Reducing Social Security PRA
Risk at the Individual Level —
Lifecycle Funds & No-Loss
Strategies
October 2006
James Poterba
MIT and
NBER
Joshua Rauh
University of
Chicago and
NBER
Steven Venti
Dartmouth and
NBER
David Wise
Harvard and
NBER
Motivation
• Lifecycle funds charge investors to rebalance
away from stocks and towards bonds as
retirement draws near
• Rapid growth of lifecycle funds in recent years
• Could these products mitigate risk in a Social
Security system with private investment
accounts (PRA)?
• Simulations based on PRVW (2005) examine
expected utility of wealth at retirement under
different PRA asset allocation rules
• Particular attention to lifecycle funds versus ageinvariant strategies
Preview of Results
• Expected utility associated with different asset allocation
strategies depends on:
–
–
–
–
the expected return on corporate stock
the relative risk aversion of the investing household
the amount of non-PRA household wealth
expenses associated with given strategy
• Usually a fixed-proportions portfolio of stocks & TIPS
yields expected utility at retirement at least as high as
that from lifecycle strategies
• Variation in expense ratios can be as important as
variation in asset allocation for determining expected
utility
Market for Target-Year Lifecycle Funds
50
$ billions
45
40
35
30
25
20
15
10
5
0
Data source: Morningstar
Asset Allocation in Target-Year
Lifecycle Funds by Retirement Year
Retirement
Year
2005
2010
2015
2020
2025
2030
2035
2040
2005Q1 Weighted Average Asset Allocation
Money Market
Bonds
Stocks
28.0%
42.0%
30.0%
15.3%
35.4%
49.4%
6.1%
35.7%
58.2%
5.7%
24.6%
69.7%
3.6%
17.2%
79.2%
4.5%
13.8%
81.7%
4.4%
10.4%
85.2%
3.5%
8.4%
88.0%
Simulating DC Account Balances:
Related Literature
• Empirical Literature
– PRVW (2005), Schrager (2006), Samwick and
Skinner (2004), Shiller (2005)
• Theoretical Literature
– Merton (1969), Samuelson (1969), Bodie,
Merton and Samuelson (1988),
– Gollier (2001), Gollier and Zeckhauser (2002)
– Campbell and Viceira (2002), Cocco, Gomes
and Maenhout (2005)
Simulation Model
• 401(k) Accumulation Profile for a Given Household (i)
return net of investing expenses
 t

Wi (63)   [1  Ri (63  j )]Ci (63  t )
t 0  j 0

35
• Contribution for a Given Household (i)
Ci (a)  0.09 * Ei (a)
assuming this is all earnings, not just
Social Security covered earnings
• Information on household earnings and wealth from the
Health and Retirement Study (HRS)
• Focus on the 1400 couples with male aged 63-72 for
which Social Security earnings histories available for
secure restricted use
Simulation Technique
• Evaluate household utility at retirement using a
standard constant relative risk aversion utility
function
Uh
W


PRA, h
 Wnon  PRA

1
1
• Find certainty equivalents accounting for the fact
that households have non-PRA wealth, given by
non-pension annuities and other financial wealth
Asset Allocation Strategies
i.
ii.
iii.
iv.
v.
vi.
vii.
viii.
ix.
x.
