Measuring
Volatility and the Cost of Retirement
By
Frank Armstrong III
NOVEMBER
2005  Few investors know whether they will be able to retire
with any level of comfort, and studies indicate that most
Americans choose to ignore the subject. The amount of investment
capital required to replace preretirement income is more than
most people think. Annual withdrawal rates of 4% to 6% require
that there be $16 to $25 of capital at work for every dollar
of income a portfolio must produce. An
individual’s income needs depend partly upon expectations
for a retirement lifestyle. Many retirees find that they
need as much or more than before retirement; a retiree probably
should not expect to be satisfied with less than 75% of
preretirement income. People more than a few years from
retirement must also account for inflation. A plan that
doesn’t account for inflation is doomed to fail. The
highest risk factor a retiree faces, and the only decision
directly under his control, is the withdrawal rate.
The
Volatility Effect
A tool
called the Monte Carlo simulation, along with a straightforward
computer spreadsheet, is enough to start focusing on solutions.
A Monte Carlo simulation uses random draws of numbers from
pools constructed with specified rates of return and volatility
(risk). Much like a lottery, values are drawn at random
from a pool of numbers to construct a single test. The process
is repeated many times, and a summary of the results provides
a quantitative estimate of the range and distribution of
the possible returns. Varying the construction of the pools
of numbers allows the planner to examine different strategies
to see which ones give a higher probability of success.
For
example, one could construct pools of numbers that have
an average rate of return of 10% and a standard deviation
of 10%. Using random draws from those pools, one can test
the survival rates of 4%, 5%, 6%, and 7% annual withdrawals.
The findings will generally confirm the pioneering 1990s
study by Phillip L. Cooley, Carl M. Hubbard, and Daniel
T. Walz that tracked failure rates against withdrawal amounts,
commencing in 1926 (using the S&P 500 and bonds in various
combinations over varying time periods). The study results
revealed that portfolio failure rates are directly related
to time horizon and withdrawal rates and are influenced
by asset allocation. One could run the simulation again
using a pool of numbers with a 10% return but a standard
deviation of 10%, 15%, and 20%, and assume a annual withdrawal
rate of 6%. At 30 years, only 1% of the trials with a 10%
standard deviation fail, but 23% fail at a standard deviation
of 20%. Failure rates soar with higher volatility. The point
is that all 10% returns are not equal (see the Exhibit).
The
simulation reveals a clear link between volatility and survival
of the portfolio at any given time horizon. Anything that
reduces portfolio volatility (given the same rate of return
and withdrawal rates) significantly enhances the probabilty
that a retiree’s nest egg will survive.
Totally
Skewed
In
the traditional analysis referred to above, one might have
assumed that half of all trials would result in greater
than expected returns, and half less. But the only case
where each trial yields the average result occurs where
there is no volatility. In that special case, every trial
survives and gets the identical result.
With
volatility, outcomes become skewed. Although one obtains
the expected rate of return across the sample, the median
return is less than the average. The higher the volatility,
the greater the sample becomes skewed at any time horizon.
So, although the average return meets expectations, the
median result is less than expected. As the number of failures
goes up, the number of extraordinary results also goes up.
A small number of portfolios will deliver much higher than
expected results, while a large number of portfolios either
fail or obtain lower than expected results.
For
example, assume an target terminal value of $100,000 for
a particular withdrawal rate, rate of return, and time horizon.
If one result yields $1 million, and nine results yield
$0 at some particular risk level, then the average return
has been achieved but nine out of 10 results are portfolio
failures.
The
importance of selecting a realistic withdrawal rate cannot
be overestimated.

If capital is insufficient, the retiree may be tempted
to increase the withdrawal rate.

A high withdrawal rate increases the probability of portfolio
failure.

Reaching for higher investment returns increases volatility,
which in turn increases the probability of portfolio failure.
Constructing
an Investment Strategy
Every
step of a financial plan must support the retiree’s
objectives. The ideal investment plan supports the required
withdrawal rate while maximizing the probability of success.
The first problem facing the retiree is that “guaranteed”
investment products are unlikely to provide sufficient total
return to meet reasonable needs. Meanwhile, equities are
too volatile to provide a reliable income stream. A combination
of stocks and bonds will probably best meet the need.
Because
at least part of the portfolio will be volatile, the issue
of risk management moves to the forefront. The first step
is to construct a “twobucket” portfolio. Bucket
1 would consist of adequate liquid reserves. Recognizing
that equity investments are too volatile to support even
moderate withdrawal rates safely, investors must temper
their portfolios with a nearriskless asset that will lower
the volatility at the portfolio level and be available to
fund withdrawals during downmarket conditions. As a minimum
liquidity requirement, highquality, shortterm bonds are
generally sufficient to cover five to seven years of income
needs at the beginning of retirement. While chasing higher
yields with longerduration or lowerquality issues may
be tempting, the enormous increase in risk often swamps
the small additional yield benefit.
An
individual who expects to draw down 6% of capital each year
for income needs should plan to have 30% to 42% of assets
in fixed investments. When the market takes a downturn,
the investor will have plenty of time for it to recover
while drawing down the bonds. This strategy protects growth
assets during market declines.
Bucket
2 would be the world equity market bucket. The design philosophy
here is to construct the equity portfolio with the highest
possible return per unit of risk. This investment policy
recognizes the impact of volatility and employs standard
portfolio construction concepts to reduce it. These wellknown
modern portfolio theory techniques include the use of multiple
asset classes with low correlations to one another. Some
planners use nine distinct global equity asset classes,
each with high expected returns at tolerable risk levels
and relatively low correlation to the others.
Withdrawal
Strategy: Preserve Volatile Assets in Down Markets
A rational
withdrawal strategy recognizes that equities are volatile
and shortterm bonds are not. Therefore, a sound strategy
is one designed to protect volatile assets during downmarket
conditions to avoid consuming excessive equity capital.
Most
financial advisors have been content to treat retirement
assets as a single portfolio with a targeted allocation,
say of 60% stocks and 40% bonds. This conception of a portfolio,
however, would lead to withdrawals on a pro rata basis from
both equity and fixed assets, regardless of market experience,
and does nothing to protect volatile assets during down
markets.
A far
superior strategy would treat the equity and bond portfolios
separately, then follow a rule for withdrawals that protects
equity capital during down markets by liquidating only bonds
during bad years. During good years, withdrawals are funded
by sales of equity shares, and any excess accumulation is
used to rebalance the portfolio back to the desired asset
allocation. Again, using spreadsheet models with Monte Carlo
simulations, this simple rule can be shown to result in
substantial incremental improvement in overall results.
Implementation
and Evaluation of Alternatives
A policy
of implementation via noload institutionalclass index
funds spreads risk as widely as possible in some of the
world’s most attractive markets while controlling
costs, preventing “style drift,” minimizing
taxes, and eliminating “management” risk.
The
Monte Carlo simulation is a powerful tool to evaluate alternative
strategies. For example, should an investor needing a 6%
withdrawal rate invest in a portfolio with a 10% return
and a 12% standard deviation, or one with an 11% return
with a 15% standard deviation? Does this answer depend on
the time horizon? Does the answer change if the withdrawal
rate changes? Monte Carlo simulations can guide an investor
to the best choice, based on personal requirements and goals.
The correct choice is the one that is most likely to succeed.
Frank
Armstrong III is the founder and principal of Investor
Solutions, Inc. (www.investorsolutions.com), a feeonly, SECregistered
investment advisor. He is also the author of The Informed
Investor: A HypeFree Guide to Constructing a Sound Financial
Portfolio (AMACOM).
