Morningstar - Summer 2019 - 60

Strategies

SCA N T R IGGE R
LAU NCH COMPANI ON V I DE OS

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What Harry Markowitz Doesn't Like
About the CAPM
Nobel laureate takes aim at an
unrealistic assumption.

QUANT U

Paul D. Kaplan
Modern Portfolio Theory and the Capital Asset
Pricing Model are two of the pillars of
modern finance. In fact, the first time that the
Nobel Memorial Prize in Economic Sciences
was awarded to financial economists in
1990, it was shared by the creator of MPT, Harry
Markowitz, and the best known of the creators
of the CAPM, William Sharpe.1 While MPT
and CAPM are related, they are distinct
theories that unfortunately are often confused.
In fact, as I discuss in this issue of Quant
U, Markowitz, the creator of MPT, has been
a leading critic of the CAPM.

CAPM, Markowitz (2005) lists the assumptions of
the CAPM and takes aim at the ones he finds
most objectionable. Markowitz writes that if one
makes the following assumptions:
A1 Transaction costs and other illiquidities can

be ignored,
A2 All investors hold mean-variance efficient portfolios,
A3 All investors hold the same (correct) beliefs about

means, variances, and correlations of returns
of securities, and
A4 Every investor can lend all she or he has or can
borrow all she or he wants at the risk-free rate.
then Conclusion 1 follows:
C1 The market portfolio is a mean-variance efficient

portfolio.
Before getting into Markowitz's critique of the
CAPM, we need to make the most important
distinction between MPT and the CAPM-
namely, the type of economic theory that each
represents. MPT is an example of normative
economics; that is, it is a model of how investors
ought to behave. In contrast, the CAPM is
an example of positive economics; it is meant
to be a description of how financial markets
and investors behave.2
Assumptions of the CAPM
All economic models are built from a set of
assumptions, and the CAPM is no exception.
Economists often debate a model's
assumptions. In a masterful critique of the

C1 also follows, Markowitz says, if A4 is replaced
by A4':
A4' Investors can sell short without limit and use the

Morningstar Summer 2019

X1 + X2 + X3 = 1
Note that this places no limits on short selling.
The allocation X1 = 1,000%, X2 = 100%, X3 = -1,000%
is allowed under assumption A4'.
Markowitz points out that in practice, investors
cannot short sell like this. This is the constraint for
i = 1, 2, 3, X i ≥ 0
EXHIB IT 1 illustrates both the budget constraint
and the prohibition against short selling when
there are three securities.

proceeds of the sale to buy long positions.

Markowitz takes aim first at assumption A4', then
at assumption A4. Here, I present his critique
of assumption A4'. I will address assumptions A3
and A4 in future issues of Quant U.
A Three-Security Example
Markowitz uses a three-security example to
illustrate his points, which he presents graphically.

1 The 1990 Nobel prize was also shared by Merton Miller.
2 For more on the distinction between normative and positive economics, see Friedman (1953).

I recast his graphical analysis in a way that
I believe makes his points clearer. Suppose that
we have three securities, which we refer
to as Security 1, Security 2, and Security 3.
For a given portfolio, let Xi denote the allocation
to Security i. Under assumption A4', the only
constraint that each investor faces is the
budget constraint that the sum of the allocations
must equal 100%:

Each corner of the triangle in EXHIBIT 1 represents
a 100% allocation to the security indicated
by the label. Each point on each side of the
triangle represents a portfolio of the two securities
at the corners that the side connects, with
a 0% allocation to the security at the remaining
corner. Each point inside of the triangle represents
a portfolio in which all three securities are
held long. Points outside of the triangle represent
portfolios that contain short positions.

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