Morningstar Magazine - August/September 2017 - 44

Strategies

Lower Risk

Higher Risk

Typically Lower Rewards
EXHIBIT 2

between risk and expected return among
portfolios generally. In fact, in general,
it should be possible to lower risk and increase
expected return.

on forecasts of return, standard deviations,
and correlations. Collectively, the values of these
parameters are sometimes known as capital
market assumptions.

So far, the only constraint that I have placed on
portfolios is that they cannot have short positions.
In this case, we say that the frontiers are
unconstrained. However, in practice, investors who
use MPT place additional constraints on the
portfolios; for example, constraining foreign stocks
to be no more than 30% of the total allocation to
stocks. Another example is placing a cap, such as
limiting the allocation to commodities at 10%.
When these sorts of constraints are imposed when
applying MPT, the resulting efficient and
inefficient frontiers fall somewhere inside of the
unconstrained frontiers.

After the fact, or ex-post, the realized returns,
standard deviations, and correlation can be quite
different from the capital market assumptions.
To illustrate this, in EXHIB IT 4 , I created
the ex-post efficient frontier from the returns on
indexes representing the 13 asset classes in
E X H I BI T 1 using monthly returns over the 10-year
period June 2007 to May 2017. Because
this efficient frontier shows actual performance,
I show 10-year compound annual return on
the vertical axis rather than one-year expected
return as shown in EXHIB IT 1 .

1

1

9
%

Dev Mkts ex-US Stocks
US Mid-Cap Stocks

REITs
Emerging Mkt Stocks

6

Commodities

US Large-Cap Stocks
EFFICIENT PORTFOLIO

MOST INEFFICIENT
PORTFOLIO

TIPS
ST Core Bonds
Cash

IT Core Bonds

3

Gbl Ex US Govt Bonds
LT Core Bonds

0
0
5
Standard Deviation

10

15

20

25
%

Source: Morningstar, author's calculations.

44

5

6

7

3

4

5

6

7

Higher Risk
Typically Higher Rewards

Source: European Securities and Market Authority

1-Year Expected Return
US Small-Cap Stocks

2

Lower Risk
Typically Lower Rewards

The Efficient and Inefficient Frontiers All long-only portfolios fall between the most
efficient and inefficient frontiers.
Ineﬃcient Frontier

4

Example of a Fund That Would Fall Into Category 2:

EXHIBIT 1

Eﬃcient Frontier

3

The Synthetic Risk and Reward
Indicator

The right-most point on the ex-post efficient
frontier represents the portfolio with
the highest compound annual return. This portfolio
is composed of about 3% U.S. midcap stocks,

Ex-Ante Versus Ex-Post Frontiers
The efficient and inefficient frontiers that E X H I BI T 1
shows are ex-ante frontiers. That is, they are based

2

Typically Higher Rewards

Morningstar August/September 2017

10-Year Compound

70% U.S. small-cap stocks, and 27% long-term
core bonds; thus, it is to the left of the most
volatile asset classes. In general, the right-most
point of an efficient frontier with compound
return or geometric mean on the vertical axis
06/2012-05/2017
is a blend of two or more asset classes.
In contrast, as EXHIB IT 1 , the right-most point
of an unconstrained ex-ante frontier is 100% in
the asset class with the greatest expected
one-year return.

In EXHIB IT 4 , I plotted the realized 10-year
compound and annualized standard deviation of
the portfolios that constitute the ex-ante frontier.
The left part falls entirely below the ex-post
frontier, and the right part represents portfolios
that were more volatile than the ex-post efficient
portfolio with the greatest compound annual
return, but with lower returns.
EXHIB IT 4 drives home the point that portfolios
that are ex-ante efficient, based on forward0looking capital market
10 assumptions, will20turn out
Annualized 5-Year Standard Deviation
to be ex-post inefficient. In other words,
the ex-ante efficient frontier is ex-post inefficient.
This is because the ex-ante frontier is
based on forecasts that are highly unlikely to
be fulfilled exactly.

Summary
A common misunderstanding of modern portfolio
theory is that the riskier the portfolio, the
higher its expected return. However, this is only
true for portfolios that lie on the ex-ante efficient
frontier. All other portfolios are inefficient so
that there need not be a relationship between risk
and expected return. Thus, there is not only
an efficient frontier but also an inefficient frontier,

30
Table of Contents for the Digital Edition of Morningstar Magazine - August/September 2017
