Portfolio Management 03 Residual Risk and Return The Information Ratio

Test ID: 7442128

Residual Risk and Return: The Information Ratio

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Rajesh Murtaniis comparing threeactivemanagers, Roobini, Durseand Lurten. Hehas gatheredthefollowing datafromthe previous period:

Manager Residual Risk Aversion Information Ratio

Roobini 0.05 0.52

Durse 0.10 0.60

Lurten 0.15 0.78

Themanager withthehighestoptimallevelofresidualriskismostlikely:

Durse. Lurten. Roobini.

Explanation

Theoptimallevelofresidualriskis calculatedasIR/ (2 × riskaversion) Roobini 0.52/(2 × 0.05) = 5.2%

Durse 0.60/(2 × 0.10) = 3.0% Lurten 0.78/(2 × 0.15) = 2.6%

Younis Kabulisanalyzing the performanceoftwoactivemanagers. ManagerAhasanex-postalphaof1.2% withatstatistic 2.15 using 10 yearsofdata. ManagerBhasanex-postalphaof1.2% withatstatistic of2.15 basedon20 yearsofdata. Whichofthefollowing statementsaboutthemanagers' informationratiosismostaccurate?

Both managers will have the same information ratio. MangerA willhavethehigherinformationratio.

ManagerB willhavethehigherinformationratio.

Explanation

Theinformationratiois calculatedasthealpha'st-statistic divided bythesquarerootofthenumberofyears. Givenidenticalt-statistics, managerA willhavethehigherinformationratio.

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ᅞ A) ᅚ B) ᅞ C) Explanation

TheIRisequaltothealpha'st-statistic divided bythesquarerootofthenumberofyearsintheregression. IR = 2.21 / 15 = 0.57

Hal calculatestheex-postalphaofhis portfolioas 0.45% withat-statistic of2.26. Hal calculatesthatthis giveshiman informationratioof 0.32. Whichofthefollowing isclosesttothenumberofyearsofdata Halusedinhisanalysis?

7. 50. 20.

Explanation

Theinformationratiois calculatedasthealpha'st-statistic divided bythesquarerootofthenumberofyearsofdata. 0.32 = 2.26 / #years

#years = 2.26 / 0.32 = 7.06 #years = 7.06 = 49.8

Whichofthefollowing statementsregarding activemanagementisleastaccurate? Theobjectiveofactivemanagement:

is to minimize residual risk.

can beexpressedasafunctionofresidualreturn, residualriskandriskaversion.

istomaximizethe valueaddedfromresidualreturn.

Explanation

Theobjectiveistomaximize valueadded whichisafunctionofresidualrisk, residualreturn, andriskaversion.

Whichofthefollowing statementsregarding theinformationratioisleastaccurate? The information ratio can be negative.

Theinformationratioforthe benchmarkisequaltoone.

Theinformationratioisaratioofresidualreturntoresidualrisk.

Explanation

Informationratioistheratioofresidualreturntoresidualrisk. Theinformationratioforthe benchmarkisequalto zero. Ex-post

informationratio can benegative (iftheex-postalphaisnegative).

½

½

½

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Question #11 of 14

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Whichofthefollowing statementsregarding the choiceofa particularactivestrategyismostaccurate?

Investors who are more risk averse will choose managers who have historically displayed a low level of risk aversion.

Investors whoaremoreriskaverse willnot consideramanager'shistoric levelofrisk

aversion.

Investors whoaremoreriskaverse will choosemanagers whohavehistorically displayedahighlevelofriskaversion.

Explanation

Investorsseektomaximize valueadded, andthedecisionisindependentofthelevelofriskaversionthemanagerhas

displayed. Investors willsimply chooseamanager withthehighestinformationratio. Theriskaversionoftheinvestor will

simplydeterminehow aggressively (or conservatively)theinvestor willimplementthemanager'sstrategy.

Whichofthefollowing statementsismostaccurate?

A negative ex ante information ratio means that the portfolio manager underperformed the benchmark for the year

Theex anteinformationratioistheratioofrealizedresidualreturntorealizedresidual

riskfora period.

Theex postalphaistheaverageoftherealizedresidualreturns.

Explanation

Theex postalphameasuresrealizedresidualreturns. Theex anteinformationratiousesexpectedresidualreturnsandrisk.

Theex postinformationratiomeasuresrealizedresidualreturnsandrisk. Anegativeex-postinformationratiomeansthatthe portfoliomanagerunderperformedthe benchmarkfortheyear.

When choosing anactivemanager, aninvestor withahighlevelofriskaversion: will choose a manager with the lowest history of residual risk exposure.

will choosethemanager withthehighestinformationratio. will choosethemanager withthehighesthistoryofresidualreturn.

Explanation

Valueaddedisindependentofthelevelofriskaversion. Allinvestors will choosethemanager withthehighestinformation

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Question #14 of 14

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Whichofthefollowing statementsregarding valueaddedismostaccurate? Foractivemanagers withthesameresidualreturn

andresidualrisk:

the value added will be higher for the manager operating a portfolio for a client

with a higher risk aversion.

the valueadded will beequal.

the valueadded will behigherforthemanageroperating a portfoliofora client witha

lowerriskaversion.

Explanation

Valueaddedis calculatedasresidualreturnlessthe penaltyforresidualrisk. The penaltyforresidualriskis proportionaltothe riskaversion. Ifresidualreturnandriskareidenticalfortwomanagers, themanager withthelowerriskaversionhasthelower penaltyand consequently, ahigher valueadded.

Inresponsetoariskaversionlevelof 0.15 forhis client, anactivemanagersetshisoptimallevelofresidualriskexposureto

3.2%. Whichofthefollowing isclosesttotheinformationratiothatthemanagerhasassumed?

0.96.

0.05. 0.48.

Explanation

Theoptimallevelofriskaversionis calculatedastheinformationratiodivided by (2 × riskaversion). 3.2 = IR / (2 × 0.15)

IR = 3.2 × 0.3 = 0.96

Whichofthefollowing statementsismostlikely correct? Theex-postalpha:

is the average of a stock's realized returns.

istheaverageofastock'srealizedexcessreturnovertheriskfreerate.

istheaverageofastock'srealizedresidualreturns.

Explanation

Theex-postalphareflectstheaverageofrealizedresidualreturns. Realizedresidualreturnsona portfolioarereturnsin