2. Motivation Should investors reduce their equity exposure as retirement approach? Bodie Merton Samuelson: –under “normal” circumstances, this is the optimal portfolio rule in a standard life cycle model –human capital, which decreases as retirement nears, provides a hedge against adverse financial outcomes This inspires Target Date Retirement Funds & default investment rules in DC plans –Vanguard: retirement date 2045 and 2015 respectively have stock allocations of 90% and 57% –Swedish PP: 100% percent in equities until 55, then gradually into fixed income

3. This paper Inserts bonds, beside equity and cash, in standard life cycle model 1. optimal portfolio share in stocks increases, or is constant, in age for reasonable parameter combinations –correlation btw permanent labour income shocks and stock returns –risk aversion –variance of income shocks 2. non investment in stocks by the young obtains without participation cost 3. large heterogeneity in optimal portfolio shares due to different work histories, especially for younger investors with relatively low saving 4. Implication: Tailored portfolio allocations rather than one-size-fits-all If default is needed, then an equally weighted portfolio is preferable

4. Previous Literature Benzoni et al (2007): long-run cointegration between labour income and stock returns Cocco (2004): presence of housing wealth Munk and Sorensen (2010): sensitivity of the expected labor income growth to the real short-term interest rate

5. Standard life cycle model power utility of consumption during life, conditional probability of survival labour income has a deterministic part, a temporary shock and a permanent shock, that can be correlated with stock returns liquidity constraints prevent from insuring against idiosyncratic shocks first pillar grants exogenous replacement ratio after retirement i.i.d. returns on stocks and risky bonds – correlated with each other riskless asset

6. Calibration (Cocco et al., 2005) Base (black), variation (red) working life 20-65, max age 100, US Mortality Tables discount factor 0.96 relative risk aversion 5, 8 variance of permanent & transitory shock to labour income σ ε ² = 0.0106 and σ n ² = 0.0738 σ ε ² = 0.042 and σ n ² = 0.30 riskless rate 0.02 expected stock and bond risk premia 0.04 and 0.02 standard deviations of asset returns σ s =0.157 and σ b = 0.08 Stock-bond return correlation ρ sb = 0.2 Stock-labour income correlation ρ sY = 0 or 0.2 –CCGM (2001) find higher values, ranging from 0.33 for households with no high-school education to 0.52 for college graduates

7. 7 Median Investment Profiles Base case –Insertion of bonds does not alter the age profile for equities Similar to Bodie et al. (1992) and Cocco et al.(2005), but risky bonds substitute for riskless asset –Prior to retirement, investment in equities in decreasing in age The asset allocation of the young is tilted towards stocks In the two decades before retirement it gradually shifts to risky bonds –After retirement, equity share is increasing in age As pension wealth is riskless, the retirees invest in stocks the more so the more financial wealth is disinvested; Flatter schedule with bequest

8. Median Investment Profiles Higher variance As the variance of labour income shocks increases: no change in the shape of age profiles savings and financial wealth increase, lowering equity investments the optimal share in stocks at 40 drops to 40% and keeps relatively constant until 65

9. Median Investment Profiles 0.2 i ncome-stock return correlation As correlation of labour income shocks increases: younger workers (20-25) accumulate stocks more slowly, since labor income is closer to an implicit holding of stocks; in high variance case, both savings and financial wealth increase, lowering the optimal equity share and restoring the decreasing profile For middle-aged workers asset allocation obtained in base case holds At 65 non financial income becomes certain (and therefore uncorrelated with stock returns), and the investor sharply rebalances her portfolio towards stocks

10. INVERTED Median Investment Profiles RRA 8; 0.2 labor income –stock returns correlation Higher risk aversion with positive correlation: upward sloping age profile for equities! age rule for bonds! median equity share never exceeds 0.2 before retirement normal variance case: workers do not participate when 20-25 higher variance: workers save more and accumulate larger financial wealth, which leads to cautious participation in the equity market

11. Implications and Evidence on Age Profile for Equities Model Implication –Interact risk aversion and correlation to obtain equity portfolio shares that decrease, increase or stay constant in age. Missing interaction may explain divergent results on empirical relationship: –Bodie and Crane (1997) downward sloping –Heaton and Lucas (2004) horizontal –Ameriks and Zeldes (2004) increasing or hump shaped

12. Implications and Evidence on Non-Participation Implication: positive correlation is essential Haliassos and Michaelides (2003): not plausible. –Without bonds, correlation needed to achieve non participation is 0.5 instead of 0.2 –Early estimates: higher correlation for more educated groups and entrepreneurs, that typically invest in stocks. –Angerer and Lam (2009): higher correlation for craftsman, operatives, managers and administrators, farm laborers, private household workers and armed forces; and education below college degree.

13. 13 Heterogeneity in portfolio shares 5 th, 50 th, 95 th percentiles of the cross-sectional distributions of portfolio shares conditional on age decreasing heterogeneity, before retirement at all ages, when background risk increases because financial wealth grows heterogeneity driven by working histories (idiosyncratic labour income shocks) together with low financial wealth to hedge them more similar optimal investments by workers with high risk aversion, because of higher financial wealth and lower heterogeneity

14. Heterogeneity in portfolio profiles Base Case “normal” labor shock variance“high” labor shock variance

15. Heterogeneity Positive income-stock returns correlation “normal” labor shock variance “high” labor shock variance

16. Heterogeneity Portfolio shares: Risk aversion 8 positive labor income –stock returns correlation (0.2)

17. 17 Welfare Costs of Suboptimal Asset Allocation magnitude of the mean welfare costs is in the range of 5-460 bp in base case –higher risk aversion 6-250 bp 1/3 has lower welfare costs than a modifed age rule (100-age)/2 Welfare costs is measured in certainty equivalent return –if management cost of optimal allocation exceeds 460bp, then 1/3 default investment option is better for all risk aversion and correlation

18. Welfare Costs of Suboptimal Asset Allocation (percentiles of financial wealth accumulated at 65) 18

19. 19 Take-aways The optimal portfolio share invested in stock need not fall in age, even in normal circumstances Optimal default investment option ought to be tied to labour income risk characterics Equally weighted strategy better than age rule