vi risk and rates of return

8/18/2019 VI Risk and Rates of Return

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Risk and Rates of Return

(Ch. 10 & 11)Stand-Alone Risk

Portfolio Risk

Risk and ReturnQuick overview of CAPM/SML


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A First Look at Risk and Return

•Standard & Poor’s 500: 90 U.S. stocks uto !9"# and "00 after t$at. Leaders in t$eirindustries and a%on& t$e lar&est 'r%s tradedon U.S. Markets.

• Sma sto!ks( Securities traded on t$e )*S+wit$ %arket caitali,ations in t$e otto%!0.

• "ord Portfoio( nternational stocks fro%all t$e worlds %a1or stock %arkets in )ort$A%erica2 +uroe2 and Asia.


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A First Look at Risk and Return(!ont’d)

• Cor#orate $onds( Lon&-ter%2 AAA-rated U.S. cororate onds wit$

%aturities of aro3i%atel4 50 4ears.

• %reasur $is: An invest%ent in

t$ree-%ont$ 6reasur4 ills.


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'aue of 100 n*ested at the +nd of1,-5

Source: Chicago Center for Research in Security Prices (CRSP) for U.S. stocks and

CPI, Global inance !ata for the "orld Inde#, $reasury bills and cor%orate bonds.


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$ottom Line

• Sma sto!ks had the hi/hest on/term returns w$ile 6-7ills $ad t$elowest lon&-ter% returns.

• Sma sto!ks had the ar/est2u!tuations in #ri!e2 w$ile 6-7ills$ad t$e lowest.

So ke %akea3a

4i/her risk reuires a hi/her return.


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n*estment Returns

6$e rate of return on an invest%ent cane calculated as follows(

8or instance2 if !2000 is invested and

!2!00 is returned after one 4ear2 t$erate of return for t$is invest%ent is(

:!2!00 ; !2000


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"hat is in*estment risk• 6wo t4es of invest%ent risk

– Stand-alone risk

– Portfolio risk

• nvest%ent risk is related to t$e %robability of earnin& a low ornegative actual return.

• %he /reater the !han!e of o3er

than e6#e!ted or ne/ati*ereturns the riskier thein*estment.


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Probability Distributions• A listin& of all ossile outco%es2 and t$e roailit4 o

eac$ occurrence.• Can e s$own &ra$icall4.

+3ected Rate of Return

Rate of

Return :


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Probability !istribution of Returns for a sto &n illustration


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?ow does it translate &ra$icall4@


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+%irical istriution of Annual Returns for U.S. Lar&e Stocks :SBP"00


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Avera&e Annual Returns for U.S. S%all Stocks2 Lar&eStocks :SBP "00


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13

A word on calculating portfolio return and portfolio risk


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14

Volatility is more tricky to compute as you shall take

into account dependence


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15


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nvest%ent Alternatives in a c$an&in& world

+cono%4 Pro. A $ C 8

Recession 0.! "." -7.08 5#.0 .0 -!#.0

7elow av& 0.5 "." 7.08 !E.0 -!F.0 -E.0

Avera&e 0.F "." 15.08 0.0 E.0 !0.0

Aove av& 0.5 "." 90.08 -!!.0 F!.0 5".0

7oo% 0.! "." 5.08 -5!.0 5.0 ED.0

6reasur4@

" diGerent asset class2 " ortfolios


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nvest%ent Alternatives in a c$an&in& world

+cono%4 Pro. $ C 8

Recession 0.! -7.08 5#.0 .0 -!#.0

7elow av& 0.5 7.08 !E.0 -!F.0 -E.0

Avera&e 0.F 15.08 0.0 E.0 !0.0

Aove av& 0.5 90.08 -!!.0 F!.0 5".0

7oo% 0.! 5.08 -5!.0 5.0 ED.0

6reasur4@

" diGerent asset class2 " ortfolios

!5.F

:F"


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Ca!uatin/ Standard ;e*iation for $

∑=

−=σ

σ==σ

=σ

)

!i

i

5

5

P

"ei/hted

A 02! -5# !52F -02E9F 02!""5 020!""57 025 -# !52F -02!9F 020E# 0200#"5

C 02F !" !52F 0205 02000 020005F

025 E0 !52F 02!# 020E09 020050

+ 02! F" !52F 02E5 02!0E 020!00

E%?%AL 020F0!!

