Modern Portfolio Theory:
Expectation vs. Reality
A White Paper by Manning & Napier
www.manning-napier.com
Unless otherwise noted, all figures are based in USD.
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Modern Portfolio Theory: Expectation vs. Reality | A White Paper by Manning & Napier
Academic studies have shown that the asset allocation
decision accounts for a meaningful portion of long-term
portfolio returns1. As such, the asset allocation decision
remains the central element of portfolio construction in
the investment industry today. While there are numerous
methods and theories designed to aid with the asset
allocation decision, Modern Portfolio Theory (MPT)
remains one of the most popular. Invented by Harry
Markowitz in the 1950s, MPT is based on several key
principles:
• Portfolios are described by various levels of expected
risk and return
• Expected risk is defined as volatility of expected returns
(i.e., standard deviation)
• “Optimal” portfolios can be constructed by either
minimizing expected risk for a given level of expected
return or maximizing return for a given level of risk.
The attractiveness and longevity of MPT likely, in part,
rests on its simplicity. The theory condenses the often
complex realm of investor goals and objectives into
quantitative expected risk and return statistics. With
these volatility and return inputs along with correlations
(a measure of how two asset classes/securities move in
relation to each other) between various asset classes,
MPT states that investors can construct portfolios that are
designed to meet their goals and objectives.
Within the scope of MPT, one portfolio is considered
superior to another if it either achieves a greater level of
expected return for a given level of expected standard
deviation or a lower level of standard deviation for a given
return. All portfolios that maximize expected return at
various volatility levels or minimize expected volatility
and various return levels are considered “optimal” and
lie on the “efficient frontier” (illustrated on the right). For
example, portfolio 3 would not be considered optimal as
portfolio 1 is expected to achieve a higher return at the
same standard deviation. Likewise, the chart illustrates
that MPT assumes that investors will demand a higher
level of expected return as a portfolio’s expected volatility
increases (i.e., investors require compensation for taking
on additional “risk”). Hence, MPT implies a positive
relationship between expected returns and expected
volatility.
Efficient Frontier
18
16
14
Optimal Portfolio 2
12
Return
MPT Background
10
Optimal Portfolio 1
8
6
Portfolio 3
4
2
0
0
5
10
15
20
25
30
35
Standard Deviation
While the following analysis focuses primarily on the
quantitative aspects of MPT (e.g., return and volatility
inputs), the theory relies on several more theoretical
assumptions which have also been debated since its
introduction. Several of these assumptions are listed
below.
• The financial markets are efficient (i.e., a security’s
market price accurately reflects its value and all the
available information about the security). While rather
elegant in theory, the concept of market efficiency has
been repeatedly contested in the industry leading to
several varieties of the “efficient market hypothesis.”
• Investors are rational and are able to accurately evaluate
the value of various securities in the context of their
own risk tolerance and market/economic fundamentals.
Observations of actual investor behavior have led
many to question the assumption of investor rationality.
In fact, the field of behavioral finance has formalized
several specific examples of irrational investor behavior
including “herding” and “anchoring bias.”
• Financial transactions including investing, lending, and
borrowing can be executed without costs. In reality, any
participant in the financial markets likely knows from
experience that transaction costs not only exist but can
meaningfully affect investment returns.
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Modern Portfolio Theory: Expectation vs. Reality | A White Paper by Manning & Napier
While some investors may consider MPT an intuitive
method for constructing portfolios, the actual applications
of MPT generally differ from that of the theory along
several notable dimensions.
• While MPT is designed to utilize expected return and
volatility assumptions, historical data is most often
utilized in practice due to the potential difficulty of
making precise, forward looking return and standard
deviation estimates.
• The number of asset classes included in portfolio
construction may have meaningful effects on the
composition of the optimal portfolio.
• Because optimal portfolios based on MPT, at times, can
be relatively undiversified (i.e., concentrated in certain
asset classes), portfolios are constructed with asset
class constraints (e.g., no more than 20% in small cap
stocks).
In general, both the use of historical data and asset class
constraints are understandable from a practical standpoint.
