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1 IIPC Cosultig AG IRR Attributio Date: November 2011 Date: November Slide 1

2 Ageda Itroductio Calculatio of IRR Cotributio to IRR IRR attributio Hypothetical example Simple example for a IRR implemetatio Critical aspects Commets ad questios Appedix: Profit ad loss attributio Refereces Cotact details ad disclaimer Date: November Slide 2

3 Itroductio Date: November Slide 3

4 Iitial commets o TWR attributio Decomposig the TWR is commo practice ad the mai method implemeted by performace attributio software providers, meas that: Portfolio ad bechmark returs are TWRs. Segmet ad stock returs are TWRs. Retur cotributios are calculated usig TWRs. Use of TWRs assumes that portfolio maager has o discretio over ay (exteral as well as iteral) cash flows. Impact of iteral as well as exteral cash flows are eutralized. Impact of over- / uderweightig of segmets or stocks is dealt by usig weights istead of cash flows. Date: November Slide 4

5 Iitial commets o MWR attributio Decomposig the MWR is ot commo practice ad ot offered by performace attributio software providers, meas that: Decomposig the MWR or TWR usig the "MWR-cocept" is ot commo practice. The effect of cash flows is ot allocated properly. The maagemet effects may be misleadig. Date: November Slide 5

6 Iitial commets o MWR Moey-weighted rate of retur (MWR) measures the retur of a portfolio i a way that the retur is sesitive to chages i the moey ivested: MWR measures the retur from a cliet s perspective where he does have cotrol over the (exteral) cash flows. MWR does ot allow a compariso across peer groups. MWR does allow a compariso agaist a bechmark (adjusted for cash flows). MWR is best measured by the iteral rate of retur (IRR). Calculatig, decomposig ad reportig MWRs is ot commo practice. MWRs are ot geerally covered by the GIPS Stadards - just for private equity ad closed ed real estate fuds. Date: November Slide 6

7 Decompositio of MWR versus TWR The MWR allows a decompositio of the portfolio retur reflectig the cliet s mai ivestmet decisio: TWR Bechmark effect => reflects the retur cotributio based o the cliet s decisio to ivest his iitial capital ito a specific bechmark strategy (correspods to the TWR bechmark retur). TWR Maagemet effect => reflects the retur cotributio based o deviatig from the bechmark strategy by asset allocatio ad stock pickig (correspods to the TWR attributio effects). MWR Timig effect => reflects the retur cotributio of chagig the iitial ivested capital ito the bechmark strategy ad ito the asset allocatio of the portfolio (correspods to the differece betwee MWR ad TWR). Date: November Slide 7

8 Decompositio of MWR Aother perspective The MWR allows also a decompositio of the portfolio retur without explicitly separatig the timig effect: MWR Bechmark effect => reflects the retur cotributio based o the cliet s decisio to ivest his capital ito a specific bechmark strategy (icludig the effect of chagig the iitial ivested capital). MWR Maagemet effect => reflects the retur cotributio based o deviatig from the bechmark strategy by asset allocatio ad stock pickig (icludig the effect of chagig the iitial ivested capital). Date: November Slide 8

9 Compariso of differet decompositio approaches TWR TWR Bechmark effect + TWR + Maagemet effects MWR Timig effect MWR MWR Bechmark effect + MWR Maagemet effects TWR Bechmark effect + Timig TWR Bechmark effect Maagemet effects + Timig Maagemet effects Date: November Slide 9

10 Geeral framework for decomposig returs (1/2) The MWR-calculatio ad MWR-attributio allow to defie a geeral framework for decomposig returs: That combies the differet views o performace (cliet versus portfolio maager). That coects the differet retur measuremet methods (TWR ad MWR). That coects the differet retur attributio methods (TWR ad MWR). That correspods to absolute profit & loss measuremet ad profit & loss attributio. Etc. Date: November Slide 10

11 Geeral framework for decomposig returs (2/2) "Odd" questios ca be better aswered usig the geeral framework for decomposig returs; icludig MWRs! The retur is positive but I lost moey - how come? The segmet retur is positive but its retur cotributio is egative - how come? Multiplyig the weights with the retur does ot lead to my absolute profit - how come? What is my o average ivested capital? Date: November Slide 11

12 Calculatio of IRR Date: November Slide 12

13 First step towards IRR attributio Calculatio of the IRR for the portfolio. Calculatio of the IRR for the bechmark => by simulatig the portfolio's cash i- ad outflows also for the bechmark. Calculatio of the excess IRR. Date: November Slide 13

