02 Portfolio Theory-putih

7/24/2019 02 Portfolio Theory-putih

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PORTFOLIO THEORY

Presented by

Prof. Eduardus Tandelilin, CWM


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ObjectivesTo understand the benefit of Diversification

To learn about constructing an efficient portfolio

To compare and contrast Diversifiable and

Non Diversifiable risk

To learn how to calculate Stocks eta and draw

!apital "arket #ine


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Put all your eggs in the onebasketand

WATCH THAT BASKET! -- Mark Twain

As we shall see in this chapter, this is probably not the best advice!

Intuitively, we all know that diversification is important when we aremanaging investments.

In fact, diversification has a profound effect on portfolio return andportfolio risk.

But, how does diversification work, exactly?


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PORTFOLIO RISK

Rate of Return Distribution

Two (W&M) stocks with perfect negative correlation (r = -1.0)

and for portfolio WM

a. Rates of Return

Stock W Stock M Portfolio WM

-10 -10

kw(%) kM(%) kP(%)

25 25 25

15 15 15

0 0 0

-10

2003 2003 2003


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b. Probability Distributions of Return

Probability

Density

Probability

Density

Probability

Density

kw kM kP

Stock WStock M Portfolio WM

0 0 015 15 15Percent Percent

Percent


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Year W kW(%) M - kM(%)Portfolio WM kP

(%)1999 40.0 -10.0 15.0

2000 -10.0 40.0 15.0

2001 35.0 -5.0 15.0

2002 -5.0 35.0 15.0

2003 15.0 15.0 15.0

Average return 15.0 15.0 15.0

Standard Deviation 22.6 22.6 0.0

Standard Deviations Portfolio ww2ww 2()2)2)22

22

2)

2) rp ++==

w1 * weighted fund invested in asset )

w2 * ) + w1* weighted fund invested in asset 2

r)(2 * correlation coefficient between asset ) and asset 2


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PORTFOLIO RISKRate of Return Distribution

Two (M&M) stocks with perfect positive correlation (r = +1.0)

and for portfolio MMc. Rates of Return

2003

Stock M Stock M Portfolio MM

kM(%) kM(%) kP(%)

25

15

0

-10

2003 2003

-10 -10

0 0

15 15

25 25


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d. Probability Distributions of Return

Probability Density

Percent

Stock M

Percent0 15

kM

Stock M Portfolio MM

Probability Density Probability Density

0 015 15Percent

kMkP


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Year M - kM(%) M kM (%)Portfolio MM - kP

(%)1999 -10.0 -10.0 -10.0

2000 40.0 40.0 40.0

2001 -5.0 -5.0 -5.0

2002 35.0 35.0 35.0

2003 15.0 15.0 15.0

Average Return 15.0 15.0 15.0



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PORTFOLIO RISK

Rate of Return Distribution

Two (W&Y) stocks with partial correlation (r = +0.65)

and for portfolio WY

e. Return

25

15

-10

Stock WkW(%)

0

Stock Stock Wk(%) kW(%)

25 25

15 15

0 02003 2003 2003

-10 -10


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f. Probability Distributions of Return

Stock W and Y

Probability Density

Portfolio WY

0 15 Percent

kP


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Year W - kW(%) Y kY(%)Portfolio WY - kP

(%)

1999 40.0 28.0 34.0

2000 -10.0 20.0 5.0

2001 35.0 41.0 38.0

2002 -5.0 -17.0 -11.0

2003 15.0 3.0 9.0

Average Return 15.0 15.0 15.0



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Correlation and Diversification

Suppose that as avery conservative, risk-averse

investor, you decide to invest all of your money in a bondmutual fund. Very conservative, indeed?

Uh,is this decision a wise one?


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The feasible set of portfoliosrepresents all portfolios

that can beconstructedfrom a given set of assets.

An efficient portfoliois one that offers the most returnfor a given amount of risk, or the least risk for a givenamount of return.

The optimal portfoliofor an investors is defined by the

tangency point between the efficient set of portfoliosand the investors highest indifference curve.

