Performance Attribution in Private Equity

Transcription

1 Performace Attributio i Private Equity Austi M. Log, III MPA, CPA, JD Parter Aligmet Capital Group 4500 Steier Rach Blvd., Ste. 806 Austi, TX Phoe Fax alog@aligmetcapital.com October 7, 2008 C:\Data\Publish\J of Perf Measuremet - IRR Performace Attributio v5 txt & exhibits.doc Page 1 of 18

2 I the public markets, time weighted rate of retur (TWRR) performace attributio has bee refied to eable the aalyst to determie the relative cotributio of the stock idex, sector allocatio ad stock selectio i order to derive the maager s cotributio to ivestmet retur, as show i Exhibit 1 (i which W M represets the weight of the market segmet; R M, the retur to the market segmet; W P, the weight of the portfolio segmet; ad R P, the retur to the portfolio market segmet). Public market performace attributio aalysis depeds, i part, o the availability of a idex as the ivestible alterative; ad, i part, o the fact that performace is measured by TWRR, which igores the timig of iterim cash flows. Neither of these critical factors applies to the private markets there is o ivestible idex i the private markets; ad the IRR computatio, which is required for private equity performace presetatio by the Global Ivestmet Performace Stadards (GIPS) of the CFA Istitute (CFAI), does take ito accout the timig ad weights of all iterim cash flows. As Exhibit 2 makes clear, TWRR is therefore ot equal to IRR i most cases with iterim cash flows. Because there is o ivestible idex for private equity, ad because TWRR is ot equal to (or eve recocilable with) IRR i most cases, the curret body of fiace literature does ot iclude a reliable method for performace attributio i the private markets. Below, this article puts forward a ew method ad meas for determiig performace attributio i the private markets that addresses the lack of a ivestible idex ad icorporates the time/cash flow attributes of the IRR computatio. The IRR Calculatio It is well established i the literature of fiace that the iteral rate of retur (IRR) of a ivestmet is calculated by: IRR = r where i= 1 CF i ( 1+ r) = 0 I Equatio 1, CF i is the cash flow at period i (usig atural sigs, so that ivestmets of capital are egative ad both distributios of capital ad termial valuatios are positive) ad is the total umber of cash flow periods. I Excel s XIRR fuctio, which was used for all of the examples below, is expressed i days ad XIRR therefore calculates IRR usig idividual dates for each cash flow. i If the ivestmet is urealized, the termial cash flow CF is take to be a distributio (i.e., a positive cash flow) equal to its valuatio o the termial date. It is also commo kowledge i the fiace idustry ad literature that the discout rate for actual IRR (r) ad the discout rate for a pro forma IRR usig the same cash flows multiplied by ay costat k (r pf ) are the same: r = r pf where (2) kcf i i= 1 ( 1+ r ) pf = 0 This is so because the relative weights of the cash flows are uchaged as a fuctio of time whe multiplied by a costat. Aother way to uderstad why multiplyig each cash flow by a costat does ot chage the IRR of a ivestmet is to look at the origial ivestmet as a bod ad the IRR as its yield to maturity. It is obvious that buyig two idetical bods at the same price o the same date ad with the same cash flows (ad thus the same yield to maturity) would result i a portfolio with the same yield to maturity as that of the uderlyig bods. The same would be true of buyig 4 bods or k bods. It is a small extesio of the priciple to apply the same otio to fractioal bods ad (1) (3) C:\Data\Publish\J of Perf Measuremet - IRR Performace Attributio v5 txt & exhibits.doc Page 2 of 18

