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ALLOCATION BASICS
THE MOST IMPORTANT DECISIONThe art and science of asset allocation is concerned with
determining the most efficient combinations of assets
for a portfolio, in other words, the combinations that
yield the highest return for a given level of risk or
the lowest level of risk for a given level of return.
Most portfolios are not efficient - they yield too little
return for the risk or too much risk for the return.
An investment portfolio that yields the highest level of
return for the risk an individual or organization is
willing to assume is the optimal portfolio for that
individual or organization.
Determining the optimal portfolio allocation is the most
important decision individual investors, endowment
managers, trustees, and fiduciaries can make. No other
investment management decision is as important.
For
an individual saving for retirement, an optimal asset
allocation can result in a more secure retirement with
less worry in pre-retirement years.
For
a non-profit organization, an optimal asset allocation
can result in higher endowment returns and more robust
endowment growth. It can also reduce the variability of
endowment returns thereby providing more reliable
program support and institutional stability.
THE BENEFITS OF DIVERSIFICATION
The benefits of diversification are sometimes
counter-intuitive. Although most investors understand
that it’s best not to keep all their eggs in one basket,
the benefits of diversification go beyond reducing the
chances of loss by not having too much invested in one
place – like Enron employees with their 401k funds all
in the company stock or the charities and investors who
had all their money with Bernie Madoff.
Diversification can offer positive benefits because it
is possible to reduce the risk of a portfolio by adding
a risky asset to it. That’s right. The lowest risk
portfolio is not necessarily the one composed of just
low risk assets. The classic case is an investor who
wants to avoid the swings of the stock market and opts
for a 100% bond portfolio. But a 100% bond portfolio is
not the lowest risk portfolio he can construct. By
adding some stocks to his portfolio, he can reduce the
total risk below what he could achieve with bonds alone,
and increase his long-term return.
This
is not as mysterious as it may seem. Diversification
offers positive benefits because returns on different
assets don’t all move together. Bond returns are often
strongest when stock returns are weakest and vice versa.
Some stock markets may go up when others go down. Real
estate returns may do well when neither stocks nor bonds
are performing. In technical parlance, when returns on
different asset classes are not highly positively
correlated, investors are likely to benefit by
diversifying their investments across the range of asset
classes. Doing so will enable them to achieve a higher
level of return with a lower level of risk than would be
achievable with a more narrowly diversified portfolio,
or even with a portfolio concentrated in just low risk
assets.
AN EXAMPLE
Consider the following example. We start with a set of
asset categories that we might choose to invest in. We
map the choices by plotting the risk and return
characteristics of the different asset classes and
combinations of classes on a graph with return plotted
on the vertical axis and risk plotted on the horizontal
axis. We use the variability of returns as
measured by standard deviation for the risk measure (see
the Risk Primer article
for why we use this measure). For the return measure, we
use the average expected return from the class. The
plots of some individual asset classes are displayed
below.
A
Map of Return and Risk Characteristics of Selected
Individual Asset Classes
Figure 1: Return/risk Map of Selected Individual Asset
Classes
Source: Advisor
Our
primary interest is not in the choices among individual
asset classes but in the choices among portfolios
constructed by combining asset classes in various ways.
For example, if we construct a portfolio divided 50/50
between U.S. large-cap stocks and intermediate-term U.S.
Treasuries, we can expect the risk and return
characteristics shown on the next chart (Figure 2). Note
that although the expected return on the mixed portfolio
is just the weighted average of the expected returns of
the two components, the risk is less than the average of
the two because of how returns on the two classes have
been correlated.
A
Map of the Return and Risk Characteristics of a Blended
Portfolio
and Selected Individual Asset Classes
Figure 2: Return/risk Map of Selected Individual Asset
Classes
Source: Advisor
If
we add a third asset class to the mix, we get even more
interesting results. If we add commodities, which have
a lower expected return than our 50/50 portfolio and
higher risk than either of the two components, we get a
portfolio with a higher expected return and with less
risk. Once again, this is due to how returns on the
three asset classes have been correlated, with
commodities showing a negative correlation to both
stocks and bonds. The results are mapped on the next
chart (Figure 3).
A
Map of the Return and Risk Characteristics of Selected
Portfolios
and Individual Asset Classes
Figure 3: Return/risk Map of Selected Portfolios and
Individual Asset Classes
Source: Advisor
As we
add more asset classes to the mix and vary the amounts
allocated to each, we get more interesting results. The
next chart (Figure 4) shows the risk and return
characteristics of more than 11,000 possible portfolios
constructed from fifteen asset classes. The 11,451
portfolios mapped in the chart were constructed by
varying the amounts allocated to each of fifteen asset
classes in various combinations. Each point on the chart
corresponds to the return and risk characteristics of a
possible portfolio.
