Performance Attribution in Private Equity

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "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 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

INVESTMENT PERFORMANCE COUNCIL (IPC) Guidance Statement on Calculation Methodology

INVESTMENT PERFORMANCE COUNCIL (IPC) Guidance Statement on Calculation Methodology Adoptio Date: 4 March 2004 Effective Date: 1 Jue 2004 Retroactive Applicatio: No Public Commet Period: Aug Nov 2002 INVESTMENT PERFORMANCE COUNCIL (IPC) Preface Guidace Statemet o Calculatio Methodology

More information

INVESTMENT PERFORMANCE COUNCIL (IPC)

INVESTMENT PERFORMANCE COUNCIL (IPC) INVESTMENT PEFOMANCE COUNCIL (IPC) INVITATION TO COMMENT: Global Ivestmet Performace Stadards (GIPS ) Guidace Statemet o Calculatio Methodology The Associatio for Ivestmet Maagemet ad esearch (AIM) seeks

More information

CHAPTER 3 THE TIME VALUE OF MONEY

CHAPTER 3 THE TIME VALUE OF MONEY CHAPTER 3 THE TIME VALUE OF MONEY OVERVIEW A dollar i the had today is worth more tha a dollar to be received i the future because, if you had it ow, you could ivest that dollar ad ear iterest. Of all

More information

How to read A Mutual Fund shareholder report

How to read A Mutual Fund shareholder report Ivestor BulletI How to read A Mutual Fud shareholder report The SEC s Office of Ivestor Educatio ad Advocacy is issuig this Ivestor Bulleti to educate idividual ivestors about mutual fud shareholder reports.

More information

where: T = number of years of cash flow in investment's life n = the year in which the cash flow X n i = IRR = the internal rate of return

where: T = number of years of cash flow in investment's life n = the year in which the cash flow X n i = IRR = the internal rate of return EVALUATING ALTERNATIVE CAPITAL INVESTMENT PROGRAMS By Ke D. Duft, Extesio Ecoomist I the March 98 issue of this publicatio we reviewed the procedure by which a capital ivestmet project was assessed. The

More information

Introducing Your New Wells Fargo Trust and Investment Statement. Your Account Information Simply Stated.

Introducing Your New Wells Fargo Trust and Investment Statement. Your Account Information Simply Stated. Itroducig Your New Wells Fargo Trust ad Ivestmet Statemet. Your Accout Iformatio Simply Stated. We are pleased to itroduce your ew easy-to-read statemet. It provides a overview of your accout ad a complete

More information

Institute of Actuaries of India Subject CT1 Financial Mathematics

Institute of Actuaries of India Subject CT1 Financial Mathematics Istitute of Actuaries of Idia Subject CT1 Fiacial Mathematics For 2014 Examiatios Subject CT1 Fiacial Mathematics Core Techical Aim The aim of the Fiacial Mathematics subject is to provide a groudig i

More information

.04. This means $1000 is multiplied by 1.02 five times, once for each of the remaining sixmonth

.04. This means $1000 is multiplied by 1.02 five times, once for each of the remaining sixmonth Questio 1: What is a ordiary auity? Let s look at a ordiary auity that is certai ad simple. By this, we mea a auity over a fixed term whose paymet period matches the iterest coversio period. Additioally,

More information

BENEFIT-COST ANALYSIS Financial and Economic Appraisal using Spreadsheets

BENEFIT-COST ANALYSIS Financial and Economic Appraisal using Spreadsheets BENEIT-CST ANALYSIS iacial ad Ecoomic Appraisal usig Spreadsheets Ch. 2: Ivestmet Appraisal - Priciples Harry Campbell & Richard Brow School of Ecoomics The Uiversity of Queeslad Review of basic cocepts

More information

I. Why is there a time value to money (TVM)?

I. Why is there a time value to money (TVM)? Itroductio to the Time Value of Moey Lecture Outlie I. Why is there the cocept of time value? II. Sigle cash flows over multiple periods III. Groups of cash flows IV. Warigs o doig time value calculatios

More information

Incremental calculation of weighted mean and variance

Incremental calculation of weighted mean and variance Icremetal calculatio of weighted mea ad variace Toy Fich faf@cam.ac.uk dot@dotat.at Uiversity of Cambridge Computig Service February 009 Abstract I these otes I eplai how to derive formulae for umerically

More information

CDs Bought at a Bank verses CD s Bought from a Brokerage. Floyd Vest

CDs Bought at a Bank verses CD s Bought from a Brokerage. Floyd Vest CDs Bought at a Bak verses CD s Bought from a Brokerage Floyd Vest CDs bought at a bak. CD stads for Certificate of Deposit with the CD origiatig i a FDIC isured bak so that the CD is isured by the Uited