3 thus to all the cash flows multiplied by ay costat k. It is importat to ote that k ca be egative, as well as positive, without affectig IRR. Fially, aother techical defiitio of IRR is the discout rate required to make the positive cash flows (PCF) resultig from the ivestmet equal to the egative cash flows (NCF) expeded i acquirig the ivestmet: NCF i = ( 1+ r) i= 1 ( r) i= 1 1+ PCF It is therefore mathematically obvious that kncf i = i ( 1+ r) i= 1 ( r) i= 1 1+ kpcf i (4) (5) The Zero-Base Time (ZBT) IRR A alterative method of IRR computatio is referred to i the private equity idustry as the zerobase time or time-zero method. I the zero-base time (ZBT) IRR method, all ivestmets i a portfolio are presumed to begi o the same date (the zero date). I a 1995 white paper etitled Opportuistic Ivestig: Performace Measuremet, Bechmarkig ad Evaluatio, Richards ad Tierey, a well-kow cosultig firm, argued that the ZBT method is the best way to determie stock selectio ability, sice it eutralizes the relative timigs of the various acquisitios i a private market portfolio. I other words, the ZBT method, by movig all ivestmets up to a commo start date, miimizes the effect of a early wier, which, i the usual IRR calculatio, ca come to domiate retur sice iceptio. Exhibit 3 illustrates the problem of a very successful early ivestmet that domiates a portfolio s retur sice iceptio, as well as the effect of applyig the ZBT method to the same cash flows. The Neutrally-Weighted Portfolio (NWP) IRR I a diversified portfolio settig, although the IRR of each ivestmet is uchaged whe all its cash flows are multiplied by a costat as show above, we have discovered that multiplyig or dividig each of the i period cash flows of each of j ivestmets i a portfolio of m ivestmets by a scalig factor f s chages the IRR of the portfolio to a costat value IRR k while leavig the IRR j of each ivestmet uchaged, as show i the equatios below: IRR k = r pf where m 1 f scfi j= i= 1 ( 1+ r ) pf, j = 0 ad f s = i= 1 k NCF Note that, i Equatio 6, NCF j represets the et cash flow of period j (some periods may have more tha oe cash flow, i which case they are etted together to result i a sigle cash flow for the period); ad f is calculated so as to result i scalig each of the ivestmets i the portfolio to cotai the same amout of ivested capital. The eutrally-weighted portfolio IRR is a costat because the relative weight of each ivestmet s cotributio to the portfolio s cash flows is the same as a fuctio of time. Sice the relative weights are the same o matter what costat is used to scale the cash flows of the idividual ivestmets (i.e., the portfolio is eutrally weighted to ay commo stadard, as j (6) C:\Data\Publish\J of Perf Measuremet - IRR Performace Attributio v5 txt & exhibits.doc Page 3 of 18

4 show i Exhibit 4), the IRR of the eutrally-weighted portfolio is a costat, as is its total value to paid i ratio (TVPI, calculated as [Distributios + Edig Value] / Paid-I Capital). This is so without regard to the value of k, icludig egative values. The umerical examples i Exhibit 4 make it clear that a eutrally-weighted portfolio, i which the cash flows of all ivestmets i a portfolio are scaled to a commo costat, has two importat fiacial ad mathematical characteristics: the IRRs of the idividual ivestmets are uchaged; ad the portfolio s IRR ad TVPI measures are costat, o matter what factor is used to scale the portfolio to a eutral weight. Combied Use of the Zero-Based Time ad Neutrally-Weighted Portfolio (ZBT-NWP Aalysis) i Private Equity Performace Attributio The ivestmet meaig of the eutrally-weighted portfolio s costat IRR ca be used as a performace diagostic by comparig it to the covetioal portfolio IRR. The differece betwee the two is caused by the relative weightig of ivestmets (or, i public stock terms, stock selectio). I private market terms, this compariso determies the relative efficiecy with which the maagers ivested their capital. If the eutrally-weighted portfolio s IRR is less that the covetioal portfolio IRR, the maagers ivested more moey i the best-performig trasactios ad less moey i the worst-performig trasactios. Coversely, if the eutrallyweighted portfolio IRR is greater tha the covetioal portfolio IRR, the maagers ivested more moey i the worst-performig trasactios ad less moey i the best-performig trasactios. Obviously, the former is preferable to the latter i terms of ivestmet efficiecy. It is also importat to ote that, for all the reasos cited above as to why the eutrally-weighted portfolio s IRR is costat, the total value to paid i ratio (TVPI) is also differet from actual ad is also a costat. I the same fashio as cited i the previous paragraph, a TVPI measure i the actual portfolio that is greater tha that of the eutrally-weighted portfolio idicates that the maagers ivested more moey i the best-performig trasactios ad less moey i the worstperformig trasactios. Coversely, if the eutrally-weighted portfolio TVPI measure is greater tha the covetioal portfolio TVPI, the maagers ivested more moey i the worstperformig trasactios ad less moey i the best-performig trasactios. Agai, the former is preferable to the latter i terms of ivestmet efficiecy. The paragraphs below show i detail how the eutrally-weighted portfolio s costat IRR, as calculated above, ad both the zero-based IRR ad actual IRR, also as calculated above, ca be used to aalyze performace attributio i the private markets i terms of: 1. relative weightig of ivestmets (i.e., stock selectio, whether the maagers put more moey i the better trasactios); 2. relative timig of ivestmets (i.e., whether the maagers track record reflects fortuate timig, rather tha ivestmet skill); ad 3. retur agaist the base portfolio (as defied i the box below). I order to aalyze performace i these terms, we eed to kow the followig: Weight Time I Neutral Weight Zero-based Portfolio base retur II Actual Zero-based Actual weights, w/ commo start date III Neutral Weight Actual Neutral-weight portfolio, w/ actual start dates IV Actual Actual Actual portfolio IRR Takig up these topics i order: C:\Data\Publish\J of Perf Measuremet - IRR Performace Attributio v5 txt & exhibits.doc Page 4 of 18

