smooth consumption across entire lifetime- Optimization problem for measured utility, with key parameter = individual’s “rate

of time preference” (we will call this parameter the “gamma” factor) Numerous academic studies/papers

- Starts with seminal paper by Yarri (1965) showing significant value to using annuities (if “fairly priced”), leading to “annuity puzzle”

- Concept that developed is the “Annuity Equivalent Wealth” metric: the additional amount of wealth that a rational consumer would require/demand to be as well-off (in measured utility) without access to fairly priced annuities (see Brown, Mitchell, Poterba, Warshawsky papers and book)

- Attempts by academics to work in other factors: need for liquidity to deal with health care spending; bequest motives; Social Security and pension income

Recent SOA project: Value of mortality risk pooling (“VoMoP”)- Georgia State professor Dani Bauer: refined the sensitivity of results to the need

for liquidity for unexpected health care expenses- Excel worksheet to calculate VoMoP / AEW (based on algorithm from “Annuity

Equivalent Wealth is the Value of Longevity Pooling: Some Analytic Approximations” by Huaxiong Huang and Moshe A. Milevsky, Working Paper, Schulich School of Business, York University, Fall 2017)

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Excel Workbook

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These calculations reflect the value of mortality pooling for retirement at age 65, based on the assumptions listed below, and using standard life-cycle methodologywith a Constant Relative Risk Aversion function. The calculations include the ability to recognize that Social Security benefits automatically provide mortality pooling, so that the risk aversion adjustments only apply to the non-SS benefits. The resulting value of mortality pooling results are therefore lower, representing the marginal utility for the pooling of non-SS benefits. For this purpose, the calculations assume that the non-SS benefits will be in the amount required to achieve a total specified final pay replacement ratio, inclusive of the specified level of SS replacement ratio.

The "value of mortality pooling" should be interpreted as the utility value gained by pooling the mortality risk for non-SS benefits through an actuarially fair annuity without any loading for expenses, profits, etc. For example, if $100,000 is the required amount to annuitize the non-SS benefits, and the "value of mortality pooling" result is +15.0%, this means that the annuity is equivalent in utility value to a lump sum amount of $115,000 -- based on all the assumptions used.

Basis for calculations

Results

Without recognition of Social Security (or other pension income)

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Assumptions

Inflation 2.00%Ben COLA 2.00%Real risk-free interest 2.00%Risk aversion (gamma) 1.00 SS repl ratio 0%

Target repl ratio 80%

Value of Mortality Pooling (retirement at 65)

Single Male

Single Female

Single Unisex

Married Couple

36.5% 32.6% 34.6% 29.4%

Results, contd.

With recognition of Social Security- Calculation methodology still under development for Excel workbook- For estimated impact, we use results from “New Evidence on the Money’s Worth

of Individual Annuities” by Olivia Mitchell, James Poterba, Mark Warshawsky and Jeffrey Brown; American Economic Review (1999) which showed that if half of the retirement wealth is “pre-annuitized” (e.g. Social Security) then the VoMoP is reduced by a factor of about x0.7

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Assumptions

Inflation 2.00%Ben COLA 2.00%Real risk-free interest 2.00%Risk aversion (gamma) 1.00 SS repl ratio 40%



Single Male

Single Female

Single Unisex

Married Couple

25.5% 22.8% 24.2% 20.6%

Sensitivity to “Gamma”

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Gamma = 0.5

Gamma = 1.0

Gamma = 2.0

Assumptions

Inflation 2.00%Ben COLA 2.00%Real risk-free interest 2.00%Risk aversion (gamma) XSS repl ratio 40%



Single Male

Single Female

Single Unisex

Married Couple

18.9% 17.0% 18.0% 15.3%


Single Male

Single Female

Single Unisex

Married Couple

25.5% 22.8% 24.2% 20.6%


Single Male

Single Female

Single Unisex

Married Couple

33.4% 29.6% 31.6% 26.9%

Insights from Behavioral Economics

“Rational economic agents” ≠ real human beings Overview of behavioral issues: “Annuitization Puzzles”; by Shlomo Benartzi,

Alessandro Previtero and Richard Thaler; Journal of Economic Perspectives (2011) Actual decisions heavily influenced by embedded psychological factors:

- Mental accounting- Prospect theory

• Reference point• Value function with loss aversion• Decision weights different from true probabilities

