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
Hisorical performance Cum. Mean Sd Dev CSFB Tremon HF Index 194.8% 10.7% 8.3% S&P 500 186.8% 10.4% 15.4% MSCI World Index 109.6% 9.2% Source: Sandard & Poor s 14.4%
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
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
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?
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
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 0 1 1 k k θ 0,1 for j = 0,..., k j 2 = σ 1 = θ + θ +... + θ 0 1 k
Exising academic evidence Gemansky, Lo, and Makarov (JFE 2004) Cov R, R = θ R + θ R +... + θ R where O 0 1 1 k k [ ] θ 0,1 for j = 0,..., k O E R = μ O Var R = σ j 1 = θ + θ +... + θ 0 1 2 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
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
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
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 8,946 974 (7,972) 0 November 3,365 3,365 0 0 December 2,837 2,837 0 0 2003 January 2,792 3,678 886 886 February 2,559 2,650 91 977 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
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
The model R O ( ( ) ) ( ( ) ) = θ0 1 + ψ0 + θ1 1 1 + 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
Esimaion ( 1 ) ( + ) R = a+ b I + b I R + η O O 1 1 1 1 1 I = 1 if R c I = 0 if R < c We derive analyic expressions for b and b + 1 1 Model predics b > b + 1 1
Figure 1. Analyic difference beween condiional beas 1.5 1.0 0.5 b b + 1 1 0.0-0.5-1.0 0.0 0.2 0.4 1.0 θ 0 0.6 0.8 0.8 0.7 1.0 ψ 0
Figure 2. Analyic residual serial correlaion 1.0 0.8 0.6 0.4 0.2 0.0 0.0 0.2 0.4 1.0 θ 0 0.6 0.8 0.8 0.7 1.0 ψ 0
Implemenaion ( 1 ) ( + ) R = a+ b I + b I R + η I I O O 1 1 1 1 1 = 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
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 139 48 78 108 85 36 53 86 G Emerging 96 50 73 94 41 30 42 69 G Esablished 288 40 67 96 258 38 53 92 G Inernaional 37 62 88 120 21 47 59 73 G Macro 46 43 79 104 53 36 48 73 Long Only 12 63 80 92 12 32 48 78 M-N 344 36 63 89 175 36 55 72 Secor 108 42 54 88 52 32 47 64 Shor-Sellers 20 51 79 86 8 34 61 66 Fund of Funds 425 43 71 108 151 35 55 74
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 1 1 1 1 1
Table 7. Size analysis of condiional serial correlaion Known Facor Unobservable Facor Monhs Monhs # 120 60 36 120 60 36 Hedge Funds E-D 210 0.02 0.02 0.02 0.02 0.02 0.02 G Emerging 137 0.04 0.04 0.03 0.04 0.04 0.03 G Esablished 534 0.02 0.02 0.02 0.02 0.02 0.02 G Inernaional 58 0.02 0.02 0.03 0.02 0.02 0.02 G Macro 92 0.02 0.02 0.02 0.03 0.02 0.02 Long Only 24 0.04 0.01 0.01 0.04 0.02 0.02 M-N 511 0.01 0.02 0.01 0.02 0.02 0.01 Secor 160 0.01 0.01 0.01 0.01 0.02 0.02 Shor-Sellers 25 0.01 0.02 0.01 0.01 0.02 0.01 Fund of Funds 567 0.02 0.01 0.01 0.02 0.01 0.01
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 1 1 1 1 1
Table 8. Power analysis under conrolled condiions Known Facor Unobservable Facor Monhs Monhs # 120 60 36 120 60 36 Hedge Funds E-D 210 0.81 0.53 0.33 0.77 0.44 0.25 G Emerging 137 0.84 0.56 0.32 0.78 0.46 0.24 G Esablished 534 0.79 0.50 0.31 0.74 0.43 0.23 G Inernaional 58 0.84 0.55 0.34 0.76 0.44 0.23 G Macro 92 0.84 0.54 0.34 0.75 0.41 0.23 Long Only 24 0.77 0.46 0.29 0.76 0.41 0.24 M-N 511 0.86 0.59 0.38 0.77 0.45 0.25 Secor 160 0.80 0.49 0.32 0.76 0.43 0.25 Shor-Sellers 25 0.79 0.48 0.28 0.76 0.44 0.23 Fund of Funds 567 0.77 0.48 0.30 0.74 0.43 0.25
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 1 1 1 1 1
Table 10. Power analysis under acual condiions # 5% 10% 20% Hedge Funds E-D 210 0.36 0.45 0.56 G Emerging 137 0.37 0.47 0.59 G Esablished 534 0.28 0.38 0.51 G Inernaional 58 0.35 0.45 0.57 G Macro 92 0.27 0.36 0.47 Long Only 24 0.39 0.48 0.61 M-N 511 0.28 0.37 0.49 Secor 160 0.26 0.36 0.49 Shor-Sellers 25 0.36 0.48 0.60 Fund of Funds 567 0.35 0.45 0.58
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?
Table 13. Cross-secional analysis of red-flagged hedge funds Coefficien p-value Coefficien p-value Consan -2.4207 0.0000-2.5149 0.0000 ln(cfvol) 0.2203 0.0287 0.3326 0.0201 Cfmu -4.9885 0.0021-5.7388 0.0316 E[r] 12.0490 0.2597 Fee -0.1135 0.4847 Incen 0.0127 0.3005 Live -0.2937 0.1656 ln(size) 0.0025 0.9082 Audi -0.1846 0.5595 Age 0.0035 0.1552 ln(wai) 0.1077 0.0672 LR saisic 8.9597 15.2337 Probabiliy(LR sa) 0.0113 0.1238 McFadden R-squared 0.0113 0.0177 # obs 3,649 2,058 # obs red-flagged 177 110 Frequency 0.0485 0.0534
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
Noe: Don chea in China