E "ransform #ariance into standard de#iation =$ (,411!&(,5! = 2,%


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Co%arin& Standardeviations

Pro.A

7

0 "." 9.D !5.F Rate of Return :<


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Comments on Standard ;e*iationas a @easure of Risk

• Standard deviation :Ji< %easures total2 orstand-alone2 risk.

• 6$e lar&er Ji is2 t$e lower t$e roailit4t$at actual returns will e closer toe3ected returns.

• Lar&er Ji is associated wit$ a wider

roailit4 distriution of returns.


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Co%arin& Risk and Return

S+C A

S+C $S+C CS+C ;@AR+

%


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CoeKcient of Iariation :CI<

A standardi,ed %easure of

disersion aout t$e e3ectedvalue2 t$at s$ows the risk #er unitof return.

rHreturn+3ected

deviationStandard

CI

σ==


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Risk Rankin/s


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llustratin& t$e CI as a Measure ofRelative Risk

Je = Jf 2 ut e is riskier because of a larger %robability

of losses. n ot$er words2 the same amount of risk(as measured


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nvestor Attitude towards Risk

Risk a*ersion ; assu%es investors dislike

risk and reuire $i&$er rates of return toencoura&e t$e% to $old riskier securities.

Risk #remium :w$ic$ serves as

co%ensation for investors to $old riskiersecurities< - the diEeren!e


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Portfolio Construction( Risk and Return

• Assu%e a t'ostock %ortfolio is created

wit$ "02000 invested euall4 in 5ortfolios.

• Portfoio’s e6#e!ted return =

wei&$ted avera&e of t$e returns of t$eortfolios co%onent assets.

•Standard deviation is a little %oretrick4 as we saw earlier..


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Calculatin& Portfolio +3ected Return

.#:!.0


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An Alternative Met$od for eter%inin&Portfolio #%ected Return

+cono%4 Pro. 7 C Port.Port.Recession 0.! -5#.0 5#.0 0.00.0

7elow

av&

0.5 -#.0 !E.0 E.0E.0

Avera&e 0.F !".0 0.0 #."#."

Aoveav&

0.5 E0.0 -!!.0 9."9."

7oo% 0.! F".0 -5!.0 !5.0!5.0

.#:!5.0


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Calculatin& Portfolio Standardeviation and CI

0."!.#

E.F CI

E.F

.#


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Co%%ents on Portfolio RiskMeasures• J = E.F is %uc$ lower t$an t$e Ji of

eit$er stock :J?6 = 50.0O JColl. = !E.5


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eneral Co%%ents aout Risk

J ≈ E" for an avera&e stock.

Most stocks are ositivel4 :t$ou&$not erfectl4< correlated wit$ t$e%arket :i.e.2 etween 0 and !


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Returns istriution for 6wo Perfectl4)e&ativel4 Correlated Stocks : = -!.0<


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Correlation


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Partial Correlation2 = 0.E"


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Creatin& a Portfolio( 7e&innin& wit$ neStock and Addin/ Random See!tedSto!ks to Portfolio

D# de!reases as sto!ks added2ecause t$e4 would not be %erfectlycorrelated wit$ t$e e3istin& ortfolio.

+3ected return of t$e ortfolio wouldre%ain relativel4 constant.

+ventuall4 t$e diversi'cation ene'ts of

addin& %ore stocks dissiates :afteraout !0 stocks


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llustratin& iversi'cation +Gects of aStock Portfolio


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7reakin& own Sources of Risk

Stand-alone risk = Market risk iversi'ale risk

• @arket risk ; ortion of a securit4sstand-alone risk t$at cannot e eli%inatedt$rou&$ diversi'cation. Measured 4eta.

• ;i*ersiGa


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8ailure to iversif4

• f an investor c$ooses to $old a one-stock

ortfolio :doesnt diversif4


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Caital Asset Pricin& Model:CAPM<

Model linkin& risk and reuired returns. CAPMsu&&ests t$at t$ere is a Securit4 Market Line:SML


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4


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41


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42


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43


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44


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45


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7eta

Measures t$e %arket risk of a stock2and s$ows a stocks volatilit4relative to t$e %arket.

