11-1 Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

11-1Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Chapter Eleven

Return, Risk and the Security

Market Line


11.1 Expected Returns and Variances

11.2 Portfolios

11.3 Announcements, Surprises and Expected Returns

11.4 Risk: Systematic and Non-systematic

11.5 Diversification and Portfolio Risk

11.6 Systematic Risk and Beta

11.7 The Security Market Line

11.8 The Capital Market Line

11.9 Portfolio Characteristics

11.10 The SML and the Cost of Capital: A Preview

11.11 Problems with the CAPM

Summary and Conclusions

Chapter Organisation


Chapter Objectives• Calculate the expected return and risk (standard

deviation) of both a single asset and a portfolio.• Distinguish between systematic and non-systematic

risk.• Explain the principle of diversification.• Explain the capital asset pricing model (CAPM).• Distinguish between the security market line (SML)

and the capital market line (CML).


Expected Return and Variance• Expected return—the weighted average of the

distribution of possible returns in the future.

• Variance of returns—a measure of the dispersion of the distribution of possible returns.

• Rational investors like return and dislike risk.


Example—Calculating Expected Return

15%

5% 0.25 15% 0.50 35% 0.25

return Expected


Example—Calculating Variance

14.14%or 0.1414

0.02


Example—Expected Return and Variance

13%0.130.250.600.050.40

6%0.060.100.600.300.40

RE

RE

B

A

Expected Returns:


Example—Expected Return and Variance

0.0216

0.13 0.25 0.60 0.13 0.05 0.40 Var

0.0384

0.06 0.10 0.60 0.06 0.30 0.40 Var

22

22

B

A

R

R

14.7%0.1470.0216

19.6%0.1960.0384

Rσ

Rσ

B

A

Variances:

Standard deviations:


Portfolios• A portfolio is a collection of assets.

• Portfolio weight is the percentage of a portfolio’s total value in a particular asset.

• An asset’s 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’s expected return and standard deviation, just as with individual assets.


Portfolio Expected Returns• The expected return of a portfolio is the weighted

average of the expected returns for each asset in the portfolio.

m

E(Rp) = ∑ wjE (Rj) j=1

• 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.


Example—Portfolio Return and Variance

Assume 50 per cent of portfolio in asset A and 50 per cent in asset B.

9.5%or0.095

0.0750.600.1250.40

RE p


Example—Portfolio Return and Variance

• Var(Rp) (0.50 x Var(RA)) + (0.50 x Var(RB)).

• By combining assets in a portfolio, the risks faced by the investor can significantly change.

2.45% or 0.0245

0.0006

0.0006

0.095 0.075 0.60 0.095 0.125 0.40 Var 22

p

p

R

R


Asset A returns

0.05

0.04

0.03

0.02

0.01

0

-

0.01

-

0.02

-

0.03

-

0.04

-

0.05

0.05

0.04

0.03

0.02

0.01

0

-

0.01

-

0.02

-

0.03

Asset B returns

0.04

0.03

0.02

0.01

0

-0.01

-0.02

-0.03

Portfolio returns:50% A and 50% B

The Effect of Diversification on Portfolio Variance


Announcements, Surprises and Expected Returns• Key Issues

– What are the components of the total return?– What are the different types of risk?

• Expected and Unexpected Returns– Total return (R) = expected return (E(R)) + unexpected return

(U).

• Announcements and News– Announcement = expected part + surprise = E(R) + U– It is the surprise component that affects a stock’s price and,

therefore, its return.


Risk• Systematic risk is the component of total risk which is

due to economy-wide factors. Also known as market risk.

• Influences a large number of assets, each to a greater or lesser extent.

• Non-systematic risk is the component of total risk which is unique to an asset or firm.

• Affects a single asset or a small group of assets.


Risk

• The distinction between systematic and non-systematic risk means can be applied to break down the surprise portion of returns:

portion systematic-nonportion systematic

return Unexpectedreturn Expectedreturn Total

RE

URER


Diversification• Diversification is the process of spreading

investments across different assets, industries and countries to reduce risk.

• Total risk = systematic risk + non-systematic risk

• Non-systematic risk can be eliminated by diversification.

• Systematic risk affects all assets and cannot be diversified away.


Standard Deviations of Monthly Portfolio Returns


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 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 or market risk.


Portfolio Diversification


Systematic Risk and Beta• The systematic risk principle states that the expected

return on a risky asset depends only on the asset’s systematic risk.

• The amount of systematic risk in an asset relative to an average risky asset is measured by the beta coefficient.

• Since assets with larger betas have greater systematic risks, they will have greater expected returns.


Systematic Risk and Beta• Example:

Std Deviation Beta

Security A 30% 0.60

Security B 10% 1.20

• Security B will have a higher risk premium and a greater expected return, despite the fact that it has less total risk than Security A.