5 I. Usig both the eutrally-weighted portfolio IRR ad the time zero IRR together elimiates both time ad ivestmet weightig. The retur to the portfolio after elimiatig the effects of both weightig/ivestmet selectio ad timig results i what we term the base portfolio. Exhibit 5 shows the result. II. As metioed above, the so-called time zero IRR (ZBT) calculatio restates all the ivestmets i a portfolio to a commo start date. The portfolio effect is to elimiate the relative timig of each of the ivestmets i determiig portfolio IRR. Cash flow weights, o the other had, remai actual. Exhibit 6 shows the result. III. The eutrally-weighted portfolio gives equal weight to each ivestmet i a portfolio, elimiatig the effect of the relative weight of each ivestmet i determiig IRR ad thus yieldig a costat portfolio IRR. As oted above, if more capital has bee ivested i the poorest ivestmets, the actual IRR of the portfolio will be less tha the portfolio scaled IRR. If the more capital has bee ivested i the best ivestmets, the actual IRR will be greater tha the portfolio scaled IRR. Exhibit 7 shows the result whe all cash flows are scaled to a commo stadard so that each ivestmet s ivested capital is the same. The timig of all cash flows is actual. Sice the 45.9% IRR of the eutrally-weighted portfolio exceeds the 43.1% IRR of the maager s portfolio, the example shows that the maager s stock selectio (i.e., relative weightig of the ivestmets i the portfolio) actually detracted from returs. I other words, aïve or eutral weightig would have yielded returs superior to the actual weightig of the portfolio s ivestmets. IV. The actual portfolio retur (i.e., the IRR usig both actual cash flow weights ad actual cash flow timig), usig the umerical example cited above, is show i Exhibit 8. With all of these figures kow, we ca aalyze the maager s performace i Exhibit 9. Note carefully that the IRRs total properly to the maager s retur i this aalysis, a property derived from the fact that the selectio IRR ad timig IRR each have oly a sigle chaged parameter, whether dollar weight or time, from the lie immediately precedig. There are thus o iterveig uexplaied factors. Usig ZBT-NWP Performace Attributio o a Actual Portfolio I the example show i Exhibit 10, performace attributio aalysis of a real-world portfolio shows that the portfolio maager did put the most moey ito the best ivestmets (II I = 112 bp of value added over the base portfolio). Timig was also good (IV II = 95 bp of value added), but timig is the ivestmet aspect least cotrollable by the maager i the private markets. ii The total maager cotributio was positive (IV I = 207 bp), although it is importat to keep i mid that this additio to performace came o top of a excellet base portfolio retur of 20.5%. I other words, the maager did extremely well, obtaiig a 20.5% IRR ad the addig 207 bp i additioal retur, although oly 112 bp of the added retur was attributable to factors withi the maager s cotrol. I portfolios with lower base returs, selectio ad timig begi to domiate the portfolio s retur, thus puttig a premium o maager skill (i the case of selectio retur) ad/or luck (i the case of timig retur). Attributio of Additioal Aspects of Performace I additio to calculatig the retur to selectio ad timig for the IRR of a idividual ivestmet or ay aggregatio of ivestmets, icludig vitages, asset classes, ivestmet strategies ad the like, ZBT-NWP portfolio aalysis ca aalyze the performace of ay of these relative to a public market idex (the opportuity cost of the same cash flows i the public C:\Data\Publish\J of Perf Measuremet - IRR Performace Attributio v5 txt & exhibits.doc Page 5 of 18

