Reducing Social Security PRA Risk at the Individual Level — Lifecycle Funds and No-Loss Strategies Pathways to a Secure Retirement Conference, August 2006, Washington, DC David Wise Harvard and NBER Steven Venti Dartmouth and NBER James Poterba MIT and NBER Joshua Rauh University of Chicago and NBER

Motivation Lifecycle funds charge investors to rebalance away from stocks and towards bonds as retirement draws near Market for these funds has grown exponentially in recent years Could these products mitigate risk in a Social Security system with private investment accounts (PRA)? This paper uses simulations to examine expected utility of wealth at retirement under different PRA asset allocation strategies Particular attention to lifecycle funds versus age- invariant strategies Simulation framework developed in PRVW (2005) to calculate and compare certainty equivalent measures of the different strategies

Preview of Results Expected utility associated with different 401(k) asset allocation strategies, and the ranking of these strategies, sensitive to: –the expected return on corporate stock –the relative risk aversion of the investing household –the amount of non-PRA wealth that the household will have available at retirement –expenses associated with given strategy There often exists a fixed-proportions portfolio of stocks and inflation-indexed government bonds that yields expected utility at retirement at least as high as that from lifecycle strategies When asset allocation is reasonably close, variation in expense ratios is more important than variation in asset allocation

Market for Target-Year Lifecycle Funds Data source: Morningstar $ billions

Asset Allocation in Target-Year Lifecycle Funds by Retirement Year

Simulating DC Account Balances: Related Literature Empirical Literature –PRVW (2005) –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)

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 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 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.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)

Simulating Equity Returns All portfolio strategies are simulated under two distributions for equity: 1.historical empirical distribution of simple annual returns, with replacement 2.same but with equity returns reduced by 300 basis points

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 –40 basis points for lifecycle funds 2. Actual average expense ratios for lifecycle funds, 74 basis points 3.High expense ratios for everything 100 basis points for stocks, bonds and TIPS 120 basis points for lifecycle funds

Baseline Expense Ratios, No Other Wealth

Various Expense Ratios, No Other Wealth

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%

Lifecycle vs. “Optimal” Strategies

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 these education groups under the high expense ratio scenario –their background wealth makes them effectively less risk averse –the lifecycle funds cost 120 basis points compared to the equity fund’s 100 basis points.

Conclusions Higher risk aversion, lower expected stock returns, lower non-PRA wealth are the factors that reduce the attractiveness of a 100% stocks 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 could be achieved by the household Households who are unable to do this on their own will not do terribly in lifecycle funds but they will lose money relative to what they could get if they executed very simple investing strategies on their own