7/30/2019 Lecture Ch.13 1

1/50

Ch.13 Return, Risk, and theSecurity Market Line

Know how to calculate expected returns Understand the impact of diversification Understand the systematic risk principle Understand the security market line

Understand the risk-return trade-off Be able to use the Capital Asset Pricing Model

1

7/30/2019 Lecture Ch.13 1

2/50

Chapter Outline

Expected Returns and Variances Portfolios

Announcements, Surprises, and ExpectedReturns Risk: Systematic and Unsystematic

Diversification and Portfolio Risk Systematic Risk and Beta The Security Market Line

2

7/30/2019 Lecture Ch.13 1

3/50

Expected Returns

Expected returns are based on theprobabilities of possible outcomes

In this context, expected means average if the process is repeated many times

The expected return does not even have tobe a possible return

n

iii R p R E

1

)(

3

7/30/2019 Lecture Ch.13 1

4/50

Expected Returns Example 1 Suppose you have predicted the following returns for

stocks C and T in three possible states of nature.What are the expected returns?

State Probability C T Boom 0.3 0.15 0.25 Normal 0.5 0.10 0.20 Recession ??? 0.02 0.01

RC = .3(.15) + .5(.10) + .2(.02) = .099 = 9.9% RT = .3(.25) + .5(.20) + .2(.01) = .177 = 17.7%

4

7/30/2019 Lecture Ch.13 1

5/50

Variance and Standard Deviation

Variance and standard deviation still measurethe volatility of returns

You can use unequal probabilities for theentire range of possibilities

Weighted average of squared deviations

n

iii R E R p

1

22 ))((

5

7/30/2019 Lecture Ch.13 1

6/50

Variance and Standard Deviation Example

Consider the previous example. What is the varianceand standard deviation for each stock?

Stock C 2

= .3(.15-.099)2

+ .5(.1-.099)2

+ .2(.02-.099)2

=.002029 = .045

Stock T 2 = .3(.25-.177) 2 + .5(.2-.177) 2 + .2(.01-.177) 2 =

.007441 = .0863

6

7/30/2019 Lecture Ch.13 1

7/50

Quick Quiz I Consider the following information:

State Probability ABC, Inc. Boom .25 .15

Normal .50 .08 Slowdown .15 .04 Recession .10 -.03

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

7

7/30/2019 Lecture Ch.13 1

8/50

Portfolios

A portfolio is a collection of assets An assets risk and return is important in how

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

measured by the portfolio expected returnand standard deviation, just as with individualassets

8

7/30/2019 Lecture Ch.13 1

9/50

Example: Portfolio Weights

Suppose you have $15,000 to invest and youhave purchased securities in the followingamounts. What are your portfolio weights ineach security?

$2000 of ABC $3000 of DEF $4000 of GHI $6000 of JKL

ABC: 2/15 = .133 DEF: 3/15 = .2 GHI: 4/15 = .267 JKL: 6/15 = .4

9

7/30/2019 Lecture Ch.13 1

10/50

Portfolio Expected Returns

The expected return of a portfolio is the weightedaverage of the expected returns for each asset in theportfolio

You can also find the expected return by finding theportfolio return in each possible state and computingthe expected value as we did with individualsecurities

m

j j jP R E w R E

1)()(

10

7/30/2019 Lecture Ch.13 1

11/50

Example: Expected PortfolioReturns

Consider the portfolio weights computed previously.If the individual stocks have the following expectedreturns, what is the expected return for the

portfolio? ABC: 19.65% DEF: 8.96% GHI: 9.67% JKL: 8.13%

E(RP) = .133(19.65) + .2(8.96) + .267(9.67) + .4(8.13)= 10.24%

11

7/30/2019 Lecture Ch.13 1

12/50

Portfolio Variance

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

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

Compute the portfolio variance and standarddeviation using the same formulas as for anindividual asset

12

7/30/2019 Lecture Ch.13 1

13/50

Example: Portfolio Variance Consider the following information

Invest 60% of your money in Asset A State Probability A B Boom .5 70% 10% Bust .5 -20% 30%

What is the expected return and standard

deviation for each asset? What is the expected return and standard

deviation for the portfolio?

