risk and returne

8/18/2019 Risk and Returne

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5-1

Chapter 5 Chapter 5

Risk andRisk andReturnReturn

© Pearson Education Limited 2004Fundamentals of Financial Management, 12/e

Created !" #regor! $% &u'leme!er, P'%(%

Carroll College, )aukes'a, )*


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After studying Chapter 5, After studying Chapter 5,

you should be able to:you should be able to:

1% +nderstand t'e relations'i -or .tradeoff eteen risk and return%

2% (efine risk and return and s'o 'o to measure t'em ! calculatinge3ected return, standard deiation, and coefficient of ariation%

5% (iscuss t'e different t!es of inestor attitudes toard risk%

4% E3lain risk and return in a ortfolio conte3t, and distinguis' eteenindiidual securit! and ortfolio risk%

6% (istinguis' eteen aoidale -uns!stematic risk and unaoidale-s!stematic risk and e3lain 'o roer diersification can eliminate oneof t'ese risks%

7% (efine and e3lain t'e caitalasset ricing model -C$PM, eta, and t'e

c'aracteristic line%8% Calculate a re9uired rate of return using t'e caitalasset ricing model

-C$PM%

:% (emonstrate 'o t'e ;ecurit! Market Line -;ML can e used to descriet'is relations'i eteen e3ected rate of return and s!stematic risk%


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Risk and ReturnRisk and Return

(efining Risk and Return

+sing Proailit! (istriutions to

Measure Risk $ttitudes =oard Risk

Risk and Return in a Portfolio Conte3t

(iersification ='e Caital $sset Pricing Model -C$PM

Efficient Financial Markets


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Defining ReturnDefining Return

*ncome receied*ncome receied on an inestmentlus an! c'ange in market ricec'ange in market rice,

usuall! e3ressed as a ercent oft'e eginning market riceeginning market rice of t'e

inestment%

((tt > -PPtt P Pt1t1

PPt1t1R ?


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Return ExampleReturn Example

='e stock rice for ;tock $ as @10@10 ers'are 1 !ear ago% ='e stock is currentl!

trading at @


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Return ExampleReturn Example

='e stock rice for ;tock $ as @10@10 ers'are 1 !ear ago% ='e stock is currentl!

trading at @


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Defining Risk Defining Risk

)'at rate of return do !ou e3ect on !our)'at rate of return do !ou e3ect on !our

inestment -saings t'is !earBinestment -saings t'is !earB

)'at rate ill !ou actuall! earnB)'at rate ill !ou actuall! earnB(oes it matter if it is a ank C( or a s'are(oes it matter if it is a ank C( or a s'are

of stockBof stockB

The ariability of returns fromThe ariability of returns from

those that are expe!ted"those that are expe!ted"


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Determining Expe!tedDetermining Expe!ted

Return #Dis!rete Dist"$Return #Dis!rete Dist"$

R ? - R i - i

R is t'e e3ected return for t'e asset,

R i is t'e return for t'e it' ossiilit!,

i is t'e roailit! of t'at returnoccurring,

n is t'e total numer of ossiilities%

n

i?1


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&o' to Determine the Expe!ted&o' to Determine the Expe!ted

Return and (tandard DeiationReturn and (tandard Deiation

;tock )

Ri Pi -Ri-Pi

%16 %10 %016

%05 %20 %007

%0< %40 %057

%21 %20 %042

%55 %10 %055

(um )"** "*+* "*+*

='ee3ectedreturn, R,for ;tock

) is %0<or


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Determining (tandardDetermining (tandard

Deiation #Risk easure$Deiation #Risk easure$

σ

? - R i R 2- i

;tandard (eiation;tandard (eiation,σ

, is a statisticalmeasure of t'e ariailit! of a distriution

around its mean%*t is t'e s9uare root of ariance%

ote, t'is is for a discrete distriution%

n

i?1


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&o' to Determine the Expe!ted&o' to Determine the Expe!ted

Return and (tandard DeiationReturn and (tandard Deiation

;tock )

Ri Pi -Ri-Pi -Ri R 2-Pi

%16 %10 %016 %00687

%05 %20 %007 %002::

%0< %40 %057 %00000

%21 %20 %042 %002::

%55 %10 %055 %00687

(um )"** "*+* "*+* "*)-./ "*)-./


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σ

? - R i R 2- i

σ

? %0182:

σ

? %1516%1516 or 15%16D15%16D

n

i?1


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Coeffi!ient of 0ariationCoeffi!ient of 0ariation

='e ratio of t'e standard deiationstandard deiation ofa distriution to t'e meanmean of t'at

distriution%

*t is a measure of RE1AT20E RE1AT20E risk%

C ? σ / RR

C of ) ? %1516%1516 / %0


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Dis!rete s" ContinuousDis!rete s" Continuous

