11.1

Chapter

11Systematic Risk & Equity Risk Premium

11.2

Key Concepts and Skills

Know how to calculate expected returnsUnderstand the impact of diversificationUnderstand the systematic risk principleUnderstand the security market lineUnderstand the risk-return trade-off

11.3

Chapter Outline

Expected Returns and VariancesPortfoliosAnnouncements, Surprises, and Expected ReturnsRisk: Systematic and UnsystematicDiversification and Portfolio RiskSystematic Risk and BetaThe Security Market LineThe SML and the Cost of Capital: A Preview

11.4

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 a possible return

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11.5

Example: Expected Returns

You have predicted the following returns on Coke and Tyco stock in three possible economic states. What are the expected returns? State Probability Coke Tyco Boom 0.3 0.15 0.25 Normal 0.5 0.10 0.20 Recession ??? 0.02 0.01

RC =

RT =

11.6

Variance and Standard Deviation

Variance and standard deviation still measure the volatility of returns

Using unequal probabilities for the entire range of possibilities

Weighted average of squared deviations

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22 ))((σ

11.7Example: Variance and Standard Deviation Consider the previous example. What are the variance (2) and

standard deviation () for Coke and Tyco? Coke stock

State Prob. C Ret. Ave Diff Diff2 Wtd Diff2

Boom 0.3 0.15 Normal0.5 0.10 Recess.O.2 0.02

Tyco stock 2 = ? = .00741 = ? =

11.8

Another Example

Consider the following information:State Probability ABC, Inc.Boom .25 .15Normal .50 .08Slowdown .15 .04Recession .10 -.03

What is the expected return?What is the variance?What is the standard deviation?

11.9

Portfolios

A portfolio is a collection of assetsAn asset’s risk and return is important in how

it affects the risk and return of the portfolioThe risk-return trade-off for a portfolio is

measured by the portfolio’ expected return and standard deviation, just as with individual assets

11.10

Example: Portfolio Weights

Suppose you have invested money and have purchased securities in the following amounts. What are your portfolio weights in each security?$2000 of IBM$3000 of MCD$4000 of GE$6000 of HP

11.11

Portfolio Expected Returns

The expected return of a portfolio is the weighted average of the expected returns for each asset 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 individual securities

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11.12

Example: Expected Portfolio ReturnsConsider the portfolio weights computed

previously. What is the expected return for the portfolio if the individual stocks have the following expected returns?IBM: 19.65%MCD: 8.96%GE: 9.67%HP: 8.13%

E(RP) =Portfolio Expected Return

11.13

Portfolio Variance

Compute the portfolio return for each state:RP = w1R1 + w2R2 + … + wmRm

Compute the expected portfolio return using the same formula as for an individual asset

Compute the portfolio variance and standard deviation using the same formulas as for an individual asset

11.14

Example: Portfolio VarianceWhat is the expected return and standard deviation

for each asset & portfolio considering the following?Invest 50% of your money in Asset AState Probability A B PortfolioBoom .4 30% -5% 12.5%Bust .6 -10% 25% 7.5%

11.15Example: Portfolio Variance #2: What is the expected return and standard deviation for a portfolio with an investment of $6000 in asset X and $4000 in asset Z?

Considering the following information State Probability X Z Boom .25 15% 10% Normal .60 10% 9% Recession .15 5% 10%

11.16

Expected versus Unexpected ReturnsRealized returns are generally not equal to

expected returnsThere is the expected component and the

unexpected (surprise) component in total (realized) returnAt any point in time, the unexpected return can be

either positive or negativeOver time, the average of the unexpected component

is zero

11.17

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 therefore its return

This is very obvious when we watch how stock prices move when an unexpected announcement is made or earnings are different than anticipated

11.18

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

11.19

Systematic Risk

Risk factors that affect a large number of assetsAlso known as non-diversifiable risk or market

riskIncludes such things as changes in GDP,

inflation, interest rates, etc.

11.20

Unsystematic Risk

Risk factors that affect a limited number of assets

Also known as unique risk, asset-specific risk, or firm-specific risk

Includes such things as labor strikes, part shortages, etc.

Can be diversified away

11.21

Returns

Total Return = expected return + unexpected return

Unexpected return = systematic portion + unsystematic portion

Therefore, total return can be expressed as follows:

Total Return = expected return + systematic portion + unsystematic portion

11.22

Diversification

Portfolio diversification =investing in several different asset classes or sectors

Diversification is not just holding a lot of assets

For example, if you own 50 internet stocks, you are not diversified

However, if you own 50 stocks that span 20 different industries, then you are diversified

11.23

The Principle of Diversification

Diversification can substantially reduce the riskiness (variability) of returns with a smaller reduction in expected returns

This reduction in risk arises because worse than expected returns from one asset are offset by better than expected returns from another

However, there is a minimum level of risk that cannot be diversified away and that is the systematic portion

