978-0134083308 Chapter 5 Solution Manual Part 1

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Chapter 2 Securities Markets and Transactions 15

Chapter 5

Modern Portfolio Concepts

 Outline

Learning Goals

I. Principles of Portfolio Planning

A. Portfolio Objectives

B. Portfolio Return and Standard Deviation

C. Correlation and Diversification

1. Correlation

2. Diversification

D. International Diversification

1. Effectiveness of International Diversification

2. Methods of International Diversification

3. Costs of International Diversification

Concepts in Review

II. The Capital Asset Pricing Model

A. Components of Risk

B. Beta: A Measure of Undiversifiable Risk

1. Deriving Beta

2. Interpreting Beta

3. Applying Beta

C. The CAPM: Using Beta to Estimate Return

1. The Equation

2. The Graph: The Security Market Line

3. Some Closing Comments

Concepts in Review

III. Traditional Versus Modern Portfolio Theory

A. The Traditional Approach

B. Modern Portfolio Theory

1. The Efficient Frontier

2. Portfolio Betas

a. Risk Diversification

16 Smart/Gitman/Joehnk • Fundamentals of Investing, Thirteenth Edition

b. Calculating Portfolio Betas

c. Interpreting Portfolio Betas

3. The Risk-Return Tradeoff: Some Closing Comments

C. Reconciling the Traditional Approach and MPT

Concepts in Review

Summary

Key Terms

Discussion Questions

Problems

Case Problems

5.1 Traditional Versus Modern Portfolio Theory: Who’s Right?

5.2 Susan Lussier’s Inherited Portfolio: Does It Meet Her Needs?

Excel@Investing

 Key Concepts

1. The concept of a portfolio, the importance of portfolio objectives, and the calculation of the return

and standard deviation of a portfolio

2. The effect of positive and negative correlation and diversification on portfolio return and risk;

demonstrating that diversification’s advantages are greater when correlation is lower

3. The aspects of international diversification, including effectiveness, methods, and benefits

4. Modern risk concepts and the use of beta to measure the relevant risk in order to assess potential

investments

5. The two basic approaches to portfolio management—traditional portfolio management versus

modern portfolio theory (MPT)

 Overview

This chapter discusses the fundamentals of planning and building a portfolio, with special attention paid to

return correlation and systematic risk.

1. The chapter begins with the definition and possible objectives of a portfolio. The instructor should

stress the concept of a risk-return tradeoff—in order to get more return, an investor must bear more

risk. The chapter emphasizes that one of the major benefits of owning a portfolio is risk reduction

through diversification. The student learns to calculate portfolio returns and the standard deviation

of a portfolio.

2. The chapter discusses how correlation, a statistical measure of the relationship between securities

in a portfolio, and diversification are used to reduce risk and increase return.

3. The chapter discusses the numerous opportunities for international investment as well as the

methods, benefits, and effectiveness of international diversification.

Chapter 2 Securities Markets and Transactions 17

4. Beta is a modern measure of risk. Instructors can use the graphic derivation of beta, which is

demonstrated in the chapter, to discuss the interpretation and use of beta. The instructor may wish to

indicate some sources for obtaining betas for individual stocks and demonstrate the computation of

the required return in class.

5. While beta is a measure of risk, the link between risk and return is made using beta and the capital

asset pricing model (CAPM). The CAPM is graphically represented by the security market line

(SML). Understanding this model should enhance the student’s ability to grasp the true significance of

the risk-return tradeoff among assets. In addition, awareness of differing investor risk preferences—

risk-indifferent, risk-averse, and risk-taking, with the great majority of investors being risk-averse—

should further enhance their understanding of the risk-return tradeoff.

6. Special attention is paid to the varying risk premiums across asset classes.

7. The next section compares traditional portfolio management with modern portfolio theory. The

traditional approach to portfolio construction emphasizes balancing the portfolio by selecting

investments from a broad cross section of industries, while modern portfolio theory relies on such

statistical concepts as expected returns, standard deviation, correlation, and portfolio betas. It might

be helpful to note that MPT postulates a specific mathematical relationship between risk and return.

The beta equation shows such a relationship, where the bi measures the beta coefficient (the

undiversifiable or systematic risk) for company i. The risk-return tradeoff bears the same relationship.

 Answers to Concepts in Review

5.1 A portfolio is simply a collection of investments. An efficient portfolio is a portfolio offering the

highest expected return for a given level of risk.

5.2 The return of a portfolio is calculated by finding the weighted average of returns of the portfolio’s

component assets:

( ) ( ) ( )

1 1 2

p n j j

r w r w r w rn w r

= ´ + ´ + ´ = ´

=(r

–r)

t=1

¸(n–1).

18 Smart/Gitman/Joehnk • Fundamentals of Investing, Thirteenth Edition

Alternatively, for a portfolio invested in just two assets, if you know the standard deviation of each

asset and the correlation between them, you can use the equation shown at the bottom of Table 5.2 to

3. Correlation refers to the statistical measure of the relationship, if any, between two series of

numbers or two random variables. The correlation between asset returns is important in determining

how the movements of individual assets in a portfolio contribute to the portfolio’s movements.