Efcient and OptimalPortolio

)%


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!ovariance and !orrelation !oefficient

=

==n

1i iBBiAAi

P)k-(k)k-(k(AB)CovCovarians

BA

AB

Cov(AB)r(AB)tCoefciennCorrelatio

==

)&


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Probability Distribution of Stocks E, F, G, Dan H

Probabilityof occurrence

!ate of !et"rn Distrib"tion

E F G H

0.1 10% 6. % 14% 2%

0.2 10 8 12 6

0.4 10 10 10 9

0.2 10 12 8 15

0.1 10 14 6 20

k = 10% 10% 10% 10%

= 0.00% 2.2% 2.2% 5%


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MEASURING THE PORTFOLIO RISK : EXAMPLE

COV (FG)=

= (6-10) (14-10) (0.1) + (8-10) (12-10) (0.2)

+ (10-10) (10-10) (0.4) + (12-10) (8-10) (0.2)

+ (14-10) (6-10) (0.1 = - 4.8

The negative sign indicates that the rates of returns on stocks F and G tendsto move in the opposite directions.

Correlation Coefficient F&G is:

=

5

1iiGGii

P)k-(k)k-(k

G

G

Cov(G)r

= /0)12022021

%0-+r34 =


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SCATTER DIAGRAM

a. Returns on E & F (r = 0) b. Returns on F & G (r = -1.0)

5 16

)/

)&

/

&

& )/ )& 2/

416

3 16

)/

)&

/

&

& )/ )& 2/ 316


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SCATTER DIAGRAM

a. Return F and H (r0.9) b. Return G and H (r-0.9)

Notes :a. Thered linesin each graph are called regression lines.

b. These graph are drawn as if each point had an equal probability of occurrence.

)/

&

)&

316

& )/ )& 2/ & )/ )& 2/

416

)&

)/

&

716 716


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THE TWO-ASSET CASE

A complicated looking but operationally simple equation can beused to determine the riskiness of a two-asset portfolio:

)1(!)1("#PortoolioBA

!!!!

p

ABrXXXX

BA ++==


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Average Return and Volatility For Portfolios

Portfolio Stan#ar# De$iation

Portfolio%&'e

cte#!et"rn

0000 0050 0100 0150 0200 0250 0300 0350

0025

0020

0015

0010

0005

0000

How Do Portfolios of These Stocks Perform?

100% !*S+!,*

.!/+P / ,M!,

100% MM+ /!P

100% W!SS

/M .!/+P

50% W!SS 50%

!*S+!,*

50% W!SS 50%MM+


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50% ireless ! 50% I""ucell

Ris# Increases it$ &'ected Return

50% ireless ! 50% Reinsurance

Ris# Decreases at First( T$en Increases as

&'ected Return Rises

Why Do Portfolios of Dierent Stocks Behave Dierently?

Average Return and Volatility For Portfolios


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Expected Return For Portfolio

( )( ) ( ) ( ) 6%$0)6-%0/&0/6/$02&0/

111 22))

=+=

+= REwREwRE p

50% ireless ! 50% I""ucell

50% ireless ! 50% Reinsurance

( )( ) ( )( ) 6$'0)6'.0/&0/6/$02&0/

111 22))

=+=

+= REwREwRE p

E$pected %et&rn o Portolio 's e Avera*eO E$pected %et&rns O e +o "tocks


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Two-Asset Portfolio StandardDeviation

2))22)

2

2

2

2

2

)

2

)

22 wwwwp ++=

2DeviationStandard

p

=

)orrelation *et+een Stoc#s In,uencesPortfolio -olatility

What is Correlation Between Wireless and mm!cell?"#$"

What is Correlation Between Wireless and %eins!rance&ro!'?("#))


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Correlation of Reinsurance Group,Immucell, and Wireless

Relative Performance of Three Stocks

0

0(5

1

1(5

2

2(5

January 000 ! December 00

Stock

Price

Re

lative

toP

ri

January

000

!eins"rance .ro"' )44"cell -or'( Wireless eleco4

Wireless and mm!cell *ove To+ether, Wireless and %eins!rance *ovein -''osite Directions

