Risk /Return Return = r = Discount rate = Cost of Capital (COC)
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Transcript of Risk /Return Return = r = Discount rate = Cost of Capital (COC)
![Page 1: Risk /Return Return = r = Discount rate = Cost of Capital (COC)](https://reader036.fdocuments.us/reader036/viewer/2022081418/5697bf711a28abf838c7dd7c/html5/thumbnails/1.jpg)
Risk /Return
Return = r = Discount rate = Cost of Capital (COC)
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Risk /Return
Return = r = Discount rate = Cost of Capital (COC)
r is determined by risk
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Risk /Return
Return = r = Discount rate = Cost of Capital (COC)
r is determined by risk
Two Extremes
• Treasury Notes are risk free = Retrun is low
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Risk /Return
Return = r = Discount rate = Cost of Capital (COC)
r is determined by risk
Two Extremes
• Treasury Notes are risk free = Retrun is low
• Junk Bonds are high risk = Return is high
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Risk
Variance & Standard Deviation
• yard sticks that measure risk
• Return is measured
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Risk
Variance & Standard Deviation
• yard sticks that measure risk
• Return is measured
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The Value of an Investment of $1 in 1900
$1
$10
$100
$1,000
$10,000
$100,000
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
Start of Year
Dol
lars
Common Stock
US Govt Bonds
T-Bills
15,578
14761
2004
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The Value of an Investment of $1 in 1900
$1
$10
$100
$1,000
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
Start of Year
Dol
lars
Equities
Bonds
Bills
719
6.81
2.80
2004
Real Returns
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Rates of Return 1900-2003
Source: Ibbotson Associates
-60%
-40%
-20%
0%
20%
40%
60%
80%
1900 1920 1940 1960 1980 2000
Year
Per
cent
age
Ret
urn
Stock Market Index Returns
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Diversification
Diversification is the combining of assets. In financial theory, diversification can reduce risk.
The risk of the combined assets is lower than the risk of the assets held separately.
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Efficient Frontier
Example Correlation Coefficient = .4Stocks % of Portfolio Avg ReturnABC Corp 28 60% 15%Big Corp 42 40% 21%
Standard Deviation = weighted avg = 33.6 Standard Deviation = Portfolio = 28.1
Additive Standard Deviation (common sense):= 28 (60%) + 42 (40%) = 33.6 WRONG
Real Standard Deviation:= (282)(.62) + (422)(.42) + 2(.4)(.6)(28)(42)(.4)
= 28.1 CORRECT
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Efficient Frontier
Example Correlation Coefficient = .4
Stocks % of Portfolio Avg Return
ABC Corp 28 60% 15%
Big Corp 42 40% 21%
Standard Deviation = weighted avg = 33.6
Standard Deviation = Portfolio = 28.1
Real Standard Deviation:
= (282)(.62) + (422)(.42) + 2(.4)(.6)(28)(42)(.4)
= 28.1 CORRECT
Return : r = (15%)(.60) + (21%)(.4) = 17.4%
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Efficient Frontier
Example Correlation Coefficient = .4
Stocks % of Portfolio Avg Return
ABC Corp 28 60% 15%
Big Corp 42 40% 21%
Standard Deviation = weighted avg = 33.6
Standard Deviation = Portfolio = 28.1
Return = weighted avg = Portfolio = 17.4%
Let’s Add stock New Corp to the portfolio
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Efficient Frontier
Example Correlation Coefficient = .3
Stocks % of Portfolio Avg Return
Portfolio 28.1 50% 17.4%
New CorpNew Corp 3030 50%50% 19% 19%
NEW Standard Deviation = weighted avg = 31.80
NEW Standard Deviation = Portfolio = 23.43
NEW Return = weighted avg = Portfolio = 18.20%
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Efficient Frontier
Example Correlation Coefficient = .3
Stocks % of Portfolio Avg Return
Portfolio 28.1 50% 17.4%
New Corp 30 50% 19%
NEW Standard Deviation = weighted avg = 31.80
NEW Standard Deviation = Portfolio = 23.43
NEW Return = weighted avg = Portfolio = 18.20%
NOTE: Higher return & Lower risk
How did we do that? DIVERSIFICATION
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Diversification
)rx()r(x Return PortfolioExpected 2211
)σσρxx(2σxσxVariance Portfolio 21122122
22
21
21
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Efficient Frontier
A
B
Return
Risk (measured as O)
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Efficient Frontier
A
B
Return
Risk
AB
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Efficient Frontier
A
BN
Return
Risk
AB
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Efficient Frontier
A
BN
Return
Risk
ABABN
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Efficient Frontier
A
BN
Return
Risk
AB
Goal is to move up and left.