- Availability heuristic- Hyperbolic discounting- Framing effects: investment vs consumption

• Investment frame – potential loss of principal• Consumption frame – insurance against out-living assets

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“Behavioral Obstacles in the Annuity Market”; by Wei-Yin Hu and Jason S. Scott;Financial Analyst Journal (2007)

“Why Don’t People Insure Late Life Consumption: A Framing Explanation of the Under-annuitization Puzzle”; by Jeffrey Brown, et al;NBER Working Paper (2008)

Framing Experiments

Practical work to potentially improve up-take of pooling products Ongoing series of on-line surveys, and papers reporting results, by Jeffrey Brown

(Univ. of Illinois) and collaborators- Participants (over age 50) provided some background information- Then presented with a series of choices made by two fictitious people- Must answer who they think made the better choice

Let’s give it a try….- Read over the page of background information you have- Then enter the version number shown at the top of the page- Then on each of the following slides, enter the person who you think made the

better choice

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Question #1

Mr. Green / consul bondor

Mr. White / savings account

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Question #2

Mr. Red / life annuityor

Mr. White / savings account

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Question #3

Mr. Orange / 20-yr. period annuityor

Mr. Blue / 35-yr. period annuity

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Question #4

Mr. Blue / 35-yr. period annuityor

Mr. Red / life annuity

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Question #5

Mr. Red / life annuityor

Mr. Orange / 20-yr. period annuity

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Results

The background papers present different “frames”- Version 1 is an investment frame- Version 2 is a consumption frame

In the survey done for the paper, the life annuity was considered the better choice as follows:

In our survey, here are the results (% where Mr. Red / life annuity was selected as better choice):

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Investment Frame

Consumption Frame

Savings account 21% 68%

20-yr. period annuity 48% 79%

35-yr period annuity 40% 73%

Consul bond 27% 70%

Investment Frame (V1)

Consumption Frame (V2)

Savings account (Q #2)

20-yr. period annuity (Q #5)

35-yr period annuity (Q #4)

Analysis of Real World Options

SOA research project: Quantitative Evaluation Framework (QE Framework)- Nearing completion- Based on stochastic modelling of various risk and reward metrics- Goal is to provide a consistent basis for comparing the outcomes of various

retirement systems- Two separate, but connected, models

• For the accumulation phase• For the payout phase

Trying to expand beyond the academic “utility models” to cover a much broader range of metrics

- Benefit risks and reward / success measures- Cost risks to sponsor

Provide guidance for researchers and practitioners in the development of newer and better system designs

- Variable and target benefit designs- Guarantees (“hard” or “soft”)- Collective risk sharing designs (investment and/or mortality risks)- New insured products (e.g. longevity annuities)- Efficient risk control features

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QE Framework: Overview of Payout Model

Goal: Create metrics that allow for comparative analysis of payout schemes for retirement accumulations

Measurement of:- Efficiency in creating lifetime income streams

• Mean, or average, levels of income• Range of dispersion / uncertainty around mean• Shortfall and “failure” risks• Year-to-year volatility risks• Sensitivity to initial conditions at time of retirement

- Balance between income benefits and death benefits- Potential cost risks to sponsors

Approach used:- Stochastic simulations, as extensions of the accumulation phase model (i.e. simulation

results for first year of retirement at age 67 are the next year’s values from the age 66 results in the accumulation model)

- Create a baseline set of results- For any payout scheme, calculate the ratio of results in each year to the baseline- Parameterized model to handle combinations of:

• Insured annuities, priced at market rates• Fixed-price annuities• Longevity annuities• Various “Structured Withdrawal Plans” (SWP’s)

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Methodology

Initial conditions- Continuity from the accumulation phase model- Yield rates at age 67 point of retirement (nominal 10-yr. Treasury, 10-yr. TIPS,

expected inflation)- Accumulation balance at retirement

• Default is for DC plan using typical TDF investment structure (10% of pay each year)

• Option to use other balance amounts (DC with different investment structure, or DB)

- Final pay at retirement, based on accumulation model Baseline set of results = “ideal” basis from participant viewpoint to minimize risk /

maximize income- Fixed price annuity (selected 5.45% interest rate, based on expected return from

a fund with 30% risk asset allocation)- Full CPI indexing (priced at average inflation expectation = 2.5%)- No death benefits

