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Principles of FinanceBS 2100

Risk & Return II

Pete HahnFaculty of FinanceRoom 5012

Cass Building

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Topics Coveed

Review Diversification

!a"o#it$ Potfolio Theoy

The Relationship Bet#een Ris" and Retun

%alidity and the Role of the C&P!

'ome &ltenative Theoies

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Com)ining stoc"s into potfolios can educe standad

deviation* )elo# the level o)tained fom a simple

#eighted aveage calculation+

Coelation coefficients ma"e this possi)le+

The vaious #eighted com)inations of stoc"s that ceate

these standad deviations constitute the set of efficientportfolios+

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Pice changes vs+ -omal disti)utionIBM - Daily % change 1988-2008

Prop

ortionofDay

s

Daily % Change

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

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'tandad Deviation %'+ ./pected Retun

Investment A

%probability

% retrn

0

2

4

6

8

10

12

14

16

18

20

-50 0 50

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Investment B

%probability

% retrn

0

2

4

6

8

10

12

14

16

18

20

-50 0 50

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Investment

%probability

% retrn

0

2

4

6

8

10

12

14

16

18

20

-50 0 50

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!al-"art

#$"

tan&ar& De'iation

()pe*te& +etrn ,%

40% in #$"

()pe*te& +etrns an& tan&ar& De'iations 'ary gi'en&ifferent eighte& *o/binations of the sto*s

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.fficient Fontie

, .fficient Potfolios all fom the same 10 stoc"s

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.fficient Fontie

tan&ar& De'iation

()pe*te& +etrn ,%

(a*h half egg shell represents the possible eighte& *o/binations for tosto*s.

he *o/posite of all sto* sets *onstittes the effi*ient frontier

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.fficient Fontie

tan&ar& De'iation

()pe*te& +etrn ,%

en&ing or $orroing at the ris free rate ,rf allos s to e)ist otsi&ethe effi*ient frontier.

rf

Lend

ing

Borro

wing

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.fficient Fontie

./ample Coelation Coefficient 4 +,

'toc"s of Potfolio &vg Retun

&BC Cop2 0 15

Big Cop ,2 ,0 21

'tandad Deviation 4 #eighted avg 4 ((+ 6R7-8

Standard Deviation = Portfolio = 28.1

Return = ei!"ted av! = Portfolio = 1#.$%

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.fficient Fontie

Pevious ./ample Coelation Coefficient 4 +,'toc"s of Potfolio &vg Retun

&BC Cop2 0 15

Big Cop ,2 ,0 21

'tandad Deviation 4 Potfolio 4 2+1

Retun 4 #eighted avg 4 Potfolio 4 1+,

9et:s &dd stoc" -e# Cop to the potfolio

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.fficient Fontie

Pevious ./ample Coelation Coefficient 4 +(


Potfolio 2+1 50 1+,

!ew or"#0 $0% 19%

-.6 'tandad Deviation 4 #eighted avg 4 (1+0 6R7-8

'( Standard Deviation = Portfolio = 2).$)

'( Return = ei!"ted av! = Portfolio = 18.20%

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.fficient FontiePevious ./ample Coelation Coefficient 4 +(


Potfolio 2+1 50 1+,

-e# Cop (0 50 13

-.6 'tandad Deviation 4 Potfolio 4 2(+,(

-.6 Retun 4 #eighted avg 4 Potfolio 4 1+20

NOTE:Highe etun ; 9o#e is"ow &i& we &o that' DIVERSIFICATION

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.fficient Fontie

*

B

Return

Risk

+,easured

as -

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.fficient Fontie

*

B

Return

Risk

*B

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.fficient Fontie

*

B

Return

Risk

*B

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.fficient Fontie

*

B

Return

Risk

*B*B

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.fficient Fontie

*

B

Return

Risk

*B

oal is to ,oveup and left.

(/

*B

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.fficient Fontie

Return

Risk

o Risk

/i!" Return

/i!" Risk

/i!" Return

o Risk

o Return

/i!" Risk

o Return

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.fficient Fontie

Return

Risk

o Risk

/i!" Return

/i!" Risk

/i!" Return

o Risk

o Return

/i!" Risk

o Return

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.fficient Fontie

Return

Risk

*

B

*B*B

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'ecuity !a"et 9ine

Return

Risk

.

rf

Risk Free

Return =

'fficient Portfolio

3arket Return = r,

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'ecuity !a"et 9ine

Return

Risk

.

rf

Risk Free

Return =

'fficient Portfolio

3arket Return = r,

*

B

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'ecuity !a"et 9ine

Return

.

rf

Risk Free

Return =

'fficient Portfolio

3arket Return = r,

B'4*1.0

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'ecuity !a"et 9ine

Return

.

rf

Risk Free

Return =

B'4*

Securit5 3arket

ine +S3-

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'ecuity !a"et 9ineReturn

B'4*

rf

1.0

S3

S3 '6uation = rf 7 B + r,

rf -

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Capital &sset Picing !odel

R = rf 7 B + r, rf -

CP"

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Capital &sset Picing !odel

rs = rf 7 9 + r, rf -

alc(late investors re)(ire& ret(rn* Ass(me the Ret(rn on the Mar+et

has ,een an& is e."ecte& to ,e 8% the Ris+-/ree Rate or the M onilts is #% an&

eta3strata 2*4

osta offee 0*$ Mar+s 5 6"encer 1*2

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Testing the C&P!

*v! Risk Pre,iu,

1:)1200;

Portfolio Beta1.0

S330

20

10

0

#n'estors

"aretPortfolio

$eta 's. 'erage +is Pre/i/

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Testing the C&P!

*v! Risk Pre,iu,

1:)1

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Testing the C&P!

*v! Risk Pre,iu,

1:

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&ltenative Theoies to the C&P!

Arbitrage Pricing Theor

./pected Ris"

Pemium 4 < f

4 Bfacto1=facto1 < f> ? Bf2=f2 < f>

? @

Retun 4 a ? )facto1=facto1> ? )f2=f2> ?@

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&)itage Picing Theoy

7stimate& ris+ "remi(ms for ta+ing on ris+ factors198-1990:

6.36"aret

.83-#nflation

.4P+eal

.5-rate()*hange

.61-rate#nterest

5.10%sprea&7iel&,r

i/+is Pre/(sti/ate&a*tor

fa*tor fr

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Three Factor !o"el'teps to Adentify Factos

1+ Adentify a easona)ly shot list of macoeconomic factos thatcould affect stoc" etuns

2+ .stimate the e/pected is" pemium on each of these factos = r

facto 1 r f * etc+>

(+ !easue the sensitivity of each stoc" to the factos = , 1 * , 2 *

etc+>+

&ltenative Theoies to the C&P!

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Thee Facto !odel

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Ho# am A doing

he ratio of the ris pre/i/ to

the stan&ar& &e'iation is *alle& the

harpe ratio9

4"e s"arpe ratio+portfolio return > risk free- ? portfolio s.d.

provides a co,parative ,easure of return to risk for different

portfolios.

p

fp rr

=+atioharpe

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Topics Coveed


The Relationship Bet#een Ris" and Retun

%alidity and the Role of the C&P!

'ome &ltenative Theoies

Compaing Potfolios

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'ee you ne/t #ee"

POF_Week_7_SB (2)

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