Afs 2016-certainty of lifestyle shared

CERTAINTY OF LIFESTYLE: CONTRASTING A SIMULATION OVER A FIXED PERIOD VERSUS MULTIPLE PERIOD MODELS

Larry R. Frank, Sr.MBA, B.S. cum laude Physics, CFP® Registered Investment Adviser, Better Financial Education

Shawn BraymanBSc, MES, Chartered Financial PlannerPresident & CEO of PlanPlus Inc.

Academy of Financial Services 2October 20-21, 2016

Similar to Long Division, there is a solution, derivation of solution, and remainder values.

Traditional Monte Carlo Simulation Cast over a fixed period

Deterministic

Stochastic


The solution to single period simulations• Use Period Life Tables to determine the length of each age’s simulation period

• Recast simulations AT EACH AGE, with a NEW simulation period

• What really seeking is the POINT SOLUTION for each age depending onprobable capital from returns over time.

How does a model doing this compare to a traditional simulation utilized today?

Academy of Financial Services 4

A series of solutions

October 20-21, 2016

Without derivation of the solution iterations or remainderValues (i.e., Terminal Portfolio Values).

All points are SOLUTIONS.

Academy of Financial Services 5

Fixed Period Calculations/SimulationOctober 20-21, 2016

• NOT a Stochastic problem … problem comes from how derivation processis viewed

• 1) There is only ONE age that a 30 year period applies to …• And it is not when retiree’s are in their 60’s – ages of common retirement.

• Result: Penalizing the spending of the many,for the sake of the few who are long lived.

• Better to make adjustments as the retiree ages – modeling review process.• 2) LAST year of simulation (29th) is 1 year = table is longer; same for 28th year

& 27th year, etc.• Results in Cash Flow errors which results in Capital Balance errors

• And these are the purposes of a model vs a single calculation/simulation


• Fixed period simulations, and deterministic calculations, ignore the influence of mortality on time period calculations.

• Fixed period simulations have only one, or a single, time period over which the calculations are performed; for example, 30 years between age 65 and 95.

• However, when one also considers the aging effect where one moves through the mortality tables as one ages, the time periods are anything but fixed.

• An error in cash flow, and resulting portfolio balances, results because the last period of a fixed period simulation is only 1 year long, while those still alive at that later age have more than 1 year of expected longevity.

• Perverse effect: Age 95 is a common reference age used in fixed period simulations. Although less than 13% of 60-year-old females may outlive age 95. The effect of using such an arbitrary “ending” age is to penalize the many, 87%, who don’t outlive age 95, by restricting their spending from the beginning at age 60

The problem with Monte Carlo Simulations as utilized today


• Stout and Mitchell (2006) used mortality tables to address the concern of an unknown planning horizon

• Frank, Mitchell and Blanchett (2012a) developed the first model integrating multiple period simulations based on an annual reference to period life tables

• Bernicke (2005) found household expenditures decline as retirees age and this decline is voluntary.

• Blanchett (2014) suggests retiree spending tends to decline with age, • consumption as part of a long-term plan and as a result of habits and

commitments. By being autonomous to income, it is not related to raises, but to a retirement budget constrained by the level of available assets.”

(Shambo 2008).• Suarez, et. al., (2015) use a fixed period methodology combined with an

n-1 time horizon; a 90% chance that you won’t have to lower your withdrawal amount in the future,

Literature Review – Mortality, Adjusting Lifestyle


• Steiner (2014) outlined an actuarial approach to calculate the withdrawal amount based on the “risk-free interest rate” and the greater of the retiree’s life expectancy and age 95.

• Waring and Siegel (2015) annually recalculated virtual annuity (ARVA). “The ARVA strategy can be derived from an annuity payout calculation, repeated each period; simulations and other fancy techniques that accept some probability of ruin are not required”.

• Pfau (2015) compared 10 alternative models, by comparing real remaining wealth after 30 years, for retirement income withdrawals estimation included decision rules and actuarial approaches. “Choosing a retirement income strategy is complicated by the fact that there is no single number that can summarize all of the characteristics of the strategy”.

Literature Review – Actuarial Methods


• Three (3) portfolios based on Money Guide Pro: i.e. Balanced allocation 50% stocks, 47% bonds and 3% cash with real return 5.92% and standard deviation 10.24%.

• Mortality tables based on Social Security Period Life Tables 2011 • The Continually Adjusting Stochastic Actuarial Model (CASAM) used the

same return assumptions but time horizon was established using mortality tables. Withdrawal is calculated for each capital balance for each year.

• A variety of approaches to mitigate income volatility: • Defensive and Moderate Growth portfolios • Different glide paths aggressive to conservative; or the opposite; • Variations in percentile mortality targets or other factors adjusting the

mortality assumption; • Floor-and-ceiling assumptions etc.

