How Do Household Portfolio Shares Vary With Age? John Ameriks The - - PowerPoint PPT Presentation

How Do Household Portfolio Shares Vary With Age? John Ameriks

The Vanguard Group john_ameriks@vanguard.com

Stephen P. Zeldes

Benjamin Rosen Professor of Finance & Economics Graduate School of Business Columbia University stephen.zeldes@columbia.edu/ www.columbia.edu/~spz1

Presentation notes: October 2005 Fall 2005 Q-Group Seminar

Introduction and motivation

• How households allocate their financial

portfolios is an increasingly important issue to economists, policymakers, and investors

• Shift from DB to DC in pensions
• Increasing emphasis on accounts/asset
• wnership as a policy solution
• Aging of the population

Our focus is on variation with age

• How should portfolio allocations change with

age?

• How do portfolio allocations change with

age?

• We examine both questions, but focus on the

second

Outline

• Economic theory, professional prescriptions,

and previous evidence

• Modeling and identification
• Data
• Results
• Conclusions

Economic Theory: Benchmark Model

• Mossin, Samuelson, Merton c. 1968
• Assumptions
• No labor income or non-tradable assets
• Stock returns i.i.d.
• CRRA utility, time invariant, time separable
• No transactions costs or other market frictions
• Benchmark Result: Fraction of wealth optimally

held in stock is constant, and thus independent

• f both age and wealth

Economic Theory: Extensions

• Human capital
• Key issue is correlation of labor income with stock market
• Non-i.i.d. asset returns (mean reversion, other patterns)
• Other utility functions (changing risk aversion, non-

separability, others)

• Transactions costs (Learning, monitoring, information,

taxes, fees)

• See Jagannathan and Kocherlakota (1996), Gollier

(2004)

Professional Advice: The longer the investment horizon, the greater the equity share should be

• Typical rule of thumb:

Stocks/financial assets = 100 – age

Share of assets in stocks vs age

20 40 60 80 100 20 40 60 80 100 age percent in stocks

“Life-cycle” / “target date” mutual funds

• Automatic reduction in equity share

(½ - 3 percentage points per year)

• Growing in popularity
• Currently ~ $45-50 billion in target date funds
• Examples include:
• Vanguard “Target Retirement” funds
• Fidelity “Freedom Funds” (2010, 2020, 2030)
• Barclays Global Investors (“LifePath Funds”)
• T. Rowe Price Funds
• TIAA-CREF Funds

Findings of Previous Studies

• Agnew, Balduzzi, and Sunden (AER, 2003)

“Age has a negative effect on the share held in equities: each

extra year translates into a lower allocation to stocks by 93 basis

• points. This is remarkably close to the practitioners’ rule of

thumb of decreasing one’s equity exposure by 1 percent for each additional year of age.”

Modeling and identification

• Solution to optimal portfolio choice problem

will be of the form ωit = f (ait, bi, t, Wit, Zit) where:

ωit = share of financial wealth in equities ait = age of person i at time t bi = birth year of person i t = calendar time Wit = financial wealth of person i at time t Zit = other state variables and person-specific characteristics

Age, time, and cohort effects

• Well known identification problem
• Arises in many literatures, particularly labor

Age, time, and cohort effects

• Age effects: the change in ωit caused by a change in ait
• How much does the optimal equity share change as a result of

an individual being one year older?

• Time effects: the change in ωit caused by a change in t
• How much does the optimal equity share at time t differ from

that at time t-1?

• Technology changes, changing cost structures, shifting

expectations, or other time-specific developments

• Cohort effects: change in ωit caused by a change in bi
• How much does the optimal equity share of someone born in

1970 differ from that of someone born in 1969 (regardless of time

• r age)?
• Could be that those with differing experiences behave differently,

(e.g. some have memories of depression or 1970’s)

Problem: ait ≡ t - bi , so impossible to separately identify these without further assumptions.

• Figs 1 – 3 show that different stories can be

consistent with the same data

Age, time, and cohort effects (cont.)

Figure 1 Hypothetical Portfolio Share Data 0.59 0.60 0.61 0.62 0.63 0.64 39 40 41 42 43 44 45 46 47 48 49 50 51

Age Fraction of assets in equity

Figure 1 Hypothetical Portfolio Share Data 0.59 0.60 0.61 0.62 0.63 0.64 39 40 41 42 43 44 45 46 47 48 49 50 51

Age Fraction of assets in equity Time effect, no age effect, no cohort effect Cross section view: flat

Cross section view (Time t + 2) Cross section view (Time t + 1) Cross section view (Time t )

Figure 1 Hypothetical Portfolio Share Data 0.59 0.60 0.61 0.62 0.63 0.64 39 40 41 42 43 44 45 46 47 48 49 50 51

Age Fraction of assets in equity cohort effect, age effect, no time effect.