More information

Chapter 5 Unit 1. IET 350 Engineering Economics. Learning Objectives Chapter 5. Learning Objectives Unit 1. Annual Amount and Gradient Functions

Chapter 5 Unit 1. IET 350 Engineering Economics. Learning Objectives Chapter 5. Learning Objectives Unit 1. Annual Amount and Gradient Functions Chapter 5 Uit Aual Amout ad Gradiet Fuctios IET 350 Egieerig Ecoomics Learig Objectives Chapter 5 Upo completio of this chapter you should uderstad: Calculatig future values from aual amouts. Calculatig

More information

Lesson 17 Pearson s Correlation Coefficient

Lesson 17 Pearson s Correlation Coefficient Outlie Measures of Relatioships Pearso s Correlatio Coefficiet (r) -types of data -scatter plots -measure of directio -measure of stregth Computatio -covariatio of X ad Y -uique variatio i X ad Y -measurig

More information

Analyzing Longitudinal Data from Complex Surveys Using SUDAAN

Analyzing Longitudinal Data from Complex Surveys Using SUDAAN Aalyzig Logitudial Data from Complex Surveys Usig SUDAAN Darryl Creel Statistics ad Epidemiology, RTI Iteratioal, 312 Trotter Farm Drive, Rockville, MD, 20850 Abstract SUDAAN: Software for the Statistical

More information

*The most important feature of MRP as compared with ordinary inventory control analysis is its time phasing feature.

*The most important feature of MRP as compared with ordinary inventory control analysis is its time phasing feature. Itegrated Productio ad Ivetory Cotrol System MRP ad MRP II Framework of Maufacturig System Ivetory cotrol, productio schedulig, capacity plaig ad fiacial ad busiess decisios i a productio system are iterrelated.

More information

Bond Valuation I. What is a bond? Cash Flows of A Typical Bond. Bond Valuation. Coupon Rate and Current Yield. Cash Flows of A Typical Bond

Bond Valuation I. What is a bond? Cash Flows of A Typical Bond. Bond Valuation. Coupon Rate and Current Yield. Cash Flows of A Typical Bond What is a bod? Bod Valuatio I Bod is a I.O.U. Bod is a borrowig agreemet Bod issuers borrow moey from bod holders Bod is a fixed-icome security that typically pays periodic coupo paymets, ad a pricipal

More information

The Arithmetic of Investment Expenses

The Arithmetic of Investment Expenses Fiacial Aalysts Joural Volume 69 Number 2 2013 CFA Istitute The Arithmetic of Ivestmet Expeses William F. Sharpe Recet regulatory chages have brought a reewed focus o the impact of ivestmet expeses o ivestors

More information

A Guide to the Pricing Conventions of SFE Interest Rate Products

A Guide to the Pricing Conventions of SFE Interest Rate Products A Guide to the Pricig Covetios of SFE Iterest Rate Products SFE 30 Day Iterbak Cash Rate Futures Physical 90 Day Bak Bills SFE 90 Day Bak Bill Futures SFE 90 Day Bak Bill Futures Tick Value Calculatios

More information

Learning objectives. Duc K. Nguyen - Corporate Finance 21/10/2014

Learning objectives. Duc K. Nguyen - Corporate Finance 21/10/2014 1 Lecture 3 Time Value of Moey ad Project Valuatio The timelie Three rules of time travels NPV of a stream of cash flows Perpetuities, auities ad other special cases Learig objectives 2 Uderstad the time-value

More information

France caters to innovative companies and offers the best research tax credit in Europe

France caters to innovative companies and offers the best research tax credit in Europe 1/5 The Frech Govermet has three objectives : > improve Frace s fiscal competitiveess > cosolidate R&D activities > make Frace a attractive coutry for iovatio Tax icetives have become a key elemet of public

More information

Investing in Stocks WHAT ARE THE DIFFERENT CLASSIFICATIONS OF STOCKS? WHY INVEST IN STOCKS? CAN YOU LOSE MONEY?

