Return decomposing of absolute-performance multi-asset class portfolios. Working Paper - Nummer: 16

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1 Return decomposng of absolute-performance mult-asset class portfolos Workng Paper - Nummer: by Dr. Stefan J. Illmer und Wolfgang Marty; n: Fnancal Markets and Portfolo Management; March 2007; Volume 21; Number 1; page Investment Performance IIPCIllmer Consultng AG Kontaktadresse Illmer Investment Performance Consultng AG Wenbergstrasse 28 CH 8200 Schaffhausen Emal stefan.llmer@pc-ag.com

2 Return decomposng of absolute-performance mult-asset class portfolos Verson as of By Dr. Stefan J. Illmer and Wolgang Marty Abstract performance portfolos. Besde the challenge to come up wth approprate nvestment strateges, asset managers also face the problem of explanng the acheved results, especally whether these results were due to luck or skll. Ths last problem s even more complex because the methods currently avalable for evaluatng the performance of an asset manager are not approprate for absolute-performance portfolos. Ths artcle addresses ths problem and presents a practcal soluton, especally for absolute-performance mult-asset class portfolos. 1. INTRODUCTION Before we present our approach for decomposng the return of absolute-performance mult-asset class portfolos, t s essental to explan what we understand by the correspondng nvestment strateges as well as to dscuss the assumptons underlyng our argumentaton. Absolute-performance mult-asset class portfolos 1 do not follow the tradtonal nvestment strategy of relatveperformance portfolos. In contrast to relatve-performance portfolos, t s not the nvestment target to manage the portfolo aganst a pre-defned (long- -term labltes. Absoluteperformance portfolos have a short-term nvestment horzon and are managed aganst a (long-term) target return -term labltes. We focus on nsttutonal nvestors or penson funds and do not address the specfc case of prvate and retal nvestors. We propose a practcal approach for decomposng the return of absolute-performance portfolos that s motvated by our experence n penson fund consultng and reportng. The followng assumptons are based on prncples of the nvestment process and are necessary for the understandng of the argumentaton pursued n ths paper: Short-term rsk averson s more crtcal than the long-term rsk profle. Although we know from theory that rsk s payng off n the long term for absolute-orented nvestors, short-term rsk averson s more relevant because the realzed performance s usually measured and reported on a much shorter tme scale than a typcal long-term tme horzon. In absolute-performance portfolo management, short-term market expectatons are more relevant than longterm market expectatons because a portfolo manager wll never be fully nvested n equtes f he expects a crash n the near future, even though hs long-term vew mght not be as gloomy. The asset manager has to take nto account hs own as well as the clent's market expectatons. The nvestor expresses hs market expectatons explctly through hs short-term expected market return and rsk fgures or at least mplctly through hs short-term rsk averson, whch may be mrrored by short-term or tactcal nvestment gudelnes. The basc prncples of the rsk-return trade-off reman vald and the asset manager acts accordngly - even f only ntutvely. Return decomposton of absolute performance mult asset class portfolos Page 2 of 13

3 In addton to hs own market expectatons, the asset manager derves the optmal reference portfolo from the nves -term market expectatons and short-term rsk averson. The above-mentoned optmal reference portfolo s thus pre-defned and, as a consequence, can be consdered as a benchmark. In comparson to the benchmark of a relatve-performance portfolo, the benchmark of an absoluteperformance portfolo s a short-term as opposed to a long-term benchmark and therefore need much more frequent rebalancng and adjustment. 2 The ntroducton of a short-term reference portfolo s the fundamental bass of our proposed method for decomposng the return of absolute-performance portfolos. 2. MAIN ISSUES WITH THE TRADITIONAL PERFORMANCE EVALUATION Apart from the challenge to come up wth approprate nvestment strateges and to run absolute-performance portfolos, the asset manager faces the problem of explanng the acheved results to the clent, especally whether these results were due to luck or skll. Ths last problem s even more complex because the qualty of the asset manager n charge of an absolute-performance portfolo s not easy to evaluate assumng that: The currently avalable or tradtonal methods for decomposng returns are used. An (absolute) long-term return target s used as the benchmark. Tables 1a and 1b llustrate the frst ssue by decomposng the return of an absolute-performance portfolo applyng a tradtonal performance attrbuton approach. In our case, the return decomposton was carred out for a sngle perod usng the method proposed by Brnson, Hood & Beebower (1986). Supposng a benchmark target return of 0%, the total excess return of the sample portfolo s 1.10%. Followng Brnson, Hood & Beebower, the excess return s splt up and attrbuted to three dfferent sources: the asset allocaton effect, the stock pckng effect and the nteracton effect. Due to the fact that the benchmark s not defned by a specfc nvestment strategy but by an absolute return target nstead, the ndvdual asset classes of the benchmark only enter wth 0% weghts nto the calculaton of the asset allocaton effect. Therefore, the asset allocaton effect s not the dfference between the returns of the passve and the actve nvestment strategy but the dfference between the absolute return of the actual asset allocaton of the portfolo and the absolute benchmark target return, whch s 0% n our case. 3 The total asset allocaton effect s then equal to the absolute return of the actual asset allocaton and s thus 0.79%. As the asset class weghts of the benchmark are 0%, t follows that good asset managers (wth good market tmng capabltes) cannot be dentfed n rsng markets, and the same argument apples to unsuccessful asset managers n fallng markets. Return decomposton of absolute performance mult asset class portfolos Page 3 of 13