DistributionsDistributions

0

0%06

0%10%16

0%2

0%26

0%5

0%56

0%4

16D 5D


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n

i?1σ

? - R i R 2

- n

ote, t'is is for a continuous

distriution 'ere t'e distriution isfor a population% R reresents t'eoulation mean in t'is e3amle%


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ContinuousContinuous

Distribution roblemDistribution roblem

$ssume t'at t'e folloing list reresents t'econtinuous distriution of oulation returnsfor a articular inestment -een t'oug' t'ereare onl! 10 returns%

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

Calculate t'e E3ected Return and;tandard (eiation for t'e population assuming a continuous distriution%


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Certaint! E9uialentCertaint! E9uialent -CE CE is t'eamount of cas' someone ould

re9uire it' certaint! at a oint intime to make t'e indiidual

indifferent eteen t'at certain

amount and an amount e3ected toe receied it' risk at t'e same

oint in time%

Risk AttitudesRisk Attitudes


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Certaint! e9uialent G E3ected alue

Risk PreferenceRisk Preference

Certaint! e9uialent ? E3ected alue

Risk *ndifferenceRisk *ndifference

Certaint! e9uialent H E3ected alue

Risk $ersionRisk $ersion

ost indiiduals are Risk $erseRisk $erse%

Risk AttitudesRisk Attitudes


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Risk Attitude ExampleRisk Attitude Example

Iou 'ae t'e c'oice eteen -1 a guaranteeddollar reard or -2 a coinfli gamle of

@100,000 -60D c'ance or @0 -60D c'ance%='e e3ected alue of t'e gamle is @60,000%

Mar! re9uires a guaranteed @26,000, or more, tocall off t'e gamle%

Raleig' is Aust as 'a! to take @60,000 or taket'e risk! gamle%

;'annon re9uires at least @62,000 to call off t'egamle%


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)'at are t'e Risk $ttitude tendencies of eac'B)'at are t'e Risk $ttitude tendencies of eac'B

Risk Attitude ExampleRisk Attitude Example

Mar! s'os .risk aersion.risk aersion ecause 'er.certaint! e9uialent H t'e e3ected alue oft'e gamle%%

Raleig' e3'iits .risk indifference.risk indifference ecause 'er.certaint! e9uialent e9uals t'e e3ected alueof t'e gamle%%

;'annon reeals a .risk reference.risk reference ecause'er .certaint! e9uialent G t'e e3ected alueof t'e gamle%%


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RP ? - 3 4 - R 4

RP is t'e e3ected return for t'e ortfolio,

3 4 is t'e eig't -inestment roortion for

t'e At' asset in t'e ortfolio,

R 4 is t'e e3ected return of t'e At' asset,

m is t'e total numer of assets in t'e

ortfolio%

Determining ortfolioDetermining ortfolio

Expe!ted ReturnExpe!ted Return

m

A?1


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(tandard Deiation(tandard Deiation

m

A?1

m

k?1PP ? 3 4 )k 4 k

3 4 is t'e eig't -inestment roortionfor t'e At' asset in t'e ortfolio,

3 k is t'e eig't -inestment roortion

for t'e kt' asset in t'e ortfolio,

4 k is t'e coariance eteen returns for

t'e At'

and kt'

assets in t'e ortfolio%


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Tip (lide: Appendix ATip (lide: Appendix A

;lides 62: t'roug' 650

and 655 t'roug' 657assume t'at t'e student

'as read $endi3 $ inC'ater 6


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3hat is Coarian!e 3hat is Coarian!e

σ

4 k ? 4 k r r 4 k

4 is t'e standard deiation of t'e At' asset in t'e ortfolio,

k is t'e standard deiation of t'e kt'

asset in t'e ortfolio,

r 4 k is t'e correlation coefficient eteen t'e

At'

and kt'

assets in t'e ortfolio%


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Correlation Coeffi!ient Correlation Coeffi!ient

A standardi6ed statisti!al measure

of the linear relationship bet'een

t'o ariables"

*ts range is from 7)"*7)"* -erfect

negatie correlation, t'roug' * * -no correlation, to 8)"*8)"* -erfect

ositie correlation%


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0arian!e 7 Coarian!e atrix 0arian!e 7 Coarian!e atrix

$ t'ree asset ortfolio"

Col 1 Col 2 Col 5

Ro 1 )1)1σ1,1 )1)2σ1,2 )1)5σ1,5

Ro 2 )2)1σ2,1 )2)2σ2,2 )2)5σ2,5

Ro 5 )5)1σ5,1 )5)2σ5,2 )5)5σ5,5

σ A,k ? is t'e coariance eteen returns for

t'e At' and kt' assets in t'e ortfolio%


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Iou are creating a ortfolio of ;tock (;tock ( and ;tock;tock

