Practical Risk-Adjusted Performance Measurement

237 Pages·2012·1.17 MB·English

by  Carl R. Bacon

Practical Risk-Adjusted
Performance Measurement
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Practical Risk-Adjusted
Performance Measurement
Carl R. Bacon
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LibraryofCongressCataloging-in-PublicationData
Bacon,CarlR.
Practicalrisk-adjustedperformancemeasurement/CarlR.Bacon.
p.cm.
Includesbibliographicalreferencesandindex.
ISBN978-1-118-36974-6(cloth)
1.Financialriskmanagement. 2.Performancestandards. 3.Riskmanagement. I.Title.
HD61.B332013
658.15(cid:3)5–dc23
2012023317
AcataloguerecordforthisbookisavailablefromtheBritishLibrary.
ISBN978-1-118-36974-6(hardback)ISBN978-1-118-39153-2(ebk)
ISBN978-1-118-39152-5(ebk) ISBN978-1-118-39137-2(ebk)
Setin11/13ptTimesbyAptaraInc.,NewDelhi,India
PrintedinGreatBritainbyTJInternationalLtd,Padstow,Cornwall,UK
Tomyparents

Contents
Preface xv
Acknowledgements xvii
1 Introduction 1
Definitionofrisk 1
Risktypes 1
Riskmanagementvriskcontrol 4
Riskaversion 4
Ex-postandex-ante 4
Dispersion 5
2 DescriptiveStatistics 7
Mean(orarithmeticmean) 7
Annualisedreturn 8
Continuouslycompoundedreturns(orlogreturns) 8
Winsorisedmean 9
Meanabsolutedeviation(ormeandeviation) 9
Variance 10
Meandifference(absolutemeandifferenceorGini
meandifference) 12
Relativemeandifference 14
Bessel’scorrection(populationorsample,norn−1) 14
Samplevariance 17
Standarddeviation(variabilityorvolatility) 17
Annualisedrisk(ortimeaggregation) 18
TheCentralLimitTheorem 19
viii Contents
Janssenannualisation 19
Frequencyandnumberofdatapoints 19
Normal(orGaussian)distribution 21
Histograms 22
Skewness(Fisher’sormomentskewness) 22
Sampleskewness 24
Kurtosis(Pearson’skurtosis) 24
Excesskurtosis(orFisher’skurtosis) 25
Samplekurtosis 25
Bera-Jarquestatistic(orJarque-Bera) 27
Covariance 28
Samplecovariance 30
Correlation(ρ) 30
Samplecorrelation 32
Upcaptureindicator 32
Downcaptureindicator 34
Upnumberratio 34
Downnumberratio 34
Uppercentageratio 35
Downpercentageratio 35
Percentagegainratio 35
Hurstindex(orHurstexponent) 35
Biasratio 37
3 SimpleRiskMeasures 43
Performanceappraisal 43
Sharperatio(rewardtovariability,Sharpeindex) 43
Royratio 46
Riskfreerate 46
AlternativeSharperatio 47
RevisedSharperatio 48
AdjustedSharperatio 48
Skewness-kurtosisratio 49
MADratio 49
Giniratio 52
Relativerisk 53
Trackingerror(ortrackingrisk,
relativerisk,activerisk) 53
Relativeskewness 54
Relativekurtosis 55