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Optimal life-cycle portfolios for heterogeneous workers
Fabio Bagliano Giovanna NicodanoUniversity of Turin & CeRP-Collegio Carlo Alberto
Carolina Fugazza University of Milano Bicocca & CeRP-CCA
2012 HSE Financial Economics Conference
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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
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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
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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
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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
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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
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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) and of σε² = 0.0106 σε²= 0.042
• & transitory shock to labour income σn² = 0.0738 σn² = 0.30
• riskless rate rf = 0.02
• expected stock and bond risk premia s0.04 and b 0.02
• standard deviations of asset returns σs=0.157 and σb = 0.08
• Stock-bond return correlation ρsb= 0.2
• Stock-labour income correlation ρsY= 0 and ρsY= 0.2
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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
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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
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Median Investment Profiles
00,10,20,30,40,50,60,70,80,9
1
20 30 40 50 60 70 80 90 100
age
"normal" labor shock variance
stocks bonds riskless
"high " labor shock variance
0
0.1
0.2
0.3
0.40.5
0.6
0.7
0.8
0.9
1
20 30 40 50 60 70 80 90 100age
stocks bonds riskless
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
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Median Investment Profiles ρsY 0.2
"normal" labor shock variance
0
0.10.2
0.30.4
0.5
0.60.7
0.80.9
1
20 30 40 50 60 70 80 90 100age
stocks bonds riskless
"high " labor shock variance
0
0.1
0.2
0.3
0.40.5
0.6
0.7
0.8
0.9
1
20 30 40 50 60 70 80 90 100age
stocks bonds riskless
•The young accumulate stocks more slowly until 25, since labor income is closer to an implicit holding of stocks;Then decreasing profile resumesAt 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
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Median Investment ProfilesRRA 8; ρsY 0.2
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
20 30 40 50 60 70 80 90 100
"normal labor income variance"
stocks bonds
"high labor income variance"
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
20 40 60 80 100
• 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
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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
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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.
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Heterogeneity in portfolio shares
• 5th, 50th, 95th 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
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Heterogeneity in portfolio profilesBase Case
“normal” labor shock variance “high” labor shock variance
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HeterogeneityPositive income-stock returns correlation
“normal” labor shock variance “high” labor shock variance
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HeterogeneityPortfolio shares: RRA 8 positive labor income –stock returns
correlation (0.2)
"high" labor income variance
00.10.20.30.40.50.60.70.80.9
1
20 40 60 80 100
"normal" labor income variance
00.10.20.30.40.50.60.70.80.9
1
20 40 60 80 100
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
20 30 40 50 60 70 80 90 100
"5th" "50th" "95th"
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
20 30 40 50 60 70 80 90 100
"5th" "50th" "95th"
"high" labor income variance
00.10.20.30.40.50.60.70.80.9
1
20 40 60 80 100
"normal" labor income variance
00.10.20.30.40.50.60.70.80.9
1
20 40 60 80 100
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
20 30 40 50 60 70 80 90 100
"5th" "50th" "95th"
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
20 30 40 50 60 70 80 90 100
"5th" "50th" "95th"
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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.
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Typical TDF portfolio allocation
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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