When Stocks *ove To+ether. Com/inin+ Them Doesn0t %ed!ce %isk*!ch


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Average Return and VolatilityFor Portfolios

Portfolio Stan#ar# De$iation

Portfolio%&

'ecte#!et"rn

0000 0050 0100 0150 0200 0250 0300 0350

0025

0020

0015

00100005

0000

50% W!SS 50%

MM+

!*S+!,* .!/+P

/ ,M!,MM+ /!P

W!SS

/M .!/+P

50% W!SS 50%

!*S+!,*

Wireless and mm!cell Correlation1 "#$"

Wireless and %eins!rance &ro!'1 ("#))


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Correlation Coefficients And RiskReduction For Two-Asset Portfolios

10%

15%

20%

25%

0% 5% 10% 15% 20% 25%

Standard Deviation of Portfolio Returns

"#$ect

edReturnonthePortfolio

is !.0

/.0 .0

is /.0


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Portfolios of MoreThanTwo Assets Five-Asset Portfolio

11

1111

&&%%

$$22))

REwREw

REwREwREwRE p

++

++=

&'ected Return of Portfolio Is Still T$e1vera2e Of &'ected Returns Of T$e T+o

Stoc#s

How s The 2ariance of Portfolio n3!enced By 4!m/er -fAssets in Portfolio?


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5

4

3

2

1

54321Asset

T$e )ovariance Ter"s Deter"ine To 1 Lar2e &tentT$e -ariance Of T$e Portfolio

Asset 1 2 3 4 51

2

3

4

55

4

3

2

154321Asset

-ariance of Individual 1ssets 1ccount Only for 345t$of t$e Portfolio -ariance

Variance Covariance Matrix

2

)

2

&

)

)2

2

&

)

)$

2

&

)

)%

2

&

)

)&

2

&

)

2)

2

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)

22

2

&

)

2$

2

&

)

2%

2

&

)

2&

2

&

)

$)

2

&

)

$2

2

&

)

2$

2

&

)

$%

2

&

)

$&

2

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%)

2

&

)

%2

2

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%$

2

&

)

2%

2

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%&

2

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&)

2

&

)

&2

2

&

)

&$

2

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)

&%

2

&

)

2&

2

&

)


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What Is a Stocks Beta?

*eta Is a easure of Syste"atic Ris#

2m

imi

=

What fBeta 5 6or Beta

76?

, e "tock -oves -ore an 1. onAvera*e /en te -arket -oves 1.(Beta 0 1)

, e "tock -oves ess an 1. on

Avera*e /en te -arket -oves 1.(Beta 2 1)

What fBeta 8 6?

, e "tock -oves 1. on Avera*e /ente -arket -oves 1.

, An 3Avera*e4 evel o %isk


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Diversifiable And Non-Diversifiable

Risk

As Number of Assets Increases, Diversification

Reduces the Importance of a Stocks Own Variance Diversifiable risk, unsystematic risk

Only an Assets CovarianceWith All Other AssetsContributes Measurably to Overall Portfolio Return

Variance Non-diversifiable risk, systematic risk


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How Risky Is an Individual Asset?

First 1''roac$ 6 1sset7s -ariance or StandardDeviation

What Really Matters Is Systematic Risk.How an Asset Covaries WithEverything Else

se Asset6s Beta


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The Impact Of Additional AssetsOn The Risk Of A Portfolio

%umber of Securities &'ssets( in Portfolio%umber of Securities &'ssets( in Portfolio

PortfolioRi

sk)

kp

%ondiversifiable Risk%ondiversifiable Risk

Diversifiable RiskDiversifiable Risk

Total riskTotal risk

1 5 10 15 20 251 5 10 15 20 25


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7al&in* %isk8 Assets "o&ld ake 'nto Acco&ntE$pected %et&rn and %isk

-ost 'nvestors 9 %isk Averse 9 #emandCompensation or Bearin* %isk

%isk Can Be #e:ned 'n -an8 /a8s

-arket "o&ld %e+ard Onl8 "8stematic %isk

Risk and Return

$%


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THE EFFICIENT PORTFOLIOS Anefficient portfoliois one that offers the most return for a given amount ofrisk, or the least risk for a given amount of return.