Methodology


Measuring Outcomes

Figure 3

Age Income #1 Income #2 Capital #1 Capital #260 40,000 50,338 1,000,000 1,000,000 65 40,000 54,410 1,087,089 1,013,317 70 40,000 59,127 1,171,947 983,278 75 40,000 63,936 1,275,613 948,301 80 40,000 68,371 1,457,028 870,028 85 40,000 73,261 1,669,919 751,391 90 40,000 70,848 2,004,363 593,62795 40,000 53,023 2,322,301 390,415

100 40,000 40,000 2,808,586 226,952105 40,000 40,000 3,481,094 69,959

Metricsat year 35 #/$ % #/$ %Failed scenarios of 1000 final 68 6.8% 99 9.9%Total failures (scenario years) 484 1.4% 694 2.0%Morality weighted failures 140 0.4% 199 0.6%Average Capital (among scenarios >0) 3,391,539 483,408 Median Capital (among scenarios >0) 2,541,153 424,151 SD Capital 3,104,342 122.2% 350,765 82.7%Average Income 40,000 75,996 Median Income 40,000 53,042 SD Income - 0.0% 32,981 62.2%Mortality Weighted Total Income 974,970 1,644,432 IRR on 5% 1.40% 2.09%IRR on 25% 4.05% 3.64%IRR on 50% 5.36% 5.39% IRR on 75% 6.64% 7.15% IRR on 95% 8.29% 9.54%

5.92% =/- 10.24 (Balanced Real), Minimum 4 years, 50%+1%/year, 68% of Amount, 10% failure, At least $40K

Median Values

#1 MC #2 CASAM


Measuring Outcomes• Failed scenarios of 1000 final: the number of scenarios that have run out of funds

in the year 35. • Total Failures (scenario years): Based on 35 years and 1000 scenarios, there are

35,000 simulation years. • Mortality weighted failures: total failures (scenario years) multiplied by the

probability of being alive. • Average Capital and Median Capital (among scenarios >0): the average or

median capital respectively in the final year (i.e. 35) from only those scenarios that have capital.

• The capital standard deviation (SD Capital) how wide in dollar and percentage terms, the capital varies in the final year.

• Average income represents the simple average between the highest and lowest income values as measured at the indicated time frame

• Median income from the 50th percentile value if all 1000 scenarios >0 • Standard Deviation (SD) of Income • Mortality weighted total income: Σ Incomen x Probability Survivaln

• Internal Rate of Return (IRR) return of both the investments and withdrawals based on the initial capital, withdrawals, then capital balances/residual.


ResultsFigure 1. Comparison of Capital Percentiles between MC and CASAM

0

200000

400000

600000

800000

1000000

1200000

1400000

1600000

60 65 70 75 80 85 90 95 100 105

Capital Percentiles 25th/95th MC#1 vs 5th/95th CASAM#2

95th:2 75th:1 25th:1 5th:2

Comparing MC with 10% failure to CASAM. CASAM withdrawals cause convergence where mortality = 1 year.


Results - constrainedApplying constraints:• Minimum 4 year mortality• 50th percentile mortality + 1

percentile per annum• 10% failure• Floor of $40,000 income

We ran 23 different scenarios testing different portfolios, constraint etc.

One result was that constraints led to either failures (requiring a minimum spending floor), or large build up in capital (limiting spending on the upside through setting a ceiling to spending). Single, fixed period, simulations do both constraints simultaneously!

Figure 25.92% =/- 10.24 (Balanced Real), Minimum 4 years, 50%+1%/year, 68% of Amount, 10% failure, At least $40K

0

200,000

400,000

600,000

800,000

1,000,000

1,200,000

1,400,000

1,600,000

1,800,000

2,000,000

60 65 70 75 80 85 90 95 100 105

Capital - CASAM #2

95th 75th 50th 25th 5th

0

200,000

400,000

600,000

800,000

1,000,000

1,200,000

1,400,000

1,600,000

1,800,000

2,000,000

60 65 70 75 80 85 90 95 100 105

Capital - MC #1

95th 75th 50th 25th 5th

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20,000

40,000

60,000

80,000

100,000

120,000

140,000

160,000

180,000

200,000

60 65 70 75 80 85 90 95 100 105

Withdrawals CASAM & MC

95th 75th 50th 25th 5th #1 MC Withdrawal


Variability of Income – Age 61Figure 4 - Age 61

graph … can't format it out ??

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10,000

20,000

30,000

40,000

50,000

60,000

70,000

3 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 97

Withdrawal Amount by Percentile below



Variability of Income – Age 85

Figure 4 - Age 85

graph … can't format it out ??

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20,000

40,000

60,000

80,000

100,000

120,000

140,000

160,000

180,000

200,000

3 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 97




• CASAM has a tear-drop pattern where ending percentile results tend to concentrate again at the later ages. This helps retirees visualize the consequences of spending levels from earlier ages and the range of incomes they may realize in retirement.

• CASAM allows increased spending at earlier years as opposed to approaches which may overly constrain income for the client.

• Fewer constraints or flexible spending means the client will have a non-zero portfolio balance at all points for the model contrasted with simulations that run out of money.

• A higher “Mortality Weighted Total Income” results in all cases using the CASAM. Retirees receive money to spend when they are more likely to be alive to enjoy it.

• A higher Internal Rate of Return in all cases using the CASAM.• In the CASAM model there is an automatic built in bequest as the

model allows additional time horizon and the client would require a portfolio balance to fund those future years of income beyond that age.

• The model approach reflects the reality of how people behave by taking multiple reviews as they age through retirement.

Summary

THANK YOU FOR ATTENDING OUR SESSION

Our contact information is:

[email protected]

[email protected]

Working paper available at http://ssrn.com/abstract=2769010

Link to summary paper in the Journal of Financial Planning, November 2016, "Combining Stochastic Simulations and Actuarial Withdrawals into One Model“

http://ssrn.com/abstract=2769010

http://www.betterfinancialeducation.com/8th-paper-simulations-versus-models

Afs 2016-certainty of lifestyle shared

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