chapter 8 risk and return. topics covered markowitz portfolio theory risk and return relationship ...
TRANSCRIPT
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Chapter 8
Risk and Return
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Topics Covered
Markowitz Portfolio Theory Risk and Return Relationship Testing the CAPM CAPM Alternatives
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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
Price changes vs. Normal distribution
Microsoft - Daily % change 1990-2001
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
Pro
port
ion
of D
ays
Daily % Change
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Markowitz Portfolio Theory
Standard Deviation VS. Expected Return
Investment A
0
2
4
6
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-50 0 50
%
prob
abili
ty
% return
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Markowitz Portfolio Theory
Standard Deviation VS. Expected Return
Investment B
0
2
4
6
8
10
12
14
16
18
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-50 0 50
%
prob
abili
ty
% return
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Markowitz Portfolio Theory
Standard Deviation VS. Expected Return
Investment C
0
2
4
6
8
10
12
14
16
18
20
-50 0 50
%
prob
abili
ty
% return
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Markowitz Portfolio Theory
Standard Deviation VS. Expected Return
Investment D
0
2
4
6
8
10
12
14
16
18
20
-50 0 50
%
prob
abili
ty
% return
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Markowitz Portfolio Theory
Coca Cola
Reebok
Standard Deviation
Expected Return (%)
35% in Reebok
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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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
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%
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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 Corp3030 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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Efficient Frontier
A
B
Return
Risk (measured as )
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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
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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Security Market Line
Return
Risk
.
rf
Risk Free
Return =
Efficient Portfolio
Market Return = rm
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Security Market Line
Return
.
rf
Risk Free
Return =
Efficient Portfolio
Market Return = rm
BETA1.0
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Security Market Line
Return
.
rf
Risk Free
Return =
BETA
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
R = rf + B ( rm - rf )
CAPM
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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 1966-91
Portfolio Beta1.0
SML
30
20
10
0
Investors
Market Portfolio
Beta vs. Average Risk Premium
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Testing the CAPM
0
5
10
15
20
2519
28
1933
1938
1943
1948
1953
1958
1963
1968
1973
1978
1983
1988
1993
1998
High-minus low book-to-market
Return vs. Book-to-MarketDollars
Low minus big
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
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Consumption Betas vs Market Betas
Stocks (and other risky assets)
Wealth = marketportfolio
Market risk makes wealth
uncertain.
Stocks (and other risky assets)
Consumption
Wealth
Wealth is uncertain
Consumption is uncertain
Standard
CAPM
Consumption
CAPM
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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