6 market) i the same way. Whe aalyzig opportuity cost retur i this way, ZBT-NWP aalysis takes o a ew meaig i which performace attributio has to do with the ifluece of market coditios ad timig o performace of a private equity portfolio relative to the public market. These are critical isights ito the quality of the maager s earigs relative to the public market idex, icludig how much of the retur relative to the idex was the result of the weights of the ivestmets i the portfolio (a measuremet of selectio skill) ad how much of the retur relative to the idex was the result of timig (a measuremet of luck, sice the maager caot ifluece the performace of the market over a particular or, ideed, ay time period. I Exhibit 11, the performace of a private equity ivestmet relative to the S&P 500 idex was calculated usig the origial Log-Nickels method iii later adopted by Veture Ecoomics as the public market equivalet (PME) retur. Note that ZBT-NWP aalysis makes it possible to separate the performace over the idex attributable to ivestmet weight ad the performace over the idex attributable to the timig with which the ivestmet cash flows occurred. I the example i Exhibit 11, the portfolio base retur performed extremely well agaist the idex, outperformig by 942 basis poits. However, the relative weights of the ivestmets i the portfolio, a measure of selectio skill, actually subtracted 814 basis poits of performace versus the idex. If these two elemets are take together, 942 bp 814 bp = 128 bp of retur over the idex is attributable to elemets of retur withi the maager s cotrol. The retur to timig i Exhibit 11, however, is a eormous 1,956 basis poits over the idex. This retur was ot withi the maager s cotrol, sice it would be impossible to kow i advace how the market would behave so as to time the private equity portfolio s cash flows to coform to its performace. The coclusio these outcomes poit to is that this maager s performace versus the idex, while truly outstadig (a total of 2,084 bp over the idex), was predomiately the result of timig ad therefore attributable almost exclusively to factors outside the maager s cotrol. To state the obvious, the track record of a maager whose performace versus the idex is the result of advetitious (ad advatageous) timig is ot as strog as the track record of a maager whose performace is the result of factors withi the maager s cotrol, iclude the relative weights of the ivestmets i the portfolio. ZBT-NWP aalysis therefore provides a importat screeig tool i reviewig private equity deal flow. Uses of ZBT-NWP Private Equity Portfolio Performace Attributio Oe use of ZBT-NWP private equity portfolio performace attributio is i the screeig of deal flow. While it might seem obvious to say so, it is critically importat to uderstad the origis of a private equity ivestmet maager s returs ad perhaps eve more importat to uderstad the maager s returs agaist the relevat public market idex. Great performace, icludig great performace versus the idex, is ot as impressive whe it was geerated by factors ot i the maager s cotrol. Coversely, great performace, icludig great performace versus the idex, that has bee geerated by factors withi the maager s cotrol represet the best hope that the maager will likely be able to replicate those returs i the future. This is particularly the case whe a maager ca demostrate a legthy track record of geeratig excellet performace usig replicable elemets of retur. Viewed i this light, the maager featured i Exhibit 11 represets a example of excellet returs versus the idex that are attributable pricipally to the vagaries of timig ad ot to factors withi the maager s cotrol. ZBT-NWP performace attributio thus provides a objective meas for discerig the truth of a track record, as opposed to takig at face value the various claims made by maagers attemptig to preset their returs i the most positive light. Aother importat use of ZBT-NWP performace attributio is to moitor the staff s cotributio to the returs of a istitutioal ivestor s private equity portfolio. The oly differece betwee usig ZBT-NWP aalysis for this purpose, as opposed to deal flow screeig, is that i deal flow C:\Data\Publish\J of Perf Measuremet - IRR Performace Attributio v5 txt & exhibits.doc Page 6 of 18

