The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 7- 1 B40.2302 Class #3 BM6 chapters 7, 8, 9 Based on slides created by Matthew Will Modified

©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill

7- 1

B40.2302 Class #3

BM6 chapters 7, 8, 9 Based on slides created by Matthew Will Modified 9/23/2001 by Jeffrey Wurgler

Introduction to Risk, Return, and the Opportunity Cost of Capital

Principles of Corporate FinanceBrealey and Myers Sixth Edition

Slides by

Matthew Will, Jeffrey Wurgler

Chapter 7



7- 3

Topics Covered

72 Years of Capital Market History Measuring Risk Portfolio Risk and Diversification Beta and Unique Risk Diversification and Value Additivity


7- 4

0.1

10

1000

1925 1933 1941 1949 1957 1965 1973 1981 1989 1997

S&PSmall CapCorp BondsLong BondT Bill

The Value of an Investment of $1 in 1926

Source: Ibbotson Associates

Inde

x

Year End

1

613

203

6.15

4.34

1.58

Real returns


7- 5

Returns 1926-1997

Source: Ibbotson Associates

-60

-40

-20

0

20

40

60

26 30 35 40 45 50 55 60 65 70 75 80 85 90 95

Common StocksLong T-BondsT-Bills

Year

Perc

enta

ge R

etur

n


7- 6

Measuring Risk

Two standard measures of risk:

Variance - Average value of squared deviations from mean.

Standard Deviation – Square root of variance, I.e. square root of average value of squared deviations from mean.


7- 7

Measuring RiskExample: Calculating variance and standard deviation.

Suppose four equally-likely outcomes:

21.2%=450= varianceofroot square=deviation Standard

450=1800/4=0)( mean from deviations squared of average=Variance

90030-20-0010+0010+

90030+40+ DeviationSquared Meanfrom DeviationReturn(3)(2)(1)


7- 8

Measuring Risk

1 1 24

12 1113

1013

3 20123456789

10111213

-50

to -4

0

-40

to -3

0

-30

to -2

0

-20

to -1

0

-10

to 0

0 to

10

10 to

20

20 to

30

30 to

40

40 to

50

50 to

60

Return %

# of Years Histogram of Annual Stock Market ReturnsHistogram of Annual Stock Market Returns


7- 9

Measuring Risk

Diversification - Strategy designed to reduce risk by spreading the portfolio across many investments. Reduces risk but not expected return.

Unique Risk - Risk factors affecting only that firm. Also called “diversifiable risk” or “idiosyncratic risk”

Market Risk - Economy-wide sources of risk that affect the overall stock market. Also called “non-diversifiable risk” or “systematic risk”


7- 10

Measuring Risk

Portfolio rateof return

=fraction of portfolioin first asset

xrate of returnon first asset

+fraction of portfolioin second asset

xrate of returnon second asset

((

(())

)

+ …


7- 11

Measuring Risk

05 10 15

Number of Securities

Port

folio

sta

ndar

d de

viat

ion


7- 12

Measuring Risk

05 10 15

Number of Securities

Port

folio

sta

ndar

d de

viat

ion

Market risk

Uniquerisk


7- 13

Portfolio Risk

)rx()r(x Return PortfolioExpected 2211

)σσρxx(2σxσxVariance Portfolio 21122122

22

21

21

In the two-asset case,

Variance PortfolioofSqrt SD Portfolio


7- 14

Portfolio RiskExample

Suppose you invest $55 in Bristol-Myers and $45 in McDonald’s. The s.d. of BM returns is 17.1% and the s.d. of McDonald’s is 20.8%. Assume they have a correlation of +1.00.

% 18.7 352.1 DeviationStandard

352.108)1x17.1x20.2(.55x.45x ]x(20.8)[(.45)

]x(17.1)[(.55) Variance Portfolio22

22


7- 15

Portfolio RiskExample

Suppose you invest $55 in Bristol-Myers and $45 in McDonald’s. The s.d. of BM returns is 17.1% and the s.d. of McDonald’s is 20.8%. Assume they have a correlation of -1.00.

0 DeviationStandard

020.8)(-1)x17.1x2(.55x.45x ]x(20.8)[(.45)

]x(17.1)[(.55) Variance Portfolio22

22


7- 16

Portfolio RiskThe shaded boxes contain variance terms; the others contain covariance terms.

12

3456

N1 2 3 4 5 6 N

STOCK

STOCKTo calculate portfolio variance add up the boxes


7- 17

Beta and Unique Risk

slope =beta

Expected

return

ExpectedMarket risk premium

10%10%- +

10%

stock

Copyright 1996 by The McGraw-Hill Companies, Inc

-10%

A security’s market risk is measured by beta, its expected sensitivity to the market.


7- 18


Market Portfolio - Portfolio of all investable assets in the economy. In practice a broad stock market index, such as the S&P Composite, is used to represent the market.

Beta - Sensitivity of a stock’s return to the return on the market portfolio.


