Fundamentals of corporate finance 10e ROSS JORDAN chap013

Chapter Outline• Expected Returns and Variances • Portfolios • Announcements, Surprises, and Expected Returns • Risk: Systematic and Unsystematic • Diversification and Portfolio Risk • S

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Return, Risk, and the Security

Market Line

Chapter

13

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Chapter Outline

• Expected Returns and Variances

• Portfolios

• Announcements, Surprises, and Expected Returns

• Risk: Systematic and Unsystematic

• Diversification and Portfolio Risk

• Systematic Risk and Beta

• The Security Market Line

• The SML and the Cost of Capital: A Preview

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Chapter Outline

• Portfolios

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Expected Returns

• Expected returns are based on the probabilities

of possible outcomes

• In this context, “expected” means average if

the process is repeated many times

• The “expected” return does not even have to be

E

1

) (

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Example: Expected

ReturnsSuppose you have predicted the following returns for stocks C and T in three possible states of the economy

2 What are the expected returns?

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Variance and Standard

Deviation

•Variance and standard deviation

measure the volatility of returns

•Using unequal probabilities for the

entire range of possible outcomes

•Weighted average of squared deviations

σ

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Example: Variance and

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Another Example

Consider the following information:

State Probability ABC, Inc (%) Boom 25 15

Normal 50 8 Slowdown 15 4 Recession 10 - 3

1 What is the expected return?

E(R) = 25(15) + 5(8) + 15(4) + 1(-3)

= 8.05%

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Another Example Consider the following information:

2 What is the variance?

Variance = σ2= 25(15-8.05)2 + 5(8-8.05)2 +

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Another Example Consider the following information:

3 What is the standard deviation?

Standard Deviation = σ = √ 26.7475

= 5.17%

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Chapter Outline

• Portfolios

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•A portfolio is a

collection of assets

•An asset’s risk and

return are important in

how they affect the risk

and return of the

portfolio

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•The risk/return

trade-off for a portfolio is

measured by the

portfolio’s expected

return and standard

deviation, just as with

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Example: Portfolio

Weights

Suppose you have $15,000 to invest and you have purchased securities in the following

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INTC: 4/15 = 267 KEI: 6/15 = 400

15/15 = 1.000

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Portfolio Expected

Returns

The expected return of a portfolio is the weighted average of the expected returns of the respective assets in the portfolio

You can also find the expected return by finding the portfolio return in each possible state and

computing the expected value as we did with

) (

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Example: Expected Portfolio Returns

Consider the portfolio weights computed previously The individual stocks have the following expected returns:

DCLK: 19.69%

KO: 5.25%

INTC: 16.65%

KEI: 18.24%

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Example: Expected Portfolio Returns

1 What is the expected return on this portfolio?

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Portfolio Variance

•Compute the expected portfolio return, the

variance, and the standard deviation using the same formula as for an individual asset

•Compute the portfolio return for each state:

RP = w1R1 + w2R2 + … + wmRm

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Variance

State Probability A B Boom 4 30% -5%

Bust 6 -10% 25%

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VarianceConsider the following information:

Bust 6 -10% 25%

1 What is the expected return for

asset A?

Asset A: E(RA) = 4(30) + 6(-10) = 6%

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Bust 6 -10% 25%

2 What is the variance for asset A?

Variance(A) = 4(30-6)2 + 6(-10-6)2

= 384

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Bust 6 -10% 25%

3 What is the standard deviation for

asset A?

Std Dev.(A) = 19.6%

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Bust 6 -10% 25%

4 What is the expected return for

asset B?

E(RB) = 4(-5) + 6(25) = 13%

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Bust 6 -10% 25%

5 What is the variance for asset B?

Variance(B) = 4(-5-13)2 + 6(25-13)2

= 216

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Bust 6 -10% 25%

6 What is the standard deviation for

asset B?

Std Dev.(B) = 14.7%

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Bust 6 -10% 25%

7 If you invest 50% of your money in Asset A, what is the expected return for the portfolio

in each state of the economy?

If 50% of the investment is in Asset A, then

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Bust 6 -10% 25%

8 If you invest 50% of your money in Asset A,

what is the expected return for the portfolio

in a boom period?

Portfolio return in boom = 5(30) + 5(-5)

= 12.5%

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Bust 6 -10% 25%

9 What is the expected return for the portfolio

as a whole (considering both states of the economy)?

Exp portfolio return = 4(12.5) + 6(7.5)

= 9.5%

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Bust 6 -10% 25%

10 What is the variance of the portfolio?

Variance of portfolio = 4(12.5-9.5)2 + 6(7.5-9.5)2

= 6

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Bust 6 -10% 25%

11 What is the standard deviation of the

portfolio?

Standard deviation = 2.45%

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Another Example

State Probability X Z Boom 25 15% 10%

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Chapter Outline

• Portfolios

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At any point in time, the unexpected return can

be either positive or negative Over time, the average of the unexpected

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Announcements and

News

•Announcements and news

contain both an expected

component and a surprise

component

•It is the surprise

component that affects a

stock’s price and

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Announcements and

News

• This surprise is very

obvious when we watch

how stock prices move

when an unexpected

announcement is made

or earnings are different

than anticipated

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Chapter Outline

• Portfolios

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Efficient Markets

• Efficient markets are a result of investors trading

on the unexpected portion of announcements

• The easier it is to trade on surprises, the more

efficient markets should be

• Efficient markets involve random price changes

because we cannot predict surprises

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Systematic Risk

•Risk factors that affect a

large number of assets

•Also known as

non-diversifiable risk or

market risk

•Includes such things as

changes in GDP,

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Unsystematic Risk

•Risk factors that affect a

limited number of assets

•Also known as unique risk and

asset-specific risk

•Includes such things as labor

strikes, part shortages, etc.