14 Calculatio of the IRR for the portfolio (1/2) 0 = EMV P 1 + IRR P Y T + T 1 t=1 C P,t 1 + IRR P Y t 0 BMV P To calculate the MWR, i the idustry differet methodologies are used where all but oe are approximatio methods for the true MWR. I the followig the iteral rate of retur methodology (IRR) as the "true" MWR is used because it is ot oly the most precise method for calculatig a MWR but the oe methodology that solves the full calculatio problem. The IRR is the retur / iterest rate that causes the edig market value ad itermediate cash flows to be discouted to the begiig market value. Date: November Slide 14

15 Calculatio of the IRR for the portfolio (2/2) BMV P = Portfolio begiig market value. EMV P = Portfolio edig market value at T. IRR P = IRR of portfolio. C P,t = Portfolio cash flow at t. Y T = Legth of measuremet period (to be measured i years 365). Y t 0 = Legth of time period betwee the begiig of the measuremet period ad the date of the cash flow (to be measured i years 365). Date: November Slide 15

16 Calculatio of the IRR for the bechmark 0 = EMV B 1 + IRR B Y T + T 1 t=1 C B,t 1 + IRR B Y t 0 BMV B where: C B,t = C P,t BMV B = Bechmark begiig market value. EMV B = Bechmark edig market value at T. IRR B = IRR of bechmark. C B,t = Bechmark cash flow at t. Here it is importat that the cash iflows (outflows) are ivested (de-ivested) accordig to the actual bechmark asset allocatio at the time of the cash flow ad that the returs of the moey ivested equal the respective returs of the uderlyig bechmark ivestmets. I additio cash flows have to be simulated for rebalacig activities. Date: November Slide 16

17 Calculatio of the excess IRR EIRR P = IRR P IRR B EIRR P = Excess IRR. Date: November Slide 17

18 Cotributio to IRR Date: November Slide 18

19 Secod step towards IRR attributio Calculatio of the profit ad loss of the differet asset classes. Calculatio of the average ivested capital for the differet asset classes. Calculatio of the asset class cotributio to the IRR for the portfolio. Calculatio of the asset class cotributio to the IRR for the bechmark. Calculatio of the asset class cotributio to the excess IRR. Date: November Slide 19

20 Calculatio of the profit ad loss PL P = EMV P BMV P T 1 C P,t PL P = Profit ad loss of portfolio. t=1 T 1 PL P = PL P,i = EMV P,i BMV P,i C P,i,t t=i Same formulas apply for the bechmark PL P,i = Profit ad loss of asset class i. EMV P,i = Edig market value of asset class i. BMV P,i = Begiig market value of asset class i. C P,i,t = Cash flow of asset class i at t. = Number of asset classes. Date: November Slide 20

21 Calculatio of the average ivested capital (1/3) AIC P = PL P IRR P AIC P = Average ivested capital of portfolio. AIC P,i = PL P,i AIC P,i = Average ivested capital of asset class i. IRR P,i IRR P,i = IRR of asset class i. Basic idea: Withi the IRR framework every cash flow series ca be trasferred to a cash flow series cosistig of two cash flows - the cash iflow at the begiig of the ivestmet period ad a cash outflow at the ed of the ivestmet period. For such a cash flow series the average ivested capital is equal to the cash iflow at the begiig of the ivestmet period. Same formulas apply for the bechmark Date: November Slide 21

22 Calculatio of the average ivested capital (2a/3) = = P&L = ad IRR = 5.00% = = Compouded with cost of capital - here equals IRR * ( %) * (- 1) / ( %)^2 IRR = 5.00% Date: November Slide 22

23 Calculatio of the average ivested capital (2b/3) P&L = * (- 1) * ( %)^ / = P&L = * (- 1) * ( %)^2-1 Date: November Slide 23

24 Calculatio of the average ivested capital (2c/3) = = / ( %)^ / ( %)^ * (- 1) * ( %)^2-1 Remark: is ot the "correct" AIC for the relevat cash flow stream as the P&L is ot but istead The differece is due to the iterest costs or earigs of the iterim cash flows - here for the first period ( ad ). Iterpretatios: Oe could have eared absolute 2.14 more if where also available for ivestmet i the first period (icreasig AIC from to ). Date: November Slide 24