7 screeig performace aalysis is doe at the deal level while i moitorig staff cotributio to a private equity portfolio the aalysis is doe at the fud level. I other words, ZBT-NWP aalysis ca isolate the returs (ad the returs relative to the idex) stemmig from weightig vitages, asset classes or idividual fuds withi the istitutioal private equity portfolio ad the returs (ad the returs relative to the idex) stemmig from the timig of the same vitages, asset classes or idividual fuds. While subjective factors will always be importat i determiig istitutioal staff icetive compesatio, ZBT-NWP performace attributio ca provide seior maagemet or the board of trustees a objective view of private equity performace attributio that separates returs due to timig (i.e., good fortue) from returs due to selectio (i.e., superior judgmet). Presumably most boards would choose to compesate the latter more liberally tha the former. Itellectual Property Rights i ZBT-NWP Performace Attributio Aalysis The performace attributio method discussed i this paper is the subject of U.S. patet 7,058,583, issued Jue 6, 2006, which is the property of Aligmet Capital Group, LLC. This publicatio is iteded solely for research purposes. For further iformatio, please log oto C:\Data\Publish\J of Perf Measuremet - IRR Performace Attributio v5 txt & exhibits.doc Page 7 of 18

8 Exhibit 1 W R I. II. III. IV. Sector M M W m * R m R M * W P W P P W P * R M * R P P Cosumer 30.0% 15.0% 4.5% 1.5% 5.4% 10.0% 18.0% 1.8% Techology 10.0% 20.0% 2.0% 6.0% 2.5% 30.0% 25.0% 7.5% Cyclical 35.0% 30.0% 10.5% 4.5% 7.0% 15.0% 20.0% 3.0% Eergy 25.0% -5.0% -1.3% -2.3% 1.3% 45.0% 5.0% 2.3% 100.0% 15.75% 9.75% 16.15% 100.0% 14.6% I. Idex retur 15.8% II. Idex ad portfolio allocatio returs 9.8% III. Stock selectio 16.2% IV. Portfolio retur 14.6% W R Attributio Market idex I. 15.8% Asset allocatio II - I -6.0% Security selectio IV - II 4.8% Maager's total retur IV 14.6% Maager's cotributio IV - I -1.2% C:\Data\Publish\J of Perf Measuremet - IRR Performace Attributio v5 txt & exhibits.doc Page 8 of 18

9 Exhibit 2 Ed of Period Period Begiig Value Amout (I) / Out Edig Value Idex Retur Idex IRR CF ($100.00) $ % ($100.00) 2 $ ($100.00) $ % ($100.00) 3 $ ($100,000.00) $89, % ($100,000.00) 4 $89, $89, $1, % $89, $1, $0.00 $1, % $ $1, $0.00 $1, % $1, TWROR IRR 2.3% -9.8% C:\Data\Publish\J of Perf Measuremet - IRR Performace Attributio v5 txt & exhibits.doc Page 9 of 18

10 Exhibit 3 Actual Zero-Base Time Period Ivstmt 1 Ivstmt 2 Portfolio Period Ivstmt 1 Ivstmt 2 Portfolio 1/1/2000 $ - $ (8.0) $ (8.0) 1/1/2000 $ (20.0) $ (8.0) $ (28.0) 1/1/2002 $ - $ 20.0 $ /1/2002 $ 25.0 $ 20.0 $ /1/2004 $ (20.0) $ - $ (20.0) 1/1/2004 $ - $ - $ - 1/1/2006 $ 25.0 $ - $ /1/2006 $ - $ - $ - $ 5.0 $ 12.0 $ 17.0 $ 5.0 $ 12.0 $ 17.0 IRR 12% 58% 42% IRR 12% 58% 27% TVPI TVPI C:\Data\Publish\J of Perf Measuremet - IRR Performace Attributio v5 txt & exhibits.doc Page 10 of 18

