Peirson Business Finance10e PowerPoint 07

8/9/2019 Peirson Business Finance10e PowerPoint 07

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Copyright 2009 McGraw-Hill Australia Pty Ltd

PPTs t/aBusiness Finance 10e

yPeirson

!lid"s pr"par"d y #arida A$htar a%d &arry 'li("r) Australia% *atio%al +%i("rsity

L"ar%i%g '"cti("s

• Understand how ris$ and r"tur% are definedand measured.

• Understand the concept of ris$ a("rsio% byinvestors.

• Explain how diversification reduces risk.

• Understand the importance of covariancebetween returns on assets to determine the

risk of a portfolio.

• Explain the concept of efficient portfolios.


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L"ar%i%g '"cti("s co%t

• Understand distinction between systematic andunsystematic risk and significance of systematicrisk.

• Explain the relationship between returns and riskproposed by the capital ass"t prici%g od"l (CA!".

• Understand the relationship between CA! and

the #aa-#r"%ch thr""-3actor od"l.• Explain the development of the #ama$#rench

three$factor model.


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,"tur%• %here is uncertainty associated with returns on shares.

Assume we can assign probabilities to the possiblereturns & given the following set of circumstances' theexpected return is

56apl" !olutio%

( )

( ) %11)1.013.0(

)2.012.0()4.011.0(

)242110.0()1.009.0(

1

=+

++

+=

= ∑=

R E x

x x

x x

P R R E

n

i

iiP"rc"%tag","tur%) R i

Proaility)P

i

) *.+

+* *.,

++ *.-+, *.,

+ *.+


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,is$• /isk is present whenever investors are not certain about the

outcome an investment will produce.

• ,is$ "asur"d y (aria%c" & how much a particular returndeviates from an expected return. Use standard deviation tomeasure risk' which is simply the s0uare root of the variance

• Using previous example' risk is given by

( )( )∑=

−=n

i

ii P R E R

1

22σ

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

( ) ( )

( )

2 22

2 2

2

Variance:

= 0.09-0.11 0.1 0.10-0.11 0.2

0.11-0.11 0.4 0.12-0.11 0.2

0.13-0.11 0.1

= 0.000 12

Standard Deviation: = 0.000 12 0.01095 1.095%

σ

σ

+

+ +

+

=


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,is$ Attitud"s

• ,is$-%"utral i%("stor p 17) #igur" 7. 1 2ne whose utility is unaffected by risk3 when chooses to

invest' investor focuses only on expected return.

• ,is$-a("rs" i%("stor p 17) #igur" 7.

1 2ne who demands compensation in the form of higherexpected returns in order to be induced into taking onmore risk.

• ,is$-s""$i%g i%("stor p 17) #igur" 7.

1 2ne who derives utility from being exposed to risk' andhence' may be willing to give up some expected returnin order to be exposed to additional risk.


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,is$ Attitud"s co%t

• %he standard assumption in finance theory is all

investors are risk averse.

1 %his does not mean an investor will refuse to bear anyrisk at all.

1 /ather' investors regards risk as something undesirable'

but may take up on board if compensated with sufficientreturn3 trade$off between risk and return.

• :%("stors; ris$ pr"3"r"%c"s

1 :%di33"r"%c" cur(" & which represents thosecombinations of expected return and risk that resultin a fixed level of expected utility for an investor.p 177) #igur" 7 < ,is$ a("rs" i%("stor


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,is$ o3 Ass"ts a%d Port3olios

• 4e now know that the risk of an individualasset is summarised by standard deviation(or variance" of returns.

• 5nvestors usually invest in a number ofassets (a portfolio" and will be concernedabout the risk of their overall portfolio.

• 6ow concerned about how these individual

risks will interact to provide us with overallportfolio risk.


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Port3olio Th"ory• Assuptio%s

1 5nvestors perceive investment opportunities in terms of aprobability distribution defined by expected return and risk.

1 5nvestors7 expected utility is an increasing function of returnand a decreasing function of risk (risk aversion".

• M"asuri%g r"tur% o3 port3olio 1 ortfolio return (R p" is a weighted average of all the expected

returns of the assets held in the portfolio

( ) ( )∑==

n

j j j p R E w R E

1

where:

= the proportion o the porto!io

inve"ted in a""et #

= the n$%&er o "ec$ritie" in the porto!io

jw

n


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Port3olio ,is$• Port3olio coprisi%g two ass"ts ris$ d"p"%ds o%

1 %he proportion of funds invested in each asset (w ". 1 %he riskiness of the individual assets (σ ,".

1 %he relationship between each asset in the portfoliowith respect to risk' correlation ( ρ ).

