FNCE30001 Lecture 4: Simple Index Model
27 Jun 2018
School
Department
Course
Professor
Single Index Models
mmmm
DrawbacksoftheMarkowityModdix
Numberofexpectedreturns n
Numberofestimatesrequired ntntnln.it2
if n25 weneed 350 estimates
The
sheernumber
ofestimates is a
problem and they're alljustestimates
hwiglemdescModelsiTheonge
statisticalrepresentations noteqmmodels
hafnenes the return on asecurity as the rum ofits expecteddunexpected
parts
ri Elri tu
ifwe include amacroeconomicmaprinvariable mwe can decomposeuncertainty
ui intouncertaintyabouttheeconomy as awhole cm auncertainty about this
particularfurin
ri ELri tfimtbi
di is calledfurini's sensitivitycoefficient
security
prices are affectedby il macroeconomic
factorsacidfirmspecific
factors
maffects all securities adis not correlated wfinfrecific
mile
Thefollowing are relevantformulae
Varlril off
Varlm Varle of LtoCed
Corrri rdidVarlm did
join
If nis amarket index Mthen our modelbecomes
Ritt aotfiknlt lilt
di is thesecurity'ssensitivitytotheindex
li is thefirm
specificremitual
El Ri xitfiElRm
Fundmanagers will want tofind nonzeroalphas dbuyhell therewltve fve x
sina.tn
qttttd
mdexmodelis true weform
portfoliopurlequally
weighted nrecurities
Rp xp tof
pRmttp
gap fpOni toLep
Define
averageidiosyncraticrink
ofthecomponentsofPtobe
top Eoiled
Whentheportfolioerrorterm is nimpytheweighted nunofindividualrecurityerror
terms
ep tEELei
Var ep Is EE
VarLei
02
Llp IE
As ni of remainsconstant but Io
As nTOLep o
of a
µDiversifiablerisk oilepttop
of
poor
systematic
Hof assets
Document Summary
Numberofestimatesrequired ntntnln. it 2 if n 25 weneed 350 estimates. If n is a market index m then our modelbecomes a o t fi knlt. Fundmanagers will want tofind nonzeroalphas d buyhell therewl tvef ve x sina. tnqttttdmdexmodelis true weformportfoliopurlequallyweighted n recurities. Rp xp tofp rm t tp gap fp oni t o lep. As ni of remainsconstant but i is thefirmspecificremitual x i t f i elrm. Aninvestor buysbells underloverpricedsecurities sothattheyarerewardeduponmktcorrection securityanalysisisinconsistent w1 mht efficiency. Activela securityanalysis overweight to a underweight a securities. Theinformationratio thenotrareturn wecanqtfromrecurityanalysiscomparedtothe firmspecificrink wevoluntarilyincur when we under or over weightsecuritiesrelative to thefamine mht index. Blacke n estimatesofexpecteddis dis a oiled oneestimateof elrond oh. Total 3n t2 estimates step0 find x o usingthemodel a oiledor ifnotgiven httpi balculatethe initialpositionofeachsecurityin theactivecomponent steps breaktheintitialpositiontomakethoseweights mm to1bydividingbytheirmini http3 balculatethe x oftheactivecomponent httphibalontatethe residualvarianceoftheactivecomponent httpsbalculatetheinitialposition in theactivecomponent eg n 25 need77estimates muchbetterthan350formarkowitz. Eurm 1of http6 balculatethe betaoftheactive component http7 adjusttheinitialposition in theactivecomponent.