)) -from earlier% Iou are inesting @2,000@2,000 in

;tock );tock ) and @5,000@5,000 in ;tock (;tock (% Rememer t'at

t'e e3ected return and standard deiation of ;tock );tock ) is


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Expe!ted ReturnExpe!ted Return

)C) ? @2,000 / @6,000 ? %4

))(( ? @5,000 / @6,000 ? %7%7

RP ? -)C)-R 93 > -))((-R R DD

RP ? -"-+% > -"; "; -/%/%

RP ? -


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=oasset ortfolio"

Col 1 Col 2Ro 1 )C) )C)σC),C) )C) )(σC),(

Ro 2 )( )C)σ(,C) )( )(σ(,(

='is reresents t'e ariance coariancematri3 for t'e toasset ortfolio%




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=oasset ortfolio"

Col 1 Col 2Ro 1 -%4-%4-%0185 -%4-%7-%0106

Ro 2 -%7-%4-%0106 -%7-%7-%0115

='is reresents sustitution into t'eariance coariance matri3%




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=oasset ortfolio"

Col 1 Col 2Ro 1 -%002: -%0026

Ro 2 -%0026 -%0041

='is reresents t'e actual element aluesin t'e ariance coariance matri3%




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σP ? %002: > -2-%0026 > %0041

σP ? ;JR=-%011


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='e )RK# a! to calculate is aeig'ted aerage like"

σP ? %4 -15%16D > %7-10%76D

σP ? 6%27 > 7%5


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;tock C ;tock ( Portfolio

ReturnReturn


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Comining securities t'at are not erfectl!,ositiel! correlated reduces risk%

Diersifi!ation and theDiersifi!ation and the

Correlation Coeffi!ient Correlation Coeffi!ient

*

E ; = M E = R E

= + R

=*ME =*ME=*ME

;EC+R*=I E;EC+R*=I E ;EC+R*=I F;EC+R*=I FCominationComination

E and FE and F


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Total Risk @ (ystemati!Total Risk @ (ystemati!

Risk 8 ?nsystemati! Risk Risk 8 ?nsystemati! Risk

=otal=otal

RiskRisk

+ns!stematic risk+ns!stematic risk

;!stematic risk;!stematic risk

; = (

( E K

F P K R = F K L * K

R E = + R

+MER KF ;EC+R*=*E; * =E PKR=FKL*K

Factors suc' as c'anges in nationseconom!, ta3 reform ! t'e Congress,or a c'ange in t'e orld situation%


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Total Risk @ (ystemati!Total Risk @ (ystemati!

Risk 8 ?nsystemati! Risk Risk 8 ?nsystemati! Risk

=otal=otal

RiskRisk

+ns!stematic risk+ns!stematic risk

;!stematic risk;!stematic risk

; = (

( E K F P K R = F K L * K

R E = + R

+MER KF ;EC+R*=*E; * =E PKR=FKL*K

Factors uni9ue to a articular coman!or industr!% For e3amle, t'e deat' of ake! e3ecutie or loss of a goernmental

defense contract%


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C$PM is a model t'at descries t'erelationship eteen risk and

e3ected -re9uired returnN in t'ismodel, a securit!s e3ected

-re9uired return is t'e riskfree rateriskfree rate

lus a remiuma remium ased on t'esystemati! risksystemati! risk of t'e securit!%

Capital AssetCapital Asset

ri!ing odel #CA$ri!ing odel #CA$


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1% Caital markets are efficient%

2% omogeneous inestor e3ectations

oer a gien eriod%

5% Risk7freeRisk7free asset return is certain-use s'ort to intermediateterm

=reasuries as a ro3!%4% Market ortfolio contains only

systemati! risksystemati! risk -use ;OP 600 *nde3or similar as a ro3!%

CA AssumptionsCA Assumptions


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Chara!teristi! 1ineChara!teristi! 1ine

ECE;; RE=+RK ;=KC&

ECE;; RE=+RK M$R&E= PKR=FKL*K

etaeta ?

RiseRise

RunRun

arroer sreadarroer sread

is 'ig'er correlationis 'ig'er correlation

C'aracteristic LineC'aracteristic Line


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Cal!ulating 9etaBCal!ulating 9etaB

on our Cal!ulator on our Cal!ulator

=ime Pd% Market M! ;tock

1


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$ssume t'at t'e reious continuousdistriution rolem reresents t'e .e3cessreturns of t'e market ortfolio -it ma! still ein !our calculator data orks'eet 2nd (ata %

Enter the excess market returns as “X”!ser"at#ns $ 9.6%, -15.4%, 26.7%, -0.2%,

20.9%, 28.3%, -5.9%, 3.3%, 12.2%, an& 10.5%. Enter the excess stck returns as “'” !ser"at#ns

$ 12%, -5%, 19%, 3%, 13%, 14%, -9%, -1%,12%, an& 10%.