11.24

Table 11.7

1 49.24 1.00

2 37.36 .76

4 29.69 .60

6 26.64 .54

8 24.98 .51

10 23.93 .49

20 21.68 .44

30 20.87 .42

40 20.46 .42

50 20.20 .41

100 19.69 .40

200 19.42 .39

300 19.34 .39

400 19.29 .39

500 19.27 .39

1,000 19.21 .39

(2)Average Standard

Deviation of AnnualPortfolio Returns

(3)Ratio of Portfolio

Standard Deviation toStandard Deviationof a Single Stock

(1)Number of Stocks

in Portfolio

%

11.25

Figure 11.1Average annualstandard deviation (%)

Diversifiable risk

Nondiversifiablerisk

Number of stocksin portfolio

49.2

23.9

19.2

1 10 20 30 40 1,000

11.26

Diversifiable Risk

The risk that can be eliminated by combining assets into a portfolio

Often considered the same as unsystematic, unique or asset-specific risk

If we hold only one asset, or assets in the same industry, then we are exposing ourselves to risk that we could diversify away

11.27

Total Risk

Total risk = systematic risk + unsystematic riskThe standard deviation of returns is a measure

of total riskFor well diversified portfolios, unsystematic

risk is very smallConsequently, the total risk for a diversified

portfolio is essentially equivalent to the systematic risk

11.28

Systematic Risk Principle

There is a reward for bearing riskThere is not a reward for bearing risk

unnecessarilyThe expected return on a risky asset depends

only on that asset’s systematic risk since unsystematic risk can be diversified away

11.29

Measuring Systematic Risk

How do we measure systematic risk?We use the beta coefficient to measure

systematic riskWhat 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

A beta > 1 implies the asset has more systematic risk than the overall market

11.30

Table 11.8

Company Beta Coefficient

McDonalds .85

Gillette .90

IBM 1.00

General Motors 1.05

Microsoft 1.10

Harley-Davidson 1.20

Dell Computer 1.35

America Online 1.75

(I)

11.31

Total versus Systematic Risk

Consider the following information: Standard Deviation BetaSecurity C 20% 1.25Security K 30% 0.95

Which security has more total risk?Which security has more systematic risk?Which security should have the higher

expected return?

11.32

Example: Portfolio Betas

Consider the previous example with the following four securitiesSecurity Weight BetaIBM .133 4.03MCD .2 0.84GE .267 1.05HP .4 0.59

What is the portfolio beta?

11.33

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 estimate the expected return?YES!

11.34

Example: Portfolio Expected Returns and Betas

0%

5%

10%

15%

20%

25%

30%

0 0.5 1 1.5 2 2.5 3

Beta

Exp

ecte

d R

etur

n

Rf

E(RA)

A

11.35Reward-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) / (A – 0) Where: E(RA)= expected return on stock A

Rf=risk-free rate of return on T-bills

A= Beta for stock A (a measure of the stock’s riskiness)

SO: (E(RA) – Rf)= return on the risk premium for stock A 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 (implying that

the asset plots below the line)?

11.36

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

“A’s ”Reward-to- Market’s Reward-to-

Risk Ratio Risk Ratio

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A

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11.37

Security Market LineThe security market line (SML) is the

representation of market equilibriumThe slope of the SML is the reward-to-risk

ratio: (E(RM) – Rf) / M

But since the Beta for the market is ALWAYS equal to one, M=1, the slope can be rewritten:

Slope = Return on the Market (E(RM)) – Risk-free rate of return (Rf) = market risk premium

OR: Market risk premium = E(RM) - Rf

11.38Capital Asset Pricing ModelThe Capital Asset Pricing Model (CAPM) defines the

relationship between risk and returnExpected return on stock A = Risk-free return +

Beta of stock A(Return on Mrkt -- Risk free return) Where: Return on the market – risk free return

= Market risk premium

E(RA) = Rf + A(E(RM) – Rf)If we know an asset’s systematic risk, we can use the

CAPM to determine its expected returnThis is true whether we are talking about financial assets

or physical assets

11.39

Factors Affecting Expected Return

Pure time value of money – measured by the risk-free rate

Reward for bearing systematic risk – measured by the market risk premium

Amount of systematic risk – measured by beta

11.40Example - CAPMConsider the betas for each of the assets given

earlier. If the risk-free rate is 6.15% and the market risk premium is 9.5%, what is the expected return for each?

Security Beta Expected ReturnIBM 4.03MCD 0.84GE 1.05HP 0.59

11.41

Figure 11.4

= E(RM) - Rf

E(R

M)

R

f

M=1.0

Asset beta (I)

Asset expectedreturn (E(Ri))

The slope of the security market line is equal to themarket risk premium, i.e., the reward for bearing anaverage amount of systematic risk. The equation describing the SML can be written:

E(Ri) = Rf + [E(RM) - Rf] X I

which is the capital asset pricing model, or CAPM.

11.42

Figure 11.4

Risk, or Beta

ExpectedReturn

11.43

Chapter 11 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 rate of 5% and a market return of 13%. What is the reward-to-risk ratio in equilibrium? What is the expected return on the asset?