Cohort view Cohort view Cohort view

Cohort view: rising

Note that this explanation requires 2 effects, previous only 1

Figure 2 Hypothetical Portfolio Share Data

0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.60 0.61 0.62 0.63 54 55 56 57 58 59 60 61 62 Age Fraction of assets in equity

Cross section view

(Time t + 2)

Cross section view: Cohort view: declining flat cohort effect, no age effect, no time effect

• r

time effect, age effect no cohort effect. ,

Cohort view Cohort view Cohort view Cross section view

(Time t + 1)

Cross section view

(Time t )

Data: Surveys of Consumer Finances

• 1962 (SFCC), 1983, 1989, 1992, 1995, 1998
• Excellent balance sheet data on representative

sample

• Includes data on
• demographic characteristics
• wealth inside and outside of pensions
• Summary statistics (Table 1)
• Average portfolio shares (Table 2)

Data: TIAA-CREF

• Large sample (~16,000) of TIAA-CREF

participants

• Up to 13 years (52 quarters) of administrative

data on

• Contributions, accumulated balances, transfers
• Smaller sample (~2000 individuals) with one-

time survey of demographics and assets

• utside of TIAA-CREF, linked to 10 years of

quarterly administrative data.

Data: TIAA-CREF

• Advantages
• Actual account balances and transaction activity (from TIAA-

CREF), not based on survey responses

• Track same people over time
• Data on both “stock” of accumulated assets and “flow” of

new contributions

• Disadvantages
• Not representative of US population
• Limited info on demographics / assets outside of TIAA-CREF
• Individuals rather than households
• Institutional rules and changes may affect behavior (e.g.

transfer restrictions)

NEW Data: Vanguard IRA Holders

• Data on population of Vanguard clients with

assets in tax-deferred individual accounts, excluding employer plans, as of 12/31/2004.

• Limit to those with at least $5,000 in one fund

account at end 2004.

• Tax-deferred balances only
• ~ 2 million records at end 2004
• Historical balance data back to 1998,

reconstructed from transactional records

• VERY PRELIMINARY

Results

• First, we document three important features
• f household portfolio behavior

Non-stockownership

• About half of U.S. households do not own

stock (Table 6), but

• The fraction of households owning stock has

risen substantially

• ~70% of non-stockowners own little financial wealth, but the rest

do have financial wealth (Table 7)

• 20% of TIAA-CREF participants owned no stock in 1987 – by

1999, less than 15% own no stock Percentage of US households owning stock 1962 1989 1992 1995 1998 2001 ~23.9% 33.3% 37.6% 41.3% 49.4% 52.2%

Heterogeneity in choices

• TIAA-CREF Flows
• Wide range of allocations is used
• Clustering at specific points (0, 25, 50, 75, 100)

Infrequency of changes (Table 8)

• ver 40 quarters
• People who make asset reallocations also tend to

make flow reallocations

Results on age patterns

• Age patterns in level of equity share
• assets (SCF, TIAA-CREF)
• flows (TIAA-CREF)
• For each, examine
• Unconditional equity share
• Probability of ownership
• Equity share conditional on ownership

Figure 10 Equity Share in Assets TIAA-CREF Data 1987-1999

Figure 11 Fraction of Participants with Equity in Assets TIAA-CREF Data 1987-1999

Figure 12 Equity Share in Assets Among Equity Holders TIAA-CREF Data 1987-1999

Note large increases in equity share of young people in the 1990’s.

Equity share in contribution flows of individuals aged 28-30 1990 1999 31% 73%

Figure 13 Equity Share in Flows TIAA-CREF Data 1987-1999

Unconditional Equity Shares in Assets

Vanguard Retirement Account Holders, 1998-2004

• Higher equity

shares vs. TC data

• Influence of time

effects/markets is again apparent

• Largest changes

appear to have

• ccurred among

the OLD

• As of 2004, the
• lder cohorts are

holding MORE equity than in 1998.

Ownership of Equity in Assets

Vanguard Retirement Account Holders, 1998-2004

• Ownership

changes are still important

• Not as dramatic

as in earlier data

• > 70% of those in

their 70s still own some equity

• Ownership

actually rose in

• lder cohorts

• Similar patterns arise in both assets and flows
• Different identifying assumptions yield very different

results

• Crucial to examine separately ownership probability and

equity share conditional on ownership

• Little evidence supporting systematically declining age

pattern over entire period, with possible exception of decreasing probability of being stockowner at later ages

Bottom line so far

Further attempts to pin down age effects

• Examining cohort and time effects (parsimony

and plausibility criteria)

• Parameterizing cohort and time effects
• Looking at individual changes

“X” shaped pattern with no time effect

Age effect Cohort effect Time effect Requires very large increasing age effects and very large declining cohort effects Rule out on the grounds of parsimony and plausibility

Using Proxies for Cohort and Time Effects Rather than Unrestricted Dummies

• Time effects: Use average stock return over

previous 3 years as proxy for time effects

• Return coefficient is economically and statistically

significant, but X shape remains

• Cohort effects: Use (10 yr) average stock

return while individual was aged 15-25 (formative years)