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Let us e3amine again t'e statisticalresults -Press 2nd and t'en ;tat

='e market e3ected return and standarddeiation is


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$n inde3 of systemati! risk systemati! risk %

*t measures t'e sensitiity of astocks returns to c'anges in returnson t'e market ortfolio%

='e betabeta for a ortfolio is siml! aeig'ted aerage of t'e indiidual

stock etas in t'e ortfolio%

3hat is 9eta 3hat is 9eta


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Chara!teristi! 1inesChara!teristi! 1ines

and Different 9etasand Different 9etas

ECE;; RE=+RK ;=KC&

ECE;; RE=+RK M$R&E= PKR=FKL*K

eta H 1eta H 1

-defensie-defensie

eta ? 1eta ? 1

eta G 1eta G 1

-aggressie-aggressie

Eac' c'aracteristicc'aracteristiclineline 'as adifferent sloe%


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RR A A is t'e re9uired rate of return for stock A,RRf f is t'e riskfree rate of return,

β A A is t'e eta of stock A -measures s!stematic

risk of stock A,

RRMM is t'e e3ected return for t'e market

ortfolio%

(e!urity arket 1ine(e!urity arket 1ine

RR A A ? RRf f > β A-RRMM RRf f


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RR A A ? RRf f > β A-RRMM RRf f

βMM ? 1%01%0

;!stematic Risk -eta

RRf f

RRMM

R e 9 u i r e d R e t u r n

R e 9 u

i r e d R e t u r n

RiskRisk

PremiumPremium

RiskfreeRiskfree

ReturnReturn


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Ktaining etas

Can use 'istorical data if ast est reresents t'ee3ectations of t'e future

Can also utiliQe serices like alue Line, *otson$ssociates, etc%

$dAusted eta

etas 'ae a tendenc! to reert to t'e mean of 1%0

Can utiliQe comination of recent eta and mean

2%22 -%8 > 1%00 -%5 ? 1%664 > 0%500 ? 1%:64 estimate

D t i ti f thD t i ti f th


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Lisa Miller at 9asket 3onders is attemtingto determine t'e rate of return re9uired !

t'eir stock inestors% Lisa is using a 7D R7D Rf f and a longterm market e3ected rate ofmarket e3ected rate of

returnreturn of 10D10D% $ stock anal!st folloing

t'e firm 'as calculated t'at t'e firm etaeta is1%21%2% )'at is t'e reuired rate of returnreuired rate of return on

t'e stock of 9asket 3ondersB

Determination of theDetermination of the

Reuired Rate of ReturnReuired Rate of Return

93 R i d93 R i d


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RR)) ? RRf f > β A-RRMM RRf f

RR)) ? 7D7D > 1%21%2-10D10D 7D7D

RR)) ? 10%:D10%:D

='e re9uired rate of return e3ceedst'e market rate of return as )s

eta e3ceeds t'e market eta -1%0%

93s Reuired93s Reuired

Rate of ReturnRate of Return



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Lisa Miller at ) is also attemting todetermine t'e intrinsic alueintrinsic alue of t'e stock%

;'e is using t'e constant grot' model% Lisa

estimates t'at t'e diidend ne3t erioddiidend ne3t eriod ill e@0%60@0%60 and t'at ) ill grogro at a constant rateof 6%:D6%:D% ='e stock is currentl! selling for @16%

)'at is t'e intrinsic alueintrinsic alue of t'e stockB*s t'e stock oer oer or underricedunderricedB


2ntrinsi! 0alue of 93 2ntrinsi! 0alue of 93



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='e stock is >0ER0A1?ED ast'e market rice -@16 e3ceeds

t'e intrinsic alueintrinsic alue -@10@10%


2ntrinsi! 0alue of 93 2ntrinsi! 0alue of 93

@0%60@0%6010%:D10%:D 6%:D6%:D

*ntrinsic*ntrinsic

aluealue?

? @10@10


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;!stematic Risk -eta

RRf f R e

9 u i r e d R e t u r n

R e

9 u i r e d R e t

u r n

(irection of Moement

(irection of Moement

;tock I;tock I -Kerriced

;tock -+nderriced



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;mallfirm Effect;mallfirm Effect

Price / Earnings EffectPrice / Earnings Effect

anuar! Effectanuar! Effect

='ese anomalies 'ae resentedserious c'allenges to t'e C$PMt'eor!%


Reuired Rate of ReturnReuired Rate of Return

risk and returne

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