4 Asset Class Benchmark Weght Portfolo Weght Benchmark or Index Return Portfolo Return Bonds EUR 0.00% 25.00% 2.00% 1.80% Bonds USD 0.00% 10.00% -0.60% 0.50% Bonds JPY 0.00% 0.00% -1.50% 0.00% Total Bonds 0.00% 35.00% 0.00% 1.43% Equtes EUR 0.00% 30.00% 2.00% 2.30% Equtes USD 0.00% 30.00% -0.60% 0.10% Equtes JPY 0.00% 5.00% -1.50% -2.50% Total Equtes 0.00% 65.00% 0.00% 0.92% Total 0.00% % 0.00% 1.10% Table 1a: Tradtonal return decomposton for an absolute-performance portfolo Asset Class Asset Allocaton Effect Stock Pckng Effect Interacton Effect Total Effect Bonds EUR 0.50% 0.00% -0.05% 0.45% Bonds USD -0.06% 0.00% 0.11% 0.05% Bonds JPY 0.00% 0.00% 0.00% 0.00% Total Bonds 0.44% 0.00% 0.06% 0.50% Equtes EUR 0.60% 0.00% 0.09% 0.69% Equtes USD -0.18% 0.00% 0.21% 0.03% Equtes JPY -0.08% 0.00% -0.05% -0.13% Total Equtes 0.35% 0.00% 0.25% 0.60% Total 0.79% 0.00% 0.31% 1.10% Table 1b: Tradtonal return decomposton for an absolute-performance portfolo The stock pckng effect can only be measured for a specfc asset class f the benchmark s also nvested n ths asset class. In other words, f the asset class weght for the benchmark s 0%, the stock pckng effect s automatcally 0% as well. 4 Wth all asset class weghts of the benchmark beng equal to 0%, the total stock pckng effect for absolute-performance portfolos s also 0%. The asset class weghts of the benchmark beng 0% complcates the ndentfcaton of good asset managers (wth good stock pckng abltes). In comparson to the asset allocaton effect, the stock pckng qualty can be assessed f the nteracton effect s consdered. Consderng the nteracton effect as the stock pckng effect s reasonable because the formula for the nteracton effect also contans the return dfferental on ndex or asset class level, but t s multpled by the asset class weght of the acutal portfolo nstead of the asset class weght of the benchmark. 5 In such a case, t s assumed that the nteracton effect fully belongs to the stock pckng effect. In summary, usng a tradtonal approach for decomposng the return of absolute- Return decomposton of absolute performance mult asset class portfolos Page 4 of 13