13

7/30/2019 Lecture Ch.13 1

14/50

Another Way to Calculate Portfolio Variance

Portfolio variance can also be calculated using thefollowing formula:

0.0529

0.10.45-1.004.06.020.010.40.20256.0

havewe1.00,-isBandAbetweenncorrelatiothat theAssuming

2

2

222

,22222

P

P

U LU LU LU U L LP CORR x x x x

13-14

7/30/2019 Lecture Ch.13 1

15/50

Different Correlation Coefficients(Corr=1)

15

7/30/2019 Lecture Ch.13 1

16/50

Different Correlation Coefficients(Corr=-1)

16

7/30/2019 Lecture Ch.13 1

17/50

Different Correlation Coefficients(Corr=0)

17

7/30/2019 Lecture Ch.13 1

18/50

Graphs of Possible Relationships BetweenTwo Stocks

18

7/30/2019 Lecture Ch.13 1

19/50

Diversification

There are benefits to diversification wheneverthe correlation between two stocks is lessthan perfect (p < 1.0)

If two stocks are perfectly positivelycorrelated, then there is simply a risk-returntrade-off between the two securities.

19

7/30/2019 Lecture Ch.13 1

20/50

Diversification Figure 13.4

20

7/30/2019 Lecture Ch.13 1

21/50

Terminology

Feasible set (also called the opportunity set) thecurve that comprises all of the possible portfoliocombinations

Efficient set the portion of the feasible set that onlyincludes the efficient portfolio (where the maximumreturn is achieved for a given level of risk, or wherethe minimum risk is accepted for a given level of return)

Minimum Variance Portfolio the possible portfoliowith the least amount of risk

21

7/30/2019 Lecture Ch.13 1

22/50

Quick Quiz II

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

What is the expected return and standarddeviation for a portfolio with an investment of $6000 in asset X and $4000 in asset Y?

22

7/30/2019 Lecture Ch.13 1

23/50

Expected versus Unexpected Returns

Realized returns are generally not equal toexpected returns

There is the expected component and theunexpected component

At any point in time, the unexpected return can beeither positive or negative

Over time, the average of the unexpectedcomponent is zero

23

7/30/2019 Lecture Ch.13 1

24/50

Announcements and News

Announcements and news contain both anexpected component and a surprisecomponent

It is the surprise component that affects astocks price and therefore its return

This is very obvious when we watch how stockprices move when an unexpectedannouncement is made or earnings aredifferent than anticipated

24

7/30/2019 Lecture Ch.13 1

25/50

Systematic Risk

Risk factors that affect a large number of assets

Also known as non-diversifiable risk or marketrisk

Includes such things as changes in GDP,inflation, interest rates, etc.

25

7/30/2019 Lecture Ch.13 1

26/50

Unsystematic Risk

Risk factors that affect a limited number of assets

Also known as unique risk and asset-specificrisk

Includes such things as labor strikes,shortages, etc.

26

7/30/2019 Lecture Ch.13 1

27/50

Returns

Total Return = expected return + unexpectedreturn

Unexpected return = systematic portion +unsystematic portion

Therefore, total return can be expressed asfollows: Total Return = expected return +systematic portion + unsystematic portion

27

7/30/2019 Lecture Ch.13 1

28/50

Diversification

Portfolio diversification is the investment inseveral 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 20different industries, then you are diversified

28

7/30/2019 Lecture Ch.13 1

29/50

Portfolio Diversification

29

7/30/2019 Lecture Ch.13 1

30/50

The Principle of Diversification Diversification can substantially reduce the

variability of returns without an equivalentreduction in expected returns

This reduction in risk arises because worsethan expected returns from one asset areoffset by better than expected returns fromanother

However, there is a minimum level of risk thatcannot be diversified away and that is thesystematic portion

30

7/30/2019 Lecture Ch.13 1

31/50

Figure 13.6 PortfolioDiversification

31

7/30/2019 Lecture Ch.13 1

32/50

Diversifiable (Unsystematic) Risk

The risk that can be eliminated by combiningassets into a portfolio

Synonymous with unsystematic, unique orasset-specific risk

If we hold only one asset, or assets in thesame industry, then we are exposing ourselvesto risk that we could diversify away

The market will not compensate investors forassuming unnecessary risk

32

7/30/2019 Lecture Ch.13 1

33/50

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 thesystematic risk

33

7/30/2019 Lecture Ch.13 1

34/50

Systematic Risk Principle

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

unnecessarily The expected return on a risky asset depends

only on that assets systematic risk sinceunsystematic risk can be diversified away