100% TIPS
100% Government Bonds
100% Large Cap Corporate Equity
(110 - Age)% Stocks, (Age+10)% TIPS
(110 - Age)% Stocks, (Age+10)% Government
Bonds
Empirical Lifecycle, Stocks and TIPS
Empirical Lifecycle, Stocks and Bonds
Feldstein “No Lose” Plan
Optimal Fixed Proportions (5% Grid)
Optimal Linear Lifecycle (5% Grid)
Simulated Equity Returns: Two
Distributions
* Empirical distribution of simple
annual returns, with replacement
* Empirical distribution with each
entry reduced by 300 basis
points, with replacement
Expense Ratio Assumptions
1. Baseline assumptions
– 32 basis points for equity mutual funds and
government bond funds (weighted mean of S&P 500
index funds from Hortaçsu and Syverson (2004))
– 40 basis points for TIPS & lifecycle funds
2. Actual average expense ratios for lifecycle
funds, 74 basis points
3.”High expense ratio” alternative:
– 100 basis points for stocks, bonds, TIPS
– 120 basis points for lifecycle funds
Baseline Expense Ratios, No Other Wealth
Investment Strategy / Risk Aversion
alpha = 2
Baseline Expense Ratios
100% TIPS
100% Government Bonds
100% Stocks
Heuristic: (110 - Age)% Stocks, rest TIPS
Heuristic: (110 - Age)% Stocks, rest Bonds
Empirical Lifecycle, Stocks and TIPS
Empirical Lifecycle, Stocks and Bonds
Feldstein"No Lose" Plan
alpha = 4
Baseline Ex pense Ratios
100% TIPS
100% Government Bonds
100% Stocks
Heuristic: (110 - Age)% Stocks, rest TIPS
Heuristic: (110 - Age) % Stocks, rest Bonds
Empirical Lifecycle, Stocks and TIPS
Empirical Lifecycle, Stocks and Bonds
Feldstein "No Lose" Plan
Empirical Stock Returns
Less
High
Than
School
College
High
and/or
and/or
School
Some
PostDegree College graduate
Empirical Stock Returns,
Reduced 300 Basis Points
Less
High
Than
School
College
High
and/or
and/or
School
Some
PostDegree College graduate
167.4
171.9
389.1
271.5
278.0
322.5
323.5
297.1
236.7
242.9
553.7
384.8
393.9
458.9
460.3
423.5
325.5
334.3
731.0
516.4
528.7
605.5
607.9
557.5
207.9
210.8
215.8
224.4
225.2
212.7
294.5
298.4
305.5
317.9
319.0
301.6
403.3
405.7
415.3
430.2
432.1
407.8
167.4
150.0
204.2
239.4
226.2
263.1
247.5
245.8
236.7
211.8
288.3
339.1
320.2
372.6
350.6
348.7
325.5
294.9
398.1
458.3
435.5
501.7
473.8
468.9
116.3
186.3
176.6
186.8
176.5
191.2
164.2
263.6
249.8
263.8
249.3
270.4
234.5
361.0
344.1
363.9
345.0
370.3
Various Expense Ratios, No Other Wealth
Investment Strategy / Risk Aversion
alpha = 2
Baseline Expense Ratios
Empirical Lifecycle, Stocks and TIPS
Empirical Lifecycle, Stocks and Bonds
Average Expense Ratios
Empirical Lifecycle, Stocks and TIPS
Empirical Lifecycle, Stocks and Bonds
High Expense Ratios
Empirical Lifecycle, Stocks and TIPS
Empirical Lifecycle, Stocks and Bonds
alpha = 4
Baseline Expense Ratios
Empirical Lifecycle, Stocks and TIPS
Empirical Lifecycle, Stocks and Bonds
Average Expense Ratios
Empirical Lifecycle, Stocks and TIPS
Empirical Lifecycle, Stocks and Bonds
High Expense Ratios
Empirical Lifecycle, Stocks and TIPS
Empirical Lifecycle, Stocks and Bonds
Empirical Stock Returns
Less
High
Than
School College
High
and/or
and/or
School Some
PostDegree College graduate
Empirical Stock Returns,
Reduced 300 Basis Points
Less
High
Than
School College
High
and/or
and/or
School Some
PostDegree College graduate
322.5
323.5
458.9
460.3
605.5
607.9
224.4
225.2
317.9
319.0
430.2
432.1
299.1
300.0
425.3
426.6
563.6
565.8
209.0
209.7
295.8