Investing in Stocks WHAT ARE THE DIFFERENT CLASSIFICATIONS OF STOCKS? WHY INVEST IN STOCKS? CAN YOU LOSE MONEY? Ivestig i Stocks Ivestig i Stocks Busiesses sell shares of stock to ivestors as a way to raise moey to fiace expasio, pay off debt ad provide operatig capital. Ecoomic coditios: Employmet, iflatio, ivetory

More information

5.4 Amortization. Question 1: How do you find the present value of an annuity? Question 2: How is a loan amortized?

5.4 Amortization. Question 1: How do you find the present value of an annuity? Question 2: How is a loan amortized? 5.4 Amortizatio Questio 1: How do you fid the preset value of a auity? Questio 2: How is a loa amortized? Questio 3: How do you make a amortizatio table? Oe of the most commo fiacial istrumets a perso

More information

CHAPTER 4: NET PRESENT VALUE

CHAPTER 4: NET PRESENT VALUE EMBA 807 Corporate Fiace Dr. Rodey Boehe CHAPTER 4: NET PRESENT VALUE (Assiged probles are, 2, 7, 8,, 6, 23, 25, 28, 29, 3, 33, 36, 4, 42, 46, 50, ad 52) The title of this chapter ay be Net Preset Value,

More information

Present Value Tax Expenditure Estimate of Tax Assistance for Retirement Saving

Present Value Tax Expenditure Estimate of Tax Assistance for Retirement Saving Preset Value Tax Expediture Estimate of Tax Assistace for Retiremet Savig Tax Policy Brach Departmet of Fiace Jue 30, 1998 2 Preset Value Tax Expediture Estimate of Tax Assistace for Retiremet Savig This

More information

Savings and Retirement Benefits

Savings and Retirement Benefits 60 Baltimore Couty Public Schools offers you several ways to begi savig moey through payroll deductios. Defied Beefit Pesio Pla Tax Sheltered Auities ad Custodial Accouts Defied Beefit Pesio Pla Did you

More information

How to use what you OWN to reduce what you OWE

How to use what you OWN to reduce what you OWE How to use what you OWN to reduce what you OWE Maulife Oe A Overview Most Caadias maage their fiaces by doig two thigs: 1. Depositig their icome ad other short-term assets ito chequig ad savigs accouts.

More information

1741 SWITZERLAND CAP WEIGHTED INDEX

1741 SWITZERLAND CAP WEIGHTED INDEX 1741 Switzerlad Idex Series 1741 SWITZERLAND CAP WEIGHTED INDEX Idex rules Status as of 1 July 2015 1741 Switzerlad Cap Weighted Idex 2 CONTENTS 1 Itroductio 3 2 Idex specificatios 4 3 Idex uiverse 5 4

More information

FM4 CREDIT AND BORROWING

FM4 CREDIT AND BORROWING FM4 CREDIT AND BORROWING Whe you purchase big ticket items such as cars, boats, televisios ad the like, retailers ad fiacial istitutios have various terms ad coditios that are implemeted for the cosumer

More information

Enhancing Oracle Business Intelligence with cubus EV How users of Oracle BI on Essbase cubes can benefit from cubus outperform EV Analytics (cubus EV)

Enhancing Oracle Business Intelligence with cubus EV How users of Oracle BI on Essbase cubes can benefit from cubus outperform EV Analytics (cubus EV) Ehacig Oracle Busiess Itelligece with cubus EV How users of Oracle BI o Essbase cubes ca beefit from cubus outperform EV Aalytics (cubus EV) CONTENT 01 cubus EV as a ehacemet to Oracle BI o Essbase 02

More information

Time Value of Money. First some technical stuff. HP10B II users

Time Value of Money. First some technical stuff. HP10B II users Time Value of Moey Basis for the course Power of compoud iterest $3,600 each year ito a 401(k) pla yields $2,390,000 i 40 years First some techical stuff You will use your fiacial calculator i every sigle

More information

Modified Line Search Method for Global Optimization

Modified Line Search Method for Global Optimization Modified Lie Search Method for Global Optimizatio Cria Grosa ad Ajith Abraham Ceter of Excellece for Quatifiable Quality of Service Norwegia Uiversity of Sciece ad Techology Trodheim, Norway {cria, ajith}@q2s.tu.o

More information

A Resource for Free-standing Mathematics Qualifications Working with %

A Resource for Free-standing Mathematics Qualifications Working with % Ca you aswer these questios? A savigs accout gives % iterest per aum.. If 000 is ivested i this accout, how much will be i the accout at the ed of years? A ew car costs 16 000 ad its value falls by 1%

More information

Amendments to employer debt Regulations

Amendments to employer debt Regulations March 2008 Pesios Legal Alert Amedmets to employer debt Regulatios The Govermet has at last issued Regulatios which will amed the law as to employer debts uder s75 Pesios Act 1995. The amedig Regulatios

More information

Subject CT5 Contingencies Core Technical Syllabus

Subject CT5 Contingencies Core Technical Syllabus Subject CT5 Cotigecies Core Techical Syllabus for the 2015 exams 1 Jue 2014 Aim The aim of the Cotigecies subject is to provide a groudig i the mathematical techiques which ca be used to model ad value

More information

I. Chi-squared Distributions

I. Chi-squared Distributions 1 M 358K Supplemet to Chapter 23: CHI-SQUARED DISTRIBUTIONS, T-DISTRIBUTIONS, AND DEGREES OF FREEDOM To uderstad t-distributios, we first eed to look at aother family of distributios, the chi-squared distributios.

