Risk & Return Pp

5/24/2018 Risk & Return Pp

1/405.1 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.

Chap ter 11

Risk andReturn



Defining Return

Income received on an investmentplus any change in market price,

usually expressed as a percent ofthe beginning market price of the

investment.

Dt+ (PtPt - 1)

Pt - 1R =



Return Example

The stock price for Stock A was $10pershare 1 year ago. The stock is currently

trading at $9.50per share and shareholdersjust received a $1 dividend. What return

was earned over the past year?

$1.00 + ($9.50$10.00)

$10.00R== 5%



Defining Risk

What rate of return do you expect on yourinvestment (savings) this year?

What rate will you actually earn?

The var iab i li ty o f returns from

those that are expected .



Determ ining Expected

Retu rn (Discrete Dist .)

R= ( Ri)( Pi)

Ris the expected return for the asset,Riis the return for the i

thpossibility,

Piis the probability of that returnoccurring,

nis the total number of possibilities.

n

I = 1



How to Determ ine the Expected

Return and Standard Deviat ion

Stock BW

Ri Pi (Ri)(Pi)

-0.15 0.10 0.015

-0.03 0.20 0.006

0.09 0.40 0.036

0.21 0.20 0.042

0.33 0.10 0.033

Sum 1.00 0.090

Theexpectedreturn, R,for Stock

BW is .09or 9%



Determ ining Standard

Dev iation (Risk Measure)

s= ( RiR)2( Pi)Standard Deviation, s, is a statistical

measure of the variability of a distributionaround its mean.

It is the square root of variance.

Note, this is for a disc rete distr ibut ion.

n

i = 1



How to Determ ine the Expected

Return and Standard Deviat ion

Stock BW

Ri Pi (Ri)(Pi) (Ri - R )2(Pi)

0.15 0.10 0.015 0.005760.03 0.20 0.006 0.00288

0.09 0.40 0.036 0.00000

0.21 0.20 0.042 0.002880.33 0.10 0.033 0.00576

Sum 1.00 0.090 0.01728



Determ ining Standard

Dev iation (Risk Measure)

n

i=1s= ( RiR)2( Pi)

s= .01728s = 0.1315or 13.15%



Coeff ic ient o f Variat ion

The ratio of the standard deviat ion ofa distribution to the mean of that

distribution.

It is a measure of RELATIVErisk.

CV = s/RCV of BW = 0.1315/ 0.09= 1.46


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5.11 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.

Disc rete versus . Con t inuous

Dist r ibut ions

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.15 0.03 9% 21% 33%

Discrete Cont inuous

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

-50%

-41%

-32%

-23%

-14%

-5%

4%

13%

22%

31%

40%

49%

58%

67%


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Cont inuous

Distr ibut ion Prob lem

Assume that the following list represents thecontinuous distribution of population returnsfor a particular investment (even thoughthere are only 10 returns).

9.6%,15.4%, 26.7%,0.2%, 20.9%,28.3%,5.9%, 3.3%, 12.2%, 10.5%

Calculate the Expected ReturnandStandard Deviat ionfor the populat ion.


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Lets Use the Calculator!Enter Data first. Press:

2nd Data

2nd CLR Work

9.6 ENTER

15.4 ENTER

26.7 ENTER

Note, we are inputting dataonly for the X variable andignoring entries for the Yvariable in this case.

Source: Courtesy of Texas Instruments


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Lets Use the Calculator!

Enter Data first. Press:

0.2 ENTER

20.9 ENTER

28.3 ENTER

5.9 ENTER

3.3 ENTER

12.2 ENTER

10.5 ENTER



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Lets Use the Calculator!

Examine Resu lts! Press:

2nd Stat

through the results.

Expected return is 9% forthe 10 observations.Population standard

deviation is 13.32%. This canbe much quicker

than calculating by hand,but slower than using aspreadsheet.



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Certainty Equ ivalen t(CE) is theamount of cash someone would

require with certainty at a point intime to make the individual

indifferent between that certain

amount and an amount expected tobe received with risk at the same

point in time.

Risk A tt itudes


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Certainty equivalent > Expected value

Risk Preference

Certainty equivalent = Expected value

Risk Indifference

Certainty equivalent < Expected valueRisk Aversion

Mostindividuals are Risk Averse.

Risk A tt itudes


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You have the choice between (1) a guaranteeddollar reward or (2) a coin-flip gamble of

$100,000 (50% chance) or $0 (50% chance).The expected value of the gamble is $50,000.

Maryrequires a guaranteed $25,000, or more, tocall off the gamble.

Raleighis just as happy to take $50,000 or takethe risky gamble.

Shannonrequires at least $52,000 to call off thegamble.

Risk A tt itude Examp le


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What are the Risk Attitude tendencies of each?

Risk A tt itude Examp le

Maryshows risk aversionbecause her

certainty equivalent < the expected value ofthe gamble.

Raleighexhibits risk indifferencebecause hercertainty equivalent equals the expected value

of the gamble.

Shannonreveals a risk preferencebecause hercertainty equivalent > the expected value ofthe gamble.


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RP= ( Wj)( Rj)

RPis the expected return for the portfolio,

Wjis the weight (investment proportion)for thejthasset in the portfolio,

Rjis the expected return of the jthasset,

mis the total number of assets in the

portfolio.

Determ ining Port fo l io

Expected Return

m

J = 1


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Standard Deviat ion

m

J=1

m

K=1sP= WjWk jk

Wjis the weight (investment proportion)for thejthasset in the portfolio,

Wkis the weight (investment proportion)

for the kthasset in the portfolio,

jkis the covariance between returns forthejthand kthassets in the portfolio.


