Fundamentals of Corporate Finance/3e,ch11

Copyright 2004 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 3e Ross, Thompson, Christensen, Westerfield and JordanSlides prepared by Sue Wright

11-1

Chapter Eleven

Return, Risk and the Security

Market Line


11-2

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

Chapter Organisation


11-3

11.11 Problems with the CAPM

11.12 Summary and Conclusions

Chapter Organisation (continued)


11-4

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).


11-5

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.


11-6

Example—Calculating Expected Return

15%

5% 0.25 15% 0.50 35% 0.25

return Expected


11-7

Example—Calculating Variance

14.14%or 0.1414

0.02


11-8

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:


11-9

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:


11-10

Portfolios

• A portfolio is a collection of assets.

• 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.


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.

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.


11-12

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


11-13

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


11-14

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


11-15

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– It is the surprise component that affects a stock’s price and,

therefore, its return.


11-16

Risk

• Systematic risk: that component of total risk which is due to economy-wide factors.

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

portion systematic-nonportion systematic

return Unexpectedreturn Expectedreturn Total

RE

URER


11-17

Standard Deviations of Monthly Portfolio Returns


11-18

Diversification

• 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.


11-19

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.


11-20

Portfolio Diversification


11-21

Systematic Risk

• 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.

Std Deviation Beta

Security A 30% 0.60

Security B 10% 1.20

• Security A has greater total risk but less systematic risk (more non-systematic risk) than Security B.


11-22

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.


11-23

Beta Coefficients for Selected Companies


11-24

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


11-25

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.


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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


11-27

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


11-28

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


11-29

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


11-30

Security Market Line (SML)Asset expectedreturn (E (Ri))

Asset

beta (i)

= E (RM) – Rf

E (RM)

Rf

M = 1.0


11-31

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


11-32

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~


11-33

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


11-34

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.


11-35

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


11-36

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


11-37

Problems with CAPM

• Difficulties in estimating beta

- thin trading

- non-constant beta• Using CAPM

- adding explanatory variables

- measure of market return

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