Indicates ho' risky a stock is if thestock is held in a 'elldi-ersied

%ortfolio.


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Co%%ents on 7eta

• f eta = !.02 t$e securit4 is 1ust as risk4as t$e %arket ortfolio.

• f eta T !.02 t$e securit4 is riskier t$an

t$e %arket ortfolio.• f eta !.02 t$e securit4 is less risk4

t$an t$e %arket ortfolio.

Most stocks $ave etas in t$e ran&e of 0."to !.".

$ f i


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Can t$e eta of a securit4 ene&ative@

• *es2 if t$e correlation etween Stock iand t$e %arket is ne&ative :i.e.2 i2% 0


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Calculatin& 7etas

• Vell-diversi'ed investors are ri%aril4concerned wit$( how a stock is expected tomove relative to the market in the future.

• Anal4sts are forced to rel4 on $istorical data.

A typical approach to estimate beta is torun a regression of the security’s pastreturns against the past returns of themarket .

• 6$e slo%e of t$e re&ression line is de'ned ast$e beta coe/cient for t$e securit4.

ll i $ C l l i f


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llustratin& t$e Calculation of7eta

.

.

.

ri

W

rM-" 0 " !0 !" 50

50

!"

!0

"

-"

-!0

Re&ression line(

ri = -5."9 !.FF rMN N

*ear rM ri

! !"!D

5 -" -!0

E !5 !

+etas with espect to the


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+etas with espect to the

-. 5 for /ndi#idua

toc0s (based on month)

data for 24–2!

6$ S it M k t Li :SML


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6$e Securit4 Market Line :SML


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V$at is t$e market risk#remium@

• ASV( Additional return over t$e risk-freerate needed to co%ensate investors forassu%in& an a-erage a%ount of risk.

• ts si,e deends on( :i< t$e erceivedrisk of t$e stock %arketO and :ii<investors de&ree of risk aversion.

• Iaries fro% 4ear to 4ear2 ut %ostesti%ates su&&est t$at it ran&esetween F and D er 4ear.

C l l ti R i d R t f


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Calculatin& Reuired Rates ofReturn

+ t d R i d R t


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+3ected vs. Reuired Returns

ll t ti t$ S it M k t


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llustratin& t$e Securit4 MarketLine

..Coll.

.?6

6-ills

.USR

SML

rM = !0."

rR8 = "."

-! 0 ! 5

.

SML( ri = "." :".0


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5

An +3a%le(


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An +3a%le(+uall4-Vei&$ted 6wo-Stock Portfolio

• Create a ortfolio wit$ "0 invested in?6 and "0 invested in Collections.

• %he


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Calculatin& Portfolio ReuiredReturns

• 6$e reuired return of a ortfolio is t$ewei&$ted avera&e of eac$ of t$e stocksreuired returns :alread4 seen efore


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8actors 6$at C$an&e t$e SML

• f investors raise inXatione3ectations 4 E2 w$at would$aen to t$e SML@

SML!

ri :<

SML5

0 0." !.0 !."

!E."!0."

D." "."

Y = E

Risk2 i



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• f in*estors’ risk a*ersionin!reased2 causin& t$e %arket riskre%iu% to increase 4 E2 w$at

would $aen to t$e SML@SML!

ri :<

SML5

0 0." !.0 !."

!E."!0."

"."

YRPM = E

Risk2 i

Ierif4in& t$e CAPM +%iricall4


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Ierif4in& t$e CAPM +%iricall4

• 6$e CAPM $as not een veri'edco%letel4.

• Statistical tests $ave role%s t$at

%ake veri'cation al%ost i%ossile.• So%e ar&ue t$at t$ere are

additional risk factors2 ot$er t$an

t$e %arket risk re%iu%2 t$at %uste considered.

Aout t$e CAPM


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Aout t$e CAPM

• nvestors see% to e concerned wit$ ot$%arket risk and total risk. 6$us2 t$e SML%a4 not roduce a correct esti%ate of r i.

ri = rR8 :rM ; rR8

vi risk and rates of return

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