5 abltes are not properly measured and, as a consequence, ths may lead to msnterpretatons and nadequate feedbacks nto the nvestment process. The tradtonal approach does not satsfy the actual requrements as far as performance evaluaton s concerned. Expected short-term return Short-term utlty functon 1 Short-term utlty functon 2 B Scenaro 2 Short-term effcent fronter Long-term target return 2 Short-term utlty functon 3 C A Scenaro 3 Long-term target return 3 Scenaro 1 Long-term target return 1 Expected short-term rsk Fgure 1: Dscrepancy between short and long-term return targets and possbltes As mentoned above, the second man ssue n evaluatng the qualty of an asset manager of an absoluteperformance portfolo s the use of an (absolute) long-term target return as a benchmark. Fgure 1 llustrates ths problem by showng three dfferent scenaros n whch a long-term target return could potentally be an unrealstc benchmark. We compare specfc long-term target returns (llustrated by the straght lnes) wth the expected shortterm returns of the portfolos on the short-term effcent fronter. For scenaro 3, we also consder three dfferent short-term utlty functons related to a specfc clent. In scenaro 1, the requred long-term target return 1 s lower than the expected return of any portfolo on the effcent fronter. From an ex-ante pont of vew, usng the long-term target return 1 as a benchmark s not reasonable because achevng a postve excess return s possble wthout any rsk consderatons or by nvestng n rsk-free assets only. In other words, on an ex-post bass, a postve excess return over the long-term target return 1 -term target return 2 s substantally above the hghest expected return of any portfolo on the effcent fronter. In ths case, not even portfolos wth a hgh level of rsk have a postve expected excess return because every effcent fronter portfolo has a negatve expected excess return. Addtonally, usng the long-term target return 2 as a benchmark s not reasonable n such a scenaro from an ex-ante pont of vew because any effcent fronter portfolo has a lower expected return than the long-term target return. In other words, a negatve ex-post excess return over the long-term target return 2 cannot be nterpreted as an ndcaton for poor asset management sklls. In an envronment where nterest rates and expected market returns are on hstorcally low levels, an asset manager faces a certan negatve excess return for a short-term perod even f he nvests n hghly rsky portfolos. Consderng the rsk averson of tradtonal, absolute-performance-orented clents, a hgh degree of portfolo rsk Return decomposton of absolute performance mult asset class portfolos Page 5 of 13

6 would not be approprate and therefore, the long-term target return 2 would not be achevable. Compared to the other above-mentoned scenaros, we see n scenaro 3 that, from an ex-ante pont of vew, the long-term target return 3 les between the mnmum and the maxmum expected return of the effcent fronter portfolos. Accordng to the effcent fronter concept, one uses the ndvdual utlty functon of a clent to represent hs rsk averson and then chooses the optmal effcent fronter portfolo as the one that s tangent to the utlty functon. Assumng the short-term utlty functon 1, the long-term target return 3 would be dentcal to the expected return of the optmal effcent fronter portfolo A. In ths unrealstc case, the long-term target return s equal to the expected return of the optmal effcent fronter portfolo, and the long-term target return 3 would be an approprate benchmark. In all other cases (for example wth the short-term utlty functons 2 and 3 n our llustraton), we are n stuatons smlar to those descrbed by scenaro 1 and 2 dscussed above. In case of utlty functon 2, the stuaton s the same as n scenaro 1 wth the expected return of the optmal effcent fronter portfolo B beng hgher than the long-term target return 3. As mentoned above, n ths stuaton t s not clear whether the ex-post excess return s due to the asset manager's decsons or not. Applyng utlty functon 3, the stuaton s the same as n scenaro 2 and the expected return of the optmal effcent fronter portfolo C s lower than the long-term target return 3. As explaned above, n ths stuaton t s agan not clear whether the excess return on an ex-post bass s due to the asset manager's decsons or not. Followng the above argumentaton on the long-term target return, we can conclude that In general, a target return used as a benchmark -term atttude towards rsk and -term utlty functon. 6 A specfc long-term target return related to an annual nterest on labltes should not be lnked to the (shortterm) rsk averson or to the (short-term) market expectatons wth respect to rsk and returns. settng an unrealstc (short-term) target return from an ex-ante perspectve may not be very motvatng for the asset manager and may lead to unntended (short-term) rsk. usng an unrealstc (short-term) target return to assess the qualty of an asset manager on an ex-post bass may lead to msnterpretatons and nadequate apprasals and thus also to nadequate feedbacks nto the nvestment process. After dscussng the two man ssues an asset manager faces when explanng the acheved results of absoluteperformance portfolos to a clent, we can conclude that the assessment of the value added by an asset manager s not possble usng a (long-term) target return as a benchmark and a tradtonal method to decompose returns. Based on the assumptons mentoned n the ntroducton, we are gong to present a method for decomposng the return of absolute- performance mult-asset class portfolos. 3. DECISION-ORIENTED RETURN DECOMPOSITION In order to decompose the returns of absolute-performance portfolos, we propose a decson-orented approach consstng of followng three steps (for more nformaton on ths decson-orented framework see Illmer & Marty (2003): Step 1: Step 2: Transform the specfc nvestment decsons nto (absolute) asset allocatons. Calculate the correspondng returns of the dfferent asset allocatons. Return decomposton of absolute performance mult asset class portfolos Page 6 of 13

