Post on 13-Apr-2018
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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$cov.>
3var.3var.3var.
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=i
ix
returnreturnxx
returnreturnxxreturnreturnxx
returnxreturnxreturnx
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&fficient Portfolio Frontier ith
=o Assets Frontier e%presses portfolio standard
deviation in terms of portfolio e%pected
return r rather than in terms ofx/.
>/
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rr
rrx
=
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33>
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rr
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rr
rr
rr
rr
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&fficient Portfolio Frontier
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*is#(*eturn =rade(Hff and
Eolding Periods
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Mutual Fund =heorem
All investors$ 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. @