POF_Week_6_SB (2)
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Transcript of POF_Week_6_SB (2)
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Principles of FinanceBS 2100
An Introduction to Risk
Pete HahnFaculty of Finance
Room 5012
Cass Building
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Topics Coveed
!ve a Centuy of Capital "a#et Histoy
"easuing Potfolio Ris#
Calculating Potfolio Ris#
Ho$ %ndividual &ecuities 'ffect Potfolio Ris#
Divesification ( )alue 'dditives
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The )alue of an %nvestment of *1 in 1+00
$1
$10
$100
$1,000
$10,000
$100,000
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
Start of Year
Dollars(
logscale)
Common Stoc
!S "o#t on%s
&'(lls
14,276
241
71
2008
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'veage "a#et Ris# Pemia ,-y county.
Risk premium, %
Country
4.855.33 5.5 5.95
6.06 6.17 6.45 6.56.88
7.52 7.628.58 8.81 8.85
9.39 9.7110.29
10.97
0123456
789
1011
Denmar
$elg*m
S.t/erlan
%
Sa
n
Cana%
a
or.a
relan
%
!
eterlan%s
#erag
e
!S
S.e%e
n
So*tfrca
*strala
"erman
7rance
aa
n
ta
l
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&ome counties pay o offe highe is#
pemiums ,i/e/ investos get a highe etunthan the is#fee o govenment -onds inthose ma#ets. $hy dont they get all the
investment money
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Dividend 3ields
Dividend yieds in t!e ".#.$. 19002008
1+00
1+04
1+0
1+0+
1+12
1+15
1+16
1+21
1+27
1+28
1+40
1+44
1+4
1+4+
1+72
1+75
1+76
1+51
1+57
1+58
1+0
1+4
1+
1++
1+82
1+85
1+86
1+61
1+67
1+68
1++0
1++4
1++
1+++
2002
2005
2006
0
1
2
4
7
5
8
6
+
10
Dividend3ield,9.
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0
70
20
0
20
70
0
60
R&teso' Return 1900(2008
#our)e* +otson $sso)i&tes
-e&r
.er)ent&/eReturn
#to)k &rket +nde Returns
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"easuing Ris#
Return %
o' -e&rs
Histogram of Annual Stock Market Returns
(1900-2008)
1 2
4
11 11
21
17
24
13
32
0
4
8
12
16
20
24
'50to'40
'40to'30
'30to'20
'20to'10
'10to0
0to10
10to20
20to30
30to40
40to50
50to60
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:;uity "a#et Ris# ,-y county.
#t&nd&rd
Devi&tiono'$n
nu&Returns,% $ver&/e Risk 1900(2008
17.0218.45 19.22 20.16
21.83 22.05 22.99 23.23 23.42 23.5123.98 24.09 25.28
28.32 29.57
33.93 34.3
0
5
10
15
20
2530
35
40
Cana%a
*strala
S.t/erlan%
!-S-
!--
Denmar
San
eterlan%s
So*tfrca
relan%
S.e%en
$elg*m
7rance
or.a
aan
tal
"erman
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Do$
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"easuing Ris#
Variance,=2 . 'veage value of s;uaed
deviations fom mean/ ' measue of volatility/
Standard Deviation,=. > The s;uaeoot of
)aiance/ 'lso? a measue of volatility/
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"easuing Ris#
Coin Toss @amecalculating vaiance and standaddeviation
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"easuing Ris#
Diversification &tategy designed to educeis# -y speading the potfolio acoss manyinvestments/
Unique Risk Ris# factos affecting only thatfim/ 'lso called Adivesifia-le is#/