However, their widespread use when constructing MPTbased portfolios may lead to actual portfolio returns and
volatility over a given time period that differ meaningfully
from those expected for optimal portfolios. Additionally,
these optimal portfolios may adjust their asset class
exposure somewhat slowly over time even as market
conditions change meaningfully. Likewise, the specific
asset classes included in the optimization process are
likely to have a significant impact on the final composition
of the optimal portfolio.
Using Historical Returns
According to MPT, the first step in determining an optimal
asset allocation is generating the required return and risk
inputs. These inputs should theoretically represent forward
looking return and volatility expectations for various
asset classes. However, most investors recognize that
accurately predicting future returns and volatility statistics
across asset classes is extremely challenging. In general,
while it may be possible to position a portfolio to take
advantage of certain short-term market return drivers or
potentially benefit from broad based long-term themes,
very few investors would likely express a great degree of
confidence if asked to predict equity returns for the next
10 to 20 years to the nearest percent. Thus, in lieu of
making forward looking return predictions most investors
utilize historical return and volatility data as inputs into
their MPT models.
Of course history isn’t static, and if a person looks back at
the fifty years from 1930 to 1980 compared to the following
twenty years (i.e., 1980 to 2000) they would probably
agree that the two periods have many notable differences.
For instance, one can point to differences in technology,
the labor markets, and the state of global trade. However,
when investors use historical data to construct optimal
portfolios, they are implicitly making the assumption that
the future will be like the present, when this has obviously
not been the case.
To illustrate this point, the charts below and on the
following page show the efficient frontiers and optimal
portfolios for the three 20 year periods from 10/1954 to
9/2014. The charts map how the efficient frontier evolved
over time and clearly show that portfolios considered
optimal during one 20 year period were meaningfully
different from the optimal portfolio in the subsequent 20
year period.
Assumptions for the scenario are as follows:
• Portfolios include 4 asset classes: Cash2, U.S.
Intermediate-Term Govt. bonds3, U.S. large cap stocks4,
U.S. small cap stocks5.
• Expected returns and volatility based on historical asset
class data from 10/1954 to 9/2014.
• Optimal portfolios designed to minimize standard
deviation at a target annualized return of 8% (i.e., the
approximate long-term return of a portfolio consisting
of 50% U.S. large caps stocks / 50% U.S. IntermediateTerm Govt. bonds).
• Charts illustrate the efficient frontier and optimal portfolio
for the three non-overlapping 20 year periods from
10/1954 to 9/2014.
Efficient Frontiers (Mean Variance
Optimization)
24
Return (Arithmetic Mean)
MPT Application
20
16
12
8
4
0
0
5
10
15
20
25
10/1994 to 9/2014
3
Standard Deviation
10/1954 to 9/1974
10/1974 to 9/1994
Modern Portfolio Theory: Expectation vs. Reality | A White Paper by Manning & Napier
Asset Allocation of Optimal Portfolio
Asset Class Returns/Standard Deviations
Asset Class
10/1954 to
9/1974
10/1974 to
9/1994
10/1994 to
9/2014
Asset Class
10/1954 to
9/1974
10/1974 to
9/1994
U.S. Large
Cap Stocks
22%
1%
16%
U.S. Small Cap
Stocks
9.4% / 19.0%
20.3% / 20.9%
U.S. Small
Cap Stocks
47%
5%
21%
Cash
3.9% / 0.5%
7.3% / 0.8%
Intermediate
Govt Bonds
10%
7%
63%
Cash
21%
87%
0%
As the illustrations show, when utilizing the parameters and
assumptions presented in the above scenario, the optimal
portfolio for achieving the 8% return target from 10/1954
to 9/1974 would have been fairly diversified across asset
classes. This hypothetical optimal portfolio based on MPT
would have provided meaningful exposure to U.S. large
and small cap stocks, as well as to cash and intermediateterm government bonds. However, in the subsequent 20
year period, an optimal portfolio would have substantially
reduced exposure to U.S. small cap stocks (transitioning
from an allocation of 47% to 5%), almost eliminated U.S.
large cap stock exposure, and been invested primarily in
cash.
