A Screen for Fraudulent Return Smoothing in the Hedge Fund Industry

Transcription

1 A Screen for Fraudulen Reurn Smoohing in he Hedge Fund Indusry Nicolas P.B. Bollen Vanderbil Universiy Veronika Krepely Universiy of Indiana May 16 h, 2006

2 Hisorical performance Cum. Mean Sd Dev CSFB Tremon HF Index 194.8% 10.7% 8.3% S&P % 10.4% 15.4% MSCI World Index 109.6% 9.2% Source: Sandard & Poor s 14.4%

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4 Regisraion wih SEC under Invesmen Advisers Ac Effecive 2/1/06 In he las five years, he Commission has brough 51 cases in which hedge fund advisers have defrauded hedge fund invesors (2005 Final Rule) Damages of a leas $1.1 billion Regisraion requiremen includes safeguards agains fraud: Deailed se of inernal conrols Compliance officer Requiring regisraion may also deer fraud by faciliaing inspecions

5 Argumens agains SEC rule May chill hedge fund indusry and reduce liquidiy provided o financial markes (Alan Greenspan) Sophisicaed invesors able o perform due diligence and make informed decision already SEC sill won be able o preven fraud (Cynhia Glassman and Paul Akins) Limied resources Risk-based screen o arge funds for examinaion no ye developed

6 This paper SEC regisraion requiremen may indicae a desire for a more acivis role This raises several imporan and relaed quesions 1. Can he SEC screen hedge funds for suspicious aciviy? 2. Does fraud leave a deecable fooprin? 3. Do exising daa provide enough saisical power o accuraely ideniy he fooprin?

7 Ouline 1. Review exising research and explain our conribuion 2. Design a specific filer for suspicious reurns 3. Documen he saisical properies of he filer 4. Apply he filer o a se of acual hedge funds

8 Exising academic evidence Gemansky, Lo, and Makarov (JFE 2004) Asse Reurns: Var R [ R] Observed Reurns: [ ] [ ] [ ] = μ+ βλ + ε, E Λ = E ε = 0 R = θ R + θ R θ R where O k k θ 0,1 for j = 0,..., k j 2 = σ 1 = θ + θ θ 0 1 k

9 Exising academic evidence Gemansky, Lo, and Makarov (JFE 2004) Cov R, R = θ R + θ R θ R where O k k [ ] θ 0,1 for j = 0,..., k O E R = μ O Var R = σ j 1 = θ + θ θ k 2 θ j= 0 j 2 k m O O σ j= 0 R m = 0 if j k θ θ if 0 m k j+ m m> k

10 Exising academic evidence Gemansky, Lo, and Makarov (JFE 2004) O = + k j = 0 j j R μ θη Documen significan θ 1 and θ 2 using MLE No way o disinguish among alernaive explanaions of serial correlaion Illiquid asses and sale prices Marking asses o model conservaively Managerial smoohing

11 Our conribuion (1) We expec a condiional smoohing algorihm Manager has more of an incenive o smooh losses han gains Gains fully repored o maximize curren managemen fee Gains fully repored o keep up wih compeiion Fraud cases ofen involve overvaluaion of asses (underreporing losses) no undervaluaion of asses (underreporing gains) Similar o accouning lieraure on managed earnings, e.g. Chandar and Bricker (JAR 2002) Resuls in a number of asymmeries in saisical fooprin ha disinguishes fraud from oher causes of serial correlaion

12 Table 1. Acual vs. repored profis from currency opions rading a NAB Monhly acual Monhly repored (Under)/Oversaemen of Cumulaive oversaemen profi/(loss) profis repored profis of porfolio value 2002 Ocober 8, (7,972) 0 November 3,365 3, December 2,837 2, January 2,792 3, February 2,559 2, March 2,774 1,797 (977) 0 April (10) 2,567 2,577 2,577 May (1,292) 4,372 5,664 8,241 June 3,390 4,558 1,168 9,409 July 12,556 7,165 (5,391) 4,018 Augus (169) 1,323 1,492 5,510 Sepember (34,780) 1,761 36,541 42,051 Ocober 13,871 5,774 (8,097) 33,954 November 3,993 7,421 3,428 37,382 December (49,106) 5,272 54,378 91,760

13 Our conribuion (2) We carefully documen he small sample properies of he saisical screen Type I error means falsely rejecing he null hypohesis examining a fund ha does no feaure condiional serial correlaion Type II error means failing o rejec he null hypohesis failing o examine a fund ha does feaure condiional serial correlaion If he screen has low power, hen he SEC will no be able o accuraely screen funds for examinaion

