1 Today Risk and Return Portfolio Theory Capital Asset Pricing Model Reading Brealey, Myers, and...
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Transcript of 1 Today Risk and Return Portfolio Theory Capital Asset Pricing Model Reading Brealey, Myers, and...
1
Today
Risk and Return • Risk and Return • Portfolio Theory• Capital Asset Pricing Model
Reading• Brealey, Myers, and Allen, Chapters 7 and 8
2
Measuring Risk
• Variance - Average value of squared deviations from mean. A measure of volatility.
• Standard Deviation - Average value of squared deviations from mean. A measure of volatility.
• Variance measures ‘Total Risk’
3
Measuring Risk
• Unique Risk - Risk factors affecting only that firm. Also called “diversifiable risk.”
• Market Risk - Economy-wide sources of risk that affect the overall stock market. Also called “systematic risk.”
• Diversification - Strategy designed to reduce risk by spreading the portfolio across many investments.
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Measuring Risk
05 10 15
Number of Securities
Po
rtfo
lio
sta
nd
ard
dev
iati
on
Market risk
Uniquerisk
5
Portfolio Risk
22
22
211221
1221
211221
122121
21
σxσσρxx
σxx2Stock
σσρxx
σxxσx1Stock
2Stock 1Stock
The variance of a two stock portfolio is the sum of these four boxes
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Portfolio Risk
Example
Suppose you invest 60% of your portfolio in Exxon Mobil and 40% in Coca Cola. The expected dollar return on your Exxon Mobil stock is 10% and on Coca Cola is 15%. The expected return on your portfolio is:
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Portfolio Risk
2222
22
211221
2112212221
21
)3.27()40(.σx3.272.181
60.40.σσρxxCola-Coca
3.272.181
60.40.σσρxx)2.18()60(.σxMobil-Exxon
Cola-CocaMobil-Exxon
Example
Suppose you invest 60% of your portfolio in Exxon Mobil and 40% in Coca Cola. The expected dollar return on your Exxon Mobil stock is 10% and on Coca Cola is 15%. The standard deviation of their annualized daily returns are 18.2% and 27.3%, respectively. Assume a correlation coefficient of 1.0 and calculate the portfolio variance.
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Portfolio RiskExample
Suppose you invest 60% of your portfolio in Exxon Mobil and 40% in Coca Cola. The expected dollar return on your Exxon Mobil stock is 10% and on Coca Cola is 15%. The standard deviation of their annualized daily returns are 18.2% and 27.3%, respectively. Assume a correlation coefficient of 1.0 and calculate the portfolio variance.
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Portfolio Return and Risk
)rx()r(x Return PortfolioExpected 2211
)σσρxx(2σxσxVariance Portfolio 21122122
22
21
21
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Portfolio RiskThe shaded boxes contain variance terms; the remainder contain covariance terms.
1
2
3
4
5
6
N
1 2 3 4 5 6 N
STOCK
STOCKTo calculate portfolio variance add up the boxes
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Beta and Unique Risk
beta
Expected
return
Expectedmarketreturn
10%10%- +
-10%+10%
stock
Copyright 1996 by The McGraw-Hill Companies, Inc
-10%
1. Total risk = diversifiable risk + market risk2. Market risk is measured by beta, the sensitivity to market changes
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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
imi
Covariance with the market
Variance of the market
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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.
15
Markowitz Portfolio Theory
Price changes vs. Normal distribution
Coca Cola - Daily % change 1987-2004
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
-9 -7 -5 -3 -1 0 2 4 6 7
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
8
10
12
14
16
18
20
-50 0 50
%
prob
abili
ty
% return
17
Markowitz Portfolio Theory
Standard Deviation VS. Expected Return
Investment B
0
2
4
6
8
10
12
14
16
18
20
-50 0 50
%
prob
abili
ty
% return
18
Markowitz Portfolio Theory
Exxon Mobil
Coca Cola
Standard Deviation
Expected Return (%)
40% in Coca Cola
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 =
Standard Deviation = Portfolio =
Return = weighted avg = Portfolio =
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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 =
Standard Deviation = Portfolio =
Return = weighted avg = Portfolio =
Let’s Add stock New Corp to the portfolio
23
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 =
NEW Standard Deviation = Portfolio =
NEW Return = weighted avg = Portfolio =
NOTE: Higher return & Lower risk
How did we do that? DIVERSIFICATION
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Efficient Frontier
A
B
Return
Risk (measured as )
25
Efficient Frontier
A
B
Return
Risk
AB
26
Efficient Frontier
A
BN
Return
Risk
AB
27
Efficient Frontier
A
BN
Return
Risk
ABABN
28
Efficient Frontier
A
BN
Return
Risk
AB
Goal is to move up and left.
WHY?
ABN
29
Efficient Frontier
Return
Risk
Low Risk
High Return
High Risk
High Return
Low Risk
Low Return
High Risk
Low Return
30
Efficient Frontier
Return
Risk
Low Risk
High Return
High Risk
High Return
Low Risk
Low Return
High Risk
Low Return
31
Efficient Frontier
Return
Risk
A
BNABABN
32
Security Market LineReturn
Risk
.
rf
Risk Free
Return =
Efficient Portfolio
Market Return = rm
33
Security Market LineReturn
.
rf
Risk Free
Return =
Efficient Portfolio
Market Return = rm
BETA1.0
34
Security Market LineReturn
.
rf
Risk Free
Return =
BETA
Security Market Line (SML)
35
Security Market LineReturn
BETA
rf
1.0
SML
SML Equation = rf + β ( rm - rf )
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Capital Asset Pricing Model
R = rf + β ( rm - rf )
CAPM
37
Testing the CAPM
Avg Risk Premium 1931-2002
Portfolio Beta1.0
SML30
20
10
0
Investors
Market Portfolio
Beta vs. Average Risk Premium
38
Testing the CAPM
Avg Risk Premium 1931-65
Portfolio Beta1.0
SML
30
20
10
0
Investors
Market Portfolio
Beta vs. Average Risk Premium
39
Testing the CAPM
Avg Risk Premium 1966-2002
Portfolio Beta1.0
SML
30
20
10
0
Investors
Market Portfolio
Beta vs. Average Risk Premium
40
Return = a + bfactor1(rfactor1) + bf2(rf2) + …
Arbitrage Pricing Theory
Alternative to CAPMAlternative to CAPM
Expected Risk
Premium = r - rf
= Bfactor1(rfactor1 - rf) + Bf2(rf2 - rf) + …
41
Arbitrage Pricing TheoryEstimated risk premiums for taking on risk factors
(1978-1990)
6.36Market
.83-Inflation
.49GNP Real
.59-rate Exchange
.61-rateInterest
5.10%spread Yield)(r
PremiumRisk EstimatedFactor
factor fr