34

7/30/2019 Lecture Ch.13 1

35/50

Measuring Systematic Risk

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

risk

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 A beta > 1 implies the asset has more systematic

risk than the overall market35

7/30/2019 Lecture Ch.13 1

36/50

High and Low Betas

36

7/30/2019 Lecture Ch.13 1

37/50

Beta Coefficients for Selected Companies

37

7/30/2019 Lecture Ch.13 1

38/50

Total versus Systematic Risk

Consider the following information:Standard Deviation Beta

Security C 20% 1.25 Security K 30% 0.95

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

expected return?

38

7/30/2019 Lecture Ch.13 1

39/50

Example: Portfolio Betas Consider the previous example with the

following four securities Security Weight Beta ABC .133 3.69 DEF .2 0.64 GHI .267 1.64

JKL .4 1.79 What is the portfolio beta? .133(3.69) + .2(.64) + .267(1.64) + .4(1.79) =

1.773 39

7/30/2019 Lecture Ch.13 1

40/50

Beta and the Risk Premium

Remember that the risk premium = expectedreturn risk-free rate

The higher the beta, the greater the riskpremium should be

Can we define the relationship between therisk premium and beta so that we canestimate the expected return?

YES!

40

7/30/2019 Lecture Ch.13 1

41/50

Portfolio Expected Returns and Betas

R f

13-41

Reward to Risk Ratio: Definition and

7/30/2019 Lecture Ch.13 1

42/50

Reward-to-Risk Ratio: Definition andExample

The reward-to-risk ratio is the slope of the lineillustrated in the previous example

Slope = (E(RA) Rf ) / ( A 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

(implying that the asset plots below the line)?

42

7/30/2019 Lecture Ch.13 1

43/50

Market Equilibrium

In equilibrium, all assets and portfolios musthave the same reward-to-risk ratio and theyall must equal the reward-to-risk ratio for themarket

M

f M

A

f A R R E R R E

)()(

43

7/30/2019 Lecture Ch.13 1

44/50

Security Market Line

The security market line (SML) is therepresentation of market equilibrium

The slope of the SML is the reward-to-riskratio: (E(RM) Rf ) / M

But since the beta for the market is ALWAYSequal to one, the slope can be rewritten

Slope = E(RM) Rf = market risk premium

44

7/30/2019 Lecture Ch.13 1

45/50

Security Market Line

45

7/30/2019 Lecture Ch.13 1

46/50

The Capital Asset Pricing Model (CAPM)

The capital asset pricing model defines therelationship between risk and return

E(RA) = Rf + A(E(RM) Rf ) If we know an assets systematic risk, we can

use the CAPM to determine its expectedreturn

This is true whether we are talking aboutfinancial assets or physical assets

46

7/30/2019 Lecture Ch.13 1

47/50

Factors Affecting Expected Return

Pure time value of money measured by therisk-free rate

Reward for bearing systematic risk measuredby the market risk premium

Amount of systematic risk measured by beta

47

7/30/2019 Lecture Ch.13 1

48/50

Example - CAPM

Consider the betas for each of the assets givenearlier. If the risk-free rate is 4.5% and the market riskpremium is 8.5%, what is the expected return foreach?

Security Beta Expected Return

ABC 3.69 4.5 + 3.69(8.5) = 35.865%

DEF .64 4.5 + .64(8.5) = 9.940%

GHI 1.64 4.5 + 1.64(8.5) = 18.440%

JKL 1.79 4.5 + 1.79(8.5) = 19.715%

13-48

7/30/2019 Lecture Ch.13 1

49/50

Quick Quiz What is the difference between systematic and

unsystematic risk? What type of risk is relevant for determining the

expected return? What is the SML? What is the CAPM? What is the

APT? 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?

49

7/30/2019 Lecture Ch.13 1

50/50

Summary There is a reward for bearing risk Total risk has two parts: systematic risk and

unsystematic risk Unsystematic risk can be eliminated through

diversification Systematic risk cannot be eliminated and is rewarded

with a risk premium Systematic risk is measured by the beta The equation for the SML is the CAPM, and it

determines the equilibrium required return for agiven level of risk