

Investment
Analysis & Portfolio Management
(FIN630)
VU
Lesson
# 35
PORTFOLIO
SELECTION
Building
a Portfolio Using Markowitz
Principles:
To select an
optimal portfolio of financial
assets using the Markowitz
analysis; investors
should;
1.
Identify optimal riskreturn
combinations available from
the set of risky assets
being
considered by
using the Markowitz
efficient frontier analysis.
This step; uses the
inputs
from, the expected returns,
variances, and covariances for a set of
securities.
2.
Choose the final portfolio
from among those in the
efficient set based on
an
investor's
preferences.
Using
the Markowitz Portfolio Selection
Model:
Even
if portfolios are selected
arbitrarily, some diversification
benefits are gained.
This
results
in a reduction of portfolio risk.
However, to take; the full
information set into
account,
we use portfolio theory as
developed by Markowitz, Portfolio
theory is nonnative,
meaning
that it tells investors; how
they should act to diversify
optimally. It is based on a
small
set of assumptions,
including;
1. A
single investment period;
for example, one
year.
2.
Liquidity of positions; for
example, there are no
transaction costs.
3.
Investor preferences based only on a
portfolio's expected return and risk;
as
measured
by variance or standard deviation.
Efficient
Portfolios:
Markowitz's
Approach to portfolio selection is
that an investor should
evaluate portfolios on
the
basis of their expected returns and
risk as measured by the standard
deviation. He was
the
first to derive the concept
of an efficient portfolio, defined as one
that, has the
smallest
portfolio
risk for a given level of
expected return or the largest expected
return for a given
level
of risk. Rational investors will
seek ethcient portfolios,
because these portfolios
are
optimized
on the two dimensions of
most importance to investors, expected
return and risk.
The
basic details of how to
derive efficient portfolios? In
brief, based on inputs
consisting
of
estimates of expected return and risk
for each security being
considered of well as the
correlation
between pairs of securities, an
optimization program varies
the weights for
each
security
until an efficient portfolio is
determined. This portfolio will
have the maximum
expected
return for a given level of
risk or the minimum risk
for a given level of
expected
return.
Selecting
an Optimal Portfolio of Risky
Assets:
Once
the efficient set of
portfolios is determined using
the Markowitz model,
investors must
select
from this set the
portfolio most appropriate
for them. The Markowitz
model does not
specify
one optimum portfolio. Rather it
generates the efficient set
of portfolios, all of
which,
by definition; are optimal
portfolios (for a given
level pf expected return or
risk).
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Investment
Analysis & Portfolio Management
(FIN630)
VU
In
economics in general and finance in
particular, we assume investors
are risk averse. This
means
that investors, if given a
choice, will not take a "fair
gamble," defined as one with
an
expected
payoff of zero and equal
probabilities of a gain or a loss. In
effect, with a fair
gamble,
the disutility from the
potential loss is greater than the
utility from the
potential
gain.
The greater the risk
aversion; the greater the
disutility from the
potential loss.
ALTERNATIVE
METHODS OF OBTAINING THE EFFICIENT
FRONTIER:
The
singleindex model provides an
alternative expression for
portfolio variance, which
is
easier
to calculate than in the
case of the Markowitz
analysis. This alternative
approach
can be
used to solve the portfolio
problem as formulated by
Markowitzdetermining the
efficient
set of portfolios. It requires
considerably fewer
calculations.
The
Single  Index
Model:
William
Sharpe, following Markowitz, developed
the singleindex model,
which relates
returns
on each security to the
returns on a common index. A broad
market index of
common
stock returns is generally
used for this purpose. Think
of the S&P 500 as this
index.
The
singleindex model can be expressed by
the following
equation:
Ri = αi
+ βiRM + еi
Where;
Ri = the return (TR) on
security i
RM = the return (TR) on
the market index:
αi = that part
of security i's .return
independent of market
performance
βi = a constant
measuring the expected change in the
dependent variable, Ri given
a
change in
the independent variable, RM
еi = the random
residual error;
The
singleindex model divides a
security's return into two
components: a unique
part,
represented by
ai and a market
related part represented by βiRM. The
unique part is a
micro
event,
affecting an individual company
but not all companies in
general. Examples
include
the
discovery of new ore reserve, a fire, a
strike, or the resignation of a
key company figure.
The
market related part, on the
other hand, is a macro event
that is broad based and
affects
all
(or; most) firms. Examples
include a Federal Reserve announcement
about the discount
rate,
a change in the prime rate, or an
unexpected announcement about
the money supply.
Given
these values, the error
term is the difference
between the lefthand side
of the
equation,
the return on security i,
arid the righthand side of
the equation, the sum of
the two
components
of return. Since the singleindex
model is, by definition,
equality, the two
sides
must
be the same.
Selecting
Optimal Asset Classesthe Asset
Allocation Decision:
The
Markowitz model is typically
thought of in terms of selecting
portfolios of individual
securities;
indeed, that is how Markowitz expected
his model to be used. As we
know,
however,
it is a cumbersome model to employ
because of the number of
covariance
estimates
needed when dealing with a
large number of individual
securities.