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Parameters: General

Asset allocation for non-insured balance (other ages will be interpolated) Percentage allocation to:Risk assets TIPS Bonds

Age 67 60% 0% 40%Age 70 55% 0% 45%Age 75 50% 0% 50%Age 80 45% 0% 55%Age 85+ 40% 0% 60%

Assumed investment expense rate 0.10%

Allocation of distribution (by percent of initial balance)Approx. ben. as %

of final payImmediate annuity -- insurance company 0.0% 0% this provides lifetime income from age 67, priced at market interest ratesImmediate annuity -- fixed rate in-plan 0.0% this provides lifetime income from age 67, but with a fixed price and cost risk for sponsorLongevity insurance 12.0% 17% this provides income from age 85, with COLA; no death benefits (prior to or after age 85)Balance to "Structured Withdrawal Plan" (SWP) 88.0% variable see below for parameters

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Parameters: Annuities

Immediate annuity -- Insurance company

Include 15-yr certain period death benefits? 1 0 = no, 1 = yes; protects against loss of annuity premium (approx.) due to "early" deathCOLA 2.5% enter fixed rate from 0% to 3%, in 0.5% increment, or enter 99% for CPI-based COLALoad for expenses/profits/contingencies 5% generally use 5% for a group annuity or 15% for a retail annuity

Immediate annuity -- Fixed rate in-plan pricing is at a fixed interest rate, producing cost risk for sponsor (e.g. typical DB plan)

Include 15-yr certain period death benefits? 1 0 = no, 1 = yes; protects against loss of annuity premium (approx.) due to "early" deathCOLA 99.0% enter fixed rate from 0% to 3%, in 0.5% increment, or enter 99% for CPI-based COLAAllocation to risk assets for in-plan funding 30% enter 30%, 50% or 70%; pricing will use expected return for this allocation

Longevity insurance -- Insurance company

COLA (applied from age 85) 2.5% enter fixed rate from 0% to 3%, in 0.5% increment, or enter 99% for CPI-based COLALoad for expenses/profits/contingencies 5% generally use 5% for a group annuity or 15% for a retail annuity

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Parameters: SWP’s

Base spend rate definition for SWP, where spend rate at each age = 1 / PV( real return discount, time period,-1,,1)Confidence

factorPV factor time period for each age IRS RMD

Life expectancy? Or fixed period? 0 0 = life expectancy; 1 = fixed periodRP2014 single life 50%

If life expectancy, choose basis 7 see options in table to right 70%If fixed period, define initial period at age 67 40 period for each age will = N - (age - 67) 90%If fixed period, define min # yrs to use 5 fixed period will decline by 1 each yr until it hits this level

RP2014 joint life 50%

PV factor real return for discount rate 70%Fixed value? Or mkt-based? 0 0 = fixed value; 1 = market-based 90%If fixed value, define expected real return on bonds 0.00% likely range = 0.00% to 2.50%Assumed return premium to recognize for risk assets 0.00% enter the full premium for risk assets, and the portion of this used will be based on asset allocation;

use zero for conservative basis which will ignore risk premium for this purposeOver-ride to base SWP spend rate, using "X% Rule" (i.e. initial spend amt = X% time initial balance, with inflation adjustment for future payments)

Over-ride applies to first N years 18 enter 99 to use the X% rule for all yearsInitial spend rate 6.50%Inflation to use

Fixed value? Or CPI? 1 0 = fixed value; 1 = CPIIf fixed value, define inflator rate 2.50%

Maximum spend rate as % of remaining funds 8.00%

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Results -- Overview

Retirement period “sliced” into three segments for analysis

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Age groupings used in analysis:

67 72 77 82 87 92 97 102 107 112 117

Expected deaths by age from a group of 67-yr. old retirees

First 15 years: ages 67 to 8126% of deaths in this age band

Next 10 years: ages 82 to 9135% of deaths in this age band

All remaining years: ages 92 and up39% of deaths in this age band

Sample Results: Group AnnuityImmediate annuity -- Insurance company

Include 15-yr certain period death benefits? 1 0 = no, 1 = yes; protects against loss of annuity premium (approx.) due to "early" deathCOLA 2.5% enter fixed rate from 0% to 3%, in 0.5% increment, or enter 99% for CPI-based COLALoad for expenses/profits/contingencies 5% generally use 5% for a group annuity or 15% for a retail annuity

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Range of income benefits as percent of baseline*:*"Baseline" benefits are based on conversion of age 67 balance to lifetime income using a fixed-price lifetime annuity, interest rate = 6.1%, no load, full CPI COLA, no death benefits. Age sub-group values are weighted averages, using deaths at each age as the weighting factor.

