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7/31/2019 Chapter 7 Slides FIN 435
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Investment Analysis &Investment Analysis &
Portfolio ManagementPortfolio Management
FIN 435 (Instructor- Saif Rahman)
Chapter 7Chapter 7
Optimal Risky PortfoliosOptimal Risky Portfolios
7/31/2019 Chapter 7 Slides FIN 435
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Market risk vs. Unique riskMarket risk vs. Unique risk
Stand-alone risk = Market risk + Firm-specific risk
The risk that remains even after extensive diversification is called
market risk, risk that is attributable to market wide risk sources.
FIN 435 (Instructor- Saif Rahman)
Such risk is also called systematic risk or nondiversifiable risk.
Measured by beta. (e.g. War, Inflation, High Interest Rates)
In contrast, the risk that can be eliminated by diversification is
called unique risk, firm-specific risk, nonsystematic risk or
diversifiable risk.
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Risk Reduction with DiversificationRisk Reduction with Diversification
Company-Specific Risk
Stand-Alone Risk
p (%)
35
FIN 435 (Instructor- Saif Rahman)2
# Stocks in Portfolio10 20 30 40 2,000+
Market Risk
20
0
7/31/2019 Chapter 7 Slides FIN 435
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TwoTwo--Security Portfolio: ReturnSecurity Portfolio: Return
Portfolio Return
Bond Weight
Bond Return
p D ED E
P
D
r
r
w
r
w wr r
FIN 435 (Instructor- Saif Rahman)
Equity Weight
Equity Return
E
E
w
r
( ) ( ) ( )p D D E EE r w E r w E r
1
n
1iiw
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= Variance of Security D
TwoTwo--Security Portfolio: RiskSecurity Portfolio: Risk
2 2 2 2 2 2 ( , )P D D E E D E D E w w w Cov r r
2D
FIN 435 (Instructor- Saif Rahman)
= Variance of Security E
= Covariance of returns forSecurity D and Security E
2
E
( , )D ECov r r
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7/31/2019 Chapter 7 Slides FIN 435
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Range of values for 1,2
+ 1.0 > r > -1.0
Correlation Coefficients: Possible ValuesCorrelation Coefficients: Possible Values
FIN 435 (Instructor- Saif Rahman)
r= . , e secur es wou e per ec ypositively correlated
Ifr= - 1.0, the securities would be perfectlynegatively correlated
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Importance of CorrelationImportance of Correlation
Correlation is important because it affects the
degree to which diversification can be achieved
using various assets.
FIN 435 (Instructor- Saif Rahman)7
Theoretically, if two assets returns are perfectly
negatively correlated, it is possible to build a
riskless portfolio with a return that is greater thanthe risk-free rate.
7/31/2019 Chapter 7 Slides FIN 435
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2
p = W12
1
2
+ W22
1
2
rp = W1r1 + W2r2 + W3r3
+ W32
3
2
ThreeThree--Security PortfolioSecurity Portfolio
FIN 435 (Instructor- Saif Rahman)
+ 2W1W2 Cov(r1r2) Cov(r1r3)+ 2W1W3Cov(r2r3)+ 2W2W3
p2 = w1
212 + w2
22
2 + 2W1W2 1 2 12
7/31/2019 Chapter 7 Slides FIN 435
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rp = Weighted average of the nsecurities
p2 = (Consider all pair-wise
In General, For an nIn General, For an n--Security PortfolioSecurity Portfolio
FIN 435 (Instructor- Saif Rahman)
covariance measures)
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TwoTwo--Security Portfolios with Different CorrelationsSecurity Portfolios with Different Correlations
13
E(r)
-
p2 = w1
212 + w2
22
2 + 2W1W2 1 2 12
FIN 435 (Instructor- Saif Rahman)
= 1%
8
St. Dev12% 20%
= .3
= -1
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The relationship depends on correlation coefficient.
-1.0 < < +1.0
The smaller the correlation, the greater the risk reduction
Portfolio Risk/Return Two Securities:Portfolio Risk/Return Two Securities:
Correlation EffectsCorrelation Effects
FIN 435 (Instructor- Saif Rahman)
Ifr = +1.0, no risk reduction is possible.
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What is the minimum level to which portfolioWhat is the minimum level to which portfolio
standard deviation can be held?standard deviation can be held?
),cov(2
),cov()(
22
2
min
EDED
EDE
rr
rrDw
FIN 435 (Instructor- Saif Rahman)
The optimal combinations result in lowest level
of risk for a given return.
The optimal trade-off is described as the efficient
frontier.
These portfolios are dominant.
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Markowitz Portfolio Selection ModelMarkowitz Portfolio Selection Model
Security Selection
First step is to determine the risk-return
FIN 435 (Instructor- Saif Rahman)
All portfolios that lie on the minimum-variance
frontier from the global minimum-variance
portfolio and upward provide the best risk-return
combinations
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The MinimumThe Minimum--Variance FrontierVariance Frontier
of Risky Assetsof Risky AssetsE(r)
Efficientfrontier
FIN 435 (Instructor- Saif Rahman)
Globalminimum
variance
portfolio Minimumvariancefrontier
Individualassets
St. Dev.
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Alternative CALsAlternative CALs (CAL with the highest reward(CAL with the highest reward--toto--
variability ratio)variability ratio)
M
E(r)
CAL (A)CAL (P)
P
M
FIN 435 (Instructor- Saif Rahman)
o aminimum variance)
A
F
P P&F A&FM
A
G
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Capital Allocation and the Separation PropertyCapital Allocation and the Separation Property
The most striking conclusion is that a portfolio manager will offer the same
risky portfolio, P, to all clients regardless of their degree of risk aversion
The result is called a separation property, it tells us that the portfolio choice
problem may be separated into two independent tasks:
FIN 435 (Instructor- Saif Rahman)
1) First determine the optimal risky portfolio
2) Then choose the allocation of the complete portfolio to risk-free
assets
An example of a situation when there is more than one optimal risky
portfolio: Risk-free lending only
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Portfolio Selection & Risk AversionPortfolio Selection & Risk Aversion
E(r)
Efficient
U U U
FIN 435 (Instructor- Saif Rahman)
risky assets
Morerisk-averseinvestor
Q
P
St. Dev
Less
risk-averseinvestor