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

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

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

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

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

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

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

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

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

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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

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

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20 30 40 50 60 70 80 90 100age

stocks bonds riskless

"high " labor shock variance

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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

Median Investment ProfilesRRA 8; ρsY 0.2

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• 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

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

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

Heterogeneity in portfolio profilesBase Case

“normal” labor shock variance “high” labor shock variance

HeterogeneityPositive income-stock returns correlation

“normal” labor shock variance “high” labor shock variance

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

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"normal" labor income variance

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"high" labor income variance

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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.

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