0%

20%

40%

60%

80%

100%

120%

140%

160%

180%

200%

0%

20%

40%

60%

80%

100%

120%

140%

160%

180%

200%

67 72 77 82 87 92 97 102 107 112 117

Income Benefits as % of Baseline(Mean value, and inter-quartile range)

Sample Results: Group Annuity, contd.

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First 15 years: ages 67 to 81 Next 10 years: ages 82 to 91 All remaining years: ages 92 and up

%tile %tile %tile95% 100.4% 95% 104.6% 95% 105.9%90% 95.7% 90% 98.9% 90% 99.9%75% 90.0% 75% 91.5% 75% 92.0%50% 83.2% 50% 83.4% 50% 83.2%25% 77.3% 25% 76.1% 25% 75.3%10% 72.6% 10% 69.7% 10% 68.1%5% 69.6% 5% 66.1% 5% 63.2%

Mean 84.1% Mean 84.1% Mean 84.0%

84.1%

30%

40%

50%

60%

70%

80%

90%

100%

110%

120%

130%

140%

150%

160%

170%

84.1%

30%

40%

50%

60%

70%

80%

90%

100%

110%

120%

130%

140%

150%

160%

170%

84.0%

30%

40%

50%

60%

70%

80%

90%

100%

110%

120%

130%

140%

150%

160%

170%

Alternate benchmarks

100% = Full baseline, no death benefit

93% = Baseline, but with death benefit

84% = Group annuitypricing, with death benefit & fixed 2.5% COLA

77% = Retail annuitypricing, with death benefit & fixed 2.5% COLA


Sensitivity to initial age 67 conditions:

Initial interest rate at age 67: Mean Mean Mean High (avg. highest quintile) 97.0% 97.3% 97.7% Medium ( avg. 20th to 80th percentile) 83.3% 83.2% 83.1% Low (avg. lowest quintile) 73.5% 73.5% 73.0%

Expected inflation at age 67: Mean Mean Mean High (avg. highest quintile) 93.4% 93.3% 93.5% Medium ( avg. 20th to 80th percentile) 83.0% 83.2% 83.2% Low (avg. lowest quintile) 77.8% 77.6% 76.9%

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Shortfall risk / "failure rate" = probability of ratio to baseline value falling below:

First 15 yrs. Next 10 yrs. Age 90 Age 95 Age 100 Age 105 Age 110(Ages 67 to 81) (Ages 82 to 91)

60% of baseline 0.6% 2.0% 47.0% 26.5% 10.4% 2.3% 0.3%50% of baseline 0.0% 0.0%40% of baseline 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%30% of baseline 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%

Volatility risk = probability that ratio to baseline value (3-yr. average) drops by more than:

First 15 yrs. Next 10 yrs. Next 10 yrs.(67 to 81) (82 to 91) (92 to 101)

Decline by 10+ percent 2.4% 2.5% 2.9%Decline by 15+ percent 0.2% 0.3% 0.6%Decline by 20+ percent 0.0% 0.0% 0.0%Decline by 25+ percent 0.0% 0.0% 0.0%

-------------- Shortfall risk (using 3-yr. avg.) ----------------- -------------- Failure rate at: -----------------

----------- Survival probability -----------

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Death benefits paid as percent of total payments

First 15 yrs. Next 10 yrs. All remaining yrs.(67 to 81) (82 to 91) (92 and up)

%tile95% 10.7% 0.0% 0.0%75% 10.7% 0.0% 0.0%50% 10.7% 0.0% 0.0%25% 10.7% 0.0% 0.0%5% 10.7% 0.0% 0.0%

Mean 10.7% 0.0% 0.0%

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Sample Results: 4% Rule


0%

20%

40%

60%

80%

100%

120%

140%

160%

180%

200%

0%

20%

40%

60%

80%

100%

120%

140%

160%

180%

200%

67 72 77 82 87 92 97 102 107 112 117


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Sample Results: 4% Rule, contd.

