Asset Market Participation and Portfolio Choice over the Life-Cycle Andreas Fagereng (Statistics Norway) Charles Gottlieb (University of Cambridge) Luigi Guiso (EIEF) WU Symposium, Vienna, August 2015
The two views Investor financial portfolio allocation over the life cycle (safe and risky investments): Practitioners view: invest heavily in stocks when young, rebalance as consumers gets older (Malkiel1996). Your age in bond Jack Bogle. Economists views - this may not always be true: Samuelson (1969), Mossin (1968), Merton (1969), but true when human capital accounted for (Merton 1971) Both views: all should participate in the risky assets markets
Merton (1971) implication: adding labor income Relevant wealth includes accumulated assets W(a) and human wealth H(a) (complete markets) Optimal share in stocks as a fraction of financial wealth is ( r) H ( a, T ) ( a) (1 ) 2 Wa ( ) And thus varies with age becasue Investors participate in stocks at all ages H ( a, T ) varies with age Wa ( ) Intuition: Human capital acts as a bond => when investors are flood with bond-like assets (at young ages) they invest a lot in stocks to attain the Merton share
Generalization of the Merton implication Does the basic Merton model implication generalize to the realistic case of uncertain and non-tradable labor income? With these features lifecycle consumption-portfolio problem has no closed form solution Over past decade a wave of computational models allow for many realistic features such as Uncertain labor income Incomplete markets (borrowing constraints) Non-standard preferences Bequests Correlated stock returns Basic Merton implication holds in these more general context
Empirical support for life cycle profile? If the risky share over the life cycle is driven by shrinking human capital (a fact of life) one would expect a strong evidence of rebalancing in the data. Haliassos et al (2001): the age profile of the risky share is relatively flat, though in some instances there does seem to be some moderate rebalancing. Empirical evidence: 1. based on cross sectional data (age vs cohort) 2. based surveys=> measurement problems. (lying about stocks and correlation of measurement error with age) 3. ignores that participation is a choice=> uncontrolled selection may contribute to failure to find evidence of rebalancing
This study: two tasks 1. Deal with the deficiencies of the empirical evidence Rely on data that should be free of most of the above concerns Model age profiles of participation and risky share accounting for time and cohort effects Account for the endogenous nature of participation Produces empirical age profiles for the portfolio share and participation with distinct patterns of adjustment Strong evidence of rebalancing along different margins 2. Propose a calibrated model that can: 1. come close to reproduce the age profile of the share and participation and the timing of adjustment along these two margins 2. is consistent with the level of the share for the stockholders
The administrative data Ideal data for our task: Long and complete household panel data from Norwegian Tax Registry, 1995-2009. No attrition due to tracking Info on all households financial assets at the single instrument level Assets ownership and value reported to the tax authority by the bank, employers, or broker where the claim sits: More difficult to conceal information (no under or non-reporting) Absence of standard measurement error Households who exit are not replaced=> some attrition because Die (main reason 62%) Divorce (25%) Leave the country (13%) Focus on two assets model: stocks and bonds
.1.2.3.4.5.6 Participation Share Participation shares in risky asset markets, selected cohorts 1940 1935 1945 1930 1955 1950 1925 1920 1960 1965 1970 25 30 35 40 45 50 55 60 65 70 75 80 85 Age
.1.2.3.4 Risky Share Conditional risky Risky share share of financial by wealth, age selected and cohorts 1965 1960 1955 1970 1950 1945 1940 1935 1930 Suggestive of time effects, unclear cohort effects, declines with age 1925 1920 25 30 35 40 45 50 55 60 65 70 75 80 85 90 Age
Conditional risky Financial share wealth, by selected age cohorts and cohort Suggestive of time effects, unclear cohort effects, declines with age
Modeling Two identification problems with the descriptive evidence in the figures 1. Separating age, time and cohort effects Impose two type of restrictions to identify the age profile 1. We follow Deaton-Paxson: add a trend and impose that deviations from trend sum to 0. 2. We impose causal mechanism on cohort effects: affected by stock market returns during impressionable years (Malmendier and Nagel, 2011, Giuliano and Spilimbergo, 2014) 2. Selection into participation: a two stage Heckman model Identification restriction: A measure of lifetime wealth (financial wealth + human capital) affects decision to participate but not the optimal share
Result: restricting cohort effects to youth experience share share share participation participation participation
Life cycle pattern of financial wealth
Key patterns: Dual adjustment Hump shape in participation => people enter and exit the stock market Participation peaks around retirement As people leave the labor market they also start leaving the stock market=> inconsistent with a once and forever participation cost Adjustment takes place along two margins with a specific timing Gradual rebalancing along the intensive margin well before retirement Exit from stocks after retirement Little wealth decumulation after retirement
Standard computational models Dynamics of the share consistent with those estimated by us but predicted level is too high Do not generate exit from the stock market and are silent about timing of exit over the life cycle Focus has been on limited (low) participation among the young Limited participation and exit among the elderly has been ignored (exception Allen Sue) We extend Cocco, Gomes and Maenhout (2005) to try account for these features by adding: 1. per-period participation cost 2. probability of tail risk 3. bequest motive
On tail risk Households in sample have had several experiences with large stock market crashes. Informed guess of tail event based on series of crashes, between 0.6% and 3.2%. Households are imperfectly diversified -> Even in years of not stock market crash some households may suffer substantial losses.
Baseline
Comparison with CGM (2005) Per period cost not enough to generate timely exit, also prob disasters needed
Estimates
Fit: estimate also disaster probability
Summing up We provide robust evidence that investors do indeed rebalance their portfolios over the life cycle Invariant to different ways to separate time, age and cohort effects Investors adjust along two margins with distinct timing Lowering the share in stocks when retirement comes into sight Exiting the stock market when they retire A model with a small per period participation cost a small age-invariant probability of disaster and relatively high risk aversion can come close to reproduce the dual pattern of adjustment and the level of the share over the life cycle