More information

Page 1. Real Options for Engineering Systems. What are we up to? Today s agenda. J1: Real Options for Engineering Systems. Richard de Neufville

Page 1. Real Options for Engineering Systems. What are we up to? Today s agenda. J1: Real Options for Engineering Systems. Richard de Neufville Real Optios for Egieerig Systems J: Real Optios for Egieerig Systems By (MIT) Stefa Scholtes (CU) Course website: http://msl.mit.edu/cmi/ardet_2002 Stefa Scholtes Judge Istitute of Maagemet, CU Slide What

More information

Comparing Credit Card Finance Charges

Comparing Credit Card Finance Charges Comparig Credit Card Fiace Charges Comparig Credit Card Fiace Charges Decidig if a particular credit card is right for you ivolves uderstadig what it costs ad what it offers you i retur. To determie how

More information

Definition. A variable X that takes on values X 1, X 2, X 3,...X k with respective frequencies f 1, f 2, f 3,...f k has mean

Definition. A variable X that takes on values X 1, X 2, X 3,...X k with respective frequencies f 1, f 2, f 3,...f k has mean 1 Social Studies 201 October 13, 2004 Note: The examples i these otes may be differet tha used i class. However, the examples are similar ad the methods used are idetical to what was preseted i class.

More information

Present Values, Investment Returns and Discount Rates

Present Values, Investment Returns and Discount Rates Preset Values, Ivestmet Returs ad Discout Rates Dimitry Midli, ASA, MAAA, PhD Presidet CDI Advisors LLC dmidli@cdiadvisors.com May 2, 203 Copyright 20, CDI Advisors LLC The cocept of preset value lies

More information

Confidence Intervals for One Mean with Tolerance Probability

Confidence Intervals for One Mean with Tolerance Probability Chapter 421 Cofidece Itervals for Oe Mea with Tolerace Probability Itroductio This procedure calculates the sample size ecessary to achieve a specified distace from the mea to the cofidece limit(s) with

More information

B1. Fourier Analysis of Discrete Time Signals

B1. Fourier Analysis of Discrete Time Signals B. Fourier Aalysis of Discrete Time Sigals Objectives Itroduce discrete time periodic sigals Defie the Discrete Fourier Series (DFS) expasio of periodic sigals Defie the Discrete Fourier Trasform (DFT)

More information

Statement of cash flows

Statement of cash flows 6 Statemet of cash flows this chapter covers... I this chapter we study the statemet of cash flows, which liks profit from the statemet of profit or loss ad other comprehesive icome with chages i assets

More information

Erik Ottosson & Fredrik Weissenrieder, 1996-03-01 CVA. Cash Value Added - a new method for measuring financial performance.

Erik Ottosson & Fredrik Weissenrieder, 1996-03-01 CVA. Cash Value Added - a new method for measuring financial performance. CVA Cash Value Added - a ew method for measurig fiacial performace Erik Ottosso Strategic Cotroller Sveska Cellulosa Aktiebolaget SCA Box 7827 S-103 97 Stockholm Swede Fredrik Weisserieder Departmet of

More information

Rainbow options. A rainbow is an option on a basket that pays in its most common form, a nonequally

Rainbow options. A rainbow is an option on a basket that pays in its most common form, a nonequally Raibow optios INRODUCION A raibow is a optio o a basket that pays i its most commo form, a oequally weighted average of the assets of the basket accordig to their performace. he umber of assets is called

More information

Module 4: Mathematical Induction

Module 4: Mathematical Induction Module 4: Mathematical Iductio Theme 1: Priciple of Mathematical Iductio Mathematical iductio is used to prove statemets about atural umbers. As studets may remember, we ca write such a statemet as a predicate

More information

MESSAGE TO TEACHERS: NOTE TO EDUCATORS:

MESSAGE TO TEACHERS: NOTE TO EDUCATORS: MESSAGE TO TEACHERS: NOTE TO EDUCATORS: Attached herewith, please fid suggested lesso plas for term 1 of MATHEMATICS Grade 12. Please ote that these lesso plas are to be used oly as a guide ad teachers

More information

REFURBISHMENTS AND AUGMENTATIONS

REFURBISHMENTS AND AUGMENTATIONS INTRODUCTION TIER WORKING PAPER No. 0 REFURBISHMENTS AND AUGMENTATIONS Workig Paper No. How Water Prices are Set provided a overview of how water prices are set o the basis of lower boud costs. As oted

