1 Public Pension Risk Dynamics Bob McCrory EFI Actuaries.

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Public Pension Risk DynamicsBob McCroryEFI Actuaries

The Model Plan

• The Model Plan• The Model Economy• Simulated Benefits,

Cost, and Funding• The Operating Region• An Initial Result:

Return Distributions Don’t Matter

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The Model Plan• All members are the same

– Hired at 37, retire at 60– Mortality and termination decrements only

• Stable member population• Simple benefits

– 50% FAP at retirement, with 2% COLA– No ancillary benefits

• Simple funding– Entry Age Normal– 8% return, 3.5% inflation, 2% merit pay increase– All demographic assumptions met exactly– Start at 100% funded (at market value) at time 0

• Simple accounting– All transactions take place at the beginning of each year

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The Model Economy• Simple and benign economic model

– Asset returns are normally distributed• Mean 8% (compound), standard deviation 11% (annual)• Equivalent to a 50% equity/50% fixed income mix from Ibbotson (2007)

– Inflation is normally distributed• Independent of returns• Mean 3.5% (compound), standard deviation 1.5% (annual)

• Model Economy is not realistic– Real returns are not normally distributed– Returns and inflation are correlated– Actuarial assumptions are met exactly

• Actuarial wind tunnel– A controlled experimental environment for testing pension plans– If we don’t understand pension behavior in this simple environment, we don’t

understand it anywhere

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Simulated Benefits

Year 0 25 50 75 100 Actuarial Projection 0.444688 0.444688 0.444688 0.444688 0.444688 Mean 0.444688 0.445407 0.444935 0.445368 0.445026 Standard Deviation 0.0 0.0167903 0.0166493 0.0166918 0.0170788 75th Percentile 0.444688 0.456838 0.455157 0.455785 0.456438 Median 0.444688 0.44532 0.444608 0.444202 0.444957 25th Percentile 0.444688 0.433621 0.434259 0.433709 0.433009

0 20 40 60 80 100

0.40

0.42

0.44

0.46

0.48

0.50

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Simulated Actuarial Cost

Year 0 25 50 75 100 Actuarial Projection 0.165275 0.165275 0.165275 0.165275 0.165275 Mean 0.165275 0.150708 0.128161 0.114998 0.0974617 SD 0.0 0.143748 0.140221 0.139323 0.134221 75th Percentile 0.165275 0.266623 0.241916 0.235827 0.192109 Median 0.165275 0.13047 0.086934 0.015328 0. 25th Percentile 0.165275 0. 0. 0. 0.

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Simulated Funded Ratio (MV)

Year 0 25 50 75 100 Actuarial Projection 1. 1. 1. 1. 1. Mean 1. 1.22554 1.84974 3.63337 9.48764 SD 0. 0.648464 2.29238 8.29702 30.6395 75th Percentile 1. 1.36507 1.70268 2.46213 5.15995 Median 1. 1.05067 1.11554 1.22023 1.42662 25th Percentile 1. 0.846691 0.884112 0.894278 0.959494

0 20 40 60 80 100

0

1

2

3

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Simulated Operating Region(Left, No Asset Smoothing; Right, with Asset Smoothing)

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First Result: Return Distributions Don’t Matter (Much)

Normally Distributed Returns

Binomially Distributed Returns

Uniformly Distributed Returns

Stable Distribution of Returns

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Risk• Investment Risk• Benefit Risk• Funding Risk• Actuarial Funding

Risk• Amortization Risk• Assumption Risk

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Investments: Risk/Reward Tradeoff

Investment Return (Vertical Axis) Plotted Against Investment Risk (Horizontal Axis)

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Investments: Risk/Reward Profile

Mean and Standard Deviation of Actuarial Cost Plotted vs. Standard Deviation of Portfolio Return, with Return Adjusted for Risk

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Funding Risk

Cost standard deviation plotted against funded ratio

0.0 0.5 1.0 1.5 2.0

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

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Actuarial Method Risk: 50% Target

Year 0 25 50 75 100 Actuarial Projection 0.304982 0.304982 0.304982 0.304982 0.304982 Mean 0.304982 0.282617 0.276308 0.275398 0.268176 SD 0.0 0.103758 0.109699 0.111005 0.117503 75th Percentile 0.304982 0.360258 0.354254 0.357421 0.353068 Median 0.304982 0.297789 0.298754 0.299528 0.292042 25th Percentile 0.304982 0.220215 0.217381 0.208125 0.201834

0 20 40 60 80 100

0.0

0.1

0.2

0.3

0.4

0.5

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Actuarial Method Risk: 150% Target

Year 0 25 50 75 100 Actuarial Projection 0.025569 0.025569 0.025569 0.025569 0.025569 Mean 0.025569 0.0773689 0.0513595 0.0374221 0.0281694 SD 0.0 0.127986 0.108583 0.0934145 0.0875339 75th Percentile 0.025569 0.127458 0.00207 0. 0. Median 0.025569 0. 0. 0. 0. 25th Percentile 0.025569 0. 0. 0. 0.