7 Step 3: Assgn the returns as well as the return dfferences to the nvestment decsons and to the relevant decson makers. Consderng our assumptons descrbed n the ntroducton, we defne a general nvestment process for absoluteperformance mult-asset class portfolos as llustrated n Fgure 2. In our sample nvestment process, we dentfy the followng fve mplct or explct nvestment decsons, wth the asset manager beng responsble for decsons 4 and 5 and the clent beng responsble for decsons 1 to 3 : Decson 1: Decson 2: Defne the (requred) long-term target return as well as the rsk profle of the clent. Defne the short-term market expectatons of the clent and deduce the short-term effcent fronter. Decson 3: Defne the short-term rsk averson of the clent and derve the short-term optmal effcent fronter portfolo and/or the short-term nvestment gudelnes. Decson 4: Defne the daly market expectatons of the asset manager and derve the daly effcent fronter. Decson 5: Derve the daly optmal effcent fronter portfolo of the asset manager n lne wth the short-term rsk averson and the short-term nvestment gudelnes of the clent. The frst decson focuses on the requred long- goal, for example the perodcal nterest necessary to serve -performance portfolo, the second nvestment decson does not focus on long-term but on short-term market expectatons. The length of the nvestment horzon may dffer from clent to clent and wll normally vary from one month to one year. Based on these short-term market expectatons, t s possble to derve a short-term effcent fronter, whch s then used n the thrd nvestment decson step to defne the short-term optmal effcent fronter portfolo dependng on -term rsk averson. Should an nvestor be unwllng or unable to formulate hs own short-term market expectatons, he can delegate ths to a consultant or to the asset manager drectly. In such a case, t s even more mportant that the delegates nvolve the clent by regularly presentng ther scenaros to hm. The short-term optmal effcent fronter portfolo can be regarded as the short-term reference portfolo or as we wll call t n the followng as the short-term benchmark. Moreover, the expected return of ths short-term benchmark can be referred to as the expected short-term target return for the next nvestment horzon because t reflects the expected return potental consderng all nvestment constrants. In step 4, the asset manager derves the daly effcent -term nvestment gudelnes. 7 Consderng the short-term rsk averson of the clent and not hs own, the asset manager defnes and mplements the daly optmal effcent fronter portfolo n step fve. It has to be emphaszed that t should be the rsk averson of the clent and not that of the asset manager that s always controllng. Ths s another dfference between absoluteand relatve-performance portfolos. The fnal and mplemented portfolo leads to the hstorcally realzed return of the portfolo, whch has to be assessed. Return decomposton of absolute performance mult asset class portfolos Page 7 of 13

8 Decson steps Output Result 1 Investment target and rsk profle of clent Long-term target return 2 Short-term market expectatons of clent Short-term effcent fronter 3 Short-term rsk averson of clent Short-term optmal portfolo and nvestment gudelnes Short-term target return 4 Daly market expectatons of asset manager Daly effcent fronter 5 Short-term rsk averson of clent Daly optmal portfolo Realzed portfolo return Fgure 2: General nvestment process of an absolute-performance portfolo In the second step of our proposed approach for a decson-orented return decomposton, hstorcal returns are calculated for the dfferent (absolute) asset allocatons as defned n the above mentoned nvestment decsons. In step 3 of the decomposton approach, we assgn the returns as well as the return dfferences to the relevant nvestment decsons and decson makers dentfed n step 1. Fgure 3 llustrates the decomposton of the return of an absolute-performance portfolo based on the abovedentfed nvestment decsons. In addton, the clent perspectve s ncorporated by not only decomposng the tmeweghted rate of return (TWR) but also the money-weghted rate of return (MWR). From a general pont of vew, we argue that Fgure 3 represents a comprehensve framework for decomposng the return of portfolos regardless of whether they are absolute- or relatve-performance portfolos. Ths framework ntegrates three dfferent perspectves: the overall clent perspectve focusng on the absolute portf the MWR of the portfolo relatve to the long-term or short- on the TWR of the portfolo relatve to the long-term or short-term benchmark (for more detals on the decomposton of the MWR, see Illmer & Marty (2003)). Followng the nvestment process shown n Fgure 2, we can dentfy the followng return dfferences whch form the bass for the assessment of the asset manager and all other decson-makers nvolved. 8 Expected excess return s the dfference between the long-term target return and the expected return of the (short-term) benchmark and shows whether the nvestment goal s achevable from an ex-ante perspectve. Estmaton error s the dfference between the ex-post benchmark return and the expected (shortterm) benchmark return and s an ndcaton for the forecastng abltes. Realzed excess return s the dfference between the ex-post money-weghted rate of return of the portfolo (so-called clent return) and the ex-post (short-term) benchmark return. It s an ndcaton of the qualty of all nvestment decsons (ncludng the tmng of external cash flows by the clent). The ex-post money-weghted rate of return of the portfolo measures the retu Fgure 3, dstngushng t more from the below-mentoned asset manager return. Return decomposton of absolute performance mult asset class portfolos Page 8 of 13

