Life Cycle Investing

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Life Cycle Investing.Hickman et. al, JPM
Winter 01
Financial Planners recommend as investor
approach retirement, portfolios should shift
toward safer categories of securities, i.e., from
small-cap to large-cap funds, and than few years
before retirement, shifting to bonds or even
Treasury bills. The problem with these
recommendation is that when to shift is a
guess. Explain the concept of risk aversion
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Life Cycle Investing.Hickman et. al, JPM
Winter 01
Life Cycle Investing and Risk Tolerance Burton
Malkeil (1996) - risk tolerance is a function of
attitude toward and his/her risk capacity. Risk
attitude is subjective but capacity is related to
investors place in the life cycle. Older
investors have less opportunity to recoup
financial losses, thus less capacity for risk
exposure. Portfolio composition will be different
at different stages of their life cycle.
Samuelson (1994)- younger investors may lean
toward equities
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Life Cycle Investing.Hickman et. al, JPM
Winter 01
Because they may work harder to compensate for
unlucky stock losses. McEnally (1985) - The
variability of ending wealth increases as the
holding period increases, i.e., risk increases
as holding period lengthens. Thorley (1995)
counters McEnally - greater risk is mainly
uncertainty about how much better equity will do
than T-bills. Only upside uncertainty as stocks
very rarely underperform bonds. Investors
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Life Cycle Investing.Hickman et. al, JPM
Winter 01
are choosing what to invest in and not whether
to Invest. Investment decisions are based on
relative performance. If X is riskier than Y, but
the return on X is always greater than Y,
relative performance determines the correct
investment choice. Probability that the higher
returns will be realized increases as the holding
period increases.
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Life Cycle Investing.Hickman et. al, JPM
Winter 01
Purpose of this Study Quantify the likelihood
that stocks will outperform bonds, and bonds will
outperform bills, etc., over various holding
periods. Analyze the interplay between the
investment horizon and the risk-return
performance over six classes of securities.
Security classes are large-cap and small-cap
intermediate and long term govt.. bonds and
corporate and Treasury bills.
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Life Cycle Investing.Hickman et. al, JPM
Winter 01
Useful for assessing the composition of
portfolios at any point in an investors life
cycle while allowing for individual differences
for risk tolerance.
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Life Cycle Investing.Hickman et. al, JPM
Winter 01
Data and Methodology Review Malkiels
results, Exhibit 2. B has higher mean and higher
standard deviation. No inference can be drawn
based on the mean-variance criteria. Decision is
based on individual risk tolerance. However, if B
is highly correlated with A, B will always be
preferred regardless of their degree of risk
aversion.
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Life Cycle Investing.Hickman et. al, JPM
Winter 01
Data Ibbotson and Sinquefield data over the
period of 1926-97 (70 years) is used. Allowed two
independent non-overlapping 30 year holding
period to analyze. Not enough observations to
draw any reliable conclusions. To remedy -
sample monthly returns with replacement was used.
Allowed as many holding periods of varied length
to examine.
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Life Cycle Investing.Hickman et. al, JPM
Winter 01
Examined holding period ranging from 1 year to
30 years, drawing 500 observations per period.
To construct a 10 year holding period, 120
months were randomly selected. For each month, a
vector of returns for each asset type (T-bills,
Intermediate Govt.. bond ...etc.) is used to
form six holding-period wealth relatives, one
corresponding to each security type. Wealth
Relative Return of 0.20, 0.40 and -0.05,
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Life Cycle Investing.Hickman et. al, JPM
Winter 01
the three year wealth relative is equal to
(1.2)(1.4)(0.95) 1.25. 1 invested at the
beginning of the period will grow to 1.25 by the
end of the period. Differences between wealth
relatives are then calculated as Small Cap -
Large Cap Large Cap - Corp. Bonds Corp. Bonds -
LT Govt.. Bonds LT Govt.. Bonds - Int. term Govt.
Bonds Int. term Govt. Bonds - Treasury Bills
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Life Cycle Investing.Hickman et. al, JPM
Winter 01
Since assets and asset classes are highly
correlated, relative returns (Rb- Ra) are
analyzed. If the distribution of pair wise return
difference is positive 100 of the time, B would
dominate regardless of the degree of risk
aversion. Explain Exhibit 3 - Correlation
matrix of assets. - Results suggest that not all
assets are mutually exclusive - Explain.
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Life Cycle Investing.Hickman et. al, JPM
Winter 01
Exhibit 4-Descriptive statistics Major
Findings ? Great difference in wealth relatives
between security classes over long holding
periods. 30 year holing period ending wealth
T-bill 3.03 vs. small-stock 120.72. No
advantage to investing in long-term over
intermediate term govt. bonds. Explain. Risk
(standard deviation) for 30 year holding period
for small stocks is 300.82 vs. 59.96 for SP.
Risk may largely offset larger return.
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Life Cycle Investing.Hickman et. al, JPM
Winter 01

