8/12/2019 POF_Week_6_SB (2)

1/38

Principles of FinanceBS 2100

An Introduction to Risk

Pete HahnFaculty of Finance

Room 5012

Cass Building

8/12/2019 POF_Week_6_SB (2)

2/38

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

8/12/2019 POF_Week_6_SB (2)

3/38

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

8/12/2019 POF_Week_6_SB (2)

4/38

8/12/2019 POF_Week_6_SB (2)

5/38

'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

8/12/2019 POF_Week_6_SB (2)

6/38

&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

8/12/2019 POF_Week_6_SB (2)

7/38

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.

8/12/2019 POF_Week_6_SB (2)

8/38

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

8/12/2019 POF_Week_6_SB (2)

9/38

"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

8/12/2019 POF_Week_6_SB (2)

10/38

:;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

8/12/2019 POF_Week_6_SB (2)

11/38

Do$

8/12/2019 POF_Week_6_SB (2)

12/38

"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/

8/12/2019 POF_Week_6_SB (2)

13/38

"easuing Ris#

Coin Toss @amecalculating vaiance and standaddeviation

8/12/2019 POF_Week_6_SB (2)

14/38

"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#/

8/12/2019 POF_Week_6_SB (2)

15/38

"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

(( (())

))

8/12/2019 POF_Week_6_SB (2)

16/38

"easuing Ris#

0

5 10 15

!u"#er of Securities

Portfolios

tand

ardd

eviation

8/12/2019 POF_Week_6_SB (2)

17/38

"easuing Ris#

0

5 10 15

!u"#er of Securities

Portfolios

tand

ardd

eviation

arket risk

Unique

risk

8/12/2019 POF_Week_6_SB (2)

18/38

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

;;;

8/12/2019 POF_Week_6_SB (2)

19/38

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 =+=

8/12/2019 POF_Week_6_SB (2)

20/38

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(=&

=

=

=

=

8/12/2019 POF_Week_6_SB (2)

21/38

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

==

=+

+

=

8/12/2019 POF_Week_6_SB (2)

22/38

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 =+=

8/12/2019 POF_Week_6_SB (2)

23/38

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.;;

8/12/2019 POF_Week_6_SB (2)

24/38

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

==

=+

+

=

8/12/2019 POF_Week_6_SB (2)

25/38

Potfolio Ris#

rrReturnort'oio?pe)ted 2211 +=

;;

8/12/2019 POF_Week_6_SB (2)

26/38

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

8/12/2019 POF_Week_6_SB (2)

27/38

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

8/12/2019 POF_Week_6_SB (2)

28/38

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%!

8/12/2019 POF_Week_6_SB (2)

29/38

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

8/12/2019 POF_Week_6_SB (2)

30/38

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

8/12/2019 POF_Week_6_SB (2)

31/38

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.

8/12/2019 POF_Week_6_SB (2)

32/38

Beta and Jni;ue Ris#

2

m

imiB

=

8/12/2019 POF_Week_6_SB (2)

33/38

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

=

8/12/2019 POF_Week_6_SB (2)

34/38

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

8/12/2019 POF_Week_6_SB (2)

35/38

:strata on Bloo"#er)

8/12/2019 POF_Week_6_SB (2)

36/38

cDonalds on Bloo"#er)

8/12/2019 POF_Week_6_SB (2)

37/38

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

8/12/2019 POF_Week_6_SB (2)

38/38

&ee you net $ee#