9 Benchmark effect s equal to the ex-post (short-term) benchmark return and can be vewed as the return contrbuton by the decson to nvest the ntal money nto a specfc (short-term) benchmark strategy. Management effect s the dfference between the ex-post tme-weghted rate of return of the portfolo and the ex-post (short-term) benchmark return and can be vewed as the return contrbuton by the actve nvestment decsons of the portfolo manager, for nstance on asset allocaton or stock selecton. The ex-post tmeweghted rate of return of the portfolo measures the return from the asset manager's perspectve and s therefore Tmng effect s the dfference between the ex-post money-weghted rate of return of the portfolo and the ex-post tme-weghted rate of return of the portfolo and can be vewed as the return contrbuton by the decson to change the amount of money nvested n the benchmark strategy and n the actve asset allocaton of the portfolo. Long-term target return Expected excess return Short-term target return Estmaton error Realzed benchmark return Realzed excess return Realzed clent return (MWR) Benchmark effect Management effect Tmng effect Realzed asset manager return (TWR) Fgure 3: Comprehensve framework for decomposng the return of portfolos 4. Practcal llustraton of the proposed decomposton approach The decomposton approach presented n ths paper s appled to an absolute-performance portfolo of a Swss Franc-based clent as of the end of The underlyng nvestment strategy follows an absolute-performance approach and nvests n three asset classes, namely cash, bonds and equtes. As reflected by the expected market returns n Table 2, the clent had a very conservatve rsk profle and a very pessmstc market outlook for the Return decomposton of absolute performance mult asset class portfolos Page 9 of 13

10 upcomng year at the end of 2002, whch was common at that date. Table 2 also ncludes the tactcal nvestment -term target return to be 5% p.a., t was very unrealstc at the end of 2002 to expect to outperform or even to reach the absolute benchmark of 5%. Asset class mnmum Tactcal gudelnes maxmum 12 months expected returns n CHF as of months realzed returns n CHF for 2003 Cash total 0.0% 41.0% Cash CHF 0.0% 29.0% 0.70% 0.32% Cash non CHF 0.0% 14.5% Euro 4.70% and USD -1.30% Euro 10.13% and USD -9.48% Bonds total 35.0% 70.5% Bonds CHF 35.0% 70.5% 0.70% 0.91% Bonds non CHF 0.0% 17.5% Euro 4.55% and USD -0.86% Euro 11.79% and USD -8.53% Equtes total 0.0% 47.0% Equtes CHF 0.0% 23.5% 5.20% 19.94% Equtes non CHF 0.0% 23.5% 3.81% 19.77% Table 2: Underlyng market expectatons and realzed market returns for Based on the long-term target return, the conservatve rsk profle and the tactcal nvestment gudelnes of the clent as well as the short-term market expectatons, we compute the short-term effcent fronter presented n Fgure We note that, due to the restrctons n the optmzaton process, the effcent fronter s below the return of some market ndces lke the Euro money market ndex (Ctgroup 3mo Euro EuroDep) and the Euro bond ndex (Ctgroup EMU 1+ Yr Gvt). Smlarly, the optmzaton does not fully nvest n the Swss equty ndces (MSCI Swtzerland and the MSCI World) because, apparently, these markets do not have an optmal rsk-return relatonshp n the optmzaton framework. For the mpact of constrants on a portfolo optmzaton problem, we refer to the example n Vörös (1987). As ndcated n Fgure 4, the clent dd not choose one of the effcent fronter portfolos but a non-effcent portfolo whch suted the clent specfc crcumstances better than the reference portfolo or the short-term benchmark. From an ex-ante pont of vew at the end of 2002, the short-term benchmark had an expected 12-month return of +1.56%. Therefore, the expected excess return was -3.44%, whch corresponds to scenaro 2 llustrated n Fgure 1. As we know today, the markets performed consderably better n 2003 than expected by many nvestors, resultng n a short-term benchmark calendar year return of +4.70% and n an estmaton error of +3.14% for Assumng that the asset manager generated an absolute return of %, we calculate a realzed excess return of +1.45% for 2003, whch s attrbuted to the asset manager due to the absence of cash n- and outflows from the clent. Fgure 5 llustrates the process of determnng the dfferent portfolos as well as the correspondng returns. Return decomposton of absolute performance mult asset class portfolos Page 10 of 13

