1. Optimal life-cycle portfolios for heterogeneous workers Fabio Bagliano Giovanna Nicodano University of Turin & CeRP-Collegio Carlo Alberto Carolina Fugazza University of Milano Bicocca & CeRP-CCA 2012 HSE Financial Economics Conference

2. Motivation The composition of household portfolios respond to permanent, industry specific labor income shocks. We study the response of optimal portfolios to heterogeneity in correlation and variance of permanent income shocks in a standard life cycle model –Cocco Gomes Menhout enriched with “risky bonds” The consensus view (Bodie Merton Samuelson) –under “normal” circumstances, investors should reduce their stock investments as they approach retirement age –rationale: human capital, which decreases as retirement nears, provides a hedge against adverse financial outcomes –Problems: –smaller holdings of stocks than predicted –non participation by the young –hardly decreasing observed investment profiles

3. Our view Optimal portfolio share in stocks increases, or is constant, in age for reasonable parameter combinations –correlation btw permanent labor income shocks and stock returns –risk aversion –variance of income shocks Bodie Teussard already find inversion, but for perfect corrrelation Rationale for this inversion: resolution of uncertainty regarding social security pension increases the equity risk bearing capacity as retirement nears Non investment in stocks by the young obtains without participation cost. –At 20 residual uncertainty concerning labor income is such that the young prefer the bond market to the stock market, that is more correlated with labour income

4. Implication Consensus view inspires Target Date Retirement Funds & default investment rules in DC plans. These are one-size-fits-all –Vanguard 2045 and 2015: stock allocations of 90% and 57% –Swedish PP: 100% in equities until 55, then gradually into fixed income Our analysis shows that –Tailored rather than one-size-fits-all portfolio allocations because of heterogeneity of labor income shocks and risk aversion –If default is needed, then an equally weighted portfolio is preferable TDF scheme delivers very low welfare costs for standard parameters, but very large ones for larger background risk

5. Previous Literature on Non Decreasing Stock Profiles 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 Here we only have bonds. –Bonds per se do not alter the consensus view. –Realistically high correlation and risk aversion without bonds do not alter consensus view. –Bonds and realistically high correlation and risk aversion alter consensus view

6. Standard life cycle model power utility of consumption during life, with uncertain length log labour income has a deterministic part, a temporary shock and a permanent shock, that can be correlated with stock returns liquidity constraints prevent from fully insure against shocks first pillar social security grants exogenous replacement ratio after retirement, depending on last labour income i.i.d. returns on stocks and risky bonds – correlated with each other riskless asset

7. Calibration (Cocco et al., 2005) Base case (black) Variation (red) working life 20-65, max age 100, US Mortality Tables discount factor  0.96 relative risk aversion  5 and  8 Var (permanent shocks) σ ε ² = 0.0106 σ ε ²= 0.042 Var transitory shock σ n ² = 0.0738 σ n ² = 0.30 riskless rate r f = 0.02 expected stock and bond risk premia  s  0.04 and  b  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 and ρ sY = 0.2

8. Support for Parametric Assumption Observed correlation between permanent labor income shocks and stock returns: –Campbell et al.(2001), Campbell & Viceira (2002): 0.33, 0.52; –Heaton & Lucas (2000): -0.07, 0.14 –Industry-specific: Davis and Willen (2000): -0.10, 0.40 8

9. 9 Median Investment Profiles Base case –Insertion of bonds does not alter the age profile for equities As in Bodie et al. (1992) and Cocco et al.(2005), but risky bonds substitute for riskless asset –Prior to retirement, investment in equities is 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

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

11. Median Investment Profiles ρ sY 0.2 The young accumulate stocks more slowly until 25, since labor income is closer to an implicit holding of stocks; Then decreasing profile resumes At 65 the investor sharply rebalances her portfolio towards stocks as pension income becomes certain high variance: both savings and financial wealth increase, lowering the optimal equity share and restoring the decreasing profile from age 20

12. Median Investment Profiles RRA 8; ρ sY 0.2 workers do not participate when 20-25 upward sloping age profile for equities median equity share never exceeds 0.2 before retirement higher variance: young workers save more and accumulate larger financial wealth, which leads to cautious participation in the equity market

13. Implications and Evidence on Age Profile for Equities 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

14. 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.

15. 15 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, 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

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

17. 17 Welfare Costs of Suboptimal Asset Allocation Comparison of suboptimal strategies with optimal one 1/N strategy of De Miguel et al. (2008) Age Rule (100-age) is equally divided between stocks and bonds TDF interpolated from observed TDF Welfare costs measured in equivalent variation of lifetime consumption.

18. Typical TDF portfolio allocation 18

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20. 20 Conclusion 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 characteristic Equally weighted strategy better than age rule and TDF when background risk is high Current analysis: –Epstein-Zin preferences to investigate driver of inversion