11 Exhibit 4 Actual Pro Forma Scaled to Mea Period Ivstmt 1 Ivstmt 2 Portfolio Times Eared Period Ivstmt 1 Ivstmt 2 Portfolio Times Eared 1/1/00 $ (4) $ - $ (4) 1/1/00 $ (3.7) $ - $ (3.7) 1/1/01 $ 2 $ (2) $ - 1/1/01 $ 1.8 $ (2.2) $ (0.4) 1/1/02 $ (8) $ 3 $ (5) 1/1/02 $ (7.3) $ 3.3 $ (4.0) 1/1/03 $ - $ (8) $ (8) 1/1/03 $ - $ (8.8) $ (8.8) 1/1/04 $ 14 $ - $ 14 1/1/04 $ 12.8 $ - $ /1/05 $ - $ 35 $ 35 1/1/05 $ - $ 38.5 $ 38.5 $ 4 $ 28 $ $ 3.7 $ 30.8 $ IRR % % 43.1% IRR 13.4% % 45.9% $ (2.0) Pro Forma Scaled to Arbitrary Period Ivstmt 1 Ivstmt 2 Portfolio Times Eared 1/1/00 $ (0.7) $ - $ (0.7) 1/1/01 $ 0.3 $ (0.4) $ (0.1) 1/1/02 $ (1.3) $ 0.6 $ (0.7) 1/1/03 $ - $ (1.6) $ (1.6) 1/1/04 $ 2.3 $ - $ 2.3 1/1/05 $ - $ 7.0 $ 7.0 $ 0.7 $ 5.6 $ IRR 13.4% % 45.9% Pro Forma Scaled to Iv 1 Pro Forma Scaled to Iv 2 Period Ivstmt 1 Ivstmt 2 Portfolio Times Eared Period Ivstmt 1 Ivstmt 2 Portfolio Times Eared 1/1/00 $ (4.0) $ - $ (4.0) 1/1/00 $ (3.3) $ - $ (3.3) 1/1/01 $ 2.0 $ (2.4) $ (0.4) 1/1/01 $ 1.7 $ (2.0) $ (0.3) 1/1/02 $ (8.0) $ 3.6 $ (4.4) 1/1/02 $ (6.7) $ 3.0 $ (3.7) 1/1/03 $ - $ (9.6) $ (9.6) 1/1/03 $ - $ (8.0) $ (8.0) 1/1/04 $ 14.0 $ - $ /1/04 $ 11.7 $ - $ /1/05 $ - $ 42.0 $ /1/05 $ - $ 35.0 $ 35.0 $ 4.0 $ 33.6 $ $ 3.3 $ 28.0 $ IRR 13.4% % 45.9% IRR 13.4% % 45.9% C:\Data\Publish\J of Perf Measuremet - IRR Performace Attributio v5 txt & exhibits.doc Page 11 of 18

12 Exhibit 5 Neutral Weight ad Zero-Based Period Ivstmt 1 Ivstmt 2 Portfolio 1/1/2000 $ (3.7) $ (2.2) $ (5.9) 1/1/2001 $ 1.8 $ 3.3 $ 5.1 1/1/2002 $ (7.3) $ (8.8) $ (16.1) 1/1/2003 $ - $ - $ - 1/1/2004 $ 12.8 $ 38.5 $ /1/2005 $ - $ - $ - $ 3.7 $ 30.8 $ 34.5 IRR 13.4% % 52.8% C:\Data\Publish\J of Perf Measuremet - IRR Performace Attributio v5 txt & exhibits.doc Page 12 of 18

13 Exhibit 6 Actual Weight ad Zero-Based Period Ivstmt 1 Ivstmt 2 Portfolio 1/1/2000 $ (4) $ (2) $ (6) 1/1/2001 $ 2 $ 3 $ 5 1/1/2002 $ (8) $ (8) $ (16) 1/1/2003 $ - $ - $ - 1/1/2004 $ 14 $ 35 $ 49 1/1/2005 $ - $ - $ 4 $ 28 $ 32 IRR 13.4% % 49.4% C:\Data\Publish\J of Perf Measuremet - IRR Performace Attributio v5 txt & exhibits.doc Page 13 of 18

