7- Diversification Index Models

8/19/2019 7- Diversification Index Models

1/26

Comm 324 --- W. SuoSlide 1Slide 1

Indices,Diversification

&Index Models


2/26


Objective

Indices

Construction

Contribution to a portfolio’s risk

How to simplify the portfolio inputs

Inde models

!ecomposition of risk

Systematic and unsystematic

!iversification Other multifactors

"ama#"rench $ factor model% etc


3/26

Comm 324 --- W. SuoSlide $Slide $

Stock Indices

&ses 'rack avera(e returns Comparin( performance of mana(ers )ase of derivatives

"actors in constructin( or usin( an Inde

*epresentative+ )road or narrow+ How is it constructed+


4/26

Slide 3 W. Suo

,amples of ,-uity Indices Canadiano S./0'S $ Composite Indeo 'S $3 4also known as 'oronto $3 or '$35o 'S 1o S./0'S 6

&So !ow 7ones Industrial 8vera(e 4$ Stocks5o Standard . /oor’s 3 Compositeo 98S!8: Compositeo 9;S, Compositeo


5/26


)ond Indices

Scotia Capital 4Canada5

=ehman )rothers

?errill =ynch

Salomon )rothers


6/26


Construction of Indices

How are stocks wei(hted+ ?arket#value wei(hted 4S./3% 98S!8:% S./0'S

Composite5 /rice wei(hted 4!7I85 ,-ually wei(hted 4@alue =ine Inde5


7/26Slide 6 W. Suo

Contrastin( 'wo nown

Stock ?arket Indicators

!ow#7ones Industrial 8vera(e 4!7I85o )e(un in 1AAB with 11 stockso 8vera(e has contained $ stocks since 12A

o Only lar(e% successful firms are in the avera(e ?isleadin( name

o Only lar(e firms are in the avera(eo 9ew firms are not includedo Some firms may be more utility than industrial firms

!7I8 !ivisor o In 12A the prices of the $ stocks were summed and divided by $o However% stock splits and stocks dividends impact the divisor


8/26Slide 7 W. Suo

Stock Splits and !7I8 !ivisor 8s an eample% consider the hypothetical stocks

Stock /rice

D3

; D1

'otal D6

8vera(e 602 E $

Stock /rice

D23

; D1

'otal D$3

8vera(e $302 E 1FG3

• If Stock • under(oes a• 2 for 1 stock

split

• 'he stock split chan(ed the price per share% butthe stockholder’s wealth has remained the same each stockholder in has twice as many

shares as beforeG

• If the divisor remains at 2% the avera(ewill drop% even thou(h the a((re(atemarket value of remains the sameG'he divisor value must drop to reflectthe stock splitG


9/26Slide 8 W. Suo

!ow#7ones Industrial 8vera(e

/ointso !7I8 is price#wei(hted

?ore wei(ht is (iven to hi(her priced stockso ,ach point represents a few pennies of stock price


10/26Slide 9 W. Suo

S./ 3 Stocks Composite Inde

"irst developed in 12$ Contained 2$$ stocks

Has been at the 3 stock level since 13F &ses a market wei(htin( scheme

,ach security’s wei(ht is based on the total market value of thefirm

Corresponds to the investment opportunities that eist in &GSG How is it calculated+


11/26Comm 324 --- W. SuoSlide 11Slide 11

S./ 3 Stocks Composite

Inde ,-uation used to calculate S./3

♦ 8utomatically adjusts for stock splits% etcG♦ )ase period with a base inde value of 1♦ Inde components chan(e sli(htly each year ♦ 3 stocks in inde are about 1F of the stocks listed on 9;S,

− )ut a((re(ate market value is J 3 of a((re(ate market value ofall stocks listed on 9;S, . 8?,



!iversification

"amous -uotes KI prefer to keep all my e((s in one basket and watch that basket

closelyGL

K!iversification is a protection a(ainst i(noranceG It makes very littlesense for those who know what they’re doin(GL

KIf you are a know#somethin( investor% able to understand business

economics and to find five to ten sensibly priced companies that

possess important lon(#term competitive advanta(es% conventional

portfolio diversification 4broadly based active portfolios5 makes nosense for youGL


13/26Comm 324 --- W. SuoSlide 1$Slide 1$

Contribution to a portfolio’s

risk "or a lar(e and diversified portfolio% it is the

covariance of the stock that contributes to the

overall risk of the portfolio+


14/26Comm 324 --- W. SuoSlide 1BSlide 1B

!iversification

*andom selection



!iversification

'he effect of random diversification



?arkowitM diversification

Can we do better than the

random selection+

?arkowitM diversification How to simplify the

approach+


17/26Comm 324 --- W. SuoSlide 1FSlide 1F

Sin(le Inde ?odel

E stock’s epected return if market’s ecess return is Mero

E the component of return due to market movements

E the component of return due to unepected firm#specificevents

and are assumed to be uncorrelated

i f M ii f i er r r r +−+=− 5454 β α


18/26Comm 324 --- W. SuoSlide 1ASlide 1A

=etN *isk premium

format

*isk /remium "ormat



= total variance

= systematic variance= unsystematic variance

?easurin( Components of *isk



?arket or systematic risk risk related to the macro economic factor or market

inde

&nsystematic or firm specific riskN risk not related to the macro factor or market inde

'otal risk E Systematic &nsystematic Risk is represented by variance (not standarddeviation)

Components of *isk



'otal *isk E Systematic &nsystematic

,aminin( /ercenta(e of

@ariance

2

22

σ

σ β M i

squared R =−



Security Characteristic =ine

Excess Returns (i)SCL

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Excess returnson market index


23/26

Comm 324 --- W. SuoSlide 2$Slide 2$

Inde ?odel and !iversification


24/26

Comm 324 --- W. SuoSlide 2BSlide 2B

Risk Reduction with

Diversification

Number ofSecurities

St. Deviation

arket Risk

!ni"ue Risk

σ#(e$)=σ#(e) % n

β$#σ#


25/26


Industry /rediction of )eta

)?O Capital ?arkets and ?errill =ynch eamples )?O 9) uses returns not risk premiums

a has a different interpretationN Q r f 41#R5

?erill =ynch’s adjusted R’N 4sample beta5

"orecastin( beta as a function of past beta

"orecastin( beta as a function of firm siMe% (rowth% levera(eetcG

Tebr ar

M

++=


26/26

?ultifactor ?odels

&se factors in addition to market return ,amples include industrial production% epected inflation etcG ,stimate a beta for each factor usin( multiple re(ression

"ama and "rench *eturns a function of siMe and book#to#market value as well as market

returns

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7- Diversification Index Models