CHAPTER FOURTEEN WHY DIVERSIFY? © 2001 South-Western College Publishing.
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Transcript of CHAPTER FOURTEEN WHY DIVERSIFY? © 2001 South-Western College Publishing.
CHAPTER FOURTEEN
WHY DIVERSIFY?
© 2001 South-Western College Publishing
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Outline Use More Than One Basket for Your Eggs
The Axiom The Concept of Risk Aversion Revisited
Preliminary Steps in Forming a Portfolio The Reduced Security Universe Security Statistics Interpreting the Statistics
The Role of Uncorrelated Securities The Variance of a Linear Combination Diversification and Utility The Concept of Dominance
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Outline
The Efficient Frontier Optimum Diversification of Risky Assets The Minimum Variance Portfolio The Effect of a Risk-free Rate The Efficient Frontier with Borrowing Different Borrowing and Lending Rates Naive Diversification The Single Index Model
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Use More Than One Basket for Your Eggs
Failure to diversify may violate the terms of fiduciary trust.
Risk aversion seems to be an instinctive trait in human beings.
Don’t put all your eggs in one basket.
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Preliminary Steps in Forming a Portfolio
Identify a collection of eligible investments known as the security universe.
Compute statistics for the chosen securities. e.g. mean of return variance / standard deviation of return matrix of correlation coefficients
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Preliminary Steps in Forming a Portfolio
Interpret the statistics.
1. Do the values seem reasonable?
2. Is any unusual price behavior expected to recur?
3. Are any of the results unsustainable?
4. Low correlations: Fact or fantasy?
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The Role of Uncorrelated Securities
The expected return of a portfolio is a weighted average of the component expected returns.
n
iiiportfolio RExRE
1
where xi = the proportion invested in security i
The Role of Uncorrelated Securities
n
iibaabbabbaap xxxxx
1
22222 12 ,
bai
ix
ab
i
i
p
and betweent coefficien ncorrelatio stock of deviation standard
stock in invested portfolio of proportion variance portfolio where
2
two-securityportfolio risk = riskA + riskB + interactive risk
The total risk of a portfolio comes from the variance of the components and from the relationships among the components.
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The Role of Uncorrelated Securitiese
xpe
cte
d re
turn
risk
betterperformance
A portfolio dominates all others if no other equally risky portfolio has a higher expected return, or if no portfolio with the same expected return has less risk.
The point of diversification is to achieve a given level of expected return while bearing the least possible risk.
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The Efficient Frontier : Optimum Diversification of Risky Assets
exp
ecte
d r
etu
rn
risk (standard deviation of returns)
impossibleportfolios
dominatedportfolios
efficient frontier
The efficient frontier contains portfolios that are not dominated.
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The Efficient Frontier : The Minimum Variance Portfolio
exp
ecte
d r
etu
rn
risk (standard deviation of returns)
single securitywith the highestexpected return
minimum varianceportfolio
The right extreme of the efficient frontier is a single security; the left extreme is the minimum variance portfolio.
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The Efficient Frontier : The Effect of a Risk-Free Rate
exp
ecte
d r
etu
rn
risk (standard deviation of returns)
dominatedportfolios
impossibleportfolios
M
Rf
C
efficient frontier:Rf to M to C
When a risk-free investment complements the set of risky securities, the shape of the efficient frontier changes markedly.
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The Efficient Frontier : The Effect of a Risk-Free Rate
In capital market theory, point M is called the market portfolio.
The straight portion of the line is tangent to the risky securities efficient frontier at point M and is called the capital market line.
Since buying a Treasury bill amounts to lending money to the U.S. Treasury, a portfolio partially invested in the risk-free rate is often called a lending portfolio.
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The Efficient Frontier with Borrowing
exp
ecte
d r
etu
rn
risk (standard deviation of returns)
dominatedportfolios
impossibleportfolios
M
Rf
C
efficient frontier:the ray from Rf through M
lending
borrowing
Buying on margin involves financial leverage, thereby magnifying the risk and expected return characteristics of the portfolio. Such a portfolio is called a borrowing portfolio.
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The Efficient Frontier : Different Borrowing and Lending Rates
exp
ecte
d r
etu
rn
dominatedportfolios
impossibleportfolios
M
RL
N
efficient frontier : RL to M, the curve to N, then the ray from N
risk (standard deviation of returns)
RB
Most of us cannot borrow and lend at the same interest rate.
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The Efficient Frontier : Naive Diversification
As portfolio size increases,total portfolio risk, on average, declines. After a certain point, however, the marginal reduction in risk from the addition of another security is modest.
tota
l ri
sk
nondiversifiablerisk
number of securities
Naive diversification is the random selection of portfolio components without conducting any serious security analysis.
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The Efficient Frontier : Naive Diversification
The remaining risk, when no further diversification occurs, is pure market risk.
Market risk is also called systematic risk and is measured by beta.
A security with average market risk has a beta equal to 1.0. Riskier securities have a beta greater than one, and vice versa.
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The Efficient Frontier : The Single Index Model
A pair-wise comparison of the thousands of stocks in existence would be an unwieldy task. To get around this problem, the single index model compares all securities to a benchmark measure.
The single index model relates security returns to their betas, thereby measuring how each security varies with the overall market.
The Efficient Frontier : The Single Index Model
Beta is the statistic relating an individual security’s returns to those of the market index.
2
,cov
m
mi
m
iimi
RR
where R = the return on the market index R = the return on security i = standard deviation of security i returns = standard deviation of market returns = correlation between security i returns and market returns
miimim
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The Efficient Frontier : The Single Index Model
E R R E R Ri f i m f
where R = riskless interest rate R = return on security i = return on the market = beta of security i
f
imi
R
The relationship between beta and expected return is the essence of the capital asset pricing model (CAPM), which states that a security’s expected return is a linear function of its beta.
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21
The Efficient Frontier : The Single Index Model
beta
E(R
i) -
Rf
secu
rity
mar
ket l
ine
+
+
-
-
0
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Review Use More Than One Basket for Your Eggs
The Axiom The Concept of Risk Aversion Revisited
Preliminary Steps in Forming a Portfolio The Reduced Security Universe Security Statistics Interpreting the Statistics
The Role of Uncorrelated Securities The Variance of a Linear Combination Diversification and Utility The Concept of Dominance
23
Review
The Efficient Frontier Optimum Diversification of Risky Assets The Minimum Variance Portfolio The Effect of a Risk-free Rate The Efficient Frontier with Borrowing Different Borrowing and Lending Rates Naive Diversification The Single Index Model