WHY?
ABN
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Efficient Frontier
Return
Risk
Low Risk
High Return
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Efficient Frontier
Return
Risk
Low Risk
High Return
High Risk
High Return
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Efficient Frontier
Return
Risk
Low Risk
High Return
High Risk
High Return
Low Risk
Low Return
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Efficient Frontier
Return
Risk
Low Risk
High Return
High Risk
High Return
Low Risk
Low Return
High Risk
Low Return
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Efficient Frontier
Return
Risk
Low Risk
High Return
High Risk
High Return
Low Risk
Low Return
High Risk
Low Return
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Efficient Frontier
Return
Risk
A
BNABABN
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Markowitz Portfolio Theory
Combining stocks into portfolios can reduce standard deviation, below the level obtained from a simple weighted average calculation.
Correlation coefficients make this possible.
The various weighted combinations of stocks that create this standard deviations constitute the set of efficient portfoliosefficient portfolios.
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Markowitz Portfolio Theory
Bristol-Myers Squibb
McDonald’s
Standard Deviation
Expected Return (%)
45% McDonald’s
Expected Returns and Standard Deviations vary given different weighted combinations of the stocks
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Efficient Frontier
Standard Deviation
Expected Return (%)
•Each half egg shell represents the possible weighted combinations for two stocks.
•The composite of all stock sets constitutes the efficient frontier
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Diversification
0
5 10 15
Number of Securities
Po
rtfo
lio
sta
nd
ard
dev
iati
on
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Diversification
0
5 10 15
Number of Securities
Po
rtfo
lio
sta
nd
ard
dev
iati
on
Market risk
Uniquerisk
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Efficient Frontier
Standard Deviation
Expected Return (%)
•Lending or Borrowing at the risk free rate (rf) allows us to exist outside the
efficient frontier.
rf
Lending
BorrowingT
S
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Efficient Frontier
Return
Risk
A
BNABABN
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Security Market Line
Return
Risk
.
rf
Efficient PortfolioRisk Free
Return =
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Security Market Line
Return
Risk
.
rf
Risk Free
Return =
Market Return = rm
Efficient Portfolio
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Security Market Line
Return
Risk
.
rf
Risk Free
Return =
Market Return = rm
Efficient Portfolio
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Security Market Line
Return
BETA
.
rf
Risk Free
Return =
Market Return = rm
Efficient Portfolio
1.0
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Risk & Beta
Market Beta = 1.0 = (Omarket)(Omarket) = Om2
(Omarket)(Omarket) Om2
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Risk & Beta
Market Beta = 1.0 = (Omarket)(Omarket) = Om2
(Omarket)(Omarket) Om2
Covariance
![Page 41: Risk /Return Return = r = Discount rate = Cost of Capital (COC)](https://reader036.fdocuments.us/reader036/viewer/2022081418/5697bf711a28abf838c7dd7c/html5/thumbnails/41.jpg)
Risk & Beta
Market Beta = 1.0 = (Omarket)(Omarket) = Om2
(Omarket)(Omarket) Om2
Stock Beta = Osm
Om2
Covariance
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Risk & Beta
Market Beta = 1.0 = (Omarket)(Omarket) = Om2
(Omarket)(Omarket) Om2
Stock Beta = Osm
Om2
Covariance
covariance of market & stock
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Beta and Unique Risk
Market Portfolio - Portfolio of all 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.
