Hedge Funds: Quantitative Insights

357 Pages·2004·1.98 MB·English

by  François-Serge Lhabitant

Hedge Funds
Quantitative Insights
Franc¸ois-Serge Lhabitant

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Hedge Funds
Quantitative Insights
Franc¸ois-Serge Lhabitant
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Lhabitant,Franc¸ois-Serge.
Hedgefunds:quantitativeinsights/byFranc¸ois-SergeLhabitant.
p. cm.
Includesbibliographicalreferencesandindex.
ISBN0-470-85667-X(alk.paper)
1.Hedgefunds. I.Title.
HG4530.L472 2004
332.64(cid:2)5–dc22 2004002909
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ISBN0-470-85667-X
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Contents
ForewordbyMarkAnson xi
Introduction xiii
Acknowledgments xvii
PARTI MEASURINGRETURNANDRISK 1
1 CharacteristicsofHedgeFunds 3
1.1 Whatarehedgefunds? 4
1.2 Investmentstyles 5
1.2.1 Thetacticaltradinginvestmentstyle 6
1.2.2 Theequitylong/shortstyle 6
1.2.3 Theevent-drivenstyle 7
1.2.4 Therelativevaluearbitragestyle 8
1.2.5 Fundsoffundsandmulti-strategyfunds 9
1.3 Thecurrentstateofthehedgefundindustry 10
2 MeasuringReturn 15
2.1 Thedifficultiesofobtaininginformation 16
2.2 Equalization,crystallizationandmultipleshareclasses 18
2.2.1 Theinequitableallocationofincentivefees 18
2.2.2 Thefreeridesyndrome 19
2.2.3 Onshoreversusoffshorefunds 20
2.2.4 Themultipleshareapproach 21
2.2.5 Theequalizationfactor/depreciationdepositapproach 22
2.2.6 Simpleequalization 26
2.2.7 Consequencesforperformancecalculation 27
2.3 Measuringreturns 27
2.3.1 Theholdingperiodreturn 27
2.3.2 Annualizing 29
2.3.3 Multiplehedgefundaggregation 30
2.3.4 Continuouscompounding 32
vi Contents
3 ReturnandRiskStatistics 35
3.1 Calculatingreturnstatistics 35
3.1.1 Centraltendencystatistics 37
3.1.2 Gainsversuslosses 39
3.2 Measuringrisk 39
3.2.1 Whatisrisk? 40
3.2.2 Range,quartilesandpercentiles 41
3.2.3 Varianceandvolatility(standarddeviation) 42
3.2.4 Sometechnicalremarksonmeasuringhistoricalvolatility/variance 43
3.2.5 Backtohistograms,returndistributionsandz-scores 45
3.3 Downsideriskmeasures 49
3.3.1 Fromvolatilitytodownsiderisk 49
3.3.2 Semi-varianceandsemi-deviation 51
3.3.3 Theshortfallriskmeasures 53
3.3.4 Valueatrisk 53
3.3.5 Drawdownstatistics 55
3.4 Benchmark-relatedstatistics 57
3.4.1 Intuitivebenchmark-relatedstatistics 57
3.4.2 Betaandmarketrisk 58
3.4.3 Trackingerror 59
4 Risk-AdjustedPerformanceMeasures 61
4.1 TheSharperatio 65
4.1.1 Definitionandinterpretation 65
4.1.2 TheSharperatioasalong/shortposition 66
4.1.3 ThestatisticsofSharperatios 67
4.2 TheTreynorratioandJensenalpha 70
4.2.1 TheCAPM 70
4.2.2 Themarketmodel 72
4.2.3 TheJensenalpha 73
4.2.4 TheTreynorratio 75
4.2.5 Statisticalsignificance 75
4.2.6 ComparingSharpe,TreynorandJensen 76
4.2.7 GeneralizingtheJensenalphaandtheTreynorratio 77
4.3 M2, M3 andGraham–Harvey 78
4.3.1 The M2 performancemeasure 78
4.3.2 GH1andGH2 80
4.4 Performancemeasuresbasedondownsiderisk 82
4.4.1 TheSortinoratio 82
4.4.2 Theupsidepotentialratio 83
4.4.3 TheSterlingandBurkeratios 84
4.4.4 ReturnonVaR(RoVaR) 84
4.5 Conclusions 85
5 Databases,IndicesandBenchmarks 87
5.1 Hedgefunddatabases 87
5.2 Thevariousbiasesinhedgefunddatabases 87
Contents vii
5.2.1 Self-selectionbias 88
5.2.2 Database/sampleselectionbias 90
5.2.3 Survivorshipbias 90
5.2.4 Backfillorinstanthistorybias 92
5.2.5 Infrequentpricingandilliquiditybias 93
5.3 Fromdatabasestoindices 95
5.3.1 Indexconstruction 95
5.3.2 Thevariousindicesavailableandtheirdifferences 98
5.3.3 Differentindices–differentreturns 110
5.3.4 Towardspurehedgefundindices 113
5.4 Fromindicestobenchmarks 116
5.4.1 Absolutebenchmarksandpeergroups 117
5.4.2 Theneedfortruebenchmarks 118
PARTII UNDERSTANDING THE NATURE OF HEDGE FUND RETURNS
ANDRISKS 121
6 CovarianceandCorrelation 123
6.1 Scatterplots 123
6.2 Covarianceandcorrelation 126
6.2.1 Definitions 126
6.2.2 Anotherinterpretationofcorrelation 131
6.2.3 TheSpearmanrankcorrelation 132
6.3 Thegeometryofcorrelationanddiversification 133
6.4 Whycorrelationmayleadtowrongconclusions 135
6.4.1 Correlationdoesnotmeancausation 135
6.4.2 Correlationonlymeasureslinearrelationships 136
6.4.3 Correlationsmaybespurious 137
6.4.4 Correlationisnotresistanttooutliers 138
6.4.5 Correlationislimitedtotwovariables 139
6.5 Thequestionofstatisticalsignificance 141
6.5.1 Sampleversuspopulation 141
6.5.2 Buildingtheconfidenceintervalforacorrelation 142
6.5.3 Correlationdifferences 144
6.5.4 Correlationwhenheteroscedasticityispresent 146
7 RegressionAnalysis 147
7.1 Simplelinearregression 148
7.1.1 Realityversusestimation 148
7.1.2 Theregressionlineinaperfectworld 150
7.1.3 Estimatingtheregressionline 151
7.1.4 Illustrationofregressionanalysis:AndorTechnology 154
7.1.5 Measuringthequalityofaregression:multiple R, R2,ANOVA
and p-values 154
7.1.6 Testingtheregressioncoefficients 158
7.1.7 ReconsideringAndorTechnology 159
7.1.8 Simplelinearregressionasapredictivemodel 161