These meaningful changes in portfolio composition are
understandable as cash provided an especially attractive
tradeoff for reaching an 8% target return during the second
20 year time period. While over the two 20 year time
periods the volatility of cash returns remained virtually
unchanged from one period to the next, absolute returns
increased from approximately 4% annualized to more than
7% over the next 20 years. As such, even though U.S.
small cap stocks generated approximately 20% returns
between 10/1974 and 9/1994, allocating the majority of the
portfolio’s assets to cash would have sufficed to come close
to the required 8% return target. Thus, a much smaller
allocation to small cap stocks was optimal given their
significantly higher volatility (i.e., a standard deviation of
approximately 21% versus 1% for cash).
Substantial variation between the allocations of the
optimal portfolios for the 10/1974 to 9/1994 and 10/1994
to 9/2014 20 year periods is also evident. While cash
returns from 10/1974 to 9/1994 were sufficient to warrant
an approximate 87% allocation in the optimal portfolio, the
optimal cash allocation decreased to 0% in the following
20 year period. Cash was largely replaced by intermediateterm government bonds in the optimal portfolio as the
Federal Funds Rate declined from approximately 15% at
the beginning of 1982 to between 0-0.25% as of 9/30/2014.
Correlations among various asset classes can play
a large role in determining the asset allocation of the
“optimal” portfolio. However, just as return and volatility
characteristics have varied over time, asset class
correlations can also differ across market environments.
For example, from 10/1974 to 9/1994 the correlation
between U.S. large cap stocks and intermediate-term
government bonds was 0.28. That correlation decreased to
-0.20 during the next 20 years. These swings in correlation
are likely to have notable effects on portfolio construction
within an MPT framework since the return and volatility
profile of various asset class combinations can vary as
their correlations change. Overall, this analysis illustrates
that asset class returns, volatility, and correlations have
varied widely even over longer-term time periods which
makes forecasting these statistics based on historical data
a challenging exercise.
Determining the Number of Asset Classes
Since MPT-based optimal portfolios can, at times, have
concentrations in a given asset class, constraints are often
imposed to construct what investors consider to be more
diversified portfolios. However, even before constraints are
placed on certain asset class allocations, an investor must
determine which asset classes will be utilized to construct
the optimal portfolio. As the table below illustrates, the
addition of even a single asset class can meaningfully
change the asset allocation of the optimal portfolio.
Asset Allocation of Optimal Portfolio
(10/1994 to 9/2014)
Asset Class
Without Long
Govt Bonds
With Long
Govt Bonds
U.S. Large Cap Stocks
16%
11%
U.S. Small Cap Stocks
21%
14%
Intermediate Govt
Bonds
63%
45%
Cash
0%
0%
Long Govt Bonds
0%
30%
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Modern Portfolio Theory: Expectation vs. Reality | A White Paper by Manning & Napier
Specifically, the scenario on the previous page analyzes
the impact of adding long-term government bonds6 to
the asset class mix utilized in the prior scenario for the
period of 10/1994 to 9/2014 (i.e., the last 20 years). It is
evident that the addition of long-term government bonds
meaningfully changes the composition of the optimal
portfolio. For example, assuming the 8% return target
utilized throughout this analysis, an optimal portfolio
which does not include long-term government bonds
would allocate approximately 21% and 63% to U.S. small
cap stocks and intermediate-term government bonds,
respectively. However, when long-term government bonds
are included, the optimal portfolio assigns a 30% allocation
to the asset class and the optimal U.S. small cap and
intermediate-term government bond allocations decline
to 14% and 45%, respectively. Thus, the number of asset
classes utilized to construct the optimal portfolio may have
a meaningful impact on its ultimate composition. In turn,
having a clear understanding of why certain asset classes
are included in the optimization process is an important
factor in analyzing the results of MPT-based portfolio
optimization.