Suppose, we assume two securities A, kA= 5% with SD A,A= 4%, and, kB= 8%

andB= 10%.

If x equals 0.75, then kp= 5.75% kp= xAkA + xBkB

= 0.75 (5%) + 0.25 (8%) = 5.75%

Next we can determineP.Substitute the given values forA,B, and rAB, and then

solve forPat different values of x. For example, in the case where rAB= 0 and x

=0.75, thenP= 3.9%.

=(0.5625) (16) + 0.0625) (100) + 2 (0.75) (0.25) (0) (4) (10)

=9.00 + 6.25 =15.25 = 3.9%

)12)1 82222

p ABrXXXX BA ++=


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Proportion ofPortfolio inSecurity 8

19alue of :

Proportion ofPortfolio inSecurity

19alue of )+:

!ase ;1r8* ;=? 5=@5 5=5 5=@5 ?= 5=@5 ;=5

;=5 ;=5 =5 @ =5 5=< =5 ?

;=? ;=> @=!5 >=5 @=!5 @= @=!5 =5

; 1 > 1; > 1; > 1;

An Example


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Illustration of Portfolio Returns, Risk,

and the Attainable Set of Portfolios c* 'ttainable Set of Risk+Return ,ombinations

,ase -.

r'/ 1*0

,ase --.

r'/ 0

,ase ---.

r'/ !1*0

k'5

a* Returns b* Risk

1002' Portfolio

'llocation1002/

Percent

k:;9kP

k'5

k'5

kP

kP

k/3

k/3

1002'

1002'

Portfolio

'llocation

Portfolio

'llocation

1002/

1002/

'4

P

/10

/10

P

'4

1002'

1002'

Portfolio

'llocation

Portfolio

'llocation

1002/

1002/

1002/1002' Portfolio

'llocation

'4P

/10

"#$ected

Return)

&2(kP

rP&2(

rP&2(

3

5 '

:

'

:

3

5

4 10

Risk) P &2(4 10

Risk) P &2(

5

3

'

:

Risk) P &2(4 10


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)8OOSI9: T8 OPTI1L PORTFOLIO

T8 FFI)I9T ST OF I9-ST9T

"#$ected PortfolioReturn) kP

/

'

,

D "

6

78easible) or

'ttainable Set

"fficient Set &/,D"(

Risk) P &2(


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RISK3RT;R9 I9DIFFR9) );R-S

=s >isk Premium 1>P for>isk * P* $0$6? >P=* 20&6

/ ) 2 $ % & ' , - .

@s >isk Premium 1>P for

>isk * P

* $0$6? >P@

* )0/6

;=

;@

5Apected >ate of >eturn( rP

&

'

,

-

.

)/

%

$2

)

>isk( p16


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SL)TI9: OPTI1L PORTFOLIO OF RISKisk( p16

B

A

-

,02

'

%2 ' - )/%02 ,0)

'D? 'D! 'D1 '! '1

'?

,


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T8 )1PIT1L 1RKT LI9Investors Equilibrium: Combining the Risk Free Asset with the Market Portfolio

>isk( P

Increasing utility

"

N

8

7

4

5

@

k"

kP

k>3

P "

;$ ;2 ;)

5Apected >ate of

>eturn( kP

>


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CAPITAL MARKET LINE (CML)

P

"

>3">3p

B

2k+kC1kkC!"#

+==

"kC

>3kC

" >isk( P/

5Apected >ate of

>eturn( kP

"


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)1L);L1TI9: *T1 )OFFI)I9T

>ealied >eturn on Stock EkE16

>ealied >eturnon the market( k"

aE * ;ntercept * +-0.6

'0))/

)'F

F

==

==

m

j

j

k

k

run

riseb

kE * aE


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Thank You..Thank You..

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02 Portfolio Theory-putih