Capital Asset Pricing Model

Capital Asset Pricing Model (CAPM)

10/17/08

Capital Asset Pricing Model

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Risk and Return State Boom Normal Recession

Probability .3 .4 .3 1.0

Company A Return 100% 15% -70%

Company B Return 20% 15% 10%

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

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Capital Asset Pricing Model

2

Find Expected Return State Boom Normal Recession

Probability

Company A Return

Company B Return

.3

100%

20%

.4 .3 1.0

15% -70%

15% 10%

E(R A ) = .3(100) + .4(15) + .3(-70) = 15% E(R B ) = .3(20) + .4(15) + .3(10) = 15% 10/17/08

Capital Asset Pricing Model

3

Find Standard Deviation Probability

Company A Return

Company B Return

Boom

.3

100%

20%

Normal

.4

15%

15%

Recession

.3

-70%

10%

State

[

1.0

]

1 .3(100 - 15) 2 + .4(15 - 15) 2 + .3(-70 - 15) 2 2

σA = = 65%

[

2

σ B = .3(20 - 15) + .4(15 - 15)

2

]

1 2 2 + .3(10 - 15)

=3.8% 10/17/08

Capital Asset Pricing Model

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Risk and Return Expected Return 15%

|

4.0%

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|

Risk

65.8%

Capital Asset Pricing Model

Standard Deviation

5

Portfolio Risk and the Phantom Egg Crusher Market

Your Portfolio

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Capital Asset Pricing Model

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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.

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Capital Asset Pricing Model

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Risk and Return State

Sun Tan Return

Umbrella Return

Probability 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.

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Capital Asset Pricing Model

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Portfolio Risk and Return State

Umbrella Return

Sun Tan Return

Probability of State

Sunny

33%

-9%

1/3

Normal

12%

12%

1/3

Rainy

-9%

33%

1/3

E[ R 50/50 ] = .5(12%) + .5(12%)

σ 50/50

= 12% ≠ .5(17.15%) + .5(17.15%) Why not?

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Capital Asset Pricing Model

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Portfolio Risk and Return State

Umbrella Return

Sun Tan Return

Probability 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%

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Capital Asset Pricing Model

No deviation from 12%!

σ 50/50 = 0

10

Lessons from Tahitian Island 1. 2. 3.

4.

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Combining securities into portfolios reduces risk. How? A portion of a stock’s variability in return is canceled by complementary variations in the return of other securities 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. Therefore, Total Risk = unsystematic + systematic diversifiable nondiversifiable firm specific market

Capital Asset Pricing Model

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Portfolio Choice U 2 U1 U 0 Expected Return

Risk

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Capital Asset Pricing Model

Standard Deviation

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Risk and Return Expected Return 2

ρ=-1 1

ρ= 1

Risk

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Capital Asset Pricing Model

Standard Deviation

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Variability of Returns Compared with Size of Portfolio Average annual standard deviation (%) 49% Unsystematic or diversifiable risk (related to company-unique events) 24% 19% Total Risk

1 10/17/08

Systematic or nondiversifiable risk (result of general market influences) 10

20 Capital Asset Pricing Model

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Number of stocks in portfolio 14

Risk & Return Expected Return

X Efficient frontier X X X X X X X X X RF --

Risk

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Std dev

Capital Asset Pricing Model

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Risk & Return Expected Return ing w o orr

B

RM --

X Efficient frontier g

din n e L

X X X

X

X

X X

X X

RF -Risk

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Std dev

Capital Asset Pricing Model

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Security Market Line: Risk/Return Trade-Off with CAPM Expected Return

SML

RF --

Systematic Risk 10/17/08

Capital Asset Pricing Model

β

17

Security Market Line: ke = RF + β(RM – RF) Expected Return

SML RM --

RF --

Systematic Risk 10/17/08

| 1

Capital Asset Pricing Model

| 2

β

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CAPM Provides a convenient measure of systematic risk of the volatility of an asset relative to the markets volatility.

β

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

β =1

Average systematic risk

β >1

High systematic risk, more volatile than the market

β <1

Low systematic risk, less volatile than the market

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Capital Asset Pricing Model

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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

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Capital Asset Pricing Model

2006 Betas:

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The SML and WACC Expected return SML = 8% 16% -15% -14% --

B A

Incorrect acceptance WACC = 15%

Incorrect rejection

R f = 7% --

β A = .60 β Firm = 1.0

β B = 1.2

Beta

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. 10/17/08

Capital Asset Pricing Model

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The SML and the Subjective Approach Expected return

SML

20% -High risk (+6%)

WACC = 14% -10% --

R f = 7% -Low risk (-4%)

Moderate risk (+0%)

Beta 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.

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Capital Asset Pricing Model

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

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Year

kH

kA

kL

kM

1

10%

10%

10%

10%

2

20%

10%

0%

10%

3

25%

20%

15%

20%

Capital Asset Pricing Model

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The Concept of Beta (cont.) Return on Stock i, k i (%) Stock H, High Risk: β = 1.5 30 --

Stock A, Average Risk: β = 1.0

20 -Stock L, Low Risk: β = 0.5

10 -| -20

| -10

0

| 10

| 20

the market,

-10 --

k i (%)

-20 --

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| 30 Return on

Capital Asset Pricing Model

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Summary of Relationship Between Risk and Return

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Capital Asset Pricing Model

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