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Level of accessible wealth as percent of final pay (inflation adjusted)(Note that the age 67 value is before the purchase of any annuities.)

0%

100%

200%

300%

400%

500%

600%

700%

800%

900%

1000%

0%

100%

200%

300%

400%

500%

600%

700%

800%

900%

1000%

67 72 77 82 87 92 97 102 107 112 117

Accessible Wealth as % of Final Pay (infl. adjusted)(Mean value, and inter-quartile range)

Sample Results: 4% Rule, contd.

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%tile95% 42.7% 75.1% 92.0%75% 36.8% 65.7% 84.6%50% 33.0% 58.7% 76.5%25% 28.9% 48.3% 60.0%5% 23.7% 30.3% 28.3%

Mean 33.0% 56.3% 79.9%

Sample Results: IRS RMD Schedule

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0%

20%

40%

60%

80%

100%

120%

140%

160%

180%

200%

0%

20%

40%

60%

80%

100%

120%

140%

160%

180%

200%

67 72 77 82 87 92 97 102 107 112 117


Sample Results: IRS RMD Schedule, contd.

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0%

100%

200%

300%

400%

500%

600%

700%

800%

900%

1000%

0%

100%

200%

300%

400%

500%

600%

700%

800%

900%

1000%

67 72 77 82 87 92 97 102 107 112 117


Sample Results: IRS RMD Schedule, contd.Shortfall risk / "failure rate" = probability of ratio to baseline value falling below:





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%tile95% 27.7% 42.6% 53.5%75% 27.1% 42.2% 53.2%50% 26.7% 41.9% 53.0%25% 26.3% 41.6% 52.8%5% 25.8% 41.2% 52.5%

Mean 26.7% 41.9% 53.0%

Newer Design Ideas

Longevity annuities- For use with SWP’s to capture cost-efficient mortality risk pooling- Papers

• “Real Longevity Insurance with a Deductible: Introduction to Advanced-Life Delayed Annuities” by Moshe Milevsky, NAAJ (2005)

• “An Annuity That People Might Actually Buy” by Anthony Webb, Guan Gong, and Wei Sun, CRR Brief (2007)

• “The Longevity Annuity: An Annuity for Everyone?” by Jason Scott, FAJ (2008) Variable benefits during payout

- Insured variable annuities (retail and group products)- Embedded within “Target Benefit” DB plan- Collective self-annuitization schemes

• “Payouts from Defined Contribution Plans: A Collective Risk-sharing Framework, by Rowland Davis, SOA (2013)

• “Optimal Retirement Tontines for the 21st Century: With Reference to Mortality Derivatives in 1693, by Moshe Milevsky and Thomas Salisbury SOA (2013)

• “Variable Payout Annuities” by Phelim Boyle, Mary Hardy, Anne MacKay, David Saunders, SOA (2015)

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Sample Results: Combo with 12% of Fund Alloc. To Longevity Anny. & Balance to SWP

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0%

20%

40%

60%

80%

100%

120%

140%

160%

180%

200%

0%

20%

40%

60%

80%

100%

120%

140%

160%

180%

200%

67 72 77 82 87 92 97 102 107 112 117


Sample Results: Combo with Longevity, contd.

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0%

100%

200%

300%

400%

500%

600%

700%

800%

900%

1000%

0%

100%

200%

300%

400%

500%

600%

700%

800%

900%

1000%

67 72 77 82 87 92 97 102 107 112 117



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First 15 years: ages 67 to 81 Next 10 years: ages 82 to 91 All remaining years: ages 92 and up

%tile %tile %tile95% 83.9% 95% 143.8% 95% 150.4%90% 83.9% 90% 129.9% 90% 132.9%75% 83.9% 75% 106.4% 75% 107.4%50% 79.4% 50% 87.2% 50% 88.0%25% 70.0% 25% 73.6% 25% 73.9%10% 63.1% 10% 63.3% 10% 65.3%5% 58.6% 5% 58.9% 5% 59.2%