More information

Terminology for Bonds and Loans

Terminology for Bonds and Loans ³ ² ± Termiology for Bods ad Loas Pricipal give to borrower whe loa is made Simple loa: pricipal plus iterest repaid at oe date Fixed-paymet loa: series of (ofte equal) repaymets Bod is issued at some

More information

Section IV.5: Recurrence Relations from Algorithms

Section IV.5: Recurrence Relations from Algorithms Sectio IV.5: Recurrece Relatios from Algorithms Give a recursive algorithm with iput size, we wish to fid a Θ (best big O) estimate for its ru time T() either by obtaiig a explicit formula for T() or by

More information

TO: Users of the ACTEX Review Seminar on DVD for SOA Exam FM/CAS Exam 2

TO: Users of the ACTEX Review Seminar on DVD for SOA Exam FM/CAS Exam 2 TO: Users of the ACTEX Review Semiar o DVD for SOA Exam FM/CAS Exam FROM: Richard L. (Dick) Lodo, FSA Dear Studets, Thak you for purchasig the DVD recordig of the ACTEX Review Semiar for SOA Exam FM (CAS

More information

Soving Recurrence Relations

Soving Recurrence Relations Sovig Recurrece Relatios Part 1. Homogeeous liear 2d degree relatios with costat coefficiets. Cosider the recurrece relatio ( ) T () + at ( 1) + bt ( 2) = 0 This is called a homogeeous liear 2d degree

More information

Domain 1: Designing a SQL Server Instance and a Database Solution

Domain 1: Designing a SQL Server Instance and a Database Solution Maual SQL Server 2008 Desig, Optimize ad Maitai (70-450) 1-800-418-6789 Domai 1: Desigig a SQL Server Istace ad a Database Solutio Desigig for CPU, Memory ad Storage Capacity Requiremets Whe desigig a

More information

Power Factor in Electrical Power Systems with Non-Linear Loads

Power Factor in Electrical Power Systems with Non-Linear Loads Power Factor i Electrical Power Systems with No-Liear Loads By: Gozalo Sadoval, ARTECHE / INELAP S.A. de C.V. Abstract. Traditioal methods of Power Factor Correctio typically focus o displacemet power

More information

Standard Errors and Confidence Intervals

Standard Errors and Confidence Intervals Stadard Errors ad Cofidece Itervals Itroductio I the documet Data Descriptio, Populatios ad the Normal Distributio a sample had bee obtaied from the populatio of heights of 5-year-old boys. If we assume

More information

Trading the randomness - Designing an optimal trading strategy under a drifted random walk price model

Trading the randomness - Designing an optimal trading strategy under a drifted random walk price model Tradig the radomess - Desigig a optimal tradig strategy uder a drifted radom walk price model Yuao Wu Math 20 Project Paper Professor Zachary Hamaker Abstract: I this paper the author iteds to explore

More information

THE TIME VALUE OF MONEY

THE TIME VALUE OF MONEY QRMC04 9/17/01 4:43 PM Page 51 CHAPTER FOUR THE TIME VALUE OF MONEY 4.1 INTRODUCTION AND FUTURE VALUE The perspective ad the orgaizatio of this chapter differs from that of chapters 2 ad 3 i that topics

More information

Forecasting. Forecasting Application. Practical Forecasting. Chapter 7 OVERVIEW KEY CONCEPTS. Chapter 7. Chapter 7

Forecasting. Forecasting Application. Practical Forecasting. Chapter 7 OVERVIEW KEY CONCEPTS. Chapter 7. Chapter 7 Forecastig Chapter 7 Chapter 7 OVERVIEW Forecastig Applicatios Qualitative Aalysis Tred Aalysis ad Projectio Busiess Cycle Expoetial Smoothig Ecoometric Forecastig Judgig Forecast Reliability Choosig the

More information

Review for College Algebra Final Exam

Review for College Algebra Final Exam Review for College Algebra Fial Exam (Please remember that half of the fial exam will cover chapters 1-4. This review sheet covers oly the ew material, from chapters 5 ad 7.) 5.1 Systems of equatios i

More information

This chapter considers the effect of managerial compensation on the desired

This chapter considers the effect of managerial compensation on the desired Chapter 4 THE EFFECT OF MANAGERIAL COMPENSATION ON OPTIMAL PRODUCTION AND HEDGING WITH FORWARDS AND PUTS 4.1 INTRODUCTION This chapter cosiders the effect of maagerial compesatio o the desired productio

