Overview of Performance Attribution. Version 2.0 Date: April 2010 Produced by: Dr. Stefan J. Illmer

Transcription

1 Overvew of erformace Attrbuto Verso 2.0 Date: Aprl 200 roduced by: Dr. Stefa J. Illmer

2 Ageda (/5). Itroducto to retur attrbuto.. erformace attrbuto: the bg pcture.2. Retur attrbuto as part of performace attrbuto.3. Defto of retur attrbuto.4. urpose of retur attrbuto.5. Retur attrbuto: the bg pcture.6. Retur attrbuto: ecessary puts.7. Cotrbuto to retur: sgle perod.8. Cotrbuto to retur: example for sgle perod.9. Uderlyg decso makg process roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 2

3 Ageda (2/5).0. Cotrbuto to excess retur.. Cotrbuto to excess retur: sgle perod.2. Startg pot: example for sgle perod.3. Asset allocato effect: example for sgle perod.4. Stock pckg effect: example for sgle perod.5. Total pcture: example for sgle perod.6. Iteracto effect - does t make sese?.7. Dfferet types of sgle factor based retur attrbuto.8. quty versus fxed come retur attrbuto.9. The ssue wth mult perod aalyss.20. Dfferet types of lkg or smoothg algorthms roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 3

4 Ageda (3/5).2. Cotrbuto to excess retur: mult perod.22. Total pcture: secod example for sgle perod.23. Startg pot: example for mult perod.24. Asset allocato effect: example for mult perod.25. Stock pckg effect: example for mult perod.26. Total pcture: example for mult perod 2. Itroducto to rsk attrbuto 2.. erformace attrbuto: the bg pcture 2.2. Rsk attrbuto as part of performace attrbuto 2.3. Defto of rsk attrbuto roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 4

5 Ageda (4/5) 2.4. urpose of rsk attrbuto 2.5. Rsk attrbuto: the bg pcture 2.6. Rsk attrbuto: ecessary puts 2.7. Some bascs 2.8. CAM rsk model 2.9. Rsk attrbuto usg CAM 2.0. Dscusso of rsk attrbuto usg CAM 2.. Types of rsk attrbuto 2.2. x-ate absolute rsk attrbuto: deftos 2.3. x-ate absolute rsk attrbuto: geeral dea 2.4. x-ate absolute rsk attrbuto usg Brso, Hood, Beebower method roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 5

6 Ageda (5/5) 2.5. x-ate relatve rsk attrbuto: geeral dea 2.6. x-ate relatve rsk attrbuto usg Brso, Hood, Beebower method 3. xample for a equty retur ad rsk attrbuto 4. xample for a fxed come retur ad rsk attrbuto roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 6

7 . Itroducto to retur attrbuto roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 7

8 erformace attrbuto: the bg pcture roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 8

9 Retur attrbuto as part of performace attrbuto erformace Attrbuto Retur Attrbuto Rsk Attrbuto Groups of FT Sector Asset Allocato Basc Idustres 0.07% Cyclcal Cosumer Goods -0.2% Cyclcal Servces -0.05% Face 0.00% Geeral Idustres 0.0% Iformato Tech 0.23% No Cyclcal Cos Goods -0.28% No Cyclcal Servces -0.38% Resources -0.22% Utltes -0.3% Other Assets 0.08% Stock Selecto -0.04% 0.26% 0.00% 0.% -0.9% -0.36% -0.5% -0.3% -0.02% 0.00% Iteracto 0.0% -0.% -0.09% 0.00% -0.4% 0.06% 0.0% 0.00% 0.00% -0.0% 0.04% -0.06% -0.3% 0.% -0.22% -0.07% -0.4% 0.00% 0.0% -0.5% -0.24% -0.4% 0.09% Total -0.79% -0.52% -0.25% -.56% Total Rsk Model : Global ortfolo Bechmark Rsk Model : Global ortfolo Trackg rror Number of Securtes Total Rsk (ex-ate) 5.76% 2.35% Number of Curreces 5 0 Factor Specfc Rsk 5.53%.40% ortfolo Value 227'447'728 -Rego 2.40% 0.9% Total Rsk (ex-ate) 5.76% 5.3% - Coutry 9.06%.3% - Factor Specfc Rsk 5.53% 5.20% - Idustry 3.07% 0.72% - Stock Specfc Rsk 2.72%.83% - Fudametal.0% 0.48% Trackg rror (ex-ate) 2.35% -Currecy 4.36% 0.52% Relatve Value at Rsk R-squared 0'878' Covarace (+/-) Stock Specfc Rsk 4.93% 2.72% 0.60%.89% Beta-adjusted Rsk 5.59% 5.3% redcted Beta.02 redcted Dvded Yeld / Rato (: 2 moths) /B Rato (B: year-ed) roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 9

10 Defto of retur attrbuto (/2) Retur attrbuto s the measuremet ad quatfcato of the hstorcal as well as expected retur cotrbutos of the dvdual steps of the vestmet process as well as of the appled facal strumets. We dstgush betwee retur cotrbuto ad attrbuto, whereby retur cotrbuto s a more or less arbtrary breakdow of the retur usg a gve breakdow of the vestmet uverse ad retur attrbuto s a decso oreted decomposto of the retur. We dstgush betwee sgle factor based attrbuto ad mult factor based attrbuto where the former approach s maly used for equty ad mult asset class portfolos ad the latter approach s used maly for fxed come portfolos. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 0

11 Defto of retur attrbuto (2/2) We dstgush betwee arthmetc ad geometrc attrbuto where the former explas the excess retur as absolute proft expressed as a percetage of the tal amout vested or as a absolute retur dfferece ad the latter explas the excess retur as absolute proft expressed as a percetage of the fal value of the bechmark or as a relatve retur dfferece. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde

12 urpose of retur attrbuto. Measuremet of retur ad sources of retur. 2. xpla o what decsos the retur ad the sources of retur are based o. 3. Support of portfolo maagemet decsos. 4. Motorg the mplemetato of the vestmet strategy. 5. Objectfcato of the dscussos o returs. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 2

13 Retur attrbuto: the bg pcture Remark: I the followg we focus o the arthmetc sgle factor based attrbuto. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 3

14 Retur attrbuto: ecessary puts Weghts of the dfferet asset classes or asset segmets for the portfolo for each perod. Weghts of the dfferet asset classes or asset segmets for the bechmark for each perod. Retur of the dfferet asset classes or asset segmets for the portfolo for each perod. Retur of the dfferet asset classes or asset segmets for the bechmark for each perod. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 4

15 Cotrbuto to retur: sgle perod R CR CR w R R CR w R ortfoloretur Cotrbuto of securty Beggweght of securty portfolo Returof securty portfolo to portfoloretur R CR CR w R R CR w R Bechmarkretur Cotrbuto of securty Beggweght of securty bechmark Returof securty bechmark to bechmarkretur R R R ( CR CR ) R xcess retur roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 5