arket Risk :conomy$ide souces of is#
that affect the oveall stoc# ma#et/ 'lso calledAsystematic is#/
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"easuing Ris#
ort'oio r&te
o' return
'r&)tion o' port'oio
in 'irst &sset
r&te o' return
on 'irst &sset
'r&)tion o' port'oio
in se)ond &sset
r&te o' return
on se)ond &sset
(( (())
))
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"easuing Ris#
0
5 10 15
!u"#er of Securities
Portfolios
tand
ardd
eviation
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"easuing Ris#
0
5 10 15
!u"#er of Securities
Portfolios
tand
ardd
eviation
arket risk
Unique
risk
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Potfolio Ris#
:!e v&ri&n)e o' & to sto)k port'oio is t!e sum o' t!ese'our oes
2
2
2
2
211221
1221
211221
12212
1
2
1
;;;
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Potfolio Ris#
+amle
#uppose you invest 60% o' your port'oio in =&(
&rt &nd 40% in +>. :!e epe)ted do&r return
on your =&(&rt sto)k is 10% &nd on +> is15%. :!e epe)ted return on your port'oio is*
%1215403.10603.Return?pe)ted =+=
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Potfolio Ris#
+amle#uppose you invest 60% o' your port'oio in =&(&rt &nd 40% in
+>. :!e epe)ted do&r return on your =&(&rt sto)k is 10% &nd
on +> is 15%. &e stan%ar% %e#(at(on of te(r ann*al(/e% %a(l
ret*rns are 19-8: an% 29-7:, resect(#el- ss*me a correlat(on
coeff(c(ent of 1-0 an% calc*late te ortfol(o #ar(ance-
222
2
2
2
211221
211221222
1
2
1
7.2940.;7.298.191
60.40.;;
7.298.191
60.40.;;&rt(=&
=
=
=
=
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Potfolio Ris#
+amle#uppose you invest 60% o' your port'oio in =&(&rt &nd 40% in
+>. :!e epe)ted do&r return on your =&(&rt sto)k is 10% &nd
on +> is 15%. :!e st&nd&rd devi&tion o' t!eir &nnu&ied d&iy
returns &re 19.8% &nd 29.7%, respe)tivey. $ssume & )orre&tion
)oe''i)ient o' 1.0 &nd )&)u&te t!e port'oio v&ri&n)e.
%23.85.564Devi&tion#t&nd&rd
5.56419.829.72.40.60
@29.7A.40
@19.8A.60B&ri&n)eort'oio
22
22
==
=+
+
=
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Potfolio Ris#
+amle
#uppose you invest 60% o' your port'oio in
?on oi &nd 40% in Co)& Co&. :!eepe)ted do&r return on your ?on oi sto)k
is 10% &nd on Co)& Co& is 15%. :!e epe)ted
return on your port'oio is*
%1215403.10603.Return?pe)ted =+=
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Potfolio Ris#
+amle#uppose you invest 60% o' your port'oio in ?on oi &nd 40% in
Co)& Co&. :!e epe)ted do&r return on your ?on oi sto)k is
10% &nd on Co)& Co& is 15%. &e stan%ar% %e#(at(on of te(r
ann*al(/e% %a(l ret*rns are 18-2: an% 27-3:, resect(#el-
ss*me a correlat(on coeff(c(ent of 1-0 an% calc*late te ortfol(o#ar(ance-
222
2
2
2
211221
211221222
1
2
1
3.2740.;3.272.181
60.40.;;
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Potfolio Ris#
+amle#uppose you invest 60% o' your port'oio in ?on oi &nd 40% in
Co)& Co&. :!e epe)ted do&r return on your ?on oi sto)k is
10% &nd on Co)& Co& is 15%. :!e st&nd&rd devi&tion o' t!eir
&nnu&ied d&iy returns &re 18.2% &nd 27.3%, respe)tivey. $ssume &
)orre&tion )oe''i)ient o' 1.0 &nd )&)u&te t!e port'oio v&ri&n)e.