297.0
402.1
403.9
268.8
269.7
381.9
383.1
509.0
511.0
189.0
189.7
267.3
268.4
365.5
367.2
263.1
247.5
372.6
350.6
501.7
473.8
186.8
176.5
263.8
249.3
363.9
345.0
244.8
230.5
346.6
326.3
468.6
442.8
174.6
165.0
246.4
233.0
341.3
323.9
221.0
208.2
312.9
294.8
425.4
402.7
158.6
150.0
223.9
211.8
311.8
296.3
Optimal Fixed Proportion and
Linear Lifecycle Strategies
Empirical Stock Returns
Less
Than
High
School
Degree
High
School College
and/or and/or
Some
PostCollege graduate
Empirical Stock Returns,
Reduced 300 Basis Points
Less
High
Than School College
High
and/or and/or
School Some
PostDegree College graduate
No Other Wealth
alpha = 2
Optimal Fixed Proportions: % Stocks (Rest TIPS)
Optimal Linear Lifecycle: Starting % St ocks
alpha = 4
Optimal Fixed Proportions: % Stocks (Rest TIPS)
Optimal Linear Lifecycle: Starting % Stocks
100%
55%
100%
55%
100%
55%
65%
55%
65%
55%
70%
55%
55%
65%
55%
65%
60%
60%
35%
80%
35%
80%
35%
80%
100%
55%
100%
55%
100%
55%
80%
55%
85%
55%
100%
55%
70%
55%
75%
55%
90%
55%
40%
75%
45%
70%
55%
65%
Annuities and Other Financial Wealth
alpha = 2
Optimal Fixed Proportions: % Stocks (Rest TIPS)
Optimal Linear Lifecycle: Starting % Stocks
alpha = 4
Optimal Fixed Proportions: % Stocks (Rest TIPS)
Optimal Linear Lifecycle: Starting % Stocks
Lifecycle vs. “Optimal” Strategies
Investment Strategy / Risk Aversion
alpha = 2
Baseline Expense Ratios
Empirical Lifecycle, Stocks and TIPS
Empirical Lifecycle, Stocks and Bonds
Optimal Fixed Proportions (Stocks and TIPS)
Optimal Linear Lifecycle
Average Expense Ratios
Empirical Lifecycle, Stocks and TIPS
Empirical Lifecycle, Stocks and Bonds
alpha = 4
Baseline Ex pense Ratios
Empirical Lifecycle, Stocks and TIPS
Empirical Lifecycle, Stocks and Bonds
Optimal Fixed Proportions (Stocks and TIPS)
Optimal Linear Lifecycle
Average Expense Ratios
Empirical Lifecycle, Stocks and TIPS
Empirical Lifecycle, Stocks and Bonds
Empirical Stock Returns
Less
High
Than
School
College
High
and/or
and/or
School
Some
PostDegree College graduate
Empirical Stock Returns,
Reduced 300 Basis Points
Less
High
Than
School
College
High
and/or
and/or
School
Some
PostDegree College graduate
322.5
323.5
389.1
298.4
458.9
460.3
553.7
423.9
605.5
607.9
731.0
562.8
224.4
225.2
224.2
220.1
317.9
319.0
317.6
311.7
430.2
432.1
430.8
421.9
299.1
300.0
425.3
426.6
563.6
565.8
209.0
209.7
295.8
297.0
402.1
403.9
263.1
247.5
256.3
256.7
372.6
350.6
363.5
364.1
501.7
473.8
490.1
489.1
186.8
176.5
193.8
197.3
263.8
249.3
274.3
278.9
363.9
345.0
374.6
381.3
244.8
230.5
346.6
326.3
468.6
442.8
174.6
165.0
246.4
233.0
341.3
323.9
Effects of Other Wealth
• Optimal fixed proportions does slightly better
than the empirical lifecycle portfolio for the
higher two education categories under baseline
expense ratios and historical equity returns
• A 100% stocks strategy dominates for high
education groups for high expense ratio case
– background wealth reduces effective risk aversion
– lifecycle funds cost 120 basis points compared to
equity fund’s 100 basis points.
Conclusions
• Higher risk aversion, lower expected stock
returns, lower non-PRA wealth reduce
attractiveness of all-stock strategy
• Avoiding high expense ratios is critical for
households saving for retirement in PRAs
• Many of the available lifecycle products
have higher expense ratios than homemade similar asset allocation strategy