25 Calculatio of the average ivested capital (3/3) AIC P 1 = % 2 1 = % = AIC P 2 = % 2 1 = % = IRR 1 P = IRR 2 P PL1 P 1 AIC = PL 2 P 2 P AIC AIC P 1 = AIC 2 P PL 1 P 2 P PL P I absolute terms the average ivested capital (AIC) of the two cash flow streams (the origial ad the trasferred oe) are ot idetical but the AIC as well as the absolute profit ad loss are multiples of each other drive by the ratio betwee the differet P&L figures. Date: November Slide 25

26 Calculatio of the cotributio to the IRR for the portfolio IRR P = PL P AIC P = PL P,i AIC P = AIC P,i AIC P IRR P,i = RC P,i RC P,i = Cotributio to IRR of asset class i. It is importat to ote that the average ivested capital of the total portfolio does ot have to be equal to the sum of the average ivested capitals of all asset classes (due to the differet implicit reivestmet assumptios). AIC P or = or AIC P,i Date: November Slide 26

27 Calculatio of the cotributio to the IRR for the bechmark IRR B = PL B AIC B = PL B,i AIC B = AIC B,i AIC B IRR B,i = RC B,i RC B,i = Cotributio to IRR of asset class i. PL B = Profit ad loss of bechmark. PL B,i = Profit ad loss of asset class i. AIC B = Average ivested capital of bechmark. AIC B,i = Average ivested capital of asset class i. Date: November Slide 27

28 Calculatio of the cotributio to the excess IRR EIRR P = IRR P IRR B = RC P,i RC B,i EIRR P = AIC P,i AIC P IRR P,i AIC B,i AIC B IRR B,i = PL P,i AIC P PL B,i AIC B Date: November Slide 28

29 IRR attributio Date: November Slide 29

30 Third ad last step towards IRR attributio Here the excess IRR is decomposed accordig to the Briso, Hood ad Beebower retur attributio methodology ad therefore split up ito the asset allocatio effect, stock pickig effect ad iteractio effect. EIRR P = IRR P IRR B = AAE P + SPE P + IAE P = AAE P,i + SPE P,i + IAE P,i AAE P = Asset allocatio effect of portfolio. AAE P,i = Asset allocatio effect of asset class i. SPE P = Stock pickig effect of portfolio. SPE P,i = Stock pickig effect of asset class i. IAE P = Iteractio effect of portfolio. IAE P,i = Iteractio effect of asset class i. Date: November Slide 30

31 Asset Allocatio Actual Passive IRR Attributio Simple framework for IRR attributio (1/5) Actual Selectio Passive Quadrat IV IRR of actual portfolio Quadrat II IRR of otioal portfolio 1 => active asset allocatio portfolio Quadrat III IRR of otioal portfolio 2 => active stock pickig portfolio Quadrat I IRR of bechmark Date: November Slide 31

32 Simple framework for IRR attributio (2/5) Quadrat IV represets the IRR of the actual portfolio which reflects all passive ad active ivestmet maagemet decisios. The calculatio of the IRR of the actual portfolio is based o the actual weights of the asset classes - expressed as cash flows - ad the respective actual returs. Quadrat III represets the IRR of the otioal portfolio 2 which reflects the active stock pickig of the portfolio assumig o active asset allocatio. The calculatio of the IRR of the otioal portfolio 2 is based o the passive weights of the asset classes - expressed as cash flows - ad the respective actual returs. Quadrat II represets the IRR of the otioal portfolio 1 which reflects the active asset allocatio of the portfolio assumig o stock pickig. The calculatio of the IRR of the otioal portfolio 1 is based o the actual weights of the asset classes - expressed as cash flows - ad the respective passive idex returs. Quadrat I represets the IRR of the bechmark. The calculatio of the IRR of the bechmark is based o the passive weights of the asset classes - expressed as cash flows - ad the respective passive idex returs. Date: November Slide 32

33 Simple framework for IRR attributio (3/5) AAE P = Quadrat II Quadrat I = IRR NP1 IRR B = RC NP1,i RC B,i IRR NP1 = IRR of otioal portfolio 1. RC NP1,i = Cotributio to IRR of asset class i. SPE P = Quadrat III Quadrat I = IRR NP2 IRR B = RC NP2,i RC B,i IRR NP2 = IRR of otioal portfolio 2. RC NP2,i = Cotributio to IRR of asset class i. Date: November Slide 33

34 Simple framework for IRR attributio (4/5) IAE P = Quadrat IV Quadrat III Quadrat II + Quadrat I IAE P = IRR P IRR NP2 IRR NP1 + IRR B IAE P = RC P,i RC NP2,i RC NP1,i + RC B,i Date: November Slide 34