A Map of Return and Risk Characteristics of 11,451
Possible Portfolios
Constructed from 15 Asset Classes
Figure 4: Return and Risk Characteristics of 11,451
Portfolios
Constructed from 15 Asset Classes
Source:
Advisor
The
possible risk and return outcomes are clearly bounded,
as Figure 4 shows. To the extreme right, outcomes are
bounded by the point determined by a 100% allocation to
the highest return/risk asset class, venture capital in
this case. To the bottom, as indicated by the turquoise
line on the chart, outcomes are bounded by those
combinations that yield the lowest return for a given
risk level—what we might term the least efficient
frontier. To the top and left, as indicated by the red
line, outcomes are bounded by those combinations that
yield the highest return for a given level of risk—the
efficient frontier. These are the optimal, most
efficient combinations. For a given risk level, no
greater return is possible from any combination of
assets. Alternatively, we can look at the efficient
frontier as mapping the lowest level of risk achievable
for a given level of return. No matter how we combine
assets, we cannot build a portfolio with less
variability than that on the efficient frontier. The
efficient frontier is exactly that; it is impossible to
achieve a point above or to the left (to the northwest)
of the efficient frontier line. It is impossible to
construct a portfolio with higher returns or lower risk.
BUILDING AN OPTIMAL PORTFOLIO
To build an optimal portfolio, then, we start with three
tasks each requiring a set of informed judgments about
the asset categories we are considering for investment.
The Asset Allocation Advisor considers a minimum
of seventeen asset classes.
First, we make judgments about the likely returns
provided by each class. (View a sample
table of the projected three-to-five year total returns
(pdf) from each asset class). Commentary on projected
returns is available in
capital
market outlook features of the
Asset Allocation Advisor. The
Advisor does not just rely on
historical returns for future projections but develops
projections based on fundamental analysis of market
conditions and valuations trends for various asset
classes. This analysis is spelled out as explicitly as
possible to allow readers to evaluate the analyses and
to make alternative projections should their judgment
differ significantly on key factors.
Second, we make judgments about the risks associated
with an investment in each class. A sample
table of the projected standard deviations of annual
returns (pdf) for each asset class is available.
Commentary regarding risk assessment is available in the
Risk section of the Advisor.
Third, we make judgments about how the various asset
classes are likely to perform relative to each other.
View a
table of the projected correlations of returns (pdf).
Commentary regarding correlations is available in the
article “Correlation” in the
Q4 2006 issue and in the Risk section of the
Advisor. Please note that the
current table of projected correlations has been revised
from that in the Q4 2006 issue.
Given a set of expected returns, risks, and
correlations, we can calculate the most efficient
combination of assets for each risk or return level. If
we map the maximum return/minimum risk levels achievable
by various asset combinations, we get the following
picture:
The red line is the efficient frontier. It represents
the maximum return/minimum risk levels that can be
achieved with any combination of assets. It is
impossible to achieve return and risk levels above the
line no matter how we combine assets. The arrow on the
chart points to the location along the efficient
frontier corresponding to a portfolio with a 15%
standard deviation of annual returns. The maximum
expected return from all portfolios with a 15% standard
deviation is indicated by this point. The maximum
expected return in this case is approximately 11.2% per
year. To achieve a higher expected return, we have to
assume more risk.
Each point along the efficient frontier has a specific
combination of assets corresponding to it – from a
mixture dominated by low risk/low return assets at the
left end of the efficient frontier to a mixture
dominated by high risk/high return assets at the right
end of the efficient frontier.
We are most interested in the portfolio that matches our
risk needs and tolerances. An investor typically will
have a minimum risk exposure necessary to achieve return
targets and a maximum risk exposure determined by what
is prudent in view of the investor’s or organization’s
circumstances and tolerances. For more on determining
your risk positions see the Risk section.
Since individuals and organizations have different risk
tolerances, we have picked a benchmark portfolio along
the efficient frontier to track over time to see how
changing market conditions, valuations, and expected
asset class returns affect the composition of the
portfolio. The benchmark portfolio is the most efficient
one yielding an expected return of ten percent. The
location of this portfolio along the efficient frontier
is marked with a star. See the
10% Portfolios for
reports on the changing composition and performance of
these portfolios.
Finally, it should be noted that calculating efficient
frontiers and the portfolios along them is not an
elementary task. Although it is possible to do simple
mean-variance optimization with a spreadsheet, more
robust calculations require advanced computational
techniques. In addition, simple mean-variance
optimization has been superseded by a new optimization
methodology, resampled efficiency, that calculates
efficient frontiers over a range of statistically
equivalent sets of assumptions and reduces the extent to
which simple mean-variance optimization results were
critically dependent on assumptions that could easily be
mis-specified. The results reported by the
Asset Allocation Advisor make
use of the more advanced optimization methodologies.
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West Hartford