Mean 76.0% Mean 92.7% Mean 94.3%

76.0%

30%

40%

50%

60%

70%

80%

90%

100%

110%

120%

130%

140%

150%

160%

170%

92.7%

30%

40%

50%

60%

70%

80%

90%

100%

110%

120%

130%

140%

150%

160%

170%

94.3%

30%

40%

50%

60%

70%

80%

90%

100%

110%

120%

130%

140%

150%

160%

170%

Alternate benchmarks

100% = Full baseline, no death benefit

93% = Baseline, but with death benefit

84% = Group annuitypricing, with death benefit & fixed 2.5% COLA

77% = Retail annuitypricing, with death benefit & fixed 2.5% COLA


Shortfall risk / "failure rate" = probability of ratio to baseline value falling below:





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%tile95% 29.3% 42.1% 49.7%75% 23.7% 36.0% 44.2%50% 21.2% 33.3% 40.2%25% 19.8% 30.8% 36.3%5% 19.0% 27.0% 30.2%

Mean 22.3% 33.6% 40.1%

Collective Payout Plan: Overview

Provides efficient pooling of individual mortality risk. Benefits provided in a form of variable annuity:

- Conditional indexing, plus- Bonus payments

Risk is shared collectively across the group of covered annuitants. Uses modest equity allocation to enhance long-term returns. Offers much more stable pricing for conversion of lump sum to

annuity stream, compared with market priced annuities – removes interest rate risk at point of retirement.

Structure provides a natural way to manage aggregate longevity risk.

http://pensionsectionnews.soa.org/Vizion5/viewer.aspx?issueID=2&pageID=27

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Collective Payout Plan: Plan Specs

Lump sum at retirement is moved into a separate fund Fund maintains constant 35% equity allocation Base annuity payments determined

- Lifetime payments- Fixed 2% COLA- Interest rate for pricing is greater of 5%, or prior year average 10-year

Treasury yield + 50 basis points Bonus payments made when plan has sufficient surplus, based on fixed

graded schedule, keyed to the plan funded status- Bonus of +5% with funded ratio of 120%- Growing to bonus of +75% with funded ratio over 175%

Temporary COLA suspension if underfunded- Suspended whenever funded ratio < 100% in 2 out of the prior 3 years- Restored when funded ratio is >105%- Rules are relaxed during initial period of fund maturation

Right to reduce regular payment is reserved to Board decision in case of extreme underfunding (never occurred in model)

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Illustration

Here is one of the simulation scenarios, from a “mature” program, with results near to the median outcome (PV of cohort benefits under collective plan = 122% of PV under group annuity)

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Years retired:1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Plan funded ratio 103% 105% 100% 98% 108% 116% 116% 121% 118% 120% 123% 128% 125% 135% 119% 130% 127% 119%COLA 2% 2% 2% 0% 2% 2% 2% 2% 2% 2% 2% 2% 2% 2% 2% 2% 2% 2%Bonus percent 0% 0% 0% 0% 0% 0% 0% 5% 0% 0% 5% 5% 5% 15% 0% 5% 5% 0%

Years retired:19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

Plan funded ratio 126% 126% 127% 118% 113% 122% 104% 98% 102% 115% 118% 115% 118% 117% 119% 101% 104%COLA 2% 2% 2% 2% 2% 2% 2% 2% 2% 2% 2% 2% 2% 2% 2% 2% 2%Bonus percent 5% 5% 5% 0% 0% 5% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0%

Benefit from group annuity:

initial benefit based on market interest rate of 3.75%; fixed

2% COLA

Base benefit from collective plan:

initial benefit based on plan interest rate of 5.00%;

contingent 2% COLA

Bonus payments

Key Simulation Results for Mature Program

Bonus payments- Frequency averages about 60%- Average bonus:

• When paid, about 18% of regular payment.• Counting non-bonus years, about 11% of regular payment

COLA suspension- Frequency averages less than 5%

Funded ratio- Generally in the range of 115% to 135%- Below 100% with about 5% probability

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Simulation Results: Compare Net Present Value

This chart shows results under the collective program for selected cohorts, assuming that the first retiree cohort entering the payout program is 10 years after the Secure Choice plan is established. The metric shown is the ratio of the net PV for benefits compared to those under a standard group annuity with a fixed 2% COLA. A value greater than 100% means the collective program provides more value (i.e. 125% means 25% higher value).