• Median yields ( 29.43 for small vs. 21.31 for
  SP) is much closer. Extreme skewness on wealth
  relatives distribution. Small stock risk is
  mainly upside risk
• Exhibit 5- Percentage of Differential Wealth
  Relatives falling below zero.
• Exhibits 4 and 5- Major Findings
• Benefits of moving to higher-risk classes as
  ones holding periods lengthens.

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Life Cycle Investing.Hickman et. al, JPM
Winter 01

• No compelling reason to move into high risk Bonds
  with longer holding periods
• Exhibit 11contains differential mean wealth
  relatives data. For 20 year hp, by investing in
  SP 500, one would expect to earn 8.82 over LT
  Corporate bonds. Median is 5.8 that indicates a
  positively skewed distribution. Upside
  uncertainly regarding the assets performance.

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Life Cycle Investing.Hickman et. al, JPM
Winter 01

• Asset Allocation and Life Cycle Investing
• Malkiel Approach
• (in their 20s) (in their 60s)
• Equity 70 Equity 30
• Bonds 25 Bonds 70
• Cash 5
• Rule of Thumb
• 100 minus your age, i.e,
• Equity 80 Equity 40
• Bonds 20 Bonds 60

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Life Cycle Investing.Hickman et. al, JPM
Winter 01

• Implied involves discrete shifts from one asset
  class to another as ones holding period shortens
  ad expected underperformance likelihood exceeds a
  critical value of 30.
• SP 500 is an indexing benchmark
• Equity 95 in SP 500
• T-bills 5

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Life Cycle Investing.Hickman et. al, JPM
Winter 01

• Exhibit 14 Mean Ending Wealth-Forty years of
  investing. Simulation is repeated 500 times.
  Modeled retirement savings by beginning with a
  portfolio initially valued at 100, then adding
  100 to the principal each month over the 40 year
  period.
• Results in Exhibit 14 are startling. Ending
  wealth for SP 500 is around 5million while
  traditional allocation models are around
  800,000.
• Traditional Models avoid underperformance only

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Life Cycle Investing.Hickman et. al, JPM
Winter 01

• by 12. Therefore, the expected cost is high in
  terms of foregone wealth, while the expected
  benefits appear insignificant.
• To determine whether the benefits are
  substantial for shorter holding period, ending
  portfolio values with various holding periods
  were computed. Exhibit 15 contains the results
  of 10, 20 30 and 40 year investment horizons.

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Life Cycle Investing.Hickman et. al, JPM
Winter 01
Summary of results Over shorter horizons,
the allocation models performs better at reducing
risk without causing the severe penalties for
ending wealth. For a 10 year horizon, the chance
that the SP will under-perform any of the three
models is 26, almost half of 40 year horizon.
Yet the implied model performs as well as SP.
For a 20 year horizon, ending wealth based
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Life Cycle Investing.Hickman et. al, JPM
Winter 01
on Implied Model (174,416) vs. SP (150,972),
while SP under-performs this portfolio by nearly
30 of the time. The traditional models severely
under-performs both the Implied model and the SP
model. All models over all horizons exhibit
positive skewness (mean exceeds median), i.e,
potential for upside gains.
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Life Cycle Investing.Hickman et. al, JPM
Winter 01
Conclusions High correlations across class of
securities make direct comparisons of mean and
variance difficult. Relative performances are
better variables to analyze. For longer holding
periods, there will be significantly huge
penalties for not pursuing risky investments,
i.e., equities.
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Life Cycle Investing.Hickman et. al, JPM
Winter 01
There seem to be little benefit, yet higher
risk, associated with investing in longer-term
bonds versus intermediate-term bonds.