Optimal life-cycle portfolios for heterogeneous workers

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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

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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 b 0.96
• relative risk aversion g 5 and g
  8
• Var (permanent shocks) and of se² 0.0106
  se² 0.042
• transitory shock to labour income sn²
  0.0738 sn² 0.30
  
• riskless rate rf 0.02
• expected stock and bond risk premia ms 0.04 and
  mb 0.02
• standard deviations of asset returns ss0.157
  and sb 0.08
• Stock-bond return correlation ?sb 0.2
• Stock-labour income correlation ?sY 0 and
  ?sY 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

• 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 ?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

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Median Investment ProfilesRRA 8 ?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

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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
high labor shock variance
normal labor shock variance
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HeterogeneityPortfolio shares RRA 8 positive
labor income stock returns correlation (0.2)
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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