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CHAPTER 4:
PORTFOLIO THEORY
Chapter 4 discusses the theory behind modern portfolio management.
Essentially,
portfolio
managers
construct
investment
portfolios
by
measuring a portfolio’s risks and returns. An understanding of the
relationship
between
portfolio
risk
and
correlation
is
critical
to
understanding modern portfolio theory.
A grasp of variance, standard
deviation, the Markowitz model, the riskfree rate, and the Capital Asset
Pricing Model (CAPM) are also needed.
Calculating Portfolio Returns
•
The expected return of a portfolio is simply the weighted average of returns on
individual assets within the portfolio, weighted by their proportionate share of the
portfolio
at the beginning of the measurement
.
Example 1:
Oliver’s portfolio holds security A, which returned 12.0% and security B, which returned
15.0%. At the beginning of the year 70% was invested in security A and the remaining
30% was invested in security B. Calculate the return of Oliver’s portfolio over the year.
R
p
= (.6x12%)+(.3x15%) = 12.9%
Example 2:
Oliver’s portfolio holds security A, which returned 12.0%, security B, which returned
15.0% and security C, which returned –5.0%. At the beginning of the year 45% was
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invested in security A, 25.0% in security B and the remaining 30% was invested in
security C. Calculate the return of Oliver’s portfolio over the year.
R
p
= (.45x12%)+(.25x15%)+(.3x(5%)) = 7.65%
Calculating Portfolio Risk
•
While there may be different definitions of risk, one widelyused measure is
called variance. Variance measures the variability of realized returns around an
average level. The larger the variance the higher the risk in the portfolio.
•
Variance is dependent on the way in which individual securities interact with each
other. This interaction is known as
covariance.
Covariance essentially tells us
whether or not two securities returns are correlated. Covariance measures by
themselves do not provide an indication of the degree of correlation between two
securities. As such, covariance is standardized by dividing covariance by the
product of the standard deviation of two individual securities. This standardized
measure is called the
correlation coefficient
.
Example 3:
Oliver’s portfolio holds security A, which returned 12.0% and security B, which returned
15.0%. At the beginning of the year 70% was invested in security A and the remaining
30% was invested in security B.
Given a standard deviation of 10% for security A, 20%
for security B and a correlation coefficient of 0.5 between the two securities, calculate the
portfolio variance.
AB
B
A
B
A
B
B
A
A
p
w
w
w
w
ρ
σ
σ
σ
σ
σ
2
2
2
2
2
2
+
+
=
(1)
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Portfolio Variance = (.7
2
x10
2
)+(.3
2
x20
2
)+(2x.7x.3x10x20x.5) = 127
Portfolio standard deviation is the square root of the portfolio variance.
%
27
.
11
127
=
=
p
σ
(2)
Equivalently:
Portfolio Standard Deviation = (127)
.5
=11.27%
The above example is for a portfolio that consists of two assets. You will find an
example of a three asset portfolio in the practice questions at the end of this chapter.
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This note was uploaded on 04/28/2010 for the course ECON FINC3017 taught by Professor Xelloss during the Spring '10 term at University of St Andrews.
 Spring '10
 Xelloss

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