Lecture Essentials of corporate finance (2/e) – Chap 11: Risk and return

Chapter 11 introduces you to risk and return. After completing this unit, you should be able to: 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.

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Risk and return

Chapter 11

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Key concepts and skills

• 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

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• Risk: Systematic and unsystematic

• Diversification and portfolio risk

• Systematic risk and beta

• The security market line (SML)

• The SML and the cost of capital: A

preview

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PPTs t/a Essentials of Corporate Finance 2e by Ross et al.

Slides prepared by David E Allen and Abhay K Singh

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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 a

possible return.

• Where:

– pi = the probability of state ‘I’ occurring

– Ri = the expected return on an asset in state i

n

i i i

R p R

E

1

) (

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Expected returns—Example

• Suppose you have predicted the following

returns for shares A and B in three possible

states of nature What are the expected

returns?

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i

iR p

) R ( E

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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.

• Standard deviation = square root of

variance.

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Variance and standard deviation—Another example

• Consider the following information:

• What is the expected return?

• What is the variance?

• What is the standard deviation?

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• 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 expected

return and standard deviation, just as

with individual assets.

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Portfolio expected returns

• The expected return of a portfolio is the weighted

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

• Weights (w j ) = percentage of portfolio invested in

each asset.

• 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

) (

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Portfolio weights: Example

• Suppose you have $15 000 to invest

and you have purchased securities in

the following amounts What are your

portfolio weights in each security?

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Portfolio Weights

Dollars % of Pf Asset Invested w(j) Double Click $2,000 13.3%

Coca Cola $3,000 20.0%

Intel $4,000 26.7%

Keithley Industries $6,000 40.0%

$15,000 100.0%

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Expected portfolio returns:

Example

• Consider the portfolio weights computed

previously If the individual shares have the

following expected returns, what is the

expected return for the portfolio?

Portfolio Weights

Dollars % of Pf w(j) x Asset Invested w(j) E( Rj ) E( Rj ) Double Click $2,000 13.3% 19.650% 2.62%

Coca Cola $3,000 20.0% 8.960% 1.79%

Intel $4,000 26.7% 9.670% 2.58%

Keithley Industries $6,000 40.0% 8.130% 3.25%

$15,000 100.0% 10.24%

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Expected portfolio return

Alternative method

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2 Apply the probabilities of each state to the

expected return of the portfolio in that

state.

3 Sum the result of step 2.

3

1 i

i P i

P

5

1 j

j j

i P

) R ( E p )

R ( E

) R ( E w )

R ( E

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Portfolio risk Variance and standard

deviation

a weighted average of the standard deviation of the component

securities’ risk.

– If it were, there would be no benefit

to diversification.

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Portfolio variance

C ompute portfolio return for each state:

R P,i = w 1 R 1,i + w 2 R 2,i + … + w m R m,i

C ompute the overall expected portfolio

return using the same formula as for

an individual asset.

C ompute the portfolio variance and

standard deviation using the same

formulas as for an individual asset

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1 Calculate expected portfolio return in each state of the economy and overall

2 Compute deviation (DEV) of expected portfolio return in each state from total expected portfolio return.

3 Square deviations (DEV^2) found in step 2.

4 Multiply squared deviations from step 3 times the probability of each state occurring (x p(i)).

5 The sum of the results from step 4 = portfolio variance.

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Expected vs unexpected

returns

• Realised returns are generally not

equal to expected returns.

• There is the expected component and

the unexpected component.

– At any point in time, the unexpected return can be either positive or negative.

– Over time, the average of the unexpected component is zero.

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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 share’s price and therefore its return.

• This is very obvious when we watch

how share prices move when an

unexpected announcement is made or earnings differ from what is anticipated.

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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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• Examples: changes in GDP, inflation

and interest rates.

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Unsystematic risk

• = diversifiable risk

• Risk factors that affect a limited number

of assets.

• Risk that can be eliminated by

combining assets into portfolios.

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• Total return = Expected return +

Unexpected return

R = E(R) + U

• Unexpected return (U) = Systematic

portion (m) + Unsystematic portion (ε)

• Total return = Expected return E(R)

+ Systematic portion m

+ Unsystematic portion ε

= E(R) + m + ε

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• For example, if you own 50 internet

company shares, you are not

diversified.

• However, if you own 50 shares that

span 20 different industries, you are

diversified.

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Standard deviations of annual portfolio returns

Table 11.7

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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 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.

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Portfolio diversification

Figure 11.1

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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.

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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.

• Total risk for a diversified portfolio is

essentially equivalent to the systematic risk.

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Systematic risk principle

• There is a reward for bearing risk.

• There is no reward for bearing risk

unnecessarily.

• The expected return on a risky asset

depends solely on that asset’s

systematic risk, since unsystematic risk can be diversified away.

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Measuring systematic risk

• How do we measure systematic risk?

• We use the beta (β) 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 market.

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Beta coefficients for selected

companies Table 11.8

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Example: Work the Web

• Many sites provide betas for

companies.

• Yahoo! Finance provides beta, plus a

lot of other information, under its profile link.

• Click on the information icon to go to

Yahoo! Finance.

– Enter a ticker symbol and get a basic

quote.

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Total vs systematic risk

• Consider the following information:

Beta

• Which security has more total risk?

• Which security has more systematic

risk?

• Which security should have the higher

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Example: Portfolio betas

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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 estimate the expected return?

– YES!

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Example: Portfolio expected

returns and betas

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Reward-to-risk ratio

• Reward-to-risk ratio:

• = Slope of line on graph

• In equilibrium, ratio should be the same for all assets.

• When E(R) is plotted against β for all

assets, the result should be a straight

line.

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Market equilibrium

• In equilibrium, all assets and portfolios must have the same reward-to-risk

ratio.

• Each ratio must equal the

reward-to-risk ratio for the market.

M

f M

A

f

R ( E

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Market equilibrium

Figure 11.3

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Security market line

• The security market line (SML) is the

representation of market equilibrium.

• The slope of the SML = reward-to-risk

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Security market line

Figure 11.4

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Capital asset pricing model

• The capital asset pricing model

(CAPM) defines the relationship

between risk and return.

• E(R A ) = R f + A (E(R M ) – R f ).

• 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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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.

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i f

M f

R

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Example: CAPM

• Consider 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? CAPM Example

Rf=6.15%

Risk Premium=9.5%

Expected Return Asset Beta

Double Click 4.03 44.435

Keithley Industries 0.59 11.755

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Quick quiz

• How do you compute the expected return and

standard deviation for an individual asset? For a

• 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?

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Chapter 11

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