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Beta and Unique Risk
2m
imiB
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Beta and Unique Risk
2m
imiB
Covariance with the market
Variance of the market
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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)
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Security Market Line
Return
BETA
rf
Risk Free
Return =
Market Return = rm
1.0
Security Market Line (SML)
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Security Market LineReturn
BETA
rf
1.0
SML
SML Equation = rf + B ( rm - rf )
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Capital Asset Pricing Model(CAPM)
R = rf + B ( rm - rf )
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Testing the CAPM
Avg Risk Premium 1931-2002
Portfolio Beta1.0
SML30
20
10
0
Investors
Market Portfolio
Beta vs. Average Risk Premium
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Testing the CAPM
Avg Risk Premium 1931-65
Portfolio Beta1.0
SML
30
20
10
0
Investors
Market Portfolio
Beta vs. Average Risk Premium
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Testing the CAPM
Avg Risk Premium 1966-2002
Portfolio Beta1.0
SML
30
20
10
0
Investors
Market Portfolio
Beta vs. Average Risk Premium
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Testing the CAPM
0.1
1
10
10019
26
1936
1946
1956
1966
1976
1986
1996
High-minus low book-to-market
Return vs. Book-to-MarketDollars(log scale)
Small minus big
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
200
3
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Measuring Betas
Hewlett Packard Beta
Slope determined from 60 months of prices and plotting the line of best fit.
Price data - Jan 78 - Dec 82
Market return (%)
Hew
lett-Packard return (%
)
R2 = .53
B = 1.35
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Measuring Betas
Hewlett Packard Beta
Slope determined from 60 months of prices and plotting the line of best fit.
Price data - Jan 83 - Dec 87
Market return (%)
Hew
lett-Packard return (%
)
R2 = .49
B = 1.33
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Measuring Betas
Hewlett Packard Beta
Slope determined from 60 months of prices and plotting the line of best fit.
Price data - Jan 88 - Dec 92
Market return (%)
Hew
lett-Packard return (%
)
R2 = .45
B = 1.70
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Measuring Betas
Hewlett Packard Beta
Slope determined from 60 months of prices and plotting the line of best fit.
Price data - Jan 93 - Dec 97
Market return (%)
Hew
lett-Packard return (%
)
R2 = .35
B = 1.69
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Measuring Betas
A T & T Beta
Slope determined from 60 months of prices and plotting the line of best fit.
Price data - Jan 78 - Dec 82
Market return (%)
A T
& T
(%)
R2 = .28
B = 0.21
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Measuring Betas
A T & T Beta
Slope determined from 60 months of prices and plotting the line of best fit.
Price data - Jan 83 - Dec 87
Market return (%)
R2 = .23
B = 0.64
A T
& T
(%)
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Measuring Betas
A T & T Beta
Slope determined from 60 months of prices and plotting the line of best fit.
Price data - Jan 88 - Dec 92
Market return (%)
R2 = .28
B = 0.90
A T
& T
(%)
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Measuring Betas
A T & T Beta
Slope determined from 60 months of prices and plotting the line of best fit.
Price data - Jan 93 - Dec 97
Market return (%)
R2 = ..17
B = .90
A T
& T
(%)
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Arbitrage Pricing Theory
Alternative to CAPMAlternative to CAPM
Expected Risk
Premium = r - rf
= Bfactor1(rfactor1 - rf) + Bf2(rf2 - rf) + …
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Arbitrage Pricing Theory
Alternative to CAPMAlternative to CAPM
Expected Risk
Premium = r - rf
= Bfactor1(rfactor1 - rf) + Bf2(rf2 - rf) + …
Return = a + bfactor1(rfactor1) + bf2(rf2) + …
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Arbitrage Pricing Theory
Estimated risk premiums for taking on risk factors
(1978-1990)
6.36Mrket
.83-Inflation
.49GNP Real
.59-rate Exchange
.61-rateInterest
5.10%spread Yield)(r
ium Risk PremEstimatedFactor
factor fr
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3 Factor Model
Fama & FrenchFama & French
Expected Return
= Bmarket(rmarket factor)
+ Bsize(rsize factor)
+ Bbook to market(rbook to market factor)
Market factor = Rm – Rf
Size Factor = R small cap – R large cap
Book to Market Factor = R high B-M stocks – R low B-M stocks