35 Simple framework for IRR attributio (5/5) O a asset class level: AAE P,i = RC NP1,i RC B,i SPE P,i = RC NP2,i RC B,i IAE P,i = RC P,i RC NP2,i RC NP1,i + RC B,i Date: November Slide 35

36 Hypothetical example Date: November Slide 36

37 Hypothetical example Assumptios (1/8) Sample multi-asset class portfolio is ivestig i two asset classes A ad B. Relevat bechmark is also ivestig i these two asset classes A ad B. The portfolio as well the bechmark are rebalaced o a yearly basis at the begiig of the caledar year. A two year period from util is cosidered. At the begiig of 2007 EUR 150 are ivested i the portfolio. At the begiig of 2008 additioal EUR 100 are ivested ito the portfolio accordig to the the curret active asset allocatio ad stock pickigs. Date: November Slide 37

38 Hypothetical example Retur calculatios (2a/8) Actual Portfolio (IRR) Period 1 Period 2 Dates Cash flow at begiig of period Cash flow at begiig of period Market value at the ed of period Asset A Asset B Portfolio Actual weights at begiig of period Actual weights at begiig of period Weights at the ed of period Asset A 50.0% 15.0% 13.2% Asset B 50.0% 85.0% 86.8% Portfolio 100.0% 100.0% 100.0% Actual retur Actual retur Cummulative retur Asset A 15.0% -5.0% 17.9% Asset B -5.0% 10.0% 12.4% Portfolio 5.0% 7.8% 13.8% Remark: egative (positive) cash flow meas cash iflow (outflow). Date: November Slide 38

39 Hypothetical example Retur calculatios (2b/8) Actual Portfolio (IRR) Period 1 Period 2 Dates Cash flow at begiig of period Cash flow at begiig of period Market value at the ed of period Asset A Asset B Portfolio Actual weights at begiig of period Actual weights at begiig of period Weights at the ed of period Asset A 50.0% 15.0% 13.2% Asset B 50.0% 85.0% 86.8% Portfolio 100.0% 100.0% 100.0% Actual retur Actual retur Cummulative retur Asset A 15.0% -5.0% 17.9% % 15% % = % = = Asset B -5.0% 10.0% 12.4% Portfolio 5.0% 7.8% 13.8% Remark: egative (positive) cash flow meas cash iflow (outflow). Date: November Slide 39

40 Hypothetical example Retur calculatios (3/8) Bechmark (IRR) Period 1 Period 2 Dates Cash flow at begiig of period Cash flow at begiig of period Market value at the ed of period Asset A Asset B Portfolio Passive weights at begiig of period Passive weights at begiig of period Weights at the ed of period Asset A 30.0% 30.0% 33.2% Asset B 70.0% 70.0% 66.8% Portfolio 100.0% 100.0% 100.0% Passive retur Passive retur Cummulative retur Asset A -20.0% 10.0% -2.2% Asset B 10.0% -5.0% 1.3% Portfolio 1.0% -0.5% 0.1% Remark: egative (positive) cash flow meas cash iflow (outflow). Date: November Slide 40

41 Hypothetical example Retur calculatios (4/8) Notioal Portfolio 1 (IRR) Period 1 Period 2 Dates Cash flow at begiig of period Cash flow at begiig of period Market value at the ed of period Asset A Asset B Portfolio Actual weights at begiig of period Actual weights at begiig of period Weights at the ed of period Asset A 50.0% 15.0% 17.0% Asset B 50.0% 85.0% 83.0% Portfolio 100.0% 100.0% 100.0% Passive retur Passive retur Cummulative retur Asset A -20.0% 10.0% -18.2% Asset B 10.0% -5.0% -2.0% Portfolio -5.0% -2.8% -7.0% Remark: egative (positive) cash flow meas cash iflow (outflow). Date: November Slide 41

42 Hypothetical example Retur calculatios (5/8) Notioal Portfolio 2 (IRR) Period 1 Period 2 Dates Cash flow at begiig of period Cash flow at begiig of period Ivestmet at the ed of period Asset A Asset B Portfolio Passive weights at begiig of period Passive weights at begiig of period Weights at the ed of period Asset A 30.0% 30.0% 27.0% Asset B 70.0% 70.0% 73.0% Portfolio 100.0% 100.0% 100.0% Actual retur Actual retur Cummulative retur Asset A 15.0% -5.0% 5.2% Asset B -5.0% 10.0% 8.7% Portfolio 1.0% 5.5% 7.7% Remark: egative (positive) cash flow meas cash iflow (outflow). Date: November Slide 42