An
alternative way to use the
Markowitz model as a selection
technique is to think in
terms
199
Investment
Analysis & Portfolio Management
(FIN630)
VU
of
asset classes, such as
domestic stocks, foreign stocks of
industrialized countries,
the
stocks of
emerging markets, bonds, and so forth.
Using, the model in this
manner, investors
decide
what asset classes to own
and what proportions of the
asset classes to
hold.
The
allocation of a portfolio's funds to
classes of assets, such as
cash equivalents,
bonds,
and equities
The
asset allocation decision
refers to the allocation of
portfolio assets to broad
asset
markets;
in other words, how much of
the portfolio's funds are to
be, invested in stocks, in
bonds,
money market assets, and so
forth. Each weight can range from
zero percent to 100
percent.
Asset allocation is one of the most;
widely used applications of
modern portfolio
theory
(MPT).
Examining
the asset allocation
decision globally leads us to
ask the following
questions:
1.
What percentage of portfolio
funds is to be invested in each of
the countries for
which
financial markets are
available toinvestors?
2.
Within each country, what
percentage of portfolio funds is to be
invested in stocks,
bonds,
bills, and other
assets?
3.
Within each of the major
asset .classes, what
percentage of portfolio funds is to
be
invested
in various individual securities?
Many
knowledgeable market observers agree
that the asset allocation
decision is the most
important
decision made by an investor.
According to some studies, for
example, the asset
allocation
decision accounts for more
than 90 percent of the
variance in quarterly returns
for
a
typical large pension
fund.
The
rationale behind this approach is
that different asset classes
offer various
potential
returns
and various levels of risk, and
the correlation coefficients
between some of these
asset
classes may be quite tow,
thereby providing beneficial
diversification effects. As
with
the
Markowitz analysis applied to
individual securities, inputs
remain a problem,
because
they
must be estimated. However, this" will
always ¥e a problem in investing,
because we
are
selecting assets to be held
over the uncertain
future.
The
Impact of Diversification on
Risk:
The
Markowitz analysis demonstrates that
the standard deviation of a portfolio is
typically
less
than the weighted average of
the standard deviations of the securities
in the portfolio.
Thus,
diversification typically reduces
the risk of a portfolioas
"the number of
portfolio
holdings
increases, portfolio risk
declines.
.
Systematic
and Nonsystematic Risk:
The
riskiness of the portfolio
generally declines as more stocks
are added, because we
are
eliminating
the nonsystematic risk, or
companyspecific risk. This is
unique risk related to
a
particular
company. However, the extent
of the risk reduction
depends upon the degree
of
correlation
among the stocks. As a general
rule, correlations among
stocks, at least domestic
stocks and
particularly large domestic stocks,
are positive, although less
than 1.0. Adding
more
stocks will reduce risk at first, but no
matter how many partially
correlated stocks we
add
to the portfolio, we can riot
eliminate all of the risk.
Variability in a security's
total
returns
that is directly associated
with overall movements in
the general market or
economy
is
called systematic risk, or
market risk, or non
diversifiable risk. Virtually
all securities
have
some systematic risk,
whether bonds or stocks, because
systematic risk
directly
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Investment
Analysis & Portfolio Management
(FIN630)
VU
encompasses
interest rate risk, market
risk, and inflation
risk.
After
the non systematic risk is
eliminated, what is left is
the non diversifiable
portion, or
the
market risk (systematic
part). This part of the
risk is inescapable, because no matter
how
well
an investor diversifies, the
risk of the overall market
cannot he avoided.
Investors
can construct a diversified portfolio and
eliminate part of the total
risk, the
diversifiable
or non market, part. As more
securities are added, the
non systematic risk
becomes
smaller and smaller, and the
total risk for the
portfolio approaches its
systematic
risk.
Since diversification cannot reduce
systematic risk, total
portfolio risk can be reduced
no
lower than the total
risk of the market
portfolio. Diversification can
substantially reduce
the
unique risk of a portfolio.
However, we cannot eliminate
systematic risk.
Clearly,
market
risk is critical to all
investors. It plays a central
role in assetpricing, because it is
the
risk
that investors can expect to be
rewarded for taking.
The
Implications of the Markowitz Portfolio
Model:
The
construction of optimal portfolios and
the selection of the best
portfolio for, an
investor
have
implications for the pricing
of financial assets. Part of the
riskiness of the,
average
stock
can be eliminated by holding a
welldiversified portfolio. This
means that part of
the
risk
of the average stock can be
eliminated and part cannot.
Investors need to focus on
that
part
of 'the risk that cannot be
eliminated by diversification, because
this is the risk
that
should
be priced in the financial
markets.
The
relevant risk of an individual
stock is its contribution to
theriskiness of a well
diversified
portfolio. The return that
should be expected on the basis of
this contribution can
be estimated by
the capital asset pricing
model.
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