14 The model R O ( ( ) ) ( ( ) ) = θ0 1 + ψ0 + θ ψ1 1 1 R I I R I I R I = 1 if R c I = 0 if R < c = μ + βλ + ε Manager repors a fracion ψ 0 of asse reurns in curren monh if hey are high, else he repors θ 0 Condiional smoohing generaes condiional serial correlaion Predicion no found in oher explanaions of smoohed reurns

15 Esimaion ( 1 ) ( + ) R = a+ b I + b I R + η O O I = 1 if R c I = 0 if R < c We derive analyic expressions for b and b Model predics b > b + 1 1

16 Figure 1. Analyic difference beween condiional beas b b θ ψ 0

17 Figure 2. Analyic residual serial correlaion θ ψ 0

18 Implemenaion ( 1 ) ( + ) R = a+ b I + b I R + η I I O O = 1 if μ+ βλ c 1 1 = 0 if μ+ βλ < c 1 1 Redefine indicaor variable Fied value of facor model can be inerpreed as unbiased esimae of asse reurn or as he reurn of non-discreionary asses

19 Table 4. Hisory lenghs of CISDM funds Live Funds Dead Funds # 25 h 50 h 75 h # 25 h 50 h 75 h Hedge Funds E-D G Emerging G Esablished G Inernaional G Macro Long Only M-N Secor Shor-Sellers Fund of Funds

20 Size analysis of condiional serial correlaion For each fund, find bes single-facor model: O O R = μ + β Λ + ε Simulae 20 asse reurn hisories for each fund: R = μ + β Λ + ξ A O E Consruc uncondiionally smoohed reurns: R = 0.5R + 0.5R S A A 1 Ask economerician o esimae condiional serial correlaion: ( 1 ) R = a+ b R + b I R + η S + S S

21 Table 7. Size analysis of condiional serial correlaion Known Facor Unobservable Facor Monhs Monhs # Hedge Funds E-D G Emerging G Esablished G Inernaional G Macro Long Only M-N Secor Shor-Sellers Fund of Funds

22 Power analysis under conrolled condiions As before, find bes single-facor model: O O R = μ + β Λ + ε And simulae 20 asse reurn hisories for each fund: R = μ + β Λ + ξ A O E Consruc condiionally smoohed reurns: ( 0.5( 1 ) ) 0.5( 1 ) R = I + I R + I R S A A 1 1 Ask economerician o esimae condiional serial correlaion ( 1 ) R = a+ b R + b I R + η S + S S

23 Table 8. Power analysis under conrolled condiions Known Facor Unobservable Facor Monhs Monhs # Hedge Funds E-D G Emerging G Esablished G Inernaional G Macro Long Only M-N Secor Shor-Sellers Fund of Funds

24 Power analysis under acual condiions For each fund, use opimal muli-facor model Simulae 20 asse reurn hisories by reordering residuals bu leaving facor observaions unchanged Consruc condiionally smoohed reurns: ( 0.5( 1 ) ) 0.5( 1 ) R = I + I R + I R S A A 1 1 Ask economerician o esimae condiional serial correlaion: ( 1 ) R = a+ b R + b I R + η S + S S

25 Table 10. Power analysis under acual condiions # 5% 10% 20% Hedge Funds E-D G Emerging G Esablished G Inernaional G Macro Long Only M-N Secor Shor-Sellers Fund of Funds

26 How many funds feaure condiional serial correlaion? Abou 4.4% of he sample a a 5% wo-sided significance level More han he 2.5% expeced under he null hypohesis Of 53 SEC fraud cases, we could obain reurns for 18 of hem 5/18 or 28% feaure significan condiional serial correlaion Wha are he properies of he flagged funds?

27 Table 13. Cross-secional analysis of red-flagged hedge funds Coefficien p-value Coefficien p-value Consan ln(cfvol) Cfmu E[r] Fee Incen Live ln(size) Audi Age ln(wai) LR saisic Probabiliy(LR sa) McFadden R-squared # obs 3,649 2,058 # obs red-flagged Frequency

28 Conclusions Saisical procedures may be available o deec fraud Power is an issue approximaely 33% under average condiions Can be viewed as a relaively low-cos bu low-power screen Analogous o IRS screens for fraud Power may be increased by running a baery of ess using alernaive managerial algorihms

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