Imposing Asset Class Constraints
To illustrate the effects that constraints can have on the
composition of the optimal portfolio, the chart below
compares constrained versus unconstrained optimal
portfolios during the 20 year periods from 10/1974 to
9/1994 and 10/1994 to 9/2014. The unconstrained portfolio
during each 20 year period utilizes the same asset classes
outlined on page 3, while the constrained portfolio imposes
the following asset class constraints.
•
•
•
When compared to the optimal unconstrained portfolio,
it is evident that the optimal constrained portfolio has
generally remained more static over time. For example,
without imposing constraints, the optimal allocation to
intermediate-term government bonds during the period of
10/1974 to 9/1994 would have been only approximately
7%. That allocation would have increased significantly to
approximately 63% during the next 20 years. In contrast,
the allocation to intermediate-term government bonds
would have remained relatively static at between 55% and
60% during each 20 year period when constraints were
added.
Looking at the actual returns and volatility characteristics
of the constrained versus unconstrained portfolios, the
effects of constraints resulted in portfolios that would
have been considered “sub-optimal” based on MPT
during both 20 year periods. For example, from 10/1974
to 9/1994, the relatively static 30% U.S. large cap
stock allocation imposed by the constraints would have
resulted in a portfolio with a higher than desired return
and volatility profile. Specifically, the “optimal” asset mix
in the constrained portfolio had a minimum return of
approximately 11% (versus the desired 8% target), along
with a standard deviation of 8% versus only 2% for the
unconstrained portfolio which held mostly cash. Despite
exceeding the target return, the constrained portfolio
would still be considered “sub-optimal” according to
MPT as investors could have achieved an 11% return
target over the period with a standard deviation of only
approximately 7%.
Maximum 10% cash
Maximum 20% U.S. small cap stocks
Minimum 30% U.S. large cap stocks.
Asset Allocation of Optimal Portfolio
100%
87%
90%
80%
63%
60%
70%
55%
60%
50%
30%
40%
30%
20%
10%
0%
1%
5%
7%
10/1974 - 9/1994 w/o Constraints
0%
10%
10/1974 - 9/1994 w/ Constraints
U.S. Large Cap Stocks
16%
31%
21%
14%
0%
10/1994 - 9/2014 w/o Constraints
U.S. Small Cap Stocks
Intermediate Govt Bond
0%
10/1994 - 9/2014 w/ Constraints
Cash
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Modern Portfolio Theory: Expectation vs. Reality | A White Paper by Manning & Napier
Conclusion
Overall, while Modern Portfolio Theory enjoys widespread
use in the investment industry, investors should keep
in mind several potential issues that may arise with the
theory’s actual application. First, the use of historical data
to generate inputs implies that future asset class returns
and volatility will reflect those of the past when, in fact,
return and volatility statistics within a given asset class can
vary greatly even over longer-term time periods. Second,
the asset classes utilized in the optimization process
can have a meaningful impact on the composition of the
optimal portfolio. As such, it is important to understand
why certain asset classes are included or excluded in the
modeling process. Lastly, imposing asset class constraints
could result in portfolios which may not truly be optimal
as defined by MPT and potentially lead to muted portfolio
adjustments in response to changing market conditions.
Ultimately, the successful application of MPT will depend
on an investor’s ability to accurately forecast future
returns and volatility statistics, utilize the “correct” mix of
asset classes, and effectively impose constraints without
resulting in portfolios considered “sub-optimal.”
When deciding the merits of MPT, investors should also
evaluate its more theoretical assumptions including the
concepts of market efficiency and investor rationality.
Numerous market bubbles and crashes over the past
century have led many investors to question the concept
of market efficiency as certain market segments at times
reached valuations which, in retrospect, were not entirely
consistent with their underlying fundamentals. Additionally,
differences between the long-term performance of various
investment products versus the actual performance of
individual investors who held those products, accounting
for their buy and sell decisions, appear somewhat contrary
to the assumption of investor rationality.
Thus, while Modern Portfolio Theory may provide investors
with information that may be useful in a specific context,
an appropriate asset allocation for a portfolio should
depend on the current market environment, as well as an
investor’s long-term goals and objectives, including their
time horizon, spending needs and specific circumstances.