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You are creating a portfolio of Stock D and StockBW (from earlier). You are investing $2,000in

Stock BW and $3,000in Stock D. Remember that

the expected return and standard deviation ofStock BWis 9%and 13.15%respectively. The

expected return and standard deviation ofStock Dis 8%and 10.65%respectively. The correlation

coefficient between BW and D is 0.75.

What is the expected return and standarddeviation of the portfolio?

Port fo l io Risk and

Expected Return Examp le


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WBW= $2,000/$5,000 = 0.4

WD= $3,000/$5,000 =0.6RP= (WBW)(RBW) + (WD)(RD)

RP= (0.4)(9%) + (0.6)(8%)

RP= (3.6%) + (4.8%) = 8.4%


Expected Return


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Portfolio variance = xBWBW + xDD

+ 2 (xBWxDBWDBWD)

Portfolio standard deviation =

xBWBW + xDD+2 (xBWxDBWDBWD)


Standard Deviat ion


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sP= (0.4)(8%) + (0.6)( 10.65%) +2 (0.4)(0.6)(0.75)(8%)(10.65%)

sP= 0.008174

= 9.04%


Standard Deviat ion


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Systematic Risk is the variability of returnon stocks or portfolios associated with

changes in return on the market as a whole.

Unsys tematic Risk is the variability of returnon stocks or portfolios not explained by

general market movements. It is avoidablethrough diversification.

Total Risk = SystematicRisk+Unsystemat icRisk

Total Risk = Sys tematic

Risk + Unsys tematic Risk


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Total

Risk

Unsystematic risk

Systematic risk

STD

DEVO

FPORTFOLIO

RETURN

NUMBER OF SECURITIES IN THE PORTFOLIO

Factors such as changes in the nations

economy, tax reform by the Congress,or a change in the world situation.




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Total

Risk

Unsystematic risk

Systematic risk

STD

DEVO

FPORTFOLIO

RETURN

NUMBER OF SECURITIES IN THE PORTFOLIO

Factors unique to a particular companyor industry. For example, the death of akey executive or loss of a governmental

defense contract.




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CAPM is a model that describes therelat ionshipbetween r iskand

expected (required) return; in thismodel, a securitys expected

(required) return is the risk-free rateplus a premium based on thesystemat ic r isk of the security.

Cap ital Asset

Pricing Model (CAPM)


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1. Capital markets are efficient.

2. Homogeneous investor expectations

over a given period.3. Risk-freeasset return is certain

(use short- to intermediate-termTreasuries as a proxy).

4. Market portfolio contains onlysystemat ic r isk (use S&P 500 Indexor similar as a proxy).

CAPM Assumpt ions


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An index of systemat ic r isk.

It measures the sensi t iv i tyof astocks returns to changes inreturns on the market portfolio.

The betafor a portfolio is simply aweighted average of the individual

stock betas in the portfolio.

What is Beta?


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EXCESS RETURNON STOCK

EXCESS RETURNON MARKET PORTFOLIO

Beta < 1(defensive)

Beta = 1

Beta > 1(aggressive)

Each characteristicline has a

different slope.

Charac ter ist ic L ines

and Dif feren t Betas


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Rjis the required rate of return for stock j,Rfis the risk-free rate of return,

bjis the beta of stock j (measuressystematic risk of stock j),

RMis the expected return for the market

portfolio.

Rj= Rf+ bj(RMRf)Securi ty Market Line


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Rj= Rf+ bj(RMRf)

bM= 1.0Systematic Risk (Beta)

Rf

RM

RequiredReturn

RiskPremium

Risk-freeReturn

Securi ty Market Line


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Obtaining Betas

Can use histor ica l dataif past best represents theexpectations of the future

Can also utilize services like Value Line, IbbotsonAssociates, etc.

Ad justed Beta

Betas have a tendency to revert to the mean of 1.0

Can utilize combination of recent betaand mean

2.22(0.7) + 1.00(0.3) = 1.554 + 0.300 = 1.854 est imate

Securi ty Market Line


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Lisa Miller at Basket Wondersis attemptingto determine the rate of return required by

their stock investors. Lisa is using a 6% Rfand a long-term market expected rate of

return of 10%. A stock analyst following the

firm has calculated that the firm betais 1.2.What is the requ ired rate of returnon the

stock of Basket Wonders?

Determ inat ion o f the

Requ ired Rate of Return


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RBW= Rf+ bj(RMRf)RBW= 6%+ 1.2(10%6%)

RBW= 10.8%

The required rate of return exceedsthe market rate of return as BWs

beta exceeds the market beta (1.0).

BWs Required

Rate o f Retu rn


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REVISION QUESTIONS1) Define a risk and return.

2)What is the definition of diversification.

3) Distinguish between systematic and unsystematic

risks. Give examples for each risk.


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4) Calculate the expected returns and standarddeviations of a two-stock portfolio. The following

data for Stock X and Stock Y as follows:

Out of a portfolio valuing RM 100,000, RM40,000 is invested in stock X and RM 60,000 in

stock Y.Stock X Stock Y

ExpectedReturn 11%

25%

Standard

Deviation15% 20%

Correlation

0.3


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5) Calculate the expected returns and standarddeviations of a two-stock portfolio. The following

data for Stock C and Stock D as follows:

Out of a portfolio valuing RM 100,000, RM60,000 is invested in stock C and RM 40,000

in stock D.

Stock C Stock DExpectedReturn 12% 20%Standard

Deviation14% 25%

C l ti 0 5

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