7- 19


2m

imiB

Covariance with the market risk premium

Variance of the market risk premium


7- 20

Diversification & Value Additivity

Value additivity holds …PV(A,B) = PV(A) + PV(B)

… since investors can diversify on their own They will not pay extra for firms that diversify And they will not pay less for firms that do

diversify, since they can “undo” its effect on their own account

Note: V.A. assumes no “synergies”

Risk and Return


Slides by


Chapter 8



7- 22

Topics Covered

Markowitz Portfolio Theory Risk and Return Relationship Testing the CAPM CAPM Alternatives

Consumption CAPM (CCAPM) Arbitrage pricing theory (APT)


7- 23

Markowitz Portfolio Theory

Can combine individual securities into portfolios that achieve at least a given expected return at the lowest possible variance.

These are called the efficient portfoliosefficient portfolios. a.k.a. mean-variance efficient portfolios.


7- 24

Markowitz Portfolio Theory

100% Bristol-Myers-Squibb

100% McDonald’s

Portfolio Standard Deviation (%)

Portfolio Expected Return (%)

45% McDonald’s, 55% Bristol-Myers-Squibb

Portfolio expected return and standard deviation depends on the weights you put on each stock.


7- 25

Efficient Frontier



•Each half egg shell represents the possible combinations of two stocks.

•As you add more stocks, you can construct more complex portfolios.

•The composite using all securities is the efficient frontier, and the portfolios on the frontier are efficient portfolios.


7- 26

Efficient Frontier•Lending or Borrowing at the risk-free rate (rf) allows us to achieve combinations that are outside the efficient frontier.

•Would never choose T, for example, when could choose S and then borrow or lend

rf

Lending

BorrowingS

T




7- 27

Security Market Line

Expected return

Beta

.

rf

rm Market Portfolio

1.0

SML


7- 28

Security Market Line / CAPMExpected return

Beta

rf

1.0

SML

SML/CAPM: E[ri ] = rf + Bi (E[rm] - rf )


7- 29

Testing the CAPM

Avg Portfolio Risk Premium 1931-65

Portfolio Beta1.0

SML30

20

10

0

Beta decile portfolios

Market Portfolio

Beta vs. Average Risk Premium


7- 30

Testing the CAPM

Avg Risk Premium 1966-91

Portfolio Beta1.0

SML

30

20

10

0

Investors

Market Portfolio

Beta vs. Average Risk Premium


7- 31

Testing the CAPM

0

5

10

15

20

25

Average Return (%)

Company size

Smallest Largest

Company Size vs. Average Return


7- 32

Testing the CAPM

0

5

10

15

20

25

Average Return (%)

Book-to-Market Ratio

Highest Lowest

Book-to-Market vs. Average ReturnBook-to-Market vs. Average Return


7- 33

Consumption Betas vs Market Betas

Stocks (and other risky assets)

Wealth = marketportfolio

Market risk makes wealth

uncertain.

Standard

CAPM


7- 34

Consumption Betas vs Market Betas


Wealth = marketportfolio

Market risk makes wealth

uncertain.


Consumption

Wealth

Wealth is uncertain

Consumption is uncertain

Standard

CAPM

Consumption

CAPM


7- 35

Arbitrage Pricing Theory

Besides CCAPM, APT is another alternative to CAPMBesides CCAPM, APT is another alternative to CAPM

Expected Risk Premium

= r - rf

= Bfactor1(rfactor1 - rf) + Bf2(rf2 - rf) + …

Return = a + bfactor1(rfactor1) + bf2(rf2) + …


7- 36

Arbitrage Pricing Theory

APT, like CCAPM, is an alternative to CAPM

If Return = a + b1*rfactor 1+ b2*rfactor 2 + …

Then Expected Return (risk premium) == ri – rf

= b1*(rfactor 1 - rf) + b2 *(rfactor 2 - rf) + …


7- 37

Arbitrage Pricing TheoryEstimated risk premiums for taking on risk factors

(1978-1990 data)

6.36Market.83-Inflation

.49GNP Real.59-rate Exchange.61-rateInterest

5.10%spread Yield)(r

ium Risk PremAnnual EstimatedFactor

factor fr

Capital Budgeting and Risk


Slides by


Chapter 9



7- 39

Topics Covered

Measuring Betas Capital Structure and COC Discount Rates for International Projects Estimating Discount Rates – What if no beta? Risk and DCF


7- 40

Company Cost of Capital

Value-additivity: Total firm value is the sum of the value of its various assets.

Note each PV on the right is evaluated at its own discount rate

PV(B)PV(A)PV(AB) valueFirm


7- 41

Company Cost of Capital Company’s average cost of capital versus

individual project cost of capital. (CAPM)

Required

Return (%)

Project Beta1.26

“Company Cost of Capital”

13

5.5

0

SML

“Average Company Beta”


7- 42

Measuring Betas

The SML shows the equilibrium relationship between expected return and risk (beta) according to the CAPM.

How to measure beta?

Typical approach: Regression analysis


7- 43

Measuring Betas

Hewlett-Packard Stock Beta

Slope (beta) estimated from a regression over 60 months of return data.

