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INVESTMENTS:Analysis and Management

Second Canadian Edition

W. Sean Cleary

Charles P. Jones

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Chapter 8

Portfolio Selection

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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.

Separate total risk into systematic and non-

systematic risk.

Learning Objectives

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Step 1: Use the Markowitz portfolio selection

model to identify optimal combinations

Step 2: Consider borrowing and lendingpossibilities

Step 3: Choose the final portfolio based on

your preferences for return relative to risk

Building a Portfolio

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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 portfolios

expected return and risk

Portfolio Theory

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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

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All other portfolios in attainable set are

dominated byefficient 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

An Efficient Portfolio

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Bx

A

Cy

Risk =

E(R)

Efficient frontier or

Efficient set

(curved line from Ato B)

Global minimum

variance portfolio(represented by

point A)

Efficient Portfolios

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Another way to use the Markowitz model is

with asset classes

Allocation of portfolio assets to broad assetcategories

Asset class rather than individual security

decisions most important for investors

Different asset classes offers various returnsand levels of risk

Correlation coefficients may be quite low

Selecting Optimal Asset Classes

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Optimal Risky Portfolios

Investor Utility Function

Efficient Frontier

E (R)

*

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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

Borrowing and Lending Possibilities

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Riskless assets can be

combined with any

portfolio in the efficientset AB

Z implies lending

Set of portfolios on line

RF to T dominates allportfolios below it

B

A

T

Risk

E(R)

RF

L

Z X

Risk-Free Lending

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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

Borrowing Possibilities

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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 investors risk-return preferences

The New Efficient Set

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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

Portfolio Choice

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Investors should focus on risk that cannot be

managed by diversification Total risk =

Systematic (non-diversifiable) risk

+

Non-systematic (diversifiable) risk

Implications of Portfolio Selection

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Systematic risk

Variability in a securitys total returns directlyassociated with economy-wide events

Common to virtually all securities

Systematic risk

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Non-Systematic Risk

Variability of a securitys 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 well-diversified portfolio

Portfolios rather than individual assets most

important

Non-Systematic Risk

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p %35

20

0

Number of securities in portfolio

10 20 30 40 ...... 100+

Total risk

Systematic Risk

Diversifiable

Risk

Portfolio Risk and Diversification

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Copyright 2005 John Wiley & Sons Canada, Ltd. All rightsreserved. Reproduction or translation of this work beyond thatpermitted by Access Copyright (The Canadian CopyrightLicensing Agency) is unlawful. Requests for further informationshould be addressed to the Permissions Department, John Wiley& Sons Canada, Ltd. The purchaser may make back-up copiesfor his or her own use only and not for distribution or resale. Theauthor and the publisher assume no responsibility for errors,omissions, or damages caused by the use of these programs orfrom the use of the information contained herein.

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