0 20 40 60 80 100

0.0

0.1

0.2

0.3

0.4

0.5

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Actuarial Method Risk by Asset Target

Cost mean and standard deviation plotted against asset target as a percentage of entry age accrued liability

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0.0

0.1

0.2

0.3

0.4

Cost Mean and SD

SD

Mean

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Amortization Risk: Immediate

Year 0 25 50 75 100 Actuarial Projection 0.165275 0.165275 0.165275 0.165275 0.165275 Mean 0.165275 0.131966 0.0976625 0.0814781 0.0581363 SD 0.0 0.321356 0.27241 0.243685 0.216961 75th Percentile 0.165275 0. 0. 0. 0. Median 0.165275 0. 0. 0. 0. 25th Percentile 0.165275 0. 0. 0. 0.

Simulated actuarial cost of the Model Plan with full and immediate amortization of any unfunded liability

0 20 40 60 80 100

0.0

0.5

1.0

1.5

2.0

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Amortization Risk: 1/20

Year 0 25 50 75 100 Actuarial Projection 0.165275 0.165275 0.165275 0.165275 0.165275 Mean 0.165275 0.151898 0.148343 0.144509 0.131955 SD 0.0 0.117818 0.131937 0.140171 0.143229 75th Percentile 0.165275 0.250299 0.267946 0.276037 0.270265 Median 0.165275 0.158868 0.145046 0.129588 0.073171 25th Percentile 0.165275 0.027093 0. 0. 0.

Simulated actuarial cost of the Model Plan with amortization of unfunded liability using a factor of 20.0

0 20 40 60 80 100

0.0

0.1

0.2

0.3

0.4

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Amortization Risk by Factor

Cost mean, median, and standard deviation plotted against amortization factor

0 5 10 15 20 250.00

0.05

0.10

0.15

0.20

0.25

0.30Cost Mean and SD by Amortization

SD

Median

Mean

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Assumption Risk: 6% Assumed

Year 0 25 50 75 100 Actuarial Projection 0.254245 0.254245 0.254245 0.254245 0.254245 Mean 0.254245 0.101265 0.0578427 0.0399899 0.0283833 SD 0.0 0.142615 0.114068 0.0952269 0.0877563 75th Percentile 0.254245 0.191202 0.049398 0. 0. Median 0.254245 0. 0. 0. 0. 25th Percentile 0.254245 0. 0. 0. 0.

Simulated actuarial cost of the Model Plan with a 6% assumed return

0 20 40 60 80 100

0.0

0.1

0.2

0.3

0.4

0.5

0.6

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Assumption Risk: 16% Assumed

Year 0 25 50 75 100 Actuarial Projection 0.032553 0.032553 0.032553 0.032553 0.032553 Mean 0.032553 0.365704 0.446121 0.465722 0.470203 SD 0.0 0.0439733 0.0216174 0.0235128 0.0263711 75th Percentile 0.032553 0.395316 0.459209 0.480333 0.485234 Median 0.032553 0.374491 0.445529 0.463056 0.467669 25th Percentile 0.032553 0.345767 0.432487 0.449443 0.451052

Simulated actuarial cost of the Model Plan with an assumed rate of return of 16%

0 20 40 60 80 100

0.0

0.1

0.2

0.3

0.4

0.5

0.6

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Assumption Risk by Assumed Rate

Cost mean, median, and standard deviation plotted against assumed rate of return

0.00 0.05 0.10 0.15 0.20

0.1

0.2

0.3

0.4

Cost Mean , Median , and SD by Assumption

SD

Median

Mean

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Actuaries Create Risk

• We fund to the riskiest asset target

• As funding increases to 100%, risk increases

• Accuracy in setting assumptions increases risk

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Summary• Pension plans are complex

dynamic systems• Behavior of these systems

is not at all obvious• Risk arises in unexpected

ways• These plans deserve study

and thought through experimentation and empirical analysis

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• Bob McCrory(206) 328-8628

bobmccrory@efi-actuaries.com• Greg Stump(484) 442-8337

gstump@efi-actuaries.com• Graham Schmidt

(415) 439-5313gschmidt@efi-actuaries.com

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