1. Reducing Social Security PRA Risk at the Individual Level — Lifecycle Funds & No-Loss Strategies October 2006 David Wise Harvard and NBER Steven Venti Dartmouth and NBER James Poterba MIT and NBER Joshua Rauh University of Chicago and NBER

2. 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 age- invariant strategies

3. 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

4. Market for Target-Year Lifecycle Funds Data source: Morningstar 0 5 10 15 20 25 30 35 40 45 50 199419951996199719981999200020012002200320042005 $ billions

5. Asset Allocation in Target-Year Lifecycle Funds by Retirement Year

6. 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)

7. 401(k) Accumulation Profile for a Given Household (i) Contribution for a Given Household (i) Simulation Model assuming this is all earnings, not just Social Security covered earnings return net of investing expenses 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

8. Simulation Technique Evaluate household utility at retirement using a standard constant relative risk aversion utility function Find certainty equivalents accounting for the fact that households have non-PRA wealth, given by non-pension annuities and other financial wealth

9. Asset Allocation Strategies i.100% TIPS ii.100% Government Bonds iii.100% Large Cap Corporate Equity iv.(110 - Age)% Stocks, (Age+10)% TIPS v.(110 - Age)% Stocks, (Age+10)% Government Bonds vi.Empirical Lifecycle, Stocks and TIPS vii.Empirical Lifecycle, Stocks and Bonds viii.Feldstein “No Lose” Plan ix.Optimal Fixed Proportions (5% Grid) x.Optimal Linear Lifecycle (5% Grid)

10. 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

11. 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

12. Baseline Expense Ratios, No Other Wealth

13. Various Expense Ratios, No Other Wealth

14. Optimal Fixed Proportion and Linear Lifecycle Strategies Empirical Stock Returns Empirical Stock Returns, Reduced 300 Basis Points Less Than High School Degree High School and/or Some College and/or Post- graduate Less Than High School Degree High School and/or Some College and/or Post- graduate No Other Wealth alpha = 2 Optimal Fixed Proportions: % Stocks (Rest TIPS) 100% 65% 70% Optimal Linear Lifecycle: Starting % Stocks 55% alpha = 4 Optimal Fixed Proportions: % Stocks (Rest TIPS) 55% 60% 35% Optimal Linear Lifecycle: Starting % Stocks 65% 60% 80% Annuities andOther FinancialWealth alpha = 2 Optimal Fixed Proportions: % Stocks (Rest TIPS) 100% 80% 85% 100% Optimal Linear Lifecycle: Starting % Stocks 55% alpha = 4 Optimal Fixed Proportions: % Stocks (Rest TIPS) 70% 75% 90% 4 45% 55% OptimalLinear Lifecycle: Starting % Stocks 55% 75% 70% 65%

15. Lifecycle vs. “Optimal” Strategies

16. 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.

17. 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 home- made similar asset allocation strategy