Returns - Jan 88 to Dec 92

Market return (%)

Hew

lett-

Pack

ard

retu

rn (%

)

R2 = 0.45

B = 1.70


7- 44

Measuring Betas

Returns - Jan 93 - Dec 97

Market return (%)

R2 = 0.35

B = 1.69

Hewlett-Packard Stock Beta

Hew

lett-

Pack

ard

retu

rn (%

)Slope (beta) estimated from a regression over 60 months of return data.


7- 45

Measuring Betas

AT&T Stock Beta


Market return (%)

R2 = 0.28

B = 0.90

A T

& T

(%

)

Slope (beta) estimated from a regression over 60 months of return data.


7- 46

Measuring Betas

AT&T Stock Beta


Market return (%)

R2 = 0.17

B = 0.90

A T

& T

(%

)Slope (beta) estimated from a regression over 60 months of return data.


7- 47

Beta Stability % IN SAME % WITHIN ONE RISK CLASS 5 CLASS 5 CLASS YEARS LATER YEARS LATER

10 (High betas) 35 69

9 18 54

8 16 45

7 13 41

6 14 39

5 14 42

4 13 40

3 16 45

2 21 61

1 (Low betas) 40 62

Source: Sharpe and Cooper (1972)


7- 48 Company Cost of Capitalsimple approach

The overall company cost of capital is based on the weighted-average beta of the individual asset / project betas.

The weights in the weighted average are determined by the % of firm value attached to each asset / project.

Example: Say firm value is split as:1/3 New ventures investment (B=2.0)1/3 Expand existing business investment (B=1.3)1/3 Plant efficiency investment (B=0.6)

Average asset beta = (1/3)*2.0 + (1/3)*1.3 + (1/3)*0.6 = 1.3This average beta determines the company cost of capital.


7- 49

Capital Structure & COC

So we’ve established how to estimate the company cost of capital.

If you owned all of firm’s securities – 100% of its equity and 100% of its debt – you would own all its assets

Think of company cost of capital as expected return on this hypothetical portfolio.


7- 50


Company cost of capital = rportfolio = rassets

rassets = rdebt (D) + requity (E)

(V) (V)

Bassets = Bdebt (D) + Bequity (E)

(V) (V)

requity = rf + Bequity ( rm - rf )

IMPORTANT

E, D, and V are all market values


7- 51


Changing capital structure can change the risk of the debt relative to the risk of the equity, but does not change the overall risk of the firm.

Changing capital structure therefore does not change the company cost of capital.

Let’s see how changes in capital structure change the costs of equity vs. debt…


7- 52

0

20

0 0.2 0.8 1.2


Expected return (%)

Bdebt Bassets Bequity

rdebt=8

rassets=12.2

requity=15

Expected Returns and Betas before refinancing


7- 53

0

20

0 0.1 0.8 1.1


Expected return (%)

BdebtBassets Bequity

rdebt=7.3

rassets=12.2requity=14.3

Expected Returns and Betas after refinancing


7- 54


Go from estimated Bequity (say, from regression) and assumed / estimated Bdebt to compute Bassets

This is called unlevering beta

To unlever beta, just remember:Bassets = Bdebt (D) + Bequity (E)

(V) (V)


7- 55

Pinnacle West Corp.

.15.51AverageIndustry 21.37. ResourcesL&PP21.43.CorpWest Pinnacle23.70. EnergyPECO15.39. EnergyOGE19.35.System ElectricNE18.65.Inc GPU19.66.Assoc UtilitiesEastern17.56. EnergyDTE20.65. EdisonedConsolidat18.30. HudsonCentral19.60. ElectricBoston ErrorStd.Bequity


7- 56

Pinnacle West Corp.Requity = rf + Bequity ( rm - rf )

= 4.5 + .51(8.0) = 8.58%(Used industry average Bequity since PW’s Bequity was

measured with lots of error)

Rdebt = can estimate as YTM on PW bonds (Bond returns often hard to observe, so hard to estimate Bdebt)

= 6.90 %


7- 57

Pinnacle West Corp.

%86.7

)58.8(57.)90.6(43.

capital ofcost company sPW'

equitydebtassets rVEr

VDr


7- 58

COC for International Projects

Same principles apply, with complications

If project is owned by US investors, they care more about project’s beta with US market. Not about project’s beta with local market.

The theory is clearest if investors are globally diversified. Then relevant beta is beta with world market.


7- 59

What if can’t calculate Beta?

Suppose a new project doesn’t match the risk of traded securities… how to discount?

Need judgment. General advice: Avoid fudge factors in discount rate. Make

unbiased cash flow forecast (i.e. right on average).

Think about determinants of asset betas. Are project cash flows more or less cyclical than usual industry project?


7- 60 Risk and DCF:Putting it all together

ExampleProject A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market risk premium of 8%, and an asset beta of .75, what is the PV of the project?

%12)8(75.6

)(

fmf rrBrr


7- 61 Risk and DCF:Putting it all together

ExampleProject A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market risk premium of 8%, and an asset beta of .75, what is the PV of the project?

%12)8(75.6

)(

fmf rrBrr

240.2 PVTotal71.2100379.7100289.31001

12% @ PV FlowCashYearAProject

Documents

The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 7- 1 B40.2302 Class #3 BM6 chapters 7, 8, 9 Based on slides created by Matthew Will Modified