More information

Bond Pricing Theorems. Floyd Vest

Bond Pricing Theorems. Floyd Vest Bod Pricig Theorems Floyd Vest The followig Bod Pricig Theorems develop mathematically such facts as, whe market iterest rates rise, the price of existig bods falls. If a perso wats to sell a bod i this

More information

Forecasting techniques

Forecasting techniques 2 Forecastig techiques this chapter covers... I this chapter we will examie some useful forecastig techiques that ca be applied whe budgetig. We start by lookig at the way that samplig ca be used to collect

More information

1 Computing the Standard Deviation of Sample Means

1 Computing the Standard Deviation of Sample Means Computig the Stadard Deviatio of Sample Meas Quality cotrol charts are based o sample meas ot o idividual values withi a sample. A sample is a group of items, which are cosidered all together for our aalysis.

More information

THE ARITHMETIC OF INTEGERS. - multiplication, exponentiation, division, addition, and subtraction

THE ARITHMETIC OF INTEGERS. - multiplication, exponentiation, division, addition, and subtraction THE ARITHMETIC OF INTEGERS - multiplicatio, expoetiatio, divisio, additio, ad subtractio What to do ad what ot to do. THE INTEGERS Recall that a iteger is oe of the whole umbers, which may be either positive,

More information

CCH Accountants Starter Pack

CCH Accountants Starter Pack CCH Accoutats Starter Pack We may be a bit smaller, but fudametally we re o differet to ay other accoutig practice. Util ow, smaller firms have faced a stark choice: Buy cheaply, kowig that the practice

More information

SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES

SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES Read Sectio 1.5 (pages 5 9) Overview I Sectio 1.5 we lear to work with summatio otatio ad formulas. We will also itroduce a brief overview of sequeces,

More information

Properties of MLE: consistency, asymptotic normality. Fisher information.

Properties of MLE: consistency, asymptotic normality. Fisher information. Lecture 3 Properties of MLE: cosistecy, asymptotic ormality. Fisher iformatio. I this sectio we will try to uderstad why MLEs are good. Let us recall two facts from probability that we be used ofte throughout

More information

Pre-Suit Collection Strategies

Pre-Suit Collection Strategies Pre-Suit Collectio Strategies Writte by Charles PT Phoeix How to Decide Whether to Pursue Collectio Calculatig the Value of Collectio As with ay busiess litigatio, all factors associated with the process

More information

Bond Mathematics & Valuation

Bond Mathematics & Valuation Bod Mathematics & Valuatio Below is some legalese o the use of this documet. If you d like to avoid a headache, it basically asks you to use some commo sese. We have put some effort ito this, ad we wat

More information

428 CHAPTER 12 MULTIPLE LINEAR REGRESSION

428 CHAPTER 12 MULTIPLE LINEAR REGRESSION 48 CHAPTER 1 MULTIPLE LINEAR REGRESSION Table 1-8 Team Wis Pts GF GA PPG PPcT SHG PPGA PKPcT SHGA Chicago 47 104 338 68 86 7. 4 71 76.6 6 Miesota 40 96 31 90 91 6.4 17 67 80.7 0 Toroto 8 68 3 330 79.3

More information

Problem Set 1 Oligopoly, market shares and concentration indexes

Problem Set 1 Oligopoly, market shares and concentration indexes Advaced Idustrial Ecoomics Sprig 2016 Joha Steek 29 April 2016 Problem Set 1 Oligopoly, market shares ad cocetratio idexes 1 1 Price Competitio... 3 1.1 Courot Oligopoly with Homogeous Goods ad Differet

More information

Simple Annuities Present Value.

Simple Annuities Present Value. Simple Auities Preset Value. OBJECTIVES (i) To uderstad the uderlyig priciple of a preset value auity. (ii) To use a CASIO CFX-9850GB PLUS to efficietly compute values associated with preset value auities.

More information

Evaluating Model for B2C E- commerce Enterprise Development Based on DEA

Evaluating Model for B2C E- commerce Enterprise Development Based on DEA , pp.180-184 http://dx.doi.org/10.14257/astl.2014.53.39 Evaluatig Model for B2C E- commerce Eterprise Developmet Based o DEA Weli Geg, Jig Ta Computer ad iformatio egieerig Istitute, Harbi Uiversity of

More information

Non-life insurance mathematics. Nils F. Haavardsson, University of Oslo and DNB Skadeforsikring

Non-life insurance mathematics. Nils F. Haavardsson, University of Oslo and DNB Skadeforsikring No-life isurace mathematics Nils F. Haavardsso, Uiversity of Oslo ad DNB Skadeforsikrig Mai issues so far Why does isurace work? How is risk premium defied ad why is it importat? How ca claim frequecy

More information

NPTEL STRUCTURAL RELIABILITY

NPTEL STRUCTURAL RELIABILITY NPTEL Course O STRUCTURAL RELIABILITY Module # 0 Lecture 1 Course Format: Web Istructor: Dr. Aruasis Chakraborty Departmet of Civil Egieerig Idia Istitute of Techology Guwahati 1. Lecture 01: Basic Statistics

More information

How To Find FINANCING For Your Business

How To Find FINANCING For Your Business How To Fid FINANCING For Your Busiess Oe of the most difficult tasks faced by the maagemet team of small busiesses today is fidig adequate fiacig for curret operatios i order to support ew ad ogoig cotracts.