43 Hypothetical example Maagemet effects (6/8) Actual Portfolio (IRR) P&L AIC IRR RC Asset A % 4.7% Asset B % 9.1% Portfolio % 13.8% Bechmark (IRR) P&L AIC IRR RC Asset A % -0.7% Asset B % 0.8% Portfolio % 0.1% Date: November Slide 43

44 Hypothetical example Maagemet effects (7/8) Notioal Portfolio 1 (IRR) P&L AIC IRR RC Asset A % -5.7% Asset B % -1.4% Portfolio % -7.0% Notioal Portfolio 2 (IRR) P&L AIC IRR RC Asset A % 1.5% Asset B % 6.2% Portfolio % 7.7% Date: November Slide 44

45 Hypothetical example Maagemet effects (8a/8) IRR-Attributio Remark: Here high IAE due to the big shifts. i the asset allocatio. AAE SPE IAE Total Asset A -4.9% 2.2% 8.1% 5.4% Asset B -2.2% 5.4% 5.2% 8.3% Portfolio -7.2% 7.6% 13.3% 13.7% Profit ad Loss Attributio Remark: IRR figures are cosistet with the absolute profit & loss figures see appedix. AAE SPE IAE Total Asset A Asset B Portfolio Date: November Slide 45

46 Hypothetical example Maagemet effects (8b/8) IRR-Attributio AAE SPE IAE Total Asset A -4.9% 2.2% 8.1% 5.4% Asset B -2.2% 5.4% 5.2% 8.3% Portfolio -7.2% 7.6% 13.3% 13.7% Profit ad Loss Attributio AAE SPE IAE Total PL NP1 PL B = = 9.9 Asset A Asset B Portfolio Date: November Slide 46

47 Simple example for a IRR implemetatio Date: November Slide 47

48 before cash flow after cash flow IRR Attributio Simple example for a IRR implemetatio (1/3) Asset allocatio i % Cash Bods Equities ' Total portfolio ' ' Cash flows Cash Bods Equities Total portfolio 1' Asset allocatio i % Cash Bods Equities ' Total portfolio 1' ' ' ' Ivestmet returs Cash -0.50% -0.50% -0.50% -0.50% Bods 3.00% 1.00% -3.00% -2.00% Equities % -8.00% 10.00% 10.00% Total portfolio -2.75% -1.51% 5.82% 6.39% Date: November Slide 48

49 Simple example for a IRR implemetatio (2/3) Remark: egative (positive) cash flow meas cash iflow (outflow). Cash flows for IRR Cash Bods Equities ' Total portfolio -1' ' Profit & Loss TWR Timig effect IRR Cotributio to IRR Cash % 0.00% -1.99% -0.17% Bods % 2.93% 1.82% 0.71% Equities % 24.01% 18.63% 9.57% Total portfolio % 2.28% 10.11% 10.11% Ivestmet Reportig based o TWR shows wodrous results: Negative TWR but absolute profit for bods ad equities. Negative TWRs for all asset classes but positive TWR for the total portfolio. Date: November Slide 49

50 Simple example for a IRR implemetatio (3/3) 30% 25% 20% 15% 10% 5% TWR Timig effect IRR 0% -5% -10% Cash Bods Equities Total portfolio Date: November Slide 50

51 Critical aspects Date: November Slide 51

52 Critical aspects Urealistic (re-)ivestmet assumptio: => explicit / realistic (re-)ivestmet assumptios (MIRR). Multiple solutios for IRR: => explicit / realistic (re-)ivestmet assumptios. IRR for bechmarks: => public market equivalet (PME) used i private equity idustry. Peer group compariso: => IRR ot desiged for peer aalysis. Risk measuremet: => IRR ot desiged for dispersio aalytics. Implied iterim asset values differ from true iterim asset value... => IRR is desiged as a average retur for the reportig period. Date: November Slide 52

53 Commets ad questios Date: November Slide 53

54 Appedix: Profit ad loss attributio Date: November Slide 54

55 Last step towards profit ad loss attributio Here the excess profit ad loss is decomposed accordig to the Briso, Hood ad Beebower retur attributio methodology ad therefore split up ito the asset allocatio effect, stock pickig effect ad iteractio effect. EPL P = PL P PL B = AAPL P + SPPL P + IAPL P = AAPL P,i + SPPL P,i + IAPL P,i AAPL P = Profit ad loss of portfolio due to asset allocatio. AAPL P,i = Profit ad loss of asset class i due to asset allocatio. SPPL P = Profit ad loss of portfolio due to stock pickig. SPPL P,i = Profit ad loss of asset class i due to stock pickig. IAPL P = Profit ad loss of portfolio due to iteractio. IAPL P,i = Profit ad loss of asset class i due to iteractio. Date: November Slide 55

