SMRE Spring 2008 1

SMRE Spring 2008 Project

An Excel Model to Estimate Expected Remaining Retirement Lifespan

By

Bruno Trenkler

SMRE Spring 2008 2

Introduction

Need a simple tool to calculate expected remaining life for retirement planning.

Available Tools Web based estimators Web based tables

Uses publicly available data for Total Population Whites

Males Females

Blacks Males Females

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Methodology

Data source is:

National Vital Statistics Reports, Vol 54, 14, April 19, 2006 (Revised March 28, 2007)

http://www.cdc.gov/nchs/data/nvsr/nvsr54/nvsr54_14.pdf

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Survival PlotPlot of All Survivor Data

0

10,000

20,000

30,000

40,000

50,000

60,000

70,000

80,000

90,000

100,000

0 10 20 30 40 50 60 70 80 90 100

Age

Su

rviv

ors

All Whites All Blacks All Females White Females Black Females All Males White Males Black Males

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Attempts to Model Survivor Function Distribution Analysis

Weibull (coeff = 0.976) 3 parameter Weibull (coeff = 0.985)

Transformations Manual

Log, Log-Log, √ , inverse √ Box-Cox

Polynomial 6th order provides R2=0.9999

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Mean Expected Life

Mean Expected Life By Age

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

0 10 20 30 40 50 60 70 80 90 100

Age (years)

Mea

n E

xpec

ted

Lif

e (y

ears

)

Total_pop Whites White_F White M Blacks Black_F Black_M

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Cubic Polynomial Fit

Max_Age

Tota

l_pop

100806040200

80

70

60

50

40

30

20

10

0

S 0.135680R-Sq 100.0%R-Sq(adj) 100.0%

Regression95% CI95% PI

Fitted Line PlotTotal_pop = 78.44 - 0.8997 Max_Age

- 0.003194 Max_Age**2 + 0.000046 Max_Age**3

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Expected Remaining Life Excel Interface

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Polynomial Model vs. Data

Comparison of Table Values and Calculated Values

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0 10 20 30 40 50 60 70 80 90 100

age

Dif

fere

nce

diff_Total_pop diff_Whites diff_White_F diff_White_M diff_Blacks diff_Black_F diff_Black_M

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Conclusions

Modeling survivor function difficult Cubic polynomial gives good results Excel program results are acceptable