2 Risk and Return Stocks

7/29/2019 2 Risk and Return Stocks

1/38

6-1

6

Corporate Financial Management 3e

Emery Finnerty Stowe

Risk and

Return: Stocks


2/38

6-2

Learning Objectives

Calculate average realized returns for asecurity.

Estimate expected returns from securities andportfolios.

Estimate the standard deviation of returns onsecurities and for portfolios.

Explain why diversification is beneficial.

Describe the efficient frontier and the CapitalMarket Line.


3/38

6-3

Risk and Return and the

Principles of Finance Diversification

Invest in a group of assets, aportfolio, to reduce yourtotal risk.

Risk-Return Trade-Off Invest in the risky market portfolio and the riskless

assetin amounts that provide the risk level youchoose.

Efficient Capital MarketsA securitys risk and retired return can be inferred

from its past realized returns.

Incremental Benefits The incremental benefits from owning a stock are its

expected future cash flows.


4/38

6-4

Risk and Return and the Principles

of Finance Time-Value-of-Money

The value of a security is the present value of itsexpected future cash flows.

Two-Sided Transactions Use a securitys fair price to compute its expected

return because a fair price does not favor eitherside of the transaction.

Self-Interested Behavior Prices are set by the highest bidder.

Valuable Ideas Look for ideas that might add value to the market.


5/38

6-5

6.2 Probability and Statistics

Random variable Something whose value in the future is subject to

uncertainty.

Probability The relative likelihood of each possible outcome

(or value) of a random variable.

Probabilities of individual outcomes cannot be

negative nor greater than 1.0. Sum of the probabilities of all possible outcomesmust equal 1.0.


6/38

6-6

Probability Concepts

Mean The long run average of the random variable.

Equals the expected value of the random variable.

Variance (and Standard Deviation) Measure the dispersion in the possible outcomes.

Standard deviation is the square-root of the variance.

Higher variance implies greater dispersion in thepossible outcomes.


7/386-7


Covariance Measures how two random variables vary

together (or co-vary). Covariance can be negative, positive or zero.

Its magnitude has no bounds.

Correlation CoefficientA standardized measure of co-variation

between two random variables.

Always lies between -1.0 and +1.0.


8/386-8


Positive Covariance (or correlation)

When one random variables outcome is above the

mean, the other is also likely to be above its mean. Negative Covariance (or correlation)

When one random variables outcome is above themean, the other is likely to be below its mean.

Zero Covariance (or correlation) There is no relationship between the outcomes of the

two random variables.


9/386-9

Computing the Basic Statistics

A security analyst has prepared the followingprobability distribution of the possible returns on

the common stock shares of two companies:Compu-Graphics Inc. (CGI) and Data Switch Corp.(DSC). Probability Return on

CGIReturn on

DSC

0.300.500.20

10%14%20%

40%16%20%


10/386-10

The Mean

Let Nrepresent the number of possibleoutcomes,

pn represent the probability of the nthoutcome,

xn represent the value of the nth

outcome.The mean of the distribution ( ) iscomputed as: n

n

N

p xn=

=

1

x

xxx

x

xx

x


11/386-11

The Mean

For CGI, the mean (or expected) return is:

Similarly, the mean return for DSC is 24.00%

= + +

=

0 30 10%) 0 50 14%) 0 20 20%)

14 00%

. ( . ( . (

.

CGI n

n

3

p xn=

=

1

x


12/386-12

The Variance and the Standard

DeviationThe variance of the distribution of returns for the stock

is computed as:

2

1

2 )( xxpN

n

nn


13/386-13

Variance and Standard

DeviationThe variance of the distribution of a random variablex

is computed as:

The standard deviation is the square-root of thevariance.

2

1

2 )( xxpN

n

nnx

2

xx


14/386-14

Variance and Standard

DeviationThe variance of CGIs returns is:

2

1

2

)( xxp

N

n

nnCGI

00.12

)1420(20.0)1414(50.0)1410(30.0 222


15/386-15

The Variance and the Standard

DeviationThe Standard Deviation of CGIs return is:

Similarly, the variance of DSCs returns is 112.00,and its standard deviation is 10.58%

%46.300.12


16/386-16

The Covariance

The Covariance of two random variablesx andy is

computed as:

))((),(1

yyxxpYXCov n

N

n

nn


17/386-17

The Covariance

The covariance of the returns on CGI and DSC is

thus:

))((),(1

, yyxxpDSCCGICov n

N

n

nnyx

00.24

)2420)(1420(20.0

)2416)(1414(50.0

)2440)(1410(30.0


18/38

6-18

The Correlation Coefficient

The Correlation Coefficient between the returns on

two random variables (x andy) is computed as:

r

x,yx.y

x y


19/38

6-19

The Correlation Coefficient

The correlation coefficient between CGI and DSC is

thus:

YX

YX YXCov

r ),(,

58.1046.3

00.24,

YXr

655.0, YXr


20/38

6-20

Summary of Results for CGI and DSC

CGI DSC

MeanStandard Deviation

14.00%3.46%

24.00%10.58%

Correlation Coefficient -0.655


21/38

6-21

6.3 Expected Return and Specific Risk

The mean return is a measure of the expectedreturnfrom the security.