1 #or a two$asset portfolio the variance is

212'12122

22

21

21

22 σ σ ρ σ σ σ wwww p ++=

where:

= the proportion o the porto!io

inve"ted in a""et

= the "tandard deviation o a""et

corre!ation &etween a""et and ret$rn"

i

i

ij

w

i

i

i j

σ

ρ =


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Port3olio ,is$ a%d ,"tur%

M"asur""%t

• Assume 8*9 of the portfolio is invested insecurity + and -*9 in security ,. 5f variances ofsecurity + and security , are *.**+8 and *.**8'respectively' and the correlation ( p1,2 " is 1*.:

#ind expected return and risk of portfolio.

• %he expected returns of the securities are *.*;and *.+, respectively.

• %he standard deviation is *.*,-.


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,"latio%ship M"asur"s• Co(aria%c"

1 + to 1+.

( )

y x xy

y x

σ σ ρ

'cov =


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Gai%s 3ro >i("rsi3icatio%• ?iversification gain is related to correlation coefficient

value.

• %he degree of risk reduction increases as the correlationbetween the rates of return on two securities decreases.

• r @ >+' /isk reduction does not occur by combiningsecurities whose returns are perfectly positively correlated.

• r @ +' /isk reduction occurs by combining securities whosereturns are less than perfectly positively correlated.

• * r +' 5f the correlation coefficient is less than +' thethird term in the portfolio variance e0uation is reduced'reducing portfolio risk.

• r @ 1+ 5f the correlation coefficient is negative' risk isreduced even more' but this is not a necessary prerequisite for diversification gains.


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PPTs t/a Business Finance 10e y Peirson


>i("rsi3icatio% with Multipl" Ass"ts

• %he more assets we incorporate into the portfolio'

the greater the diversification benefits are.• %he key is the correlation between each pair of

assets in the portfolio.

• 4ith n assets' there will be an n B n covariance

matrix.• %he properties of the variance$covariance matrix

are

1 5t will contain n2 terms.

1 %he two covariance terms for each pair of assets areidentical.

1 5t is symmetrical about the main diagonal that containsn variance terms.


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>i("rsi3icatio% with Multipl"

Ass"ts co%t

• #or a diversified portfolio' the variance ofthe individual assets contributes little tothe risk of the portfolio.

1 #or example' in a :*$asset portfolio there are:* (n" variance terms and ,-:* (n2 n"covariance terms.

• %he risk depends largely on the

covariances between the returns on theassets.


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!yst"atic a%d +%syst"atic ,is$

• 5ntuitively' we should think of risk as comprising

• !yst"atic ris$ Component of total risk that is due toeconomy$wide factors. (non$diversifiable risk"

• +%syst"atic ris$ Component of total risk that is uni0ueto firm and is removed by holding a well$diversifiedportfolio.

• %he returns on a well$diversified portfolio will vary due to

the effects of market$wide or economy$wide factors.•


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,is$ o3 a% :%di(idual Ass"t

• %he risk contribution of an asset to a portfolio is largely

determined by the covariance between the return on thatasset and the return on the holder7s existing portfolio

• 4ell$diversified portfolios will be representative of themarket as a whole. %hus' the relevant measure of risk isthe covariance between the return on the asset and thereturn on the market

( ) pi pi pi R RCov σ σ ρ ' ' =

( ) M i R RCov '


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&"ta

Beta is a measure of a security7s systematic risk'

describing the amount of risk contributed by thesecurity to the market portfolio.

Cov(R i ' R M " can be scaled by dividing it by the

variance of the return on the market. %his is the

asset7s beta (β i "

( )2

'

i M

i

M

Cov R Rβ

σ =

where:= ret$rn on the %ar*et porto!io

= ret$rn on the partic$!ar a""et

M

i

R

R


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Co%structio% o3 a Port3olio• Th" opportu%ity s"t

1 %he set of all feasible portfolios that can beconstructed from a given set of risky assets.


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?alu" at ,is$ ?a,

• A relatively new measure of the riskiness of an

asset or portfolio.• ?efined as Dthe worst loss that is possible under

normal market conditions during a given timeperiod7.

• /e0uires standard deviation of the return on theasset or portfolio.

• %ypically assumes returns are normally

distributed.• Using the normal distribution and the standard

deviation' can calculate a worst$case scenario.


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?alu" at ,is$ co%t

• 5nvestment of +*m in CurFon has an estimatedreturn of Fero and a standard deviation of ,*9 (,m".

• Assume returns are normally distributed and badmarket conditions expected :9 of the time.

• 4orst outcome under normal conditions is a loss of

+.8-: (from normal tables" multiplied by standarddeviation of ,m.

• 4orst outcome is loss of .,)m or an investmentvalue of 8.G+m.

• Ha/ was not used effectively by 6AI in the foreignexchange scandal & poor implementation andexecution.


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Th" Prici%g o3 ,is$y Ass"ts

• 4hat determines the expected rate of returnon an individual asset=

• /isky assets will be priced such that there is arelationship between returns and systematic

risk.• 5nvestors need to be sufficiently compensated

for taking on the risks associated with theinvestment.


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Th" Capital Mar$"t Li%"

• Combining the efficient frontier with preferences'

investors choose an optimal portfolio.