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Yr 10 Yr 20 Yr 30 Yr 4099% 109% 120% 140% 143%90% 107% 115% 131% 132%75% 106% 113% 126% 126%50% 105% 110% 122% 121%25% 105% 108% 117% 116%10% 104% 106% 112% 111%1% 103% 102% 103% 102%

Average 105% 110% 122% 121%

Prob. < 100% 0.0% 0.6% 0.3% 0.5%

---- Cohort retiring in year: ---- Results when plan is “mature”

Observations

Benefits- Virtually always better, on a PV basis, when compared with a standard group

annuity- Year-to-year variability is not excessive

Generational equity- As with all collective plans, a mature plan produces better benefits than during

the initial years, due to the need to build reserve balances- However, unlike with an accumulation program, the early retiree cohorts can still

be assured of better payout results than under a standard group annuity• Lump sum cash flows into the plan carry an implicit reserve• COLA suspension rules can be more favorable for early cohorts (to balance

the lower likelihood and level of bonuses, on average) Governance: the plan can operate almost completely with fixed rules, eliminating the

need for discretionary decisions

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Version 1

Introduction

On the following slides you will be asked questions. In each case, two people have made

permanent decisions on how to invest a portion of their money in retirement. You are asked to judge

which person has made a better choice. In all scenarios, each person has some savings and receives

$1,000 each month in social security, in addition to the portion of savings mentioned in each

question. Each person has chosen a different way to invest this portion ($100,000) of their savings.

They have already set aside money to leave for their children when they die. The choices are

intended to be financially equivalent and based on personal preferences for investing in retirement.

Life annuity

Mr. Red: Mr. Red invests $100,000 in an account which earns $650 each month for as long as he

lives. He can only withdraw the earnings he receives, not the invested money. When he dies, the

earnings will stop and his investment will be worth nothing.

20-year period annuity

Mr. Orange: Mr. Orange invests $100,000 in an account which earns $650 each month for 20 years.

He can only withdraw the earnings he receives, not the invested money. After 20 years, the earnings

will stop and his investment will be worth nothing. However, if he dies before then, he may leave

remaining earnings to charity.


Mr. Blue: Mr. Blue invests $100,000 in an account which earns $500 each month for 35 years. He

can only withdraw the earnings he receives, not the invested money. After 35 years, the earnings will

stop and his investment will be worth nothing. However, if he dies before then, he may leave

remaining earnings to charity.

Consol bond

Mr. Green: Mr. Green invests $100,000 in an account which earns a 5% interest rate. He can only

withdraw the interest he receives, not the invested money. When he dies, he may leave the remaining

earnings, which continue forever, to charity.

Savings account

Mr. White: Mr. White invests $100,000 in an account which earns a 4% interest rate. He can

withdraw some or all of the invested money at any time. When he dies, he may leave any remaining

money to

charity.

Version 2

Introduction

On the following slides you will be asked questions. In each case, two people have made

permanent decisions on how to spend a portion of their money in retirement. You are asked to judge

which person has made a better choice. In all scenarios, each person has some savings and can spend

$1,000 each month from social security in addition to the portion of income mentioned in each

question. Each person has chosen a different financial product for a portion ($100,000) of their

savings. They have already set aside money to leave for their children when they die. The choices are

intended to be financially equivalent and based on personal preferences for spending in retirement.

Life annuity

Mr. Red: Mr. Red pays $100,000 at retirement so he can spend $650 each month for as long as he

lives in addition to social security. When he dies, there will be no more payments.


Mr. Orange: Mr. Orange pays $100,000 at retirement so he can spend $650 each month until he is

85 years old in addition to social security. When he turns 85, he will have no additional money left to

spend. However, if he dies before he is 85, he may leave remaining payments to charity.


Mr. Blue: Mr. Blue pays $100,000 at retirement so he can spend $500 each month until he is 100

years old in addition to social security. When he turns 100, he will have no additional money left to

spend. However, if he dies before he is 100, he may leave remaining payments to charity.

Consol bond

Mr. Green: Mr. Green pays $100,000 at retirement so he can spend $400 each month for as long as

he lives in addition to social security. When he dies, he may leave remaining payments, which will

continue forever, to charity.

Savings account

Mr. White: Mr. White pays $100,000 at retirement so he can choose an amount to spend each month

in addition to social security. How long his money lasts depends on how much he spends. If he

spends only $400 per month, he has money for as long as he lives. When he dies, he may leave the

remainder to charity. If he spends $650 per month, he has money only until age 85. He can

spend down faster or slower than each of these options.

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