16 Cotrbuto to retur: example for sgle perod ortfolo Bechmark erformace Weght Cotrbuto erformace Weght Cotrbuto Total Cash 0.50% 0.00% 0.05% 0.0% 6.00% 0.0% 0.04% Domestc Bods.00% 22.00% 0.22% 3.00% 20.00% 0.60% -0.38% Foreg Bods 3.00% 0.00% 0.30% 2.00% 5.00% 0.30% 0.00% Domestc qutes -0.50% 7.00% -0.09% -0.0% 4.00% -0.0% -0.07% Foreg qutes 2.00% 2.00% 0.24% 4.00% 6.00% 0.64% -0.40% Mortages 5.00% 5.00% 0.25% 0.50% 3.00% 0.02% 0.24% Real state.00% 6.00% 0.6% 2.00% 20.00% 0.40% -0.24% Commodtes -2.00% 4.00% -0.48% -0.00% 4.00% -0.40% -0.08% rvate quty 2.00% 3.00% 0.06%.00%.00% 0.0% 0.05% Hedge Fuds.00%.00% 0.0% 3.00%.00% 0.03% -0.02% Total 0.73% 00.00% 0.73%.59% 00.00%.59% -0.86% Remark: Cotrbutos may be calculated for ay segmets or decso but should reflect the vestmet process. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 6

17 Uderlyg decso makg process It s commo practce to assume the followg three step decso makg process ad to decompose the excess retur accordgly. Step: Bechmark selecto (weghts of asset classes). 2. Step: Asset allocato (over- ad uderweghtg of asset classes). 3. Step: Stock pckg (over- ad uderweghtg of stocks wth asset classes). Remark: The aalyss ca be adjusted to ay decso makg process > see e.g. portfolo attrbuto. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 7

18 Cotrbuto to excess retur Asset allocato effect Cotrbuto to excess retur due to the over- ad uderweghtg of asset classes. Stock pckg effect Cotrbuto to excess retur due to the over- ad uderweghtg of stocks wth asset classes. Iteracto effect Cotrbuto to excess retur due to the over- ad uderweghtg of out- or uderperformg asset classes. Remark: Cotrbutos may be calculated for ay segmets or decso but should reflect the vestmet process. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 8

19 Cotrbuto to excess retur: sgle perod (/2) R R R R AA S IA Total Total Total R R AA AA AA AA S IA + S + S + S Total (w (R [(w + Total + IA w R w + IA IA ) R ) w ) (R Total R )] Remark: There are dfferet ways for calculatg the maagemet effects. Here the methodology of Brso, Hood ad Beebower was used. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 9

20 Cotrbuto to excess retur: sgle perod (2/2) AA Total Total asset allocato effect S Total Total stock pckg effect IA Total Total t eracto effect AA S IA R Asset allocato effect of asset class Stock pckg effect of asset class Iteracto effect of asset class xcess retur of asset class roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 20

21 Startg pot: example for sgle perod ortfolo Bechmark Maagemet ffects erformace Weght Cotrbuto erformace Weght Cotrbuto Asset allocato Stock pckg Iteracto Total Cash 0.0% 6.00% 0.0% 0.0% 6.00% 0.0% 0.00% 0.00% 0.00% 0.00% Domestc Bods 3.00% 20.00% 0.60% 3.00% 20.00% 0.60% 0.00% 0.00% 0.00% 0.00% Foreg Bods 2.00% 5.00% 0.30% 2.00% 5.00% 0.30% 0.00% 0.00% 0.00% 0.00% Domestc qutes -0.0% 4.00% -0.0% -0.0% 4.00% -0.0% 0.00% 0.00% 0.00% 0.00% Foreg qutes 4.00% 6.00% 0.64% 4.00% 6.00% 0.64% 0.00% 0.00% 0.00% 0.00% Mortages 0.50% 3.00% 0.02% 0.50% 3.00% 0.02% 0.00% 0.00% 0.00% 0.00% Real state 2.00% 20.00% 0.40% 2.00% 20.00% 0.40% 0.00% 0.00% 0.00% 0.00% Commodtes -0.00% 4.00% -0.40% -0.00% 4.00% -0.40% 0.00% 0.00% 0.00% 0.00% rvate quty.00%.00% 0.0%.00%.00% 0.0% 0.00% 0.00% 0.00% 0.00% Hedge Fuds 3.00%.00% 0.03% 3.00%.00% 0.03% 0.00% 0.00% 0.00% 0.00% Total.59% 00.00%.59%.59% 00.00%.59% 0.00% 0.00% 0.00% 0.00% Remark: Here o bets, everythg s dexed. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 2

22 Asset allocato effect: example for sgle perod ortfolo Bechmark Maagemet ffects erformace Weght Cotrbuto erformace Weght Cotrbuto Asset allocato Stock pckg Iteracto Total Cash 0.0% 0.00% 0.0% 0.0% 6.00% 0.0% 0.00% 0.00% 0.00% 0.00% Domestc Bods 3.00% 22.00% 0.66% 3.00% 20.00% 0.60% 0.06% 0.00% 0.00% 0.06% Foreg Bods 2.00% 0.00% 0.20% 2.00% 5.00% 0.30% -0.0% 0.00% 0.00% -0.0% Domestc qutes -0.0% 7.00% -0.02% -0.0% 4.00% -0.0% 0.00% 0.00% 0.00% 0.00% Foreg qutes 4.00% 2.00% 0.48% 4.00% 6.00% 0.64% -0.6% 0.00% 0.00% -0.6% Mortages 0.50% 5.00% 0.03% 0.50% 3.00% 0.02% 0.0% 0.00% 0.00% 0.0% Real state 2.00% 6.00% 0.32% 2.00% 20.00% 0.40% -0.08% 0.00% 0.00% -0.08% Commodtes -0.00% 4.00% -0.40% -0.00% 4.00% -0.40% 0.00% 0.00% 0.00% 0.00% rvate quty.00% 3.00% 0.03%.00%.00% 0.0% 0.02% 0.00% 0.00% 0.02% Hedge Fuds 3.00%.00% 0.03% 3.00%.00% 0.03% 0.00% 0.00% 0.00% 0.00% Total.34% 00.00%.34%.59% 00.00%.59% -0.25% 0.00% 0.00% -0.25% Remark: Here portfolo returs equals the bechmark retur. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 22

23 Stock pckg effect: example for sgle perod ortfolo Bechmark Maagemet ffects erformace Weght Cotrbuto erformace Weght Cotrbuto Asset allocato Stock pckg Iteracto Total Cash 0.50% 6.00% 0.03% 0.0% 6.00% 0.0% 0.00% 0.02% 0.00% 0.02% Domestc Bods.00% 20.00% 0.20% 3.00% 20.00% 0.60% 0.00% -0.40% 0.00% -0.40% Foreg Bods 3.00% 5.00% 0.45% 2.00% 5.00% 0.30% 0.00% 0.5% 0.00% 0.5% Domestc qutes -0.50% 4.00% -0.07% -0.0% 4.00% -0.0% 0.00% -0.06% 0.00% -0.06% Foreg qutes 2.00% 6.00% 0.32% 4.00% 6.00% 0.64% 0.00% -0.32% 0.00% -0.32% Mortages 5.00% 3.00% 0.5% 0.50% 3.00% 0.02% 0.00% 0.4% 0.00% 0.4% Real state.00% 20.00% 0.20% 2.00% 20.00% 0.40% 0.00% -0.20% 0.00% -0.20% Commodtes -2.00% 4.00% -0.48% -0.00% 4.00% -0.40% 0.00% -0.08% 0.00% -0.08% rvate quty 2.00%.00% 0.02%.00%.00% 0.0% 0.00% 0.0% 0.00% 0.0% Hedge Fuds.00%.00% 0.0% 3.00%.00% 0.03% 0.00% -0.02% 0.00% -0.02% Total 0.83% 00.00% 0.83%.59% 00.00%.59% 0.00% -0.76% 0.00% -0.76% Remark: Here portfolo weghts equals bechmark weghts. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 23

24 Total pcture: example for sgle perod ortfolo Bechmark Maagemet ffects erformace Weght Cotrbuto erformace Weght Cotrbuto Asset allocato Stock pckg Iteracto Total Cash 0.50% 0.00% 0.05% 0.0% 6.00% 0.0% 0.00% 0.02% 0.02% 0.04% Domestc Bods.00% 22.00% 0.22% 3.00% 20.00% 0.60% 0.06% -0.40% -0.04% -0.38% Foreg Bods 3.00% 0.00% 0.30% 2.00% 5.00% 0.30% -0.0% 0.5% -0.05% 0.00% Domestc qutes -0.50% 7.00% -0.09% -0.0% 4.00% -0.0% 0.00% -0.06% -0.0% -0.07% Foreg qutes 2.00% 2.00% 0.24% 4.00% 6.00% 0.64% -0.6% -0.32% 0.08% -0.40% Mortages 5.00% 5.00% 0.25% 0.50% 3.00% 0.02% 0.0% 0.4% 0.09% 0.24% Real state.00% 6.00% 0.6% 2.00% 20.00% 0.40% -0.08% -0.20% 0.04% -0.24% Commodtes -2.00% 4.00% -0.48% -0.00% 4.00% -0.40% 0.00% -0.08% 0.00% -0.08% rvate quty 2.00% 3.00% 0.06%.00%.00% 0.0% 0.02% 0.0% 0.02% 0.05% Hedge Fuds.00%.00% 0.0% 3.00%.00% 0.03% 0.00% -0.02% 0.00% -0.02% Total 0.73% 00.00% 0.73%.59% 00.00%.59% -0.25% -0.76% 0.4% -0.86% Remark: Maagemet effects should reflect the vestmet process. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 24

25 Iteracto effect - does t make sese? Iteracto effect s ot a "rest" term whch ca ot be assged to a specfc maagemet decso. Iteracto effect s the result of the "teracto" of more tha oe decso. I case of a herarchcal vestmet process the teracto effect may be assged to a specfc maagemet decso. Depedg o the aalytcs software the teracto effect may be assged to a specfc maagemet decso or smoothed by default - but ths may lead to mss-terpretatos. Remark: Hadlg of teracto effect should reflect the vestmet process. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 25

26 Dfferet types of sgle factor based retur attrbuto Sgle factor based retur attrbuto methods dffer wth respect to the way the excess retur s decomposed, for example: Brso ad Fachler > opportuty costs cosdered f calculatg the asset allocato effect. Brso, Hood ad Beebower > opportuty cost of 0% cosdered f calculatg the asset allocato effect. Karosky ad Sger > troducg currecy selecto ad rsk premum. etc. Remark: Retur attrbuto methodology should reflect the vestmet process. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 26

27 quty versus fxed come retur attrbuto "quty retur attrbuto" s maly doe for equty ad mult asset class portfolos usg a sgle factor based retur attrbuto method because here the explaatory accuracy of mult factor based retur attrbuto methods are lmted, the vestmet process s more herarchcal ad the dvdual steps of the vestmet process are more depedet from each other. "Fxed come retur attrbuto" s maly doe for fxed come portfolos usg a mult factor based retur attrbuto method because of the hgh explaatory accuracy ad because the depedeces betwee the dfferet factors may be very relevat for the fdgs of the performace aalyss. Remark: "quty retur attrbuto" s also applcable to fxed come portfolos but t eeds a dfferet terpretato. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 27

28 The ssue wth mult perod aalyss (/2) If cosderg more tha oe reportg perod oe has to aggregate the dfferet retur cotrbutos of the dfferet perods to get the retur cotrbutos for the total perod. The ssue s that the addto of the retur cotrbutos of the dfferet sub-perods do ot add up wth the retur cotrbuto for the total perod because the compoudg effect (ter-temporary cross-product) would be mssg. There s o commo way of compoudg the maagemet effects of the sub-perods ad therefore dfferet aalytcs softwares mght come up wth dfferet results. Remark: If usg geometrcal retur cotrbuto / attrbuto there s o ssue wth the ter-temporary cross-product. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 28

29 The ssue wth mult perod aalyss (2/2) erod ortfolo Bechmark xcess 5.00% 3.00% 2.00% % 3.00% 2.00% % 3.00% 2.00% % 3.00% 2.00% % 3.00% 2.00% % 3.00% 2.00% % 3.00% 2.00% % 3.00% 2.00% % 3.00% 2.00% Compoudg 5.5% Total 55.3% 30.48% 24.66% roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 29

30 Dfferet types of lkg or smoothg algorthms There s a bg debate the dustry o how to lk the sub-perod cotrbutos or o how to smooth the ter-temporary cross-product. Below are examples for curretly used algorthms: by Davd R. Carño by Jose G. Mechero by Adrew S. B. Frogello by GRA (Groupe de Recherche e Attrbuto de erformace) by Bruce J. Febel etc. Remark: Lkg or smoothg algorthms have o lk to the decso makg process ad therefore o ecoomcal terpretato. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 30

31 Cotrbuto to excess retur: mult perod (/2) Mult-perod cotrbuto [pror cumulated cotrbuto x ( + bechmark retur curret perod)] + [curret perod cotrbuto x ( + pror cumulated portfolo retur)] > Referece for the lkg approach: Ivestmet erformace Measuremet ; by Bruce J. Febel RM RM T AAM SM IAM T Total T Total T Total T RM AAM AAM SM IAM T Total T Total T Total T Total T ( + R ) + R ( + RM ) T + SM Total ( + RT ) + AAT ( + RMT ) Total ( + RT ) + ST ( + RMT ) Total ( + R ) + IA ( + RM ) T Total T T + IAM T T Total T T roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 3

32 Cotrbuto to excess retur: mult perod (2/2) R RM AA AAM S SM IA IAM RM R T T Total T Total T Total T Total T Total T Total T T T xcess retur for subperod T Cumulated excess retur utl T Total asset allocato effect for subperod T Cumulated asset allocato effect utl T Total stock pckg effect for subperod T Cumulated total stock pckg effect utl T Total teracto effect for subperod T Cumulated total teracto effect utl T Cumulated portfolo retur utl T Bechmark retur for subperod T roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 32

33 Total pcture: secod example for sgle perod ortfolo Bechmark Maagemet ffects erformace Weght Cotrbuto erformace Weght Cotrbuto Asset allocato Stock pckg Iteracto Total Lqudtät 0.50% 0.00% 0.05% 0.0% 6.00% 0.0% 0.00% 0.02% 0.02% 0.04% Oblgatoe CHF.50% 22.00% 0.33% 0.50% 20.00% 0.0% 0.0% 0.20% 0.02% 0.23% Oblgatoe Fremdwähruge 3.00% 0.00% 0.30% 4.50% 5.00% 0.68% -0.23% -0.23% 0.08% -0.38% Akte Schwez 2.00% 7.00% 0.34% 2.50% 4.00% 0.35% 0.08% -0.07% -0.02% -0.0% Akte Auslad 0.50% 2.00% 0.06% -2.00% 6.00% -0.32% 0.08% 0.40% -0.0% 0.38% Hypotheke 0.50% 5.00% 0.03% 0.50% 3.00% 0.02% 0.0% 0.00% 0.00% 0.0% Immoble 2.00% 6.00% 0.32%.50% 20.00% 0.30% -0.06% 0.0% -0.02% 0.02% Rohstoffe 6.00% 4.00% 0.24% 3.00% 4.00% 0.2% 0.00% 0.2% 0.00% 0.2% rvate quty 2.00% 3.00% 0.06% 0.50%.00% 0.0% 0.0% 0.02% 0.03% 0.06% Hedge Fuds.00%.00% 0.0% -.50%.00% -0.02% 0.00% 0.03% 0.00% 0.03% Total.74% 00.00%.74%.24% 00.00%.24% -0.0% 0.59% 0.0% 0.50% Remark: Maagemet effects should reflect the vestmet process. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 33

34 Startg pot: example for mult perod ortfolo Bechmark Maagemet ffects erformace Weght Cotrbuto erformace Weght Cotrbuto Asset allocato Stock pckg Iteracto Total Cash 0.20% 6.00% 0.0% 0.20% 6.00% 0.0% 0.00% 0.00% 0.00% 0.00% Domestc Bods 3.52% 20.00% 0.7% 3.52% 20.00% 0.7% 0.00% 0.00% 0.00% 0.00% Foreg Bods 6.59% 5.00% 0.98% 6.59% 5.00% 0.98% 0.00% 0.00% 0.00% 0.00% Domestc qutes 2.40% 4.00% 0.34% 2.40% 4.00% 0.34% 0.00% 0.00% 0.00% 0.00% Foreg qutes.92% 6.00% 0.33%.92% 6.00% 0.33% 0.00% 0.00% 0.00% 0.00% Mortages.00% 3.00% 0.03%.00% 3.00% 0.03% 0.00% 0.00% 0.00% 0.00% Real state 3.53% 20.00% 0.70% 3.53% 20.00% 0.70% 0.00% 0.00% 0.00% 0.00% Commodtes -7.30% 4.00% -0.28% -7.30% 4.00% -0.28% 0.00% 0.00% 0.00% 0.00% rvate quty.5%.00% 0.02%.5%.00% 0.02% 0.00% 0.00% 0.00% 0.00% Hedge Fuds.46%.00% 0.02%.46%.00% 0.02% 0.00% 0.00% 0.00% 0.00% Total 2.84% 00.00% 2.84% 2.84% 00.00% 2.84% 0.00% 0.00% 0.00% 0.00% Remark: Here o bets, everythg s dexed. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 34

35 Asset allocato effect: example for mult perod ortfolo Bechmark Maagemet ffects erformace Weght Cotrbuto erformace Weght Cotrbuto Asset allocato Stock pckg Iteracto Total Cash 0.20% 0.00% 0.02% 0.20% 6.00% 0.0% 0.0% 0.00% 0.00% 0.0% Domestc Bods 3.52% 22.00% 0.78% 3.52% 20.00% 0.7% 0.07% 0.00% 0.00% 0.07% Foreg Bods 6.59% 0.00% 0.65% 6.59% 5.00% 0.98% -0.33% 0.00% 0.00% -0.33% Domestc qutes 2.40% 7.00% 0.4% 2.40% 4.00% 0.34% 0.07% 0.00% 0.00% 0.07% Foreg qutes.92% 2.00% 0.25%.92% 6.00% 0.33% -0.08% 0.00% 0.00% -0.08% Mortages.00% 5.00% 0.05%.00% 3.00% 0.03% 0.02% 0.00% 0.00% 0.02% Real state 3.53% 6.00% 0.56% 3.53% 20.00% 0.70% -0.4% 0.00% 0.00% -0.4% Commodtes -7.30% 4.00% -0.28% -7.30% 4.00% -0.28% 0.00% 0.00% 0.00% 0.00% rvate quty.5% 3.00% 0.05%.5%.00% 0.02% 0.03% 0.00% 0.00% 0.03% Hedge Fuds.46%.00% 0.02%.46%.00% 0.02% 0.00% 0.00% 0.00% 0.00% Total 2.49% 00.00% 2.49% 2.84% 00.00% 2.84% -0.35% 0.00% 0.00% -0.35% Remark: Here portfolo returs equals the bechmark retur. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 35

36 Stock pckg effect: example for mult perod ortfolo Bechmark Maagemet ffects erformace Weght Cotrbuto erformace Weght Cotrbuto Asset allocato Stock pckg Iteracto Total Cash.00% 6.00% 0.06% 0.20% 6.00% 0.0% 0.00% 0.05% 0.00% 0.05% Domestc Bods 2.52% 20.00% 0.50% 3.52% 20.00% 0.7% 0.00% -0.20% 0.00% -0.20% Foreg Bods 6.09% 5.00% 0.9% 6.59% 5.00% 0.98% 0.00% -0.08% 0.00% -0.08% Domestc qutes.49% 4.00% 0.2% 2.40% 4.00% 0.34% 0.00% -0.3% 0.00% -0.3% Foreg qutes 2.5% 6.00% 0.4%.92% 6.00% 0.33% 0.00% 0.08% 0.00% 0.08% Mortages 5.53% 3.00% 0.7%.00% 3.00% 0.03% 0.00% 0.4% 0.00% 0.4% Real state 3.02% 20.00% 0.60% 3.53% 20.00% 0.70% 0.00% -0.0% 0.00% -0.0% Commodtes -6.72% 4.00% -0.25% -7.30% 4.00% -0.28% 0.00% 0.04% 0.00% 0.04% rvate quty 4.04%.00% 0.04%.5%.00% 0.02% 0.00% 0.03% 0.00% 0.03% Hedge Fuds 2.0%.00% 0.02%.46%.00% 0.02% 0.00% 0.00% 0.00% 0.00% Total 2.67% 00.00% 2.67% 2.84% 00.00% 2.84% 0.00% -0.7% 0.00% -0.7% Remark: Here portfolo weghts equals bechmark weghts. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 36

37 Total pcture: example for mult perod ortfolo Bechmark Maagemet ffects erformace Weght Cotrbuto erformace Weght Cotrbuto Asset allocato Stock pckg Iteracto Total Lqudtät.00% 0.00% 0.0% 0.20% 6.00% 0.0% 0.0% 0.05% 0.03% 0.09% Oblgatoe CHF 2.52% 22.00% 0.55% 3.52% 20.00% 0.7% 0.07% -0.20% -0.02% -0.5% Oblgatoe Fremdwähruge 6.09% 0.00% 0.6% 6.59% 5.00% 0.98% -0.33% -0.07% 0.02% -0.38% Akte Schwez.49% 7.00% 0.25% 2.40% 4.00% 0.34% 0.07% -0.3% -0.03% -0.08% Akte Auslad 2.5% 2.00% 0.30%.92% 6.00% 0.33% -0.08% 0.08% -0.02% -0.02% Hypotheke 5.53% 5.00% 0.28%.00% 3.00% 0.03% 0.02% 0.4% 0.09% 0.25% Immoble 3.02% 6.00% 0.48% 3.53% 20.00% 0.70% -0.4% -0.0% 0.02% -0.22% Rohstoffe -6.72% 4.00% -0.25% -7.30% 4.00% -0.28% 0.00% 0.04% 0.00% 0.04% rvate quty 4.04% 3.00% 0.2%.5%.00% 0.02% 0.03% 0.03% 0.05% 0.% Hedge Fuds 2.0%.00% 0.02%.46%.00% 0.02% 0.00% 0.00% 0.00% 0.00% Total 2.47% 00.00% 2.47% 2.84% 00.00% 2.84% -0.35% -0.7% 0.5% -0.37% Remark: Maagemet effects should reflect the vestmet process. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 37

38 2. Itroducto to rsk attrbuto roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 38

39 erformace attrbuto: the bg pcture roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 39

40 Rsk attrbuto as part of performace attrbuto erformace Attrbuto Retur Attrbuto Rsk Attrbuto Groups of FT Sector Asset Allocato Basc Idustres 0.07% Cyclcal Cosumer Goods -0.2% Cyclcal Servces -0.05% Face 0.00% Geeral Idustres 0.0% Iformato Tech 0.23% No Cyclcal Cos Goods -0.28% No Cyclcal Servces -0.38% Resources -0.22% Utltes -0.3% Other Assets 0.08% Stock Selecto -0.04% 0.26% 0.00% 0.% -0.9% -0.36% -0.5% -0.3% -0.02% 0.00% Iteracto 0.0% -0.% -0.09% 0.00% -0.4% 0.06% 0.0% 0.00% 0.00% -0.0% 0.04% -0.06% -0.3% 0.% -0.22% -0.07% -0.4% 0.00% 0.0% -0.5% -0.24% -0.4% 0.09% Total -0.79% -0.52% -0.25% -.56% Total Rsk Model : Global ortfolo Bechmark Rsk Model : Global ortfolo Trackg rror Number of Securtes Total Rsk (ex-ate) 5.76% 2.35% Number of Curreces 5 0 Factor Specfc Rsk 5.53%.40% ortfolo Value 227'447'728 -Rego 2.40% 0.9% Total Rsk (ex-ate) 5.76% 5.3% - Coutry 9.06%.3% - Factor Specfc Rsk 5.53% 5.20% - Idustry 3.07% 0.72% - Stock Specfc Rsk 2.72%.83% - Fudametal.0% 0.48% Trackg rror (ex-ate) 2.35% -Currecy 4.36% 0.52% Relatve Value at Rsk R-squared 0'878' Covarace (+/-) Stock Specfc Rsk 4.93% 2.72% 0.60%.89% Beta-adjusted Rsk 5.59% 5.3% redcted Beta.02 redcted Dvded Yeld / Rato (: 2 moths) /B Rato (B: year-ed) roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 40

41 Defto of rsk attrbuto Rsk attrbuto s the measuremet ad quatfcato of the hstorcal as well as expected rsk cotrbutos of the dvdual steps of the vestmet process as well as of the appled facal strumets. We dstgush betwee rsk cotrbuto ad attrbuto, whereby rsk cotrbuto s a more or less arbtrary breakdow of the rsk usg a gve breakdow of the vestmet uverse ad rsk attrbuto s a decso oreted decomposto of the rsk. We dstgush betwee sgle factor based attrbuto ad mult factor based attrbuto where the former approach s maly used for mult asset class portfolos ad the latter approach s used maly for equty ad fxed come portfolos. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 4

42 urpose of rsk attrbuto. Idetfcato of rsks. 2. Measuremet of rsk ad sources of rsk. 3. xpla o what decsos the rsk ad the sources of rsk are based o. 4. Support of portfolo maagemet decsos. 5. Motorg the mplemetato of the vestmet strategy. 6. Objectfcato of the dscussos o rsk. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 42

43 Rsk attrbuto: the bg pcture Rsk attrbuto Sgle factor based attrbuto Mult factor based attrbuto Weghts ad covaraces of segmets Factor exposures ad factor covaraces Remark: I the followg we focus o sgle factor based attrbuto. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 43

44 Rsk attrbuto: ecessary puts Weghts of the dfferet asset classes or asset segmets for the portfolo for the relevat perod. Weghts of the dfferet asset classes or asset segmets for the bechmark for the relevat perod. stmated covaraces betwee asset classes or asset segmets for the portfolo ad the bechmark for the relevat perod. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 44

45 Some bascs (/3) The absolute rsk of a portfolo s ofte estmated, measured or expressed usg the statstcal measure varace (or volatlty). σ 2 2 [ ] or σ( R ) R ( R ) ( R ) ( R ( R )) ( ) 2 Varace s easy to terpret, s measured uts of retur ad s easy to estmate. Ofte t s assumed that returs are logormal dstrbuted ad therefore that the varace ca be best estmated usg the ubased estmator. σ 2 2 ( R ) ( R R) or σ( R ) ( R R) 2 roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 45

46 roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 46 Sce covaraces are addtve the rsk of a portfolo ca easly be decomposed. For rsk attrbuto oly varaces ca be used ad f returs are ot ucorrelated a lot of covaraces have to be decomposed whch ca ot be assged clearly. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) j j j j j j 2 R R,R R Correl w w R w R,R Cov R w w R w R,R Cov R w w R R w R j j j j j j σ σ + σ σ + σ σ σ Some bascs (2/3)

47 Some bascs (3/3) Relatve rsk s ofte estmated, measured or expressed usg the statstcal measure trackg error,.e. the varace (volatlty) of the excess returs of the portfolo versus the bechmark, ad ca easly be decomposed. R R σ σ 2 2 R 2 ( R) σ ( R R ) 2 2 ( R) σ ( R ) + σ ( R ) 2 Cov( R,R ) Rsk models ofte are desged usg the CAM- ad ATtheory, of course other types of rsk models are also used. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 47

48 roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 48 CAM rsk model CAM based rsk model (hstorcal securtes weghts ad securtes returs). ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) σ σ σ + σ σ 2 2 T 2 j j j j w.... w R....,R R Cov ,R R Cov.... R w.... w R,R R Cov w w R w R R w R

49 roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 49 Decomposg the absolute rsk for predefed segmets "k", e.g. assets, asset classes, sectors, styles, durato buckets, etc. Decomposg the relatve rsk follows the same procedure as descrbed before. > How does factor "k" cotrbute to the absolute or relatve rsk? Rsk attrbuto usg CAM ( ) ( ) ( ) ( ) + σ σ m k k k k m k 2 2 k 2 m k k k k k k k k,r R Cov w w R w R R w R

50 Dscusso of rsk attrbuto usg CAM stmato of lots of covaraces. Avalablty of log tme seres for all securtes. Itegrato of ew securtes s dffcult. "Slce ad dce" decomposto s ot possble,.e. rsk attrbuto has be redesged f chagg perspectve. "Look through" rsk decomposto s ot possble. Fracto of the o-assgable covaraces ca be substatal. Radom dstrbuted covaraces have ormally o ecoomcal value. Neglect of mportat rsk factors, aalyss s ofte data drve. Smple rsk model whch s ormally easy to estmate. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 50

51 Types of rsk attrbuto Rsk attrbuto x-post aalyss x-ate aalyss Absolute rsk Decomposto of volatlty ad excess volatlty Relatve rsk Decomposto of trackg error Absolute rsk attrbuto Relatve rsk attrbuto roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 5

52 x-ate rsk attrbuto: deftos x-ate absolute rsk s measured usg the varace x-ate excess rsk s measured usg the varace (varace tackg error) x-ate absolute excess rsk dfferece betwee the absolute rsk of two portfolos x-ate relatve excess rsk Varace (varace trackg error) of the retur dffereces of two portfolos Remark: Also other rsk fgures lke VaR ca be decomposed. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 52

53 x-ate absolute rsk attrbuto: geeral dea Step : Calculate the absolute rsk for the portfolo ad for the bechmark ad aalyze the dvdual fgures ad ther dfferece. Step 2: Furthermore decompose the fgures accordg to maagemet actvtes or/ad asset classes. [ w K w ] w [ w K w ] Cov M w Cov w M w Cov Cov xpected cov arace xpected cov arace matrx matrx for for portfolo bechmark roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 53

54 x-ate absolute rsk attrbuto usg the Brso, Hood, Beebower method (/4) Absolute excess rsk absolute rsk of portfolo - absolute rsk of bechmark R A R A w j R A w j Cov (, j) w w Cov (, j) j j Absolute excess rsk rsk cotrbuto due to asset allocato + rsk cotrbuto due to stock pckg + rsk cotrbuto due to teracto R R + R + R A AA A S A IA A roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 54

55 x-ate absolute rsk attrbuto usg the Brso, Hood, Beebower method (2/4) Absolute excess rsk cotrbuto due to asset allocato R AA A j [( w w ) ( w w )] Cov (, j) j j Absolute excess rsk cotrbuto due to stock pckg R S A w j w j [ Cov (, j) Cov (, j) ] Absolute excess rsk cotrbuto due to teracto R IA A j [( w w ) ( w w )] [ Cov (, j) Cov (, j) ] j j roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 55

56 x-ate absolute rsk attrbuto usg the Brso, Hood, Beebower method (3/4) Absolute excess rsk cotrbuto due to asset allocato for asset class R AA A () [ ( w w ) ( w w )] Cov (, j) j j j Absolute excess rsk cotrbuto due to stock pckg for asset class R S A [ ] () w w Cov (, j) Cov (, j) j j roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 56

57 x-ate absolute rsk attrbuto usg the Brso, Hood, Beebower method (4/4) Absolute excess rsk cotrbuto due to teracto for asset class R IA A () [ ( w w ) ( w w )] [ Cov (, j) Cov (, j) ] j j > assumg dstrbuted covaraces by rows j roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 57

58 roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 58 [ ],, w w w w Cov Cov Cov Cov w w w w M M K K Step : Geerate a log/short portfolo where the log posto cossts of the portfolo ad the short posto s the correspodg bechmark. Step 2: Calculate ad aalyse the absolute rsk for ths log/short portfolo. Step 3: Furthermore decompose the fgures accordg to maagemet actvtes or/ad asset classes. x-ate relatve rsk attrbuto: geeral dea

59 x-ate relatve rsk attrbuto usg the Brso, Hood, Beebower method (/5) Relatve rsk trackg error of the portfolo versus the bechmark absolute rsk of portfolo + absolute rsk of bechmark - dversfcato effect portfolo versus bechmark R R T R w j ( ;B) + R w D Cov ( ;B) or matrx otato Cov, (, j) + w w Cov (, j) 2 w w Cov (, j) w, Cov Cov w [ w w ] ( 2 2 matrx) ; for,..., A A j, j Cov B j j j roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 59

60 x-ate relatve rsk attrbuto usg the Brso, Hood, Beebower method (2/5) Relatve rsk relatve rsk cotrbuto due to asset allocato + relatve rsk cotrbuto due to stock pckg + relatve rsk cotrbuto due to teracto R R + R + R R AA R S R IA R roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 60

61 x-ate relatve rsk attrbuto usg the Brso, Hood, Beebower method (3/5) Relatve rsk cotrbuto due to asset allocato R AA R 0 j, ( w w ) ( Cov (, j) + Cov (, j) 2 Cov (, j) ) (, j) + ( w w ) ( w w ) Cov (, j) 0 0 Cov j j 2 0 J, ( w w ) Cov (, j) j ( w w ) ( w w ) Cov (, j) or matrx otato j j, 0 Cov Cov [ 0 w w ] ( 2 2 matrx ) Cov Cov w w [ w w ] [ Cov (, j) ] [ w w ] ( matrx) ; for,...,, ; for,..., roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 6

62 x-ate relatve rsk attrbuto usg the Brso, Hood, Beebower method (4/5) Relatve rsk cotrbuto due to stock pckg R S R 2 w w w w Cov (, j) + w w Cov (, j) w w Cov j j j j J j j (, j), ( Cov (, j) + Cov (, j) 2 Cov (, j) ), j or matrx otato Cov w, Cov Cov w [ w w ] ( 2 2 matrx) ; for,...,, Cov roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 62

63 x-ate relatve rsk attrbuto usg the Brso, Hood, Beebower method (5/5) Relatve rsk cotrbuto due to teracto R IA R R R R R [ w w ] [ 0 w w ] Cov Cov Cov Cov Cov Cov Cov Cov Cov w, Cov Cov w [ w w ] ; for,..., AA R S R,,, Cov, w w Relatve rsk cotrbuto due to maagemet actvtes for asset class by summg up all covaraces for the row, w 0 w roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 63

64 3. xample for a equty retur ad rsk attrbuto roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 64

65 xample for a equty retur ad rsk attrbuto (/6) ortfolo Retur Attrbuto ffects Attrbuto by MSCI Sector Attrbuto by 5 World Regos NAM (ID) Composte World MSCI, actve, madates Currecy CHF Asset Allocato -0.96% -.0% M AM Retur ortfolo 8.28% Stock Selecto 0.3% -0.59% BNCHMARK MSCI World CHF Retur Bechmark 9.60% Iteracto -0.49% 0.28% RIOD Retur Relatve -.32% Total -.32% -.32% (Average over-/uderweght) Attrbuto Aalyss - by MSCI Sector.5%.5% Asset Allocato Stock Selecto.0%.0% 0.5% 0.5% 0.0% 0.0% -0.5% -0.5% -.0% -.0% -.5% Cosumer Dscretoary Cosumer Staples ergy Facals Health Care Idustrals Iformato Techology Materals Telecomm Servces Utltes Cash -.5% Cosumer Dscretoary Cosumer Staples ergy Facals Health Care Idustrals Iformato Techology Materals Telecomm Servces Utltes Cash Total Rsk Aalyss (ed perod) ortfolo Bechmark Attrbuto Aalyss - by 5 World Regos Number of Securtes 67 '550 Number of Curreces 8 0 ortfolo Value 84'334'09 Total Rsk (ex-ate) 8.8% 8.2% - Factor Specfc Rsk 8.66% 8.8% - Stock Specfc Rsk 2.39%.02% Trackg rror (ex-ate) 2.57% Value at Rsk (at 95%) 3'570'469 R-squared 0.98 Beta-adjusted Rsk 8.64% 8.2% redcted Beta.02 redcted Dvded Yeld / Rato (: 2 moths) /B Rato (B: year-ed) % 0.4% 0.2% 0.0% -0.2% -0.4% -0.6% -0.8% -.0% -.2% Asset Allocato Stock Selecto Asa ex Japa urope Japa North Amerca Cash Total Importat Remark: Dffereces betwee attrbuto returs ad the returs of the offcal performace measuremet tool are usual. They ca be explaed by the two systems usg two dfferet methodologes ad by traday tradg gas or losses. Above fgures are subject to future chages. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 65

66 xample for a equty retur ad rsk attrbuto (2/6) by MSCI Sector Average Average Relatve Absolute Absolute Dfferece Dfferece F Weght Weght Weght F Retur Retur F- - Tot Cosumer Dscretoary 2.03% 2.8% -0.5% 5.58% 23.07% -7.49% 3.47% Cosumer Staples 8.83% 9.26% -0.43% 7.74% 5.09% 2.65% -4.5% ergy 8.29% 7.4% 0.88% 0.5% 3.30% -2.79% -6.30% Facals 2.70% 22.94% -.24% 23.90% 24.94% -.04% 5.34% Health Care.73% 2.53% -0.80% 9.60% 7.3% 2.29% -2.30% Idustrals 0.45% 9.7% 0.74% 34.93% 24.08% 0.85% 4.48% Iformato Techology 2.33% 2.49% -0.6% 25.06% 32.79% -7.73% 3.9% Materals 4.84% 4.53% 0.3% 23.% 30.33% -7.22% 0.73% Telecomm Servces 6.5% 5.24% 0.9% 5.02% 2.64% 2.38% -6.96% Utltes 2.44% 3.72% -.28% 34.09% 5.45% 8.64% -4.5% Cash.2% 0.00%.2% 8.94% 0.00% 8.94% -9.60% Total 00.00% 00.00% 0.00% 8.28% 9.60% -.32% 0.00% Import remarks: - The weght umbers gves a overvew of the average weght vested the dfferet groups (e.g. sectors) wth daly weghts averaged over the chose perod. - The absolute retur umbers gve a overvew of the group's absolute performace (e.g. sector) wth thc chose tme perod (portfolo ad bechmark) - The dfferece F- compares the group's performace of the portfolo to the group's performace the bechmark wth the chose tme perod. - The dfferece - Tot compares the group's performace the bechmark wth the performace of the total bechmark wth the chose tme perod. lease ote that cash s cluded the relevat coutry or regoal groups ad show as "other assets" else (e.g. sectors). Cocerg dervatves, oly futures are splt up at the momet; dervatves (call or put optos) are ot yet cluded. Moreover, llqud securtes as prvate placemets are ot yet take to accout. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 66

67 xample for a equty retur ad rsk attrbuto (3/6) by MSCI Sector Asset Allocato Cosumer Dscretoary 0.00% Cosumer Staples 0.05% ergy 0.00% Facals -0.0% Health Care 0.20% Idustrals -0.04% Iformato Techology -0.2% Materals 0.0% Telecomm Servces -0.% Utltes 0.02% Cash -0.78% Total -0.96% Stock Selecto -0.86% 0.28% -0.9% -0.2% 0.35% 0.99% -0.9% -0.28% 0.2% 0.74% 0.00% 0.3% Iteracto -0.03% 0.03% -0.02% 0.0% -0.03% 0.2% 0.0% -0.08% -0.08% -0.4% 0.00% -0.49% Total -0.89% 0.36% -0.2% -0.30% 0.52%.07% -.% -0.35% 0.02% 0.35% -0.78% -.32% Import remarks: Asset Allocato ffect s the porto of portfolo excess retur that s attrbutable to takg dfferet group bets from the bechmark. A overweght of a group (e.g. SI sector "Chemcals" ) that outperforms the whole bechmark (e.g. SI) wll geerate a postve asset allocato effect. Securty Selecto ffect s the porto of portfolo excess retur attrbutable to choosg dfferet securtes wth groups from the bechmark. A overweght of a well-performg securty (e.g. Novarts) comparso to ts group bechmark (e.g. SI sector "Chemcals") wll geerate a postve stock selecto effect. Iteracto ffect s the porto of the portfolo excess retur whch s ot attrbutable to asset allocato ot stock selecto. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 67

68 xample for a equty retur ad rsk attrbuto (4/6) by 5 World Regos Average Average Relatve Absolute Absolute Dfferece F Weght Weght Weght F Retur Retur F- Asa ex Japa.86% 3.6% -.30% 2.52% 3.5% -8.99% urope 27.62% 28.92% -.30% 25.40% 24.36%.04% Japa 9.83% 8.74%.09% 20.6% 2.75% -.59% North Amerca 59.48% 59.7% 0.3% 5.99% 6.38% -0.39% Cash.2% 0.00%.2% 8.94% 0.00% 8.94% Total 00.00% 00.00% 0.00% 8.28% 9.60% -.32% Dfferece - Tot.9% 4.76% 2.5% -3.23% -9.60% 0.00% Import remarks: - The weght umbers gves a overvew of the average weght vested the dfferet groups (e.g. sectors) wth daly weghts averaged over the chose perod. - The absolute retur umbers gve a overvew of the group's absolute performace (e.g. sector) wth the chose tme perod (portfolo ad bechmark) - The dfferece F- compares the group's performace of the portfolo to the group's performace the bechmark wth the chose tme perod. - The dfferece - Tot compares the group's performace the bechmark wth the performace of the total bechmark wth the chose tme perod. lease ote that cash s cluded the relevat coutry or regoal groups ad show as "other assets" else (e.g. sectors). Cocerg dervatves, oly futures are splt up at the momet; dervatves (call or put optos) are ot yet cluded. Moreover, llqud securtes as prvate placemets are ot yet take to accout. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 68

69 xample for a equty retur ad rsk attrbuto (5/6) by 5 World Regos Asset Allocato Asa ex Japa -0.0% urope -0.04% Japa -0.09% North Amerca 0.0% Cash -0.78% Total -.0% Stock Selecto Iteracto -0.56% 0.30% 0.34% -0.07% -0.6% -0.08% -0.20% 0.00% -0.59% 0.4% 0.00% 0.28% Total -0.36% 0.23% -0.33% -0.05% -0.78% -.32% Import remarks: Asset Allocato ffect s the porto of portfolo excess retur that s attrbutable to takg dfferet group bets from the bechmark. A overweght of a group (e.g. SI sector "Chemcals" ) that outperforms the whole bechmark (e.g. SI) wll geerate a postve asset allocato effect. Securty Selecto ffect s the porto of portfolo excess retur attrbutable to choosg dfferet securtes wth groups from the bechmark. A overweght of a well-performg securty (e.g. Novarts) comparso to ts group bechmark (e.g. SI sector "Chemcals") wll geerate a postve stock selecto effect. Iteracto ffect s the porto of the portfolo excess retur whch s ot attrbutable to asset allocato ot stock selecto. roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 69

70 xample for a equty retur ad rsk attrbuto (6/6) Rsk Model: Global ortfolo Bechmark Rsk Model: Global ortfolo Trackg rror Number of Securtes 67 '550 Total Rsk (ex-ate) 8.8% 2.57% Number of Curreces 8 0 Factor Specfc Rsk 8.66%.50% ortfolo Value 84'334'09 - Rego.50% 0.8% Total Rsk (ex-ate) 8.8% 8.2% - Coutry 6.98% 0.83% - Factor Specfc Rsk 8.66% 8.8% - Idustry 2.64% 0.77% - Stock Specfc Rsk 2.39%.02% - Fudametal.44% 0.78% Trackg rror (ex-ate) 2.57% - Currecy 8.42% 0.27% Relatve Value at Rsk 3'570'469 - Covarace (+/-) 9.35% 0.52% R-squared 0.98 Stock Specfc Rsk 2.39% 2.08% Beta-adjusted Rsk 8.64% 8.2% redcted Beta.02 redcted Dvded Yeld / Rato (: 2 moths) /B Rato (B: year-ed) xplcato of rsk model: Factor rsk s a stadard devato that s measured by multplyg the 5-year exposure of the compoets of a portfolo to each rsk factor ad by multplyg these fgures by the exterally determed rsk of each factor. The Trackg rror s measured smlarly except that t s the dfferece betwee portfolo ad bechmark exposure that s multpled. Specfc Rsk s the stadard devato that measures the volatlty of the rsk ot captured by the factor model. The model cossts of 3 regoal, 2 coutry, 38 dustry ad 8 fudametal factors (market cap, 4-year / growth, /, B/, 5- year yeld, log term debt, 5-year RO varablty ad 5-year eargs varablty). roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 70

71 4. xample for a fxed come retur ad rsk attrbuto roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 7

72 xample for a fxed come retur ad rsk attrbuto(/6) Name (ID) Sample Fxed Icome Bechmark J Morga Global Traded erod to Currecy urope - uro RTURN OVRVIW RTURN ATTRIBUTION FFCTS RISK ATTRIBUTION FFCTS Retur F -0.25% Yeld 0.0% Rsk ortfolo 5.04% Retur -0.3% Durato 0.0% Rsk Bechmark 5.28% Retur Relatve -0.2% Term Structure -0.2% Trackg rror 0.49% Sector -0.25% Qualty -0.02% Other Spread 0.07% Currecy -0.2% Hedgg 0.2% Selecto 0.8% roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 72

73 xample for a fxed come retur ad rsk attrbuto(2/6) ANALYSIS - WIGHTS AND DURATION (NDING RIOD) Currecy F Weght Weght Rel Weght F Durato Durato Rel Durato Swtzerlad uro 28.62% 37.37% -8.75% Uted Kgdom 0.98% 6.5% 4.83% Demark 0.00% 0.7% -0.7% Norway 0.00% 0.00% 0.00% Swede 2.23% 0.63%.60% Czech Republc Hugary olad Uted States 25.0% 2.56% 3.45% Caada.37% 2.0% -0.64% Japa 30.94% 3.22% -0.28% Australa 0.6% 0.36% 0.25% Hog Kog New Zealad Sgapore South Korea Mexco South Afrca Others Total 00 % 00 % 0% roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 73

74 xample for a fxed come retur ad rsk attrbuto(3/6) ANALYSIS 2 - RTURN ATTRIBUTION FFCTS (WHOL RIOD) Currecy F Retur Retur Yeld Durato Term Other Sector Qualty Structure Spread Currecy Hedgg Selecto TOTAL Swtzerlad uro Uted Kgdom Demark Norway Swede Czech Republc Hugary olad Uted States Caada Japa Australa Hog Kog New Zealad Sgapore South Korea Mexco South Afrca Others Total roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 74

75 xample for a fxed come retur ad rsk attrbuto(4/6) ANALYSIS 3- INDIVIDUAL BONDS (BGINNING RIOD) Descrpto Currecy ID Coupo Maturty rce Retur Selecto % Weght FRANC % uro F92997* % -0.30% 5.0% DFA ACS BANK Japa M* % 0.53% 4.99% UNITD STATS T Uted States 92828GX % 0.53% 4.79% BAYRISCH LNDB Japa M* % 0.28% 4.50% UNITD STATS T Uted States 92828CA % 0.09% 4.08% SAIN % uro S2932* % -0.9% 3.80% KFW INTL FINANC Japa M* % -0.0% 3.57% KSORTFINANS Japa M* % 0.25% 3.56% JAAN HIGHWAY Uted States M* % 0.5% 3.35% NTHRLANDS 4.0 uro NN00228* % 0.02% 3.9% SAIN % uro S296* % 0.3% 2.89% BK ND GMNT Japa % 0.0% 2.88% INTRAMR DV B Japa M* % -0.03% 2.42%.9 % MDIUM T Japa 3508CQ % 0.07% 2.42% COUNCIL OF URO Uted States M* % 0.20% 2.30% NATIONWID LIF Uted Kgdom M* %.09% 2.2% USTRIA 4.25% uro LAI002* % -0.02%.99% GN LC CA CO Japa B032Z % 0.02%.97% G CAITAL UK Uted Kgdom M* % 0.76%.95% UROAN INVT B Japa M* % -0.2%.93% UR CASH uro URCASH % 0.00%.4% roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 75

76 xample for a fxed come retur ad rsk attrbuto(5/6) ANALYSIS 4 - TRACKING RROR ATTRIBUTION (ND OF RIOD) Currecy (Trackg rror, p.a.) Durato Term Structure Sector Qualty Other Spread Currecy Covarace Total Swtzerlad uro 0.23% 0.4% 0.0% 0.00% 0.06% 0.00% -0.8% 0.24% Uted Kgdom 0.02% 0.07% 0.03% 0.0% 0.00% 0.00% -0.05% 0.09% Demark 0.02% 0.02% 0.00% 0.00% 0.00% 0.00% -0.02% 0.02% Norway 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% Swede 0.0% 0.0% 0.00% 0.00% 0.00% 0.04% 0.0% 0.05% Czech Republc Hugary olad Uted States 0.% 0.08% 0.5% 0.03% 0.03% 0.02% -0.4% 0.2% Caada 0.05% 0.04% 0.00% 0.00% 0.00% 0.04% -0.06% 0.06% Japa 0.4% 0.27% 0.06% 0.00% 0.00% 0.02% -0.4% 0.30% Australa 0.0% 0.0% 0.00% 0.00% 0.00% 0.02% 0.0% 0.04% Hog Kog New Zealad Sgapore South Korea Mexco South Afrca Others Covarace 0.06% 0.07% 0.08% 0.0% 0.02% 0.29% 0.38% 0.8% Total 0.30% 0.33% 0.9% 0.03% 0.06% 0.07% -0.25% 0.49% Trackg rror (Aual Std Dev) 0.49% VaR Aalyss (95%) ercet Value ortfolo Total Rsk (Aual Std Dev) 5.04% Oe Moth Relatve VaR 0.28% 65 Bechmark Total Rsk (Aual Std Dev) 5.28% Oe Moth VaR 2.87% 672 roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 76

77 xample for a fxed come retur ad rsk attrbuto(6/6) ANALYSIS 5- INDIVIDUAL BONDS (ND OF RIOD) Descrpto % Weght SDOL Coupo Maturty Coutry Currecy Sector Qualty rce Marg Rsk Marg T UROAN INVT BK M* YY JY SUR Aaa Hgh KFW.559 M* D JY AGCY Aaa Rsk UROAN INVT BK.598 M* YY JY SUR Aaa DFA ACS BANK M* I JY ABS Aaa UR BUND FG0806BL D UR TRA Aaa CFWD USD-UR, FX0769 US UR TRA Aaa CFWD GB-UR, FX0768 GB UR TRA Aaa LIF 0 Yr Glt GT0803LI GB GB TRA Aaa SAIN % OBLS S2932* S UR TRA Tsy TS 0 Yr JGB JB0803TS J JY TRA Aaa CBT TNOT FUTR TY0803TY US USD TRA Aaa UNITD STATS TRAS FT US USD TRA Tsy BAYRISCH LNDBK 4.52 M* D JY B Aaa UR BOBL FG D UR TRA Aaa KSORTFINANS M* NO JY F Aa KFW INTL FINANC M* D JY AGCY Aaa INTRAMR DV BK M* YY JY SUR Aaa CFWD SK-UR, FX0770 S UR TRA Aaa % MDIUM TRM NO CQ CA JY TRA Aaa GN LC CA COR B032Z US JY F Aaa UK % GILT D.499 SB6NNR* GB GB TRA Tsy BK ND GMNTN NL JY B Aaa JY CASH JYCASH J JY CASH Aaa FRANC % OAT 5.46 F92997* FR UR TRA Tsy CBT T2NT FUTR TU0803TU US USD TRA Aaa roduced by: Dr. Stefa J. Illmer Date: Aprl 200 Slde 77