The expected return on DSC is 1.7 times

higher than the expected return on CGI. The standard deviation is a measure of the

specific riskof the security.

The specific risk of DSC is 3 times higherthan the specific risk of CGI.

The returns on DSC and CGI are negativelycorrelated.


22/38

6-22

6.4 Investment Portfolios

100% in CGI

100% in DSC

10.00%

12.00%

14.00%

16.00%

18.00%

20.00%

22.00%

24.00%

26.00%

0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00%

Risk

Return


23/38

6-23

Summary of Results for CGI and DSC

DSC has higher returns and higher riskthan CGI.

Without going further, the onlyrecommendation that we have is avariation on the old Wall Street saying

you can sleep well or eat well.As we will see in a minute, modern

portfolio theory can add much more value.


24/38

6-24

Portfolios of Securities

A portfolio is a combination of two or moresecurities.

Combining securities into a portfolio reducesrisk.

An efficient portfoliois one that has the highestexpected return for a given level of risk.

We will look at two-asset portfolios in fair detail.

Our results will hold forn-asset portfolios.


25/38

6-25

Portfolio Weights

Suppose you have $600 to invest.

You buy $400 worth of CGI stock and

$200 worth of DSC stock. Let CGI be stock no. 1 and DSC be stock

no. 2.

w and w1 20 667 0 333= = = =$400

$600.

$200

$600.


26/38

6-26

Expected Return of the Portfolio

The portfolios expected return is:

2111 )1( rwrwrp


27/38

6-27

Expected Return of the Portfolio

The expected return of the portfolio of CGIand DSC is:

%2431%14

32 pr

%33.17pr


28/38

6-28

Portfolio Risk

The risk of the portfolio (as measured by itsstandard deviation) is:

212111

2

2

2

1

2

1

2

1 ),()1(2)1( RRCorrwwwwp

As you can see, p is not a simpleweighted average of1 and 2.


29/38

6-29

Portfolio Risk

The risk of the portfolio of $400 worth of CGI stockand $200 worth of DSC stock is:

)58.10)(46.3)(655.0(3132258.103146.3322222

p

%67.2p


30/38

6-30

Diversification of Risk

Note that while the expected return of theportfolio is between those of CGI and DSC, its

risk is less than either of the two individualsecurities.

Combining CGI and DSC results in a substantialreduction of risk - diversification!

This benefit of diversification stems primarilyfrom the fact that CGI and DSCs returns are

negatively correlated.


31/38

6-31

Portfolio Expected Return

The expected return of the portfolio depends on:

The expected return of the securities in the

portfolio. The portfolio weights.

The risk of the portfolio depends on:

The risk of the securities in the portfolio.

The portfolio weights.

The correlation coefficient of the returns onthe securities.


32/38

6-32

Effect of Portfolio Weights on its

Expected Return and RiskPortfolio Weights PortfoliosCGI DSC Expected

Return

Standard

Deviation1.00

0.75

0.67

0.500.25

0.00

0.00

0.25

0.33

0.500.75

1.00

14.00%

16.50%

17.33%

19.00%21.50%

24.00%

3.46%

2.18%

2.64%

4.36%7.40%

10.58%


33/38

6-33

Portfolio Expected Return and

Risk

10.00%

12.00%

14.00%

16.00%

18.00%

20.00%

22.00%

24.00%

26.00%

0 .00 % 2.0 0% 4.0 0% 6.00 % 8.00 % 1 0.0 0

%

12.00

%

100% in CGI

100% in DSC

75% in CGI

25% in DSC


34/38

6-34

Correlation Coefficient and

Portfolio RiskAll else being the same, the lower the

correlation coefficient, the lower is the risk

of the portfolio. Recall that the expected return of the portfolio

is not affected by the correlation coefficient.

Thus, lower the correlation coefficient,greater is the diversification of risk.


35/38

6-35

Perfect Positive Correlation

When the returns on two stocks areperfectly positively correlated, there is no

diversification of the risk. The risk of the portfolio is then simply the

weighted average of the risk of the

individual assets.2111

2

2

2

1

2

1

2

1 )1(2)1( wwwwp

2111 )1(

wwp


36/38

6-36

Perfect Positive Correlation

1 2

2r

1r

2111 )1( wwp


37/38

6-37

Perfect Negative Correlation

When the returns on two stocks areperfectly negatively correlated, it is

possible to diversify away ALL of the riskby appropriate weighting of the two stocks.

2111

2

2

2

1

2

1

2

1 )1(2)1( wwwwp There exists a w1 such that:

0)1(2)1(2111

2

2

2

1

2

1

2

1

2 wwww

p


38/38

Perfect Negative Correlation

1 2

2r

1r

0)1(2)1( 21112

2

2

1

2

1

2

1 wwww

21

1*

1

w

2 Risk and Return Stocks

Documents

Transcript of 2 Risk and Return Stocks