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Chapter Outline

• Portfolios

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•Portfolio diversification is the investment in

several different asset classes or sectors

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•For example, if you

own 5 airline stocks,

you are not diversified

•However, if you own 50

stocks that span 20

different industries,

then you are

diversified

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Total Risk

•Total risk = systematic risk + unsystematic risk

•The standard deviation of returns is a measure

of total risk

•For well-diversified portfolios, unsystematic

risk is very small

•Consequently, the total risk for a diversified portfolio is essentially equivalent to just the

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The Principle of Diversification

• Diversification can substantially reduce the

variability of returns without an equivalent

reduction in expected returns

• This reduction in risk arises because

worse-than-expected returns from one asset are offset by than-expected returns from another

better-• However, there is a minimum level of risk that

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Chapter Outline

• Portfolios

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Measuring Systematic

Risk

How do we measure systematic risk?

We use the beta coefficient What does beta tell us?

• A beta of 1 implies the asset has the same

systematic risk as the overall market

• A beta < 1 implies the asset has less

systematic risk than the overall market

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Actual Company Betas

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Work the Web Example

•Many sites provide betas for companies

•Yahoo Finance provides beta, plus a lot of

other information under its Key Statistics link

•Click on the web surfer to go to Yahoo

Finance

• Enter a ticker symbol and get a basic quote

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Total vs Systematic Risk

Standard Deviation Beta

1 Which security has more total risk?

K because the standard deviation

is greater than C

2 Which security has more systematic risk?

C because the beta is larger than K

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Total vs Systematic Risk

Standard Deviation Beta

3 Which security should have the higher expected return?

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Example: Portfolio Betas

Consider the previous example with the following four securities:

Security Weight Beta DCLK 133 2.685

KO 2 0.195 INTC 267 2.161 KEI 4 2.434

What is the portfolio beta?

.133(2.685) + 2(.195) + 267(2.161) + 4(2.434)

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Beta and the Risk

Premium

Remember that the risk premium =

expected return – risk-free rate

The higher the beta, the greater the risk

premium should be

Can we define the relationship between the risk premium and beta so that we can

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Chapter Outline

• Portfolios

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Example: Portfolio Expected Returns and Betas: The SML

E(RA)

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Security Market Line

• The security market line (SML) is the

representation of market equilibrium

• The slope of the SML is the reward-to-risk ratio: (E(RM) – Rf) / βM

• But since the beta for the market is ALWAYS equal

to one, the slope can be rewritten:

Slope = E(RM) – Rf = market risk premium

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Reward-to-Risk Ratio:

Definition and Example

• The reward-to-risk ratio is the slope of the line

illustrated in the previous example

• Slope = (E(RA) – Rf) / (βA – 0)

• Reward-to-risk ratio for previous example =

(20 – 8) / (1.6 – 0) = 7.5

• What if an asset has a reward-to-risk ratio of 8

(implying that the asset plots above the line)?

• What if an asset has a reward-to-risk ratio of 7

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Market Equilibrium

In equilibrium, all assets and portfolios must have the same reward-to-risk ratio, and they all must equal the reward-to-

risk ratio for the market

M

f M

) (

)

=

−

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Chapter Outline

• Portfolios

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The Capital Asset Pricing

Model (CAPM)

The capital asset pricing model defines

the relationship between risk and return:

E(RA) = Rf + βA(E(RM) – Rf)

If we know an asset’s systematic risk, we can use the CAPM to determine its expected return

This is true whether we are talking about

financial assets or physical assets

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What is the expected return for each?

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The CAPM

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Quick Quiz

How do you compute the expected return and

standard deviation for an individual asset? For a portfolio?

What is the difference between systematic and unsystematic risk?

What type of risk is relevant for determining the expected return?

Consider an asset with a beta of 1.2, a risk-free

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Comprehensive Problem

1 The risk free rate is 4%, and the required return

on the market is 12% What is the required

return on an asset with a beta of 1.5?

2 What is the reward/risk ratio?

3 What is the required return on a portfolio

consisting of 40% of the asset above and the rest

in an asset with an average amount of systematic risk?

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Expected return on a portfolio

) (

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Slope = E(RM) – Rf = market risk premium

CAPM = E(RA) = Rf + β A(E(RM) – Rf)

M

f M

) (

)

=

−

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Key Concepts and Skills

•Calculate expected returns

•Describe the impact of diversification

•Define the systematic risk principle

•Construct the security market line

•Evaluate the risk-return trade-off

•Compute the cost of equity using the Capital

Asset Pricing Model

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1 Measuring portfolio returns

2 Using Std Dev and Variance to

measure portfolio risk

3 Diversification can significantly reduce

unsystematic risk

What are the most important topics of this chapter?

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5 The slope of the Security Market Line

= the market risk premium

6 The Capital Asset Pricing Model

(CAPM) provides us a measurement

of a stock’s required rate of return.

What are the most important topics of this chapter?

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Questions?

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