More information

Solving Logarithms and Exponential Equations

Solving Logarithms and Exponential Equations Solvig Logarithms ad Epoetial Equatios Logarithmic Equatios There are two major ideas required whe solvig Logarithmic Equatios. The first is the Defiitio of a Logarithm. You may recall from a earlier topic:

More information

CHAPTER 3: FINANCIAL ANALYSIS WITH INFLATION

CHAPTER 3: FINANCIAL ANALYSIS WITH INFLATION Up to ow, we have mostly igored iflatio. However, iflatio ad iterest are closely related. It was oted i the last chapter that iterest rates should geerally cover more tha iflatio. I fact, the amout of

More information

I apply to subscribe for a Stocks & Shares ISA for the tax year 20 /20 and each subsequent year until further notice.

I apply to subscribe for a Stocks & Shares ISA for the tax year 20 /20 and each subsequent year until further notice. IFSL Brooks Macdoald Fud Stocks & Shares ISA Trasfer Applicatio Form IFSL Brooks Macdoald Fud Stocks & Shares ISA Trasfer Applicatio Form Please complete usig BLOCK CAPITALS ad retur the completed form

More information

Lesson 15 ANOVA (analysis of variance)

Lesson 15 ANOVA (analysis of variance) Outlie Variability -betwee group variability -withi group variability -total variability -F-ratio Computatio -sums of squares (betwee/withi/total -degrees of freedom (betwee/withi/total -mea square (betwee/withi

More information

(VCP-310) 1-800-418-6789

(VCP-310) 1-800-418-6789 Maual VMware Lesso 1: Uderstadig the VMware Product Lie I this lesso, you will first lear what virtualizatio is. Next, you ll explore the products offered by VMware that provide virtualizatio services.

More information

I apply to subscribe for a Stocks & Shares NISA for the tax year 2015/2016 and each subsequent year until further notice.

I apply to subscribe for a Stocks & Shares NISA for the tax year 2015/2016 and each subsequent year until further notice. IFSL Brooks Macdoald Fud Stocks & Shares NISA trasfer applicatio form IFSL Brooks Macdoald Fud Stocks & Shares NISA trasfer applicatio form Please complete usig BLOCK CAPITALS ad retur the completed form

More information

Online Banking. Internet of Things

Online Banking. Internet of Things Olie Bakig & The Iteret of Thigs Our icreasigly iteretcoected future will mea better bakig ad added security resposibilities for all of us. FROM DESKTOPS TO SMARTWATCHS Just a few years ago, Americas coducted

More information

Lesson 12. Sequences and Series

Lesson 12. Sequences and Series Retur to List of Lessos Lesso. Sequeces ad Series A ifiite sequece { a, a, a,... a,...} ca be thought of as a list of umbers writte i defiite order ad certai patter. It is usually deoted by { a } =, or

More information

Vladimir N. Burkov, Dmitri A. Novikov MODELS AND METHODS OF MULTIPROJECTS MANAGEMENT

Vladimir N. Burkov, Dmitri A. Novikov MODELS AND METHODS OF MULTIPROJECTS MANAGEMENT Keywords: project maagemet, resource allocatio, etwork plaig Vladimir N Burkov, Dmitri A Novikov MODELS AND METHODS OF MULTIPROJECTS MANAGEMENT The paper deals with the problems of resource allocatio betwee

More information

Estimating Probability Distributions by Observing Betting Practices

Estimating Probability Distributions by Observing Betting Practices 5th Iteratioal Symposium o Imprecise Probability: Theories ad Applicatios, Prague, Czech Republic, 007 Estimatig Probability Distributios by Observig Bettig Practices Dr C Lych Natioal Uiversity of Irelad,

More information

Capital Gains Taxation and Corporate Investment

Capital Gains Taxation and Corporate Investment Uiversity of Chicago Law School Chicago Uboud Coase-Sador Workig Paper Series i Law ad Ecoomics Coase-Sador Istitute for Law ad Ecoomics 2016 Capital Gais Taxatio ad Corporate Ivestmet David A. Weisbach

