Diversify Portfolio

7/26/2019 Diversify Portfolio

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Lecture 5: Portfolio

Diversification and Supporting

Financial Institutions


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Portfolio Diversification

All that should matter to an investor is the

performance of the entire portfolio.

Mean and variance of portfolio matter

La of large num!ers means that spreading

over man" independent assets reduces ris#$

has no effect on e%pected return.


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&'uall"()eighted Portfolio

)hen Asset *eturns are

Independent + Same ,ariance Same dollar value in each asset

*e!alancing each period

Portfolio e%pected return e'uals average of

asset e%pected returns

Portfolio standard deviation e'uals asset

standard deviation divided !"

S'uare root rule

n


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Investment -ompanies as

Providers of Diversification Investment trusts !efore /012s3

Mutual funds especiall" inde% funds3

-losed end investment companies

4nit investment trusts

All these institutions can ena!le small

investors to overcome transactions cost andlumpiness pro!lems in achieving diversifiedportfolios


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Dou!ts a!out Diversification

-omplete diversification ould impl"

holding much in fi%ed incomes$ real estate$

etc. ut hasn6t stoc# mar#et outperformedthese7


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&'uit" Premium Pu88le

9eometric average real stoc# mar#et return

/;/(/00;: ;.2< Siegel =a!le /(/3.

9eometric average real fi%ed(income return

/;/(/00;: /.;< Siegel =a!le /(>3

&'uit" premium ? ;.2


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Dominance of Stoc#s over Fi%ed

Incomes7 o thirt"("ear period since /@/(/B/

hen the return on either long(term or

short(term !onds e%ceeded that on e'uities.Siegel p. /53


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Surve" of Institutional Investors$

Shiller$ /00@C=here is no thirt"("ear period since /B2 in

hich 4S government !onds have

outperformed stoc#s. Eave "ou heardroughl" this claim even if details$ such asthe use of @2 "ears3 are different7

/. es$ often 5>. es$ once or tice >>BB(0B: 2.< per "ear.

*eal stoc# mar#et appreciation rate for 4S /0>B(0B: 1.@< per "ear.

Philippe Gorion and )illiam 9oet8mann$

Journal of Finance51:05@(2$ /000.3

So$ 4S e'uit" premium ma" reflect a selection !ias.


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Hptimal Portfolio Diversification

in 9eneral -ase Drop assumption of e'ual eighting$

independence and e'ual variance

Putxidollars in ith asset$I?/$..$n$ here the

xisum to /.

Portfolio e%pected value ?

Portfolio variance to assets3 ?

3.&/

i

n

i

i returnx=

3$cov.3/.>3var.3/.3var. >///>>

//

>

/ returnreturnxxreturnxreturnx ++


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Portfolio ,ariance$ =hree Assets

Portfolio variance ?

3/here.

3$cov.>

3$cov.>3$cov.>

3var.3var.3var.

@

/

@>@>

@/@/>/>/

@

>

@>

>

>/

>

/

=

+

++

++

=i

ix

returnreturnxx

returnreturnxxreturnreturnxx

returnxreturnxreturnx


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&fficient Portfolio Frontier ith

=o Assets Frontier e%presses portfolio standard

deviation in terms of portfolio e%pected

return r rather than in terms ofx/.

>/

>/

rr

rrx

=

/>>

>/

/>

>

>

>

>/

/>

/

>

>/

>>

3

33>

33

rr

rrrr

rr

rr

rr

rr

+

+

=


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&fficient Portfolio Frontier


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*is#(*eturn =rade(Hff and

Eolding Periods


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Mutual Fund =heorem

All investors$ regardless of ris# preferences$

ill hold a com!ination of the ris#less asset

and the tangenc" portfolio of all ris#"assets.

=herefore$ onl" one asset need !e made

availa!le to investors: a mutual fund thatholds the tangenc" portfolio.


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-apital Asset Pricing Model

-APM3 -APM Asserts that all investors hold their

optimal portfolio

-onse'uence of the mutual fund theorem:all investors hold the same portfolio of ris#"

assets$ the tangenc" portfolio

=herefore the -APM sa"s that the tangenc"portfolio e'uals the mar#et portfolio


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eta

=he -APM implies that the e%pected return

on the ith asset is determined from its !eta.

eta i3 is the regression slope coefficient

hen the return on the ith asset is regressed

on the return on the mar#et.

Fundamental e'uation of the -APM:3. fmifi rrrr +=


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Do Mutual Funds Eold Hptimal

Portfolio7 -ompletel" diversified funds do not e%ist

Mutual funds are classified into e'uit"

funds$ fi%ed(income funds$ etc

Mutual funds are further classified into

st"les: groth$ income$ !lue(chip$ etc.

Inde% funds account invest in stoc# price

inde%es$ such as S+P 522


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Inde% Funds

@52 !illion$ or < of stoc# mar#et

invested in e'uit" inde% funds in >222.

Much of this is in specialt" inde% funds$such as Internet funds.

Some other !roadl" diversified funds$

hoever$ ma" su!stitute for mar#et inde%funds.


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Alfred -oles /0/(/01

ale 6/@

Investment advisor$

- Founded &conometric

Societ"$ -olesFoundation

Econometrica/0@@C-an Stoc# Mar#etForecasters Forecast7


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Surve" of Individual Investors

/000C=r"ing to time the mar#et$ to get out !efore it

goes don and in !efore it goes up$ is:

/. A smart thing to doJ I can reasona!l"e%pect to !e a success at it. //. ot a smart thing to doJ I can6t

reasona!l" e%pect to !e a success at it. @

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