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Chapter 7,8Risk and return
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Rate of return
Cash return = ending price + cash distribution
(dividend)beginning price
Rate of return = cash return / beginning price
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Expected rate of return
Expected rate of return
Example:
E(r) = (-10% x 0.2) + (12% x 0.3)+ ( 22% x 0.5)=
12.6%
n
i
iirPrfreturnectedrateo1
exp
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Variance and standard deviation
To measure the risk of an investment, we use
the variance and the standard deviation
Variance
Standard deviation
i
n
i
i Prr 2_
1
2 )(
2
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Variance and standard deviation
(cont.)
Example:
= 0.183 = 18.3%
10.)15.50(.20.)15.30(.40.)15.15(.20.)15.00(.10.)15.20.( 22222
0335.0
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The weak form EMH
The weak form EMH states that all past
security market information is fully reflected
into security prices.
It means all price and volume information is
already reflected into the security prices.
It means the investor cannot use the past
information to earn an abnormal return.
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The semi-strong form EMH
This form states that all publicly availableinformation such as the past information, thefinancial statements, news, announcementsabout firm, industry, country, estimation on
future earning, etc. is fully reflected into thesecurity prices.
It means the investor cannot use the publiclyavailable information to earn the abnormal
return. The semi-strong form includes the weak form
EMH
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The strong-form EMH
This form states that all publicly and privately
(insider)available information is fully reflected
into the security prices.
It means that the investor cannot use any kind
of information to earn the abnormal return
even though it is the insider information .
This form includes both the weak-form EMH
and the strong-form EMH
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The expected return of a portfolio
Equation
: the proportion of the asset i
: the expected return of the asset i
Example: E(r) = (1/2x12%)+(1/2x8%)=10%
))((...))(())(()( 2211 nnportfolio rxEwrxEwrxEwrE
iW
)(irE
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Standard deviation (risk level-) of a
portfolios return
Equation: (assumption with two assets 1 and 2in the portfolio)
: the proportion of asset i in the portfolio
: the standard deviation of asset i : correlation coefficient of the rate of return
between asset i and j
212,121
2
2
2
2
2
1
2
1 2 wwwwportfolio
iw
iji,
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Standard deviation (risk level-) of a
portfolios return (cont.)
Example: this portfolio has two assets: 1 and 2
= 0.187 = 18.7% Correlation coefficient is 0.75
)2.2.75.5.5.2()2.5(.)2.5(. 2222 xxxxxxx
035.
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Correlation coefficient
Equation of correlation coefficient
Covariance:
Example:
Cov(i,j) = (6-10)(14-10)0.1+(8-10)(12-10)0.2+(10-10)(10-10)0.4+(12-10)(8-10)0.2+(14-10)(6-10)0.1 = -4.8
= -4.8 / (2.2)x(2.2) = -1
ji
ji
jiariance
),(cov,
tjjt
n
t
iit PrrrrjiCov )()(),(_
1
_
ji,
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Correlation coefficient (cont.)
Probability of occurrence Rate of return distribution
Stock 1 Stock 2
0.1 6.0% 14.0%
0.2 8.0 12.0
0.4 10.0 10.0
0.2 12.0 8.0
0.1 14.0 6.0
Expected rate of return 10.0% 10.0%
Standard deviation 2.2% 2.2%
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Correlation coefficient (cont.)
If correlation is -1, diversification is extremely
effective in reducing risk.
If correlation is zero, there is a significant
value in diversification.
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Two categories of risk
There are two categories of risk of aninvestment: the systematic risk (non-diversifiable risk) and the unsystematic risk
(diversifiable risk) The systematic risk contributes to the risk the
market portfolio
The unsystematic risk doesnt contribute tothe risk of the market portfolio
Total risk = systematic risk + unsystematic risk
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The systematic risk (non-diversifiable
risk)
The systematic risk impacts almost all of the
investments.
This is the common element of investment
returns that causes the returns to be correlated.
The returns of some investments are more
sensitive to systematic risk than those of other
investments This risk contributes to the standard deviation of
the large diversified portfolio
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The unsystematic risk (diversifiable
risk)
The return of an investment changes because
of a specific event of the investment
This risk contributes almost nothing to the
standard deviation of the large diversified
portfolio
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Systematic risk and beta
Beta measures the relation between the
return of an investment and that of the
market portfolio
The beta of a risk free bond is zero
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Systematic risk and beta
Beta coefficient for selected companies
Company Yahoo finance Microsoft money
central
Computers and software
Apple Inc. (AAPL) 2.91 2.58
Dell Inc (DELL) 1.81 1.37
Hewlett Packard (HPQ) 1.27 1.47
UtilitiesAmerican Electric Power Co.
(AEP)
0.74 0.73
Duke Energy Corp.(DUK) 0.40 0.56
Center Energy (CNP) 0.82 0.91
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Calculating portfolio beta
Equation
: the proportion of the portfolio invested inasset I
: the beta coefficient for asset i
Example: = (0.50x1.20)+(0.25x0.70)+(0.25x0.25)=
0.8375
nnportfolio WWW ...2211
iW
i
.port
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The capital asset pricing model (CAPM)
The CAMP provides a theory how risk andexpected return are connected.
Equation:
Expected return on risky asset j = risk free rate ofreturn + beta for the asset j x (expected return on themarket portfoliorisk free rate or return)
: market risk premium
Ex. E(r, home depot) = 0.03 +0.92(0.5)=7.6%
))(()( fmarketassetjfassetj rrErrE
))(( fmarket rrE
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The security market line (SML)
E(r)
SML
Beta
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The security market line (SML) (cont.)
The straight line relationship between the
beta and expected return is called the SML
The SML is simply a graphical representation
of the CAMP