56 Asset Allocatio Actual Passive IRR Attributio Simple framework for profit ad loss attributio (1/5) Actual Selectio Passive Quadrat IV P&L of actual portfolio Quadrat II P&L of otioal portfolio 1 => active asset allocatio portfolio Quadrat III P&L of otioal portfolio 2 => active stock pickig portfolio Quadrat I P&L of bechmark Date: November Slide 56

57 Simple framework for profit ad loss attributio (2/5) Quadrat IV represets the P&L of the actual portfolio which reflects all passive ad active ivestmet maagemet decisios. The calculatio of the P&L of the actual portfolio is based o the actual weights of the asset classes - expressed as cash flows - ad the respective actual returs. Quadrat III represets the P&L of the otioal portfolio 2 which reflects the active stock pickig of the portfolio assumig o active asset allocatio. The calculatio of the P&L of the otioal portfolio 2 is based o the passive weights of the asset classes - expressed as cash flows - ad the respective actual returs. Quadrat II represets the P&L of the otioal portfolio 1 which reflects the active asset allocatio of the portfolio assumig o stock pickig. The calculatio of the P&L of the otioal portfolio 1 is based o the actual weights of the asset classes - expressed as cash flows - ad the respective passive idex returs. Quadrat I represets the P&L of the bechmark. The calculatio of the P&L of the bechmark is based o the passive weights of the asset classes - expressed as cash flows - ad the respective passive idex returs. Date: November Slide 57

58 Simple framework for profit ad loss attributio (3/5) AAPL P = Quadrat II Quadrat I = PL NP1 PL B = PL NP1,i PL B,i PL NP1 = Profit ad loss of otioal portfolio 1. PL NP1,i = Profit ad loss of asset class i. SPPL P = Quadrat III Quadrat I = PL NP2 PL B = PL NP2,i PL B,i PL NP2 = Profit ad loss of otioal portfolio 2. PL NP2,i = Profit ad loss of asset class i. Date: November Slide 58

59 Simple framework for profit ad loss attributio (4/5) IAPL P = Quadrat IV Quadrat III Quadrat II + Quadrat I IAPL P = PL P PL NP2 PL NP1 + PL B IAPL P = PL P,i PL NP2,i PL NP1,i + PL B,i Date: November Slide 59

60 Simple framework for profit ad loss attributio (5/5) O a asset class level: AAPL P,i = PL NP1,i PL B,i SPPL P,i = PL NP2,i PL B,i IAPL P,i = PL P,i PL NP2,i PL NP1,i + PL B,i Date: November Slide 60

61 Refereces Date: November Slide 61

62 Refereces Determiats of Portfolio Performace ; i: Fiacial Aalysts Joural; July 1986; by G. Briso, R. Hood & G. Beebower. Measuremet ; by Bruce J. Feibel. Decomposig the Moey-Weighted Rate of Retur ; i: Joural of Performace Measuremet; Summer 2003; page 42-50; by Stefa J. ad Wolfgag Marty. Decomposig the Moey-Weighted Rate of Retur ; at the Performace Attributio Risk Maagemet 11th Aual; 5th of November 2003; by Stefa J.. Decomposig the Moey-Weighted Rate of Retur - a Update ; i: Joural of Performace Measuremet; Fall 2009; page 22-29; by Stefa J.. Date: November Slide 62

63 Cotact details ad disclaimer Date: November Slide 63

64 Cotact details Cosultig AG Weibergstrasse 28 CH Schaffhause Switzerlad Dr. Stefa Joachim Tel. +41 / 79 / stefa.illmer@iipc-ag.com Date: November Slide 64

65 Disclaimer This documet was produced by Cosultig AG (hereafter "IIPC- AG") with the greatest of care ad to the best of its kowledge ad belief. However, IIPC-AG provides o guaratee with regard to its cotet ad completeess ad does ot accept ay liability for losses which might arise from makig use of this iformatio. This documet is provided for iformatio purposes oly ad is for the exclusive use of the recipiet. It does ot costitute a offer or a recommedatio to buy or sell fiacial istrumets or bakig services. It is expressly ot iteded for persos who, due to their atioality or place of residece, are ot permitted access to such iformatio uder local law. Date: November Slide 65