7/14/2015Capital Asset Pricing Model1 Capital Asset Pricing Model (CAPM) E[R i ] = R F + β i (R M...

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03/16/22 Capital Asset Pricing Model 1 Capital Asset Pricing Model (CAPM) E[R i ] = R F + β i (R M – R F )
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Transcript of 7/14/2015Capital Asset Pricing Model1 Capital Asset Pricing Model (CAPM) E[R i ] = R F + β i (R M...

04/19/23 Capital Asset Pricing Model 1

Capital Asset Pricing Model(CAPM)

E[Ri] = RF + βi (RM – RF)

04/19/23 Capital Asset Pricing Model 2

Risk and Return

State ProbabilityCompany A

ReturnCompany B

Return

Boom .3 100% 20%

Normal .4 15% 15%

Recession .3 -70% 10%

1.0

1. Find the expected return for Company A and B.2. Find the standard deviation for Company A and B.

04/19/23 Capital Asset Pricing Model 3

Find Expected Return

State ProbabilityCompany A

ReturnCompany B

Return

Boom .3 100% 20%

Normal .4 15% 15%

Recession .3 -70% 10%

1.0

15%

.3(10) .4(15) .3(20) )E(R

15%

.3(-70) .4(15) .3(100) )E(RA

B

04/19/23 Capital Asset Pricing Model 4

Find Standard Deviation

State ProbabilityCompany A

ReturnCompany B

Return

Boom .3 100% 20%

Normal .4 15% 15%

Recession .3 -70% 10%

1.0

21

222B

21

222A

15)-.3(10 15)-.4(15 15)-.3(20

65%

15)-.3(-70 15)-.4(15 15)-.3(100

=3.8%

04/19/23 Capital Asset Pricing Model 5

Risk and Return

Expected

Return

15%

4.0% Risk 65.8%

StandardDeviation

| |

04/19/23 Capital Asset Pricing Model 6

Portfolio Risk and the Phantom Egg Crusher

Your Portfolio Market

04/19/23 Capital Asset Pricing Model 7

Lessons from P.E.C.

1. Assets are not held in isolation; rather, they are held as parts of portfolios.

2. Assets are priced according to their value in a portfolio.

3. Investors are concerned about how the portfolio of stocks perform--not individual stocks.

04/19/23 Capital Asset Pricing Model 8

Risk and Return

StateSun Tan Return

Umbrella

ReturnProbability

of State

Sunny 33% -9% 1/3

Normal 12% 12% 1/3

Rainy -9% 33% 1/3

Expected return for Sun Tan Company = 12%Expected return for Umbrella Company = 12%Standard deviation for Sun Tan Company = 17.15%Standard deviation for Umbrella Company = 17.15%

Find the expected return and standard deviation for a portfolio which invests half its money in the Sun Tan and half its money in Umbrella Company.

04/19/23 Capital Asset Pricing Model 9

Portfolio Risk and Return

not?Why

.5(17.15%) .5(17.15%)

12%

.5(12%) .5(12%) RE

50/50

50/50

StateSun Tan Return

Umbrella

ReturnProbability

of State

Sunny 33% -9% 1/3

Normal 12% 12% 1/3

Rainy -9% 33% 1/3

04/19/23 Capital Asset Pricing Model 10

Portfolio Risk and Return

StateSun Tan Return

Umbrella

ReturnProbability

of State

Sunny 33% -9% 1/3

Normal 12% 12% 1/3

Rainy -9% 33% 1/3

State Return

Sunny .5(33) + .5( - 9) = 12%

Normal .5(12) + .5(12) = 12%

Rainy .5( - 9) + .5(33) = 12%

0

12%! fromdeviation No

50/50

04/19/23 Capital Asset Pricing Model 11

Lessons from Tahitian Island1. Combining securities into portfolios reduces risk.

2. How? A portion of a stock’s variability in return is canceled by complementary variations in the return of other securities

3. However, since to some extent stock prices (and returns) tend to move in tandem, not all variability can be eliminated through diversification.

or

Even investors holding diversified portfolios are exposed to the risk inherent in the overall performance of the stock market.

