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IAPMPGP17

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Day4

Problems Ch.7P6 P10,P17,P18,P19,ConceptChecks2and3Ch.7P6 P10,P17,P18,P19,ConceptChecks2and3 CompleteyourExcelsheet Whatistherelationbetweencorrelationmatrixandvariancecovariancematrix?(inmatrixnotation) So that given one, you can find the other when large number

of assets are involved.

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Summarizing GivenaforecastofratesofreturnandestimatesofriskGivenaforecastofratesofreturnandestimatesofriskonvarioussecurities, Draw the opportunity set (envelope portfolios) Calculate the optimal risky portfolio Allocate funds between risky portfolio and risk-free asset Calculate the break-up of the entire portfolio wrt every asset

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SupposethattwoportfoliomanagerswhoworkforSupposethattwoportfoliomanagerswhoworkforcompetinginvestmenthousescomeupwithtwodifferentEfficientFrontiers(EF)anditturnsoutthatAsoptimalportfolioliestothenorthwestofBs.Hencegivenachoice,investorswillprefertheoptimalportfolioofA Wh t h ld b d f thi t ? What should be made of this outcome? Should it be attributed to better security analysis by A?

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Systematicvs.Idiosyncratic Eachinvestmentcarriestwodistinctrisks:Eachinvestmentcarriestwodistinctrisks: Systematicriskismarketwideandpervasivelyinfluencesvirtuallyallsecurityprices. Examples are interest rates and the business cycle.

Idiosyncraticrisk(akafirmspecificrisk,diversifiablerisk)involvesunexpectedeventspeculiartoasinglesecurityoralimitednumberofsecurities. Examples are the loss of a key contract or a change in

government policy toward a specific industry.

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Diversificationreducesonlyfirmspecificrisk

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Why? Wealreadyhavethetoolstoanswerthis!Wealreadyhavethetoolstoanswerthis! Whenallriskisfirmspecific,powerofdiversificationisunlimited

Wheneconomywideriskfactorsinduceacorrln,thenwhathappens?

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RiskReductionofEquallyWeightedPortfolios CorrelationlimitsthepowerofdiversificationCorrelationlimitsthepowerofdiversification

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SupposethattheuniverseofavailableriskysecuritiesSupposethattheuniverseofavailableriskysecuritiesconsistsofalargenumberofstocks,identicallydistributedwithE(r)=15%,=60%andacommoncorrln =0.5A) What is the systematic risk in this security universe?B) Consider an equally weighted portfolio of 25 such stocks.

Will hi b ffi i ?Will this be efficient?C) In such a case, what will be the optimal efficient portfolio?

And what is the maximum attainable Sharpe ratio? (say rf=7%)D) Can we consider such a universe with ve corrlns?

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Howtomeasuresystematicrisk? EnterCAPM!EnterCAPM!

In market equilibrium, investors are only rewarded for bearing systematic risk the type of risk that cannot be diversified away.

They should not be rewarded for bearing idiosyncratic risk, since this uncertainty can be mitigated through appropriate diversificationdiversification.

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BillSharpe,oneoftheoriginatorsoftheCAPM,inanBillSharpe,oneoftheoriginatorsoftheCAPM,inaninterviewwiththeDowJonesAssetManager:Butthefundamentalidearemainsthattheresnoreasontoexpectrewardjustforbearingrisk.Otherwise,youdmakealotofmoneyinLasVegas.Iftheresrewardforrisk,itsgottobespecial.Theresgottobesomeeconomicsbehinditorelsetheworldisaverycrazyplace.Idontthinkdifferentlyelsetheworldisaverycrazyplace.Idon tthinkdifferentlyaboutthosebasicideasatall.Sharpe(1998)

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Objectivesofanyriskreturnmodel AbilitytocategorizeinvestmentsAbilitytocategorizeinvestments

Based on how their returns vary with different risk factors, after identifying these risk factors in the first place

Getonestepclosertothefairpriceofanasset Evaluateanactivemanagersperformance

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