More information

International Delegation A summary for financial advisers

International Delegation A summary for financial advisers Iteratioal Delegatio A summary for fiacial advisers Cotets Please ote For fiacial adviser use oly. It should ot be distributed to, or relied upo by, retail cliets. AXA Wealth Iteratioal is the brad used

More information

Lecture Notes CMSC 251

Lecture Notes CMSC 251 We have this messy summatio to solve though First observe that the value remais costat throughout the sum, ad so we ca pull it out frot Also ote that we ca write 3 i / i ad (3/) i T () = log 3 (log ) 1

More information

Chapter 6: Variance, the law of large numbers and the Monte-Carlo method

Chapter 6: Variance, the law of large numbers and the Monte-Carlo method Chapter 6: Variace, the law of large umbers ad the Mote-Carlo method Expected value, variace, ad Chebyshev iequality. If X is a radom variable recall that the expected value of X, E[X] is the average value

More information

Swaps: Constant maturity swaps (CMS) and constant maturity. Treasury (CMT) swaps

Swaps: Constant maturity swaps (CMS) and constant maturity. Treasury (CMT) swaps Swaps: Costat maturity swaps (CMS) ad costat maturity reasury (CM) swaps A Costat Maturity Swap (CMS) swap is a swap where oe of the legs pays (respectively receives) a swap rate of a fixed maturity, while

More information

CREATIVE MARKETING PROJECT 2016

CREATIVE MARKETING PROJECT 2016 CREATIVE MARKETING PROJECT 2016 The Creative Marketig Project is a chapter project that develops i chapter members a aalytical ad creative approach to the marketig process, actively egages chapter members

More information

Chapter 7 Methods of Finding Estimators

Chapter 7 Methods of Finding Estimators Chapter 7 for BST 695: Special Topics i Statistical Theory. Kui Zhag, 011 Chapter 7 Methods of Fidig Estimators Sectio 7.1 Itroductio Defiitio 7.1.1 A poit estimator is ay fuctio W( X) W( X1, X,, X ) of

More information

Confidence Intervals for One Mean

Confidence Intervals for One Mean Chapter 420 Cofidece Itervals for Oe Mea Itroductio This routie calculates the sample size ecessary to achieve a specified distace from the mea to the cofidece limit(s) at a stated cofidece level for a

More information

The Stable Marriage Problem

The Stable Marriage Problem The Stable Marriage Problem William Hut Lae Departmet of Computer Sciece ad Electrical Egieerig, West Virgiia Uiversity, Morgatow, WV William.Hut@mail.wvu.edu 1 Itroductio Imagie you are a matchmaker,

More information

hedge fund indexing January 2010

hedge fund indexing January 2010 hedge fud idexig Jauary 2010 Emergig from oe of the most sigificat market dislocatios to date, hedge fuds as a whole successfully capitalized o opportuities i 2009, recoupig much of their 2008 losses ad

More information

Annuities Under Random Rates of Interest II By Abraham Zaks. Technion I.I.T. Haifa ISRAEL and Haifa University Haifa ISRAEL.

Annuities Under Random Rates of Interest II By Abraham Zaks. Technion I.I.T. Haifa ISRAEL and Haifa University Haifa ISRAEL. Auities Uder Radom Rates of Iterest II By Abraham Zas Techio I.I.T. Haifa ISRAEL ad Haifa Uiversity Haifa ISRAEL Departmet of Mathematics, Techio - Israel Istitute of Techology, 3000, Haifa, Israel I memory

More information

CHAPTER 3 DIGITAL CODING OF SIGNALS

CHAPTER 3 DIGITAL CODING OF SIGNALS CHAPTER 3 DIGITAL CODING OF SIGNALS Computers are ofte used to automate the recordig of measuremets. The trasducers ad sigal coditioig circuits produce a voltage sigal that is proportioal to a quatity

More information

9.8: THE POWER OF A TEST

9.8: THE POWER OF A TEST 9.8: The Power of a Test CD9-1 9.8: THE POWER OF A TEST I the iitial discussio of statistical hypothesis testig, the two types of risks that are take whe decisios are made about populatio parameters based

More information

In nite Sequences. Dr. Philippe B. Laval Kennesaw State University. October 9, 2008

In nite Sequences. Dr. Philippe B. Laval Kennesaw State University. October 9, 2008 I ite Sequeces Dr. Philippe B. Laval Keesaw State Uiversity October 9, 2008 Abstract This had out is a itroductio to i ite sequeces. mai de itios ad presets some elemetary results. It gives the I ite Sequeces

More information