1 Today Risk and Return Portfolio Theory Capital Asset Pricing Model Reading Brealey, Myers, and...
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![Page 1: 1 Today Risk and Return Portfolio Theory Capital Asset Pricing Model Reading Brealey, Myers, and Allen, Chapters 7 and 8.](https://reader036.fdocuments.us/reader036/viewer/2022062308/56649d3f5503460f94a18f4e/html5/thumbnails/1.jpg)
1
Today
Risk and Return • Risk and Return • Portfolio Theory• Capital Asset Pricing Model
Reading• Brealey, Myers, and Allen, Chapters 7 and 8
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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’
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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.
![Page 4: 1 Today Risk and Return Portfolio Theory Capital Asset Pricing Model Reading Brealey, Myers, and Allen, Chapters 7 and 8.](https://reader036.fdocuments.us/reader036/viewer/2022062308/56649d3f5503460f94a18f4e/html5/thumbnails/4.jpg)
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Measuring Risk
05 10 15
Number of Securities
Po
rtfo
lio
sta
nd
ard
dev
iati
on
Market risk
Uniquerisk
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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.
![Page 9: 1 Today Risk and Return Portfolio Theory Capital Asset Pricing Model Reading Brealey, Myers, and Allen, Chapters 7 and 8.](https://reader036.fdocuments.us/reader036/viewer/2022062308/56649d3f5503460f94a18f4e/html5/thumbnails/9.jpg)
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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.
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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
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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
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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
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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 =
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 )
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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 LineReturn
Risk
.
rf
Risk Free
Return =
Efficient Portfolio
Market Return = rm
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Security Market LineReturn
.
rf
Risk Free
Return =
Efficient Portfolio
Market Return = rm
BETA1.0
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Security Market LineReturn
.
rf
Risk Free
Return =
BETA
Security Market Line (SML)
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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
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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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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) + …
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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