• %his can be enhanced by introducing a risk$freeasset

1 %he opportunity set for investors is expanded andresults in a new efficient frontier & capital ar$"t li%" (C!J".

• %he C!J represents the efficient set of all

portfolios that provides the investor with the bestpossible investment opportunities when a risk$free asset is available.


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Th" CAPM a%d th" !"curity

Mar$"t Li%" !ML

• 5n e0uilibrium' the expected return on a risky asset i(or an inefficient portfolio"' is given by the securitymarket line

( ) ( ) ( ) M i M

f M f i R R R R E R R E 'cov

−+=

σ

where:

( ) = the e.pected ret$rn on the th ri"*+ a""et

( ' ) = the covariance &etween ret$rn"

on th ri"*+ a""et and the %ar*et porto!io

i

i M

E R i

Cov R R

i


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• %he covariance term is the only explanatory factor in

the e0uation that is specific to asset i .• As Cov(R i 'R M " is the risk of an asset held as part of the

market portfolio' and σ 2 M is the risk of the market

portfolio' beta (β ι) measures the risk of i relative to therisk of the market as a whole.

• 4e can thus write the !"curity Mar$"t Li%" (

•


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Port3olio &"ta• %he systematic risk (beta" of a portfolio is

calculated as the weighted average of the betas of the individual assets in the portfolio

∑=

=n

i

ii p w

1

β β

where:

n$%&er o a""et" in the porto!io

= proportion o the c$rrent %ar*et va!$eo porto!io p con"tit$ted &+ the i th a""et

i

n

w

=


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:pl""%tatio% o3 th" CAPM• %he three components of the CA! Rf ' β e and E (Rm"

1 Rf %he government securities current yield whose termto maturity matches the life of the proposed proKect.

1

e Use market model to estimate beta by obtaining timeseries data on the rates of return on shares and marketportfolio. Lence' number of years and the length of periodis significant over which returns are calculated.

1 E Rm %wo ways to calculate

(+" Use average return in share market index over a long periodof time.

(," Estimate market risk premium directly over a long period oftime.

• Lowever' test and empirical studies have found problemswith CA! implementation' and concerns have led tointroducing new model introduction.


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,is$) ,"tur% a%d th" CAPM

• %he capital market will only reward investors for

bearing risk that cannot be eliminated bydiversification.

• Unsystematic risk can be diversified away' socapital market will not reward investors for

taking this type of firm specific risk.

• Lowever' CA! states the reward for bearingsystematic risk is a higher expected return'consistent with the idea of higher risk re0uires

higher return.


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T"sts o3 th" CAPM

• Early empirical evidence was supportive of CA!

in explaining asset pricing.

• ,oll;s criti@u" (+)GG" criticised methodology oftesting CA! empirically.

• !ost tests of the CA! can only determine whetherthe market portfolio used is efficient.

• 5n response' researchers implementedmethodological refinements & CA! seems

untestable' given /oll7s criti0ue.• Lowever' CA! is a useful tool when thinking about

asset returns.


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#aa-#r"%ch Thr""-#actor Mod"l

• #aa a%d #r"%ch (+))," provide evidence on

factors that explain asset returns & no support forCA!' support for firm siFe' leverage' ME' IHM!H'though not definitive.

• #aa a%d #r"%ch (+)):" leads to the most common

three$factor model

• 5ncludes the CA!' market factor' a small minuslarge portfolio factor (

( ) ( ) ( ) ( ) ,it ft i M Mt ft i S ih E R R E R R E SMB E HMLβ β β − = − +


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#aa-#r"%ch Thr""-#actor Mod"l

co%t

• %his model is supported by Australian data relative toCA! Gau%t (,**-".

• 4hile the three$factor model is empirically robust' itsuffers from difficult economic interpretation & 4hy

do company siFe and IHM!H explain asset returns=

• %he fact that #ama$#rench includes market factor'along with ambiguity of role of other factors issupportive of CA!.

• %he three$factor model is now very common inempirical research.


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!uary

• Port3olio th"ory diversification reduces risk.

1 ?iversification works best with negative or low positivecorrelations between assets and asset classes.

• ,is$ ca% " di(id"d i%to two cat"gori"s

1 !yst"atic ris$ & cannot be diversified away.

1 +%syst"atic ris$ & can be diversified away.

•


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!lid"s pr"par"d y #arida A$htar a%d &arry 'li("r Australia% *atio%al +%i("rsity

!uary co%t

• CA! uses asset7s beta and assumes linear

relationship between expected return and riskrelative to market' measured by beta.

• #ama1#rench three$factor model is a contemporaryversion of the multi$factor (A%" model.

1 Ney factors are the market excess return' return ona small minus large portfolio' return on a high minuslow market to book portfolio.

• Although CA! has its shortfall' it does providessome important insights into the link between riskand return. Lence' there is no perfect model.

Peirson Business Finance10e PowerPoint 07

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