Optimal life-cycle portfolios for heterogeneous workers

Carolina Fugazza Fabio Bagliano Giovanna NicodanoCeRP-Collegio Carlo Alberto and University of Turin

Financial Innovation and Market DynamicsCentro Baffi Carefin ConSoB 2012

MotivationShould 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 modelhuman capital, which decreases as retirement nears, provides a hedge against adverse financial outcomes

This inspires Target Date Retirement Funds & default investment rules in DC plansVanguard: 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

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 combinationscorrelation btw permanent labour income shocks and stock returnsrisk 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

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

Standard life cycle modelpower 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 returnsliquidity constraints prevent from insuring against idiosyncratic shocksfirst pillar grants exogenous replacement ratio after retirementi.i.d. returns on stocks and risky bonds correlated with each otherriskless asset

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

*Median Investment Profiles Base case

Insertion of bonds does not alter the age profile for equitiesSimilar to Bodie et al. (1992) and Cocco et al.(2005), but risky bonds substitute for riskless assetPrior to retirement, investment in equities in decreasing in ageThe asset allocation of the young is tilted towards stocks In the two decades before retirement it gradually shifts to risky bondsAfter retirement, equity share is increasing in ageAs 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 Higher varianceAs 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

Median Investment Profiles0.2 income-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 holdsAt 65 non financial income becomes certain (and therefore uncorrelated with stock returns), and the investor sharply rebalances her portfolio towards stocks

INVERTED Median Investment ProfilesRRA 8; 0.2 labor income stock returns correlationHigher 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

Implications and Evidence on Age Profile for EquitiesModel 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) horizontalAmeriks and Zeldes (2004) increasing or hump shaped

Implications and Evidence on Non-ParticipationImplication: 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.

*Heterogeneity in portfolio shares5th, 50th, 95th percentiles of the cross-sectional distributions of portfolio shares conditional on agedecreasing heterogeneity, before retirement at all ages, when background risk increases because financial wealth growsheterogeneity driven by working histories (idiosyncratic labour income shocks) together with low financial wealth to hedge themmore similar optimal investments by workers with high risk aversion, because of higher financial wealth and lower heterogeneity

Heterogeneity in portfolio profilesBase Casenormal labor shock variancehigh labor shock variance

HeterogeneityPositive income-stock returns correlationnormal labor shock variancehigh labor shock variance

HeterogeneityPortfolio shares: Risk aversion 8 positive labor income stock returns correlation (0.2)

*Welfare Costs of Suboptimal Asset Allocation

magnitude of the mean welfare costs is in the range of 5-460 bp in base casehigher risk aversion 6-250 bp1/3 has lower welfare costs than a modifed age rule (100-age)/2Welfare costs is measured in certainty equivalent returnif management cost of optimal allocation exceeds 460bp, then 1/3 default investment option is better for all risk aversion and correlation

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

*Take-aways

The optimal portfolio share invested in stock need not fall in age, even in normal circumstancesOptimal default investment option ought to be tied to labour income risk charactericsEqually weighted strategy better than age rule