%21.80.477Devi&tion#t&nd&rd
0.47718.227.32.40.60
@27.3A.40
@18.2A.60B&ri&n)eort'oio
22
22
==
=+
+
=
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Potfolio Ris#
rrReturnort'oio?pe)ted 2211 +=
;;
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Potfolio Ris#
:ample Coelation Coefficient /7&toc#s 9 of Potfolio 'vg Retun
'BC Cop 26 09 159
Big Cop 72 709 219
Retun E ,159.,/0. ,219.,/7. 18/79
&tandad Deviation Potfolio 26/1
Real &tandad DeviationE
,262.,/2. ,722.,/72. 2,/7.,/.,26.,72.,/7.
26/1 C!RR:CT
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Potfolio Ris#
:ample Coelation Coefficient /7&toc#s 9 of Potfolio 'vg Retun
'BC Cop 26 09 159
Big Cop 72 709 219
&tandad Deviation $eighted avg 44/
&tandad Deviation Potfolio 26/1
Retun $eighted avg Potfolio 18/79
Gets 'dd stoc# e$ Cop to the potfolio
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Potfolio Ris#
:ample Coelation Coefficient /4&toc#s 9 of Potfolio 'vg Retun
Potfolio 26/1 509 18/79
e$ Cop 40 509 1+9
:I &tandad Deviation $eighted avg 41/60
:I &tandad Deviation Potfolio 24/74:I Retun $eighted avg Potfolio 16/209
!T:E Highe etun ( Go$e is#
Ho$ did $e do that D%):R&%F%C'T%!
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Potfolio Ris#
&e sa%e% ;oes conta(n #ar(ance terms< te rema(n%erconta(n co#ar(ance terms-
1
2
3
4
5
6
1 2 3 4 5 6
S$%&'
S&=C
&o calc*late
ortfol(o
#ar(ance a%%
* te ;oes
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Beta and Jni;ue Ris#
;eta
+ecte%
ret*rn
+ecte%
maretret*rn
10:10:' >
- 10:>10:
stoc
&op(ri)*t 1++, #( $*e c-ra./ill &o"panies Inc
'10:
1- &otal r(s ?
%(#ers(f(a;le r(s >
maret r(s
2- @aret r(s (s
meas*re% ; ;eta,
te sens(t(#(t tomaret canges
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Beta and Jni;ue Ris#
&rket ort'oio ( ort'oio o' & &ssets in t!e
e)onomy. +n pr&)ti)e & ro&d sto)k m&rket
inde, su)! &s t!e # Composite, is used
to represent t!e m&rket.
>et& ( #ensitivity o' & sto)ks return to t!e
return on t!e m&rket port'oio.
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Beta and Jni;ue Ris#
2
m
imiB
=
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Beta and Jni;ue Ris#
Cov&ri&n)e it! t!e
m&rket
B&ri&n)e o' t!e m&rket
2
m
im
iB
=
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Beta ,o K.
,1. ,2. ,4. ,7. ,5. ,. ,8.
Poduct of
Deviation &;uaed deviations
Deviation fom aveage deviation fom aveage
"a#et 'nchovy L fom aveage 'nchovy L fom aveage etuns"onth etun etun ma#et etun etun ma#et etun ,cols 7 5.
1 69 119 109 149 100 140
2 7 6 2 7 12
4 12 1+ 10 18 100 180
7 14 6 15 7 120
5 2 4 0 1 0 0
6 7 4 27
'veage 2 2 Total 407 75
)aiance =m2 407M 50/8
Covaiance = im 75M 8
Beta ,K. = imM=m2 8M50/8 1/5
&alculatin) t*e variance of t*e "arket returns and t*e covariance
#et.een t*e returns on t*e "arket and t*ose of Anc*ov( 2ueen3 Beta is t*e ratio of
t*e variance to t*e covariance 4i3e31 5 6 7i"87"29
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:strata on Bloo"#er)
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cDonalds on Bloo"#er)
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48
Topics Coveed
!ve a Centuy of Capital "a#et Histoy
"easuing Potfolio Ris#
Calculating Potfolio Ris#
Ho$ %ndividual &ecuities 'ffect Potfolio Ris#
Divesification ( )alue 'dditives
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&ee you net $ee#