14 Exhibit 7 Neutral Weight ad Actual Time Period Ivstmt 1 Ivstmt 2 Portfolio 1/1/2000 $ (3.3) $ - $ (3.3) 1/1/2001 $ 1.7 $ (2.0) $ (0.3) 1/1/2002 $ (6.7) $ 3.0 $ (3.7) 1/1/2003 $ - $ (8.0) $ (8.0) 1/1/2004 $ 11.7 $ - $ /1/2005 $ - $ 35.0 $ 35.0 $ 3.3 $ 28.0 $ 31.3 IRR 13.4% % 45.9% C:\Data\Publish\J of Perf Measuremet - IRR Performace Attributio v5 txt & exhibits.doc Page 14 of 18

15 Exhibit 8 Actual Weight ad Actual Time Period Ivstmt 1 Ivstmt 2 Portfolio 1/1/2000 $ (4) $ - $ (4) 1/1/2001 $ 2 $ (2) $ - 1/1/2002 $ (8) $ 3 $ (5) 1/1/2003 $ - $ (8) $ (8) 1/1/2004 $ 14 $ - $ 14 1/1/2005 $ - $ 35 $ 35 $ 4 $ 28 $ 32 IRR % % 43.1% C:\Data\Publish\J of Perf Measuremet - IRR Performace Attributio v5 txt & exhibits.doc Page 15 of 18

16 Exhibit 9 Weight Time Explaatio I Neutral Weight Zero-based Portfolio base retur 52.8% II Actual Zero-based Actual weights, w/ commo start date 49.4% III Neutral Weight Actual Neutral-weight portfolio, w/ actual start dates 45.9% IV Actual Actual Actual portfolio IRR 43.1% I Base Retur 52.8% II - I Selectio (relative weightig) -3.3% IV - II Timig -6.4% IV Maager's retur 43.1% IV - I Maager's cotributio -9.7% C:\Data\Publish\J of Perf Measuremet - IRR Performace Attributio v5 txt & exhibits.doc Page 16 of 18

17 Exhibit 10 $ Time Explaatio I Neutral Weight Zero-based Idex of portfolio 20.54% II Actual Zero-based Actual weights, commo start date 21.66% III Neutral Weight Actual Neutral-weight portfolio, actual start dates (timig) 23.73% IV Actual Actual Actual weights, actual timig (covetioal IRR) 22.61% I Portfolio idex 20.54% II - I Selectio (relative weightig) agaist portfolio idex 1.12% IV - II Timig 0.95% IV Maager's retur 22.61% IV - I Maager's cotributio 2.07% IV - III Selectio (relative weightig) agaist actual outcome -1.12% C:\Data\Publish\J of Perf Measuremet - IRR Performace Attributio v5 txt & exhibits.doc Page 17 of 18

18 Exhibit 11 Retur > Idex Moey Time Explaatio I Neutral Weight Zero-based Portfolio base retur 9.4% II Actual Zero-based Actual weights, commo start date 1.3% III Neutral Weight Actual Neutral-weight portfolio, actual start dates 50.9% IV Actual Actual Actual weights, actual timig 20.8% Retur > Idex I Portfolio base retur 9.4% II-I Selectio -8.1% IV-II Timig 19.6% IV Maager's retur 20.8% IV-I Maager's cotributio 11.4% i XIRR returs for time periods less tha oe year must be aualized i order to be expressed i terms cosistet with XIRR returs for time periods greater tha oe year. ii Actually, perfect timig would suggest luck, rather tha skill. Timig, i this aalytical method, is simply a meas of isolatig the effect of oe compoet of the retur computatio. iii Iveted i 1992 ad perfected i 1993 by Austi Log ad Craig Nickels, who were the maagig the private equity portfolio of The Uiversity of Texas System. Available i the Research sectio of the Aligmet Capital Group Web site ( as A Private Equity Bechmark, by Austi Log ad Craig Nickels, published at the AIMR Veture Capital Coferece i Sa Fracisco, February 13, C:\Data\Publish\J of Perf Measuremet - IRR Performace Attributio v5 txt & exhibits.doc Page 18 of 18