INVESTMENTS:
Analysis and Management
Second Canadian Edition
W. Sean Cleary
Charles P. Jones
Chapter 8
Portfolio Selection
Learning Objectives
• State three steps involved in building a portfolio.
• Apply the Markowitz efficient portfolio selection
model.
• Describe the effect of risk-free borrowing and
lending on the efficient frontier.
• Discuss the separation theorem and its
importance to modern investment theory.
• Separate total risk into systematic and nonsystematic risk.
Portfolio Selection
• Diversification is key to optimal risk
management
• Analysis required because of the infinite
number of portfolios of risky assets
• How should investors select the best risky
portfolio?
• How could riskless assets be used?
Building a Portfolio
• Step 1: Use the Markowitz portfolio selection
model to identify optimal combinations
• Step 2: Consider borrowing and lending
possibilities
• Step 3: Choose the final portfolio based on
your preferences for return relative to risk
Portfolio Theory
• Optimal diversification takes into account all
available information
• Assumptions in portfolio theory



A single investment period (one year)
Liquid position (no transaction costs)
Preferences based only on a portfolio’s
expected return and risk
An Efficient Portfolio
• Smallest portfolio risk for a given level of
expected return
• Largest expected return for a given level of
portfolio risk
• From the set of all possible portfolios

Only locate and analyze the subset known as
the efficient set
•
Lowest risk for given level of return
An Efficient Portfolio
• All other portfolios in attainable set are
dominated by efficient set
• Global minimum variance portfolio

Smallest risk of the efficient set of portfolios
• Efficient set

Segment of the minimum variance frontier
above the global minimum variance portfolio
Efficient Portfolios
x
E(R) A
y
C
Risk = 
B
• Efficient frontier or
Efficient set
(curved line from A
to B)
• Global minimum
variance portfolio
(represented by
point A)
Selecting an Optimal Portfolio of
Risky Assets
• Assume investors are risk averse
• Indifference curves help select from efficient
set



Description of preferences for risk and return
Portfolio combinations which are equally
desirable
Greater slope implies greater risk aversion
Selecting an Optimal Portfolio of
Risky Assets
• Markowitz portfolio selection model



Generates a frontier of efficient portfolios
which are equally good
Does not address the issue of riskless
borrowing or lending
Different investors will estimate the efficient
frontier differently
•
Element of uncertainty in application
Selecting Optimal Asset Classes
• Another way to use the Markowitz model is
with asset classes

Allocation of portfolio assets to broad asset
categories
•

Asset class rather than individual security
decisions most important for investors
Different asset classes offers various returns
and levels of risk
•
Correlation coefficients may be quite low
Optimal Risky Portfolios
Investor Utility Function
E (R)
Efficient Frontier
*

Borrowing and Lending Possibilities
• Risk-free assets



Certain-to-be-earned expected return, zero
variance
No correlation with risky assets
Usually proxied by a Treasury Bill
•
Amount to be received at maturity is free of
default risk, known with certainty
• Adding a risk-free asset extends and changes
the efficient frontier
Risk-Free Lending
L
B
E(R)
T
Z
X
• Riskless assets can be
combined with any
portfolio in the efficient
set AB

Z implies lending
• Set of portfolios on line
RF to T dominates all
portfolios below it
RF
A
Risk
Impact of Risk-Free Lending
• If wRF placed in a risk-free asset:
 Expected portfolio return
E(R p )  w RFRF  (1 - w RF )E(R X )
▪ Risk of the portfolio
 p  (1 - w RF ) X
• Expected return and risk of the portfolio with lending
is a weighted average
Borrowing Possibilities
• Investor no longer restricted to own wealth
• Interest paid on borrowed money


Higher returns sought to cover expense
Assume borrowing at RF
• Risk will increase as the amount of borrowing
increases

Financial leverage
The New Efficient Set
• Risk-free investing and borrowing creates a
new set of expected return-risk possibilities
• Addition of risk-free asset results in


A change in the efficient set from an arc to a
straight line tangent to the feasible set without
the riskless asset
Chosen portfolio depends on investor’s riskreturn preferences
Portfolio Choice
• The more conservative the investor, the more
that is placed in risk-free lending and the less
in borrowing
• The more aggressive the investor, the less
that is placed in risk-free lending and the
more in borrowing

Most aggressive investors would use leverage
to invest more in portfolio T
The Separation Theorem
• Investors use their preferences (reflected in
an indifference curve) to determine their
optimal portfolio
• Separation Theorem


The investment decision regarding which risky
portfolio to hold is separate from the financing
decision
Allocation between risk-free asset and risky
portfolio separate from choice of risky
portfolio, T
Separation Theorem
• All investors


Invest in the same portfolio
Attain any point on the straight line RF-T-L by
either borrowing or lending at the rate RF,
depending on their preferences
• Risky portfolios are not tailored to each
individual’s taste
Implications of Portfolio Selection
• Investors should focus on risk that cannot be
managed by diversification
• Total risk =

Systematic (non-diversifiable) risk
+

Non-systematic (diversifiable) risk
Systematic risk
• Systematic risk


Variability in a security’s total returns directly
associated with economy-wide events
Common to virtually all securities
Non-Systematic Risk
• Non-Systematic Risk


Variability of a security’s total return not
related to general market variability
Diversification decreases this risk
• The relevant risk of an individual stock is its
contribution to the riskiness of a welldiversified portfolio

Portfolios rather than individual assets most
important
Portfolio Risk and Diversification
p %
Total risk
35
Diversifiable
Risk
20
Systematic Risk
0
10
20
30
40
......
Number of securities in portfolio
100+
Appendix 8-A: Modern Portfolio Theory
and the Portfolio Management Process
• Demonstrated by the impact on regulations
governing the investment behaviour of professional
money managers
• Require them to adhere to “prudence, loyalty,
reasonable administrative cost, and diversification”
• Portfolio management process:




Designing an investment policy
Developing and implementing an asset mix
Monitoring the economy, the markets, and the client
Adjusting the portfolio and measuring performance
Copyright
Copyright © 2005 John Wiley & Sons Canada, Ltd. All rights
reserved. Reproduction or translation of this work beyond that
permitted by Access Copyright (The Canadian Copyright
Licensing Agency) is unlawful. Requests for further information
should be addressed to the Permissions Department, John Wiley
& Sons Canada, Ltd. The purchaser may make back-up copies
for his or her own use only and not for distribution or resale. The
author and the publisher assume no responsibility for errors,
omissions, or damages caused by the use of these programs or
from the use of the information contained herein.