Measuring Systemic 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 market.


Beta Coefficients for Selected Companies


Example—Portfolio Beta Calculations

Amount PortfolioShare Invested Weights Beta

(1) (2) (3) (4) (3) (4)

ABC Company $6 000 50% 0.90 0.450

LMN Company 4 000 33% 1.10 0.367

XYZ Company 2 000 17% 1.30 0.217

Portfolio $12 000 100% 1.034


Example—Portfolio Expected Returns and Betas• Assume you wish to hold a portfolio consisting of

asset A and a riskless asset. Given the following information, calculate portfolio expected returns and portfolio betas, letting the proportion of funds invested in asset A range from 0 to 125 per cent.

• Asset A has a beta of 1.2 and an expected return of 18 per cent.

• The risk-free rate is 7 per cent.• Asset A weights: 0 per cent, 25 per cent, 50 per cent,

75 per cent, 100 per cent and 125 per cent.


Example—Portfolio Expected Returns and Betas

Proportion Proportion Portfolio Invested in Invested in Expected Portfolio Asset A (%) Risk-free Asset (%) Return (%) Beta

0 100 7.00 0.00

25 75 9.75 0.30

50 50 12.50 0.60

75 25 15.25 0.90

100 0 18.00 1.20

125 –25 20.75 1.50


Return, Risk and Equilibrium• Key issues:

– What is the relationship between risk and return?– What does security market equilibrium look like?

• The ratio of the risk premium to beta is the same for every asset. In other words, the reward-to-risk ratio for the market is constant and equal to:

i

fi RRE

ratiok Reward/ris


Example—Asset Pricing• Asset A has an expected return of 12 per cent and a beta of 1.40.

Asset B has an expected return of 8 per cent and a beta of 0.80. Are these two assets valued correctly relative to each other if the risk-free rate is 5 per cent?

• Asset B offers insufficient return for its level of risk, relative to A. B’s price is too high; therefore, it is overvalued (or A is undervalued).

0.0375 0.80

0.05 0.08 :B

0.05 1.40

0.05 0.12 :A


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)/ßM.

• But since the beta for the market is ALWAYS equal to one, the slope can be rewritten.

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


Security Market Line (SML)

Asset expectedreturn (E (Ri))

Asset

beta (i)

= E (RM) – Rf

E (RM)

Rf

M = 1.0


The Capital Asset Pricing Model (CAPM)• An equilibrium model of the relationship between risk

and return.

• What determines an asset’s expected return?– The risk-free rate—the pure time value of money– The market risk premium—the reward for bearing systematic

risk– The beta coefficient—a measure of the amount of

systematic risk present in a particular asset.

ifMfi RRERRE CAPM


Calculation of Systematic Risk

MMii / R ,R ~~Cov

Where:Cov = covariance

i = random distribution of return for asset i

M = random distribution of return for the market

M = standard deviation of market return

R~

R~


Covariance and Correlation• The covariance term measures how returns change

together—measured in absolute terms.• The correlation coefficient measures how returns

change together—measured in relative terms.• Correlation coefficient ranges between –1.0 and +1.0.

Where i = standard deviation of the return on asset i.

MiMiiM /R ,R σσ~~

Covρ


Security Market Line versus Capital Market Line

ifMfi

pMfMfp

βRRERRE

RRERRE

SML

/ CML

• SML explains the expected return for all assets.

• CML explains the expected return for efficient portfolios.


Risk of a Portfolio

Variance of a two-asset portfolio is calculated as:

weighted variance of the expected return for

each asset in the portfolio

+

twice the weighted covariance of the expected

return on the first asset with the expected

return on the second


Example—Risk of a Portfolio

Weighting Std Deviation

Asset A 0.3 0.26

Asset B 0.7 0.13

The covariance of the expected returns between A and B is 0.017.

0.1466 dev Std

0.0215

0.00714 0.008281 0.006084

0.0170.70.32 0.130.7 0.260.3 Variance 22


Problems with CAPM• Difficulties in estimating beta

- thin trading

- non-constant beta.

• Using CAPM

- adding explanatory variables

- measure of market return.

• Where are we?

- Despite its limitations, CAPM is still highly regarded

- To discard the CAPM is to surely ‘throw the baby out with the

bath water.’


Summary and Conclusions• The reward for bearing risk is the risk premium on an

asset.

• The total risk associated with an asset has two parts: systematic risk and non-systematic risk.

• Non-systematic risk can be eliminated by diversification.

• The risk premium on an asset is determined by its systematic risk.

• The SML tells us the reward offered in financial markets for bearing risk.

• The SML is a benchmark for which we can compare the returns expected from real asset investments to determine if they are desirable.

Documents

11-1 Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan