7/14/2015capital asset pricing model1 capital asset pricing model (capm) e[r i ] = r f + β i (r m...
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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