Moreover, while making precise forward looking asset
class return predictions has proved challenging for most
investors, we believe that an active, disciplined investment
process that takes into account current market conditions
has the potential to identify attractive securities and market
segments across a variety of market environments.
Analysis by Manning & Napier.
Morningstar, Inc. is a global investment research firm providing data, information, and analysis of stocks and mutual funds. ©2014 Morningstar, Inc. All rights reserved. The information contained herein: (1) is
proprietary to Morningstar and/or its content providers; (2) may not be copied, adapted or distributed; and (3) is not warranted to be accurate, complete or timely. Neither Morningstar nor its content providers are
responsible for any damages or losses arising from any use of this information, except where such damages or losses cannot be limited or excluded by law in your jurisdiction. Past financial performance is no
guarantee of future results.
1
As an example, “Determinants of Portfolio Performance II, An Update” published in the May-June 1991 issue of the Financial Analysts Journal.
2
Cash data is reflective of the Ibboston Associates SBBI U.S. 30 Day Treasury Bill Index, which is an unmanaged index representing the U.S. 30 Day Treasury Bills. The index is constructed as a one-bill portfolio
containing the shortest-term bill having not less than one month to maturity. The Index returns do not reflect any fees or expenses. Index returns provided by Morningstar.
3
U.S. Intermediate Government Bond data is reflective of the Ibbotson Associates SBBI U.S. Intermediate-Term Government Bond Index, which is an unmanaged index representing the U.S. intermediate-term
government bond market. The index is constructed as a one bond portfolio consisting of the shortest-term non-callable government bond with no less than 5 years to maturity. The Index returns do not reflect any
fees or expenses. Index returns provided by Morningstar.
4
U.S. Large Cap Stock data is reflective of the Ibbotson Associates ABBI U.S. Large Cap Index, which is an unmanaged index representing the S&P 500 Index. The S&P 500 Total Return Index is an unmanaged,
capitalization-weighted measure of 500 widely held common stocks listed on the New York Stock Exchange, American Stock Exchange, and the Over-the-Counter market. The Index returns assume daily reinvestment of dividends and do not reflect any fees or expenses. S&P Dow Jones Indices LLC, a subsidiary of the McGraw Hill Financial, Inc., is the publisher of various index based data products and services and has
licensed certain of its products and services for use by Manning & Napier. All such content Copyright ©2014 by S&P Dow Jones Indices LLC and/or its affiliates. All rights reserved. Neither S&P Dow Jones Indices
LLC, Dow Jones Trademark Holdings LLC, their affiliates nor their third party licensors make any representation or warranty, express or implied, as to the ability of any index to accurately represent the asset class
or market sector that it purports to represent and none of these parties shall have any liability for any errors, omissions, or interruptions of any index or the data included therein. The Index returns do not reflect any
fees or expenses. Index returns provided by Morningstar.
5
U.S. Small Cap Stock data is reflective of the Ibbotson Associates SBBI U.S. Small Cap Index, which is an unmanaged index representing the U.S. small cap stock market. Index returns are the total return
achieved by the DFA U.S. Micro Cap Portfolio net of fees and expenses, defined as the lowest 5% of the market defined as the aggregate of the NYSE, NYSE Amex Equities, and NASDAQ National Market System,
or companies smaller than the 1,500th largest U.S. Company in the same universe. Prior to 2001, the portfolio is defined as the lowest 20% of the market. Prior to 1982, returns are before-transaction-cost and do
not include fees or expenses. Index returns do not reflect any fees of expenses Index and are provided by Morningstar.
6
U.S. Long Government Bond data is reflective of the Ibbotson Associates SBBI U.S. Long-Term Government Bond Index, which is an unmanaged index representing the U.S. long-term government bond market.
The index is constructed as a one bond portfolio consisting of the shortest-term non-callable government bond with no less than 20 years to maturity. The Index returns do not reflect any fees or expenses. Index
returns provided by Morningstar.
Approved CAG-CM PUB049 (11/14)
6