Generally speaking, combining assets with returns that are not highly correlated with each other

produces a portfolio that has less risk than do the individual assets that make up the portfolio.

5.4 Diversification is a process of risk reduction achieved by including in the portfolio a variety

of investments having returns that are less than perfectly positively correlated with each other.

5.5 A portfolio’s return is always a simple weighted average of the returns of the assets in the portfolio.

In other words, a portfolio’s return will be somewhere between the return of the asset with the highest

return and the asset with the lowest return. But that statement is not necessarily true when it comes to

A portfolio’s return will always range between the return that the lowest-earning asset produces

and the return that the highest-earning asset produces. Where in this range a portfolio’s return lands

Chapter 2 Securities Markets and Transactions 19

(a) When assets in the portfolio are perfectly positively correlated, the portfolio’s

standard deviation will fall between the asset with the highest standard deviation and

(b) When assets in the portfolio have returns that are uncorrelated with each other (and

indeed even when the assets’ returns are simply less than perfectly positively

perfectly negatively correlated, there will be some combination of assets that produces

5.6 International diversification can often provide the benefits of higher returns and reduced risk.

There are several methods for achieving international portfolio diversification. International

diversification can be achieved by investing directly abroad in either U.S. dollar-denominated or in

foreign currency securities. Transaction costs for the direct purchase of foreign stocks can be quite

5.7 a. Diversifiable (unsystematic) risk is the part of an investment’s risk that the investor can

eliminate through diversification. Also called firm-specific risk, this kind of risk can be

eliminated by holding a diversified portfolio of assets. As an example, suppose that there are

b. Undiversifiable (systematic) risk refers to macroeconomic events or forces such as war, inflation,

or political events that affect nearly all investments. Undiversifiable risk, which cannot be

eliminated by holding a diversified portfolio, is the risk that matters most. Because investors can

5.8 Beta is a measure of systematic or undiversifiable risk. It is found by relating the historical returns on

a security with the historical returns for the market: in general, the higher the beta, the riskier the

security.

The market return refers to the return on a broad portfolio of stocks, and it is typically measured

20 Smart/Gitman/Joehnk • Fundamentals of Investing, Thirteenth Edition

By definition, the beta for the overall market is 1.0, and other betas are viewed in relation to this

benchmark. The positive or negative sign on a beta indicates whether the stock’s return changes in the

5.9 Betas are typically positive and range in value between 0.5 and 1.75. Most securities have positive

5.10 The capital asset pricing model (CAPM) links together risk and return to help investors make

investment decisions. It describes the relationship between required return and systematic risk, as

measured by beta. The equation for the CAPM is:

Expected return

on investment =Risk-free

rate

Beta for

investment

+ê

Expected Market

return

–

Risk-free

rate

[ ( )].

i rf j m rf

r r b r r= + ´ –

As beta increases, so does the required return for a given investment. The risk premium for the

specific asset,

[b  (rm  RF)], is the amount by which return increases above the risk-free rate to compensate for

the investment’s undiversifiable risk, as measured by beta. Risk premiums range from over

13% for small company stocks to under 2% for long-term government bonds. Investors in Treasury

bills do not earn a risk premium.

The security market line (SML) is a graphic representation of the CAPM and shows the required

return for each level of beta.

5.11 CAPM provides only a rough forecast of future returns, in part because the inputs that the model

requires are typically estimated using historical data. Investors who use the CAPM may make

subjective adjustments to the model’s predictions based on other information that they possess.

5.12 Traditional portfolio management emphasizes “balancing” the portfolio. The traditional portfolio

includes a wide variety of stocks and/or bonds that emphasize diversification between industries. The

securities selected are usually high quality and issued by stable, established companies and/or

5.13 Modern portfolio theory (MPT) is based on the use of statistical measures including mathematical

concepts such as correlation (of rates of return) and beta. Combining securities with less than perfect

Chapter 2 Securities Markets and Transactions 21

The feasible or attainable set of all possible portfolios refers to the risk-return

combinations achievable with all possible portfolios. It is derived by first calculating the return and

risk of all possible portfolios and plotting them on a set of risk-return axes (see Figure 5.7).

5.14 The efficient frontier consists of all efficient portfolios (those that maximize the portfolio’s return for

each risk level). Thus, the efficient frontier is part of the feasible set—indeed the most desirable part

Plotting an investor’s utility function or risk indifference curves on the graph with the

5.15 The two kinds of risk associated with a portfolio are diversifiable (or unsystematic) risk and

undiversifiable (or systematic) risk. Diversifiable (unsystematic) risk is the risk unique to each

investment that can be eliminated through diversification, by selecting stocks possessing different

5.16 Beta is an index that, according to the CAPM, measures the expected change in a security’s or

portfolio’s return relative to a change in the market return. For example, if a security has a beta of 2.0

5.17 Modern portfolio theory requires the use of sophisticated computer programs and mathematical

techniques that are beyond the reach of the average individual investor. On the other hand, the

(1) Determine how much risk he or she is willing to bear.

(3) Using beta, assemble a diversified portfolio consistent with an acceptable level of risk.

 Suggested Solutions to Discussion Questions

Answers will vary with student responses.