• Return coefficient is economically small, other

estimates basically unchanged

Using Proxies for Cohort and Time Effects Rather than Unrestricted Dummies

• Cohort effects: Replace cohort effect with

year-of-entry effect

• Year-of-entry effect
• Statistically and economically significant
• Related to stock market patterns immediately prior

to year of entry

Using Proxies for Cohort and Time Effects Rather than Unrestricted Dummies

Year-of-Entry Effects and the Stock Market

• 1.00
• 0.50

0.00 0.50 1.00 1.50 Jun-63 Jun-64 Jun-65 Jun-66 Jun-67 Jun-68 Jun-69 Jun-70 Jun-71 Jun-72 Jun-73 Jun-74 Jun-75 Jun-76 Jun-77 Jun-78 Jun-79 Jun-80 Jun-81 Jun-82 Jun-83 Jun-84 Jun-85 Jun-86 Jun-87 Jun-88 Jun-89 Jun-90 Jun-91 Jun-92 Jun-93 Jun-94 Jun-95 Jun-96 Jun-97 Jun-98

Date Log of real S&P 500 cumulative return index (Dec 1964=0)

• 0.10
• 0.05

0.00 0.05 0.10 0.15 0.20 0.25

Year of entry effect (1985=0)

log real S&P 500 cumulative year-of-entry effects in assets year-of-entry effects in flows

Individual Changes in Equity Exposure (based on individual transaction data)

• Decompose ACt into the sum of five different

effects

• Market Effect
• Passive Flow Effect
• Active Flow Effect
• Withdrawal Effect
• Transfer Effect

Individuals in Accumulation Phase (no annuitizations or withdrawals) Table 9

• Very few individuals took active steps to decrease equity

positions; even fewer saw an actual decline.

• Vast majority of individuals did nothing or took active steps

to increase equity allocations as they aged over these 9 years.

• Note: These results most comparable to regression results

that include cohort effects but no time effects.

• Evidence of reductions in equity share prior to

annuitizations and withdrawals

• % of sample ↑ ≈ % of sample ↓ , but
• size of decreases (-35%) much larger
• But recall, restrictions prevent large changes out
• f TIAA, but not out of CREF.
• May be due to big prior market increases having

pushed up equity allocations. Individuals in the Decumulation Phase (With Withdrawals and/or Annuitizations) Table 10

Conclusions

• A seemingly simple question, but not so

simple to answer because

• Three properties of individual portfolio behavior
• nonstockownership
• heterogeneity
• infrequency of action
• Identification issues
• age, time, and cohort effects
• Lack of perfect data (i.e. panel data tracking all

components of wealth over entire lifetimes)

Excluding time effects yields an upward sloping age profile

• We reject resulting “X” shaped time and

cohort patterns on grounds of parsimony and plausibility

• We conclude that time effects belong in the

specification

Excluding cohort effects appears to yield a downward sloping age profile …

• Agnew, Balduzzi, Sunden (2003)
• Exclude cohort effects
• Look at asset shares 1994-1998
• Conclude that results consistent with declining

age effects and thus with financial planner advice

• We disagree with this conclusion…

Why we disagree… Consider first patterns for 25-55 year olds

• For 1994-1998, we also see a declining age profile
• But for 1987-1993, we see an increasing profile !
• Resembles Figure 3

Possible explanations

• People came to realize that optimal profile

should be declining, so young increased equity shares

• But no evidence that planned subsequent declines

actually occurred (recall only 14% made two or more active changes)

Possible explanations

• Young responded more strongly than old to changes

in economic environment

• Consistent with significant year of entry effects

related to recent returns

• During and after stock market boom in 1994-1998,

allocations of young higher than those of old

• After stock market crash of 1987, allocations of young lower

than those of old

• New entrants represent a greater fraction of young people

than they do of older people

• Decline disappears when look at balanced panel (no new

entrants)

• Under this interpretation, NO evidence of declining

age effects among 25-55 year olds

Why we disagree… Consider next patterns for 55-70 year olds

• Across all individuals, equity share is declining

Why we disagree… Consider next patterns for 55-70 year olds

• But all of the decline is in the probability of stock ownership
• And none of it is in the equity share conditional on ownership

• Even decline in ownership probabilities may be

partly due to cohort effects (earlier generation less likely to hold stocks throughout lives)

• We do find evidence that a small set of people

make large active transfers out of equity prior to annuitizations and withdrawals

• Need to keep in mind restrictions on TIAA

transfers and withdrawals, availability of annuity Why we disagree… Consider next patterns for 55-70 year olds

Conclusions

• No evidence supporting gradual, systematic

decline in equity shares with age

• At best, based on TIAA-CREF data, there is

some evidence of people shifting completely

• ut of equity around retirement as they begin to

withdraw or annuitize their money

• Most recent Vanguard data shows that equity

exposure among the old is still not uniformly decreasing (more to come…)

Future work

• Infrequency of decisions
• Investigate carefully how individuals choose their

allocation when first join a plan, or open an account

• Model fixed transaction costs or inertia that would

lead to infrequent changes

• Explore differences across taxable / tax deferred

registrations