4. Therefore,

Total Risk = unsystematic + systematic

diversifiable nondiversifiable

firm specific market

04/19/23 Capital Asset Pricing Model 12

Portfolio Choice

Expected

Return

Risk

StandardDeviation

01 2 U UU

04/19/23 Capital Asset Pricing Model 13

Risk and Return

Expected

Return

Risk

StandardDeviation

ρ = - 1

1

2

ρ= 1

04/19/23 Capital Asset Pricing Model 14

Variability of Returns Compared with Size of Portfolio

1 10 20 25

49% -

24% -

19% -

Systematic or nondiversifiable risk (result of general market influences)

Unsystematic or diversifiablerisk (related to company-unique events)

Total Risk

Number of stocksin portfolio

Average annual standard deviation (%)

04/19/23 Capital Asset Pricing Model 15

Risk & ReturnExpected

Return

Efficient frontier

Risk Std dev

X XX X X

X X X X

RF --

X

04/19/23 Capital Asset Pricing Model 16

Risk & ReturnExpected

Return

Efficient frontier

Risk Std dev

X XX X X

X X X X

RF --

Lending

Borrowing

XRM --

04/19/23 Capital Asset Pricing Model 17

Security Market Line: Risk/ReturnTrade-Off with CAPM

Expected Return

Systematic Risk

RF --

SML

β

04/19/23 Capital Asset Pricing Model 18

Security Market Line: E[Ri] = RF + βi (RM – RF)

Expected Return

Systematic Risk

RF --

SML

RM --

1 2| | β

04/19/23 Capital Asset Pricing Model 19

CAPMProvides a convenient measure of systematic risk of the volatility of an

asset relative to the markets volatility.

is this measure--gauges the tendency of a security’s return to move in tandem with the overall market’s return.

Average systematic risk

High systematic risk, more volatile than the market

Low systematic risk, less volatile than the market

1

1

1

04/19/23 Capital Asset Pricing Model 20

Betas for a Five-year Period(1987-1992)Company Name (1987-1992) Beta

Tucson Electric Power 0.65

California Power & Lighting 0.70

Litton Industries 0.75

Tootsie Roll 0.85

Quaker Oats 0.95

Standard & Poor’s 500 Stock Index

1.00

Procter & Gamble 1.05

General Motors 1.15

Southwest Airlines 1.35

Merrill Lynch 1.65

Roberts Pharmaceutical 1.90

2006 Betas:

04/19/23 Capital Asset Pricing Model 21

The SML and WACCExpected

return

16% --

14% --

7% --

15% --

fR

A

B

Incorrectrejection

= 8%

SML

WACC = 15%

Beta1.0 Firm 1.2 B.60 A

Incorrectacceptance

If a firm uses its WACC to make accept/reject decisions for all types of projects, it will have a tendency toward incorrectly accepting risky projects and incorrectly rejecting less risky projects.

04/19/23 Capital Asset Pricing Model 22

The SML and the Subjective Approach

Expected

return

14% --

10% --

7% --fR

Low risk(-4%)

SML

Beta

WACC =

Moderate risk(+0%)

High risk(+6%)

20% --

With the subjective approach, the firm places projects into one of several risk classes. The discount rate used to value the project is then determined by adding (for high risk) or subtracting (for low risk) an adjustment factor to or from the firm’s WACC.

04/19/23 Capital Asset Pricing Model 23

Finding Beta for Three Companies: High, Average, and Low Risk & Market

Year

1 10% 10% 10% 10%

2 20% 10% 0% 10%

3 25% 20% 15% 20%

HR AR LR MR

04/19/23 Capital Asset Pricing Model 24

The Concept of Beta (cont.)

Return on Stock i,

Return on the market

(%)iR

(%) mR

30 --

20 --

10 --

0

-10 --

-20 --

-20 -10| |

10 20 30| | |

Stock L, Low Risk: β = 0.5

Stock A, Average Risk: β = 1.0

Stock H, High Risk: β = 1.5

04/19/23 Capital Asset Pricing Model 25

Summary of Relationship Between Risk and Return