Chapter 7,8 – Risk and Return

8/10/2019 Chapter 7,8 Risk and Return

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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

Chapter 7,8 – Risk and Return

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