chapter 8 risk and return. topics covered markowitz portfolio theory risk and return relationship ...
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Chapter 8
Risk and Return
Topics Covered
Markowitz Portfolio Theory Risk and Return Relationship Testing the CAPM CAPM Alternatives
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.
Markowitz Portfolio Theory
Price changes vs. Normal distribution
Microsoft - Daily % change 1990-2001
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-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
Markowitz Portfolio Theory
Standard Deviation VS. Expected Return
Investment A
0
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-50 0 50
%
prob
abili
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% return
Markowitz Portfolio Theory
Standard Deviation VS. Expected Return
Investment B
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-50 0 50
%
prob
abili
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% return
Markowitz Portfolio Theory
Standard Deviation VS. Expected Return
Investment C
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-50 0 50
%
prob
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% return
Markowitz Portfolio Theory
Standard Deviation VS. Expected Return
Investment D
0
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-50 0 50
%
prob
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% return
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
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
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
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%
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
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%
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
Efficient Frontier
A
B
Return
Risk (measured as )
Efficient Frontier
A
B
Return
Risk
AB
Efficient Frontier
A
BN
Return
Risk
AB
Efficient Frontier
A
BN
Return
Risk
ABABN
Efficient Frontier
A
BN
Return
Risk
AB
Goal is to move up and left.
WHY?
ABN
Efficient Frontier
Return
Risk
Low Risk
High Return
High Risk
High Return
Low Risk
Low Return
High Risk
Low Return
Efficient Frontier
Return
Risk
Low Risk
High Return
High Risk
High Return
Low Risk
Low Return
High Risk
Low Return
Efficient Frontier
Return
Risk
A
BNABABN
Security Market Line
Return
Risk
.
rf
Risk Free
Return =
Efficient Portfolio
Market Return = rm
Security Market Line
Return
.
rf
Risk Free
Return =
Efficient Portfolio
Market Return = rm
BETA1.0
Security Market Line
Return
.
rf
Risk Free
Return =
BETA
Security Market Line (SML)
Security Market LineReturn
BETA
rf
1.0
SML
SML Equation = rf + B ( rm - rf )
Capital Asset Pricing Model
R = rf + B ( rm - rf )
CAPM
Testing the CAPM
Avg Risk Premium 1931-65
Portfolio Beta1.0
SML
30
20
10
0
Investors
Market Portfolio
Beta vs. Average Risk Premium
Testing the CAPM
Avg Risk Premium 1966-91
Portfolio Beta1.0
SML
30
20
10
0
Investors
Market Portfolio
Beta vs. Average Risk Premium
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
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
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) + …
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