11 Expected Return Ctgroup 3 Mo Euro EuroDep TR CHF Ctgroup EMU 1+ Yr Gvt TR n Euros CHF Ctgroup Sw tzerland 1+ Yr Gvt TR Ctgroup 3 Mo Sfr EuroDep TR Short-term reference portfolo Ctgroup U.S. 1+ Yr Gvt TR CHF Ctgroup 3 Mo US$ EuroDep TR CHF MSCI Sw tzerland TR MSCI World TR CHF Standard Devaton (Rsk) Fgure 4: Short-term effcent fronter Long-term target return Labltes plus costs p.a. => 5.00% Short-term market expectatons on Short-term Effcent fronter on Expected excess return => -3.44% Short-term rsk averson on => short-term target return Short-term optmal portfolo wth an expected return on => 1.56% Estmaton error => +3.14% 12 months realzed return of the short-term optmal portfolo for 2003 => 4.70% 12 months realzed market returns for 2003 Realzed excess return => +1.45% 12 months realzed return of the actual portfolo for 2003 => 6.15% Actual portfolo for 2003 (ncludng tactcal asset allocaton and stock pckng) Fgure 5: Investment process and return decomposton over tme Return decomposton of absolute performance mult asset class portfolos Page 11 of 13

12 5. SUMMARY AND CONCLUSIONS We have presented evdence that the tradtonal decomposton approach leads to dssatsfyng results and msnterpretatons when appled to absolute-performance portfolos. Wthout an alternatve approach for evaluatng the performance of an asset manager, t s not possble to conclude whether the absolute return s due to skll or luck. Not usng a short-term benchmark would mply that one never looks back at one's own past market expectatons. Our approach for decomposng the return of absolute-performance portfolos allows not only to quantfy the value added by the dfferent decson makers but, more mportantly, also makes the nvestor more aware of the - addtonal and may be unntended nvestment rsk he faces when the long-term target return cannot be acheved n the short-term. In summary, we conclude that we cannot avod the benchmark concept for absolute-performance portfolos. Ths last statement mght be controversal but may nvte those who dsagree to present an alternatve approach for the return decomposton of absolute-performance mult-asset class portfolos. Acknowledgements We would lke to thank the anonymous referees as well as Marcel Roost from Credt Susse for ther valuable comments and dscusson ponts. References Brnson, G., Hood, R. and Beebower, G.: Determnants of Portfolo Performance. Fnancal Analysts Journal, 42(4), (1986) Brnson, G., Snger, B. and Beebower, G.: Determnants of Portfolo Preference II: An Update. Fnancal Analysts Journal, 47(3), (1991) Illmer, S. and Marty, W.: Decomposng the Money-Weghted Rate of Return. Journal of Performance Measurement, Summer, (2003) Vörös, J.: The explct dervaton of the effcent portfolo fronter n the case of degeneracy and general sngularty. European Journal of Operatonal Research, 32, (1987) Endnotes 1 In the followng, we abbrevate the term "absolute-performance mult-asset class portfolos" wth "absoluteperformance portfolos" and "relatve-performance mult-asset class portfolos" wth "relatve-performance 2 T he hgher rebalancng or adjustment frequency mples a larger effort n managng an absolute-performance portfolo because market expectatons and rsk averson have to be surveyed more often. At frst sght, ths can be understood as an advantage of absolute-performance portfolos because, deally, the hgher rebalancng frequency s also connected wth more clent contact. In contrast to ths, the asset manager of a relatveperformance portfolo normally communcates rather rarely wth the clent because both orentate themselves Return decomposton of absolute performance mult asset class portfolos Page 12 of 13

13 at long-term parameters such as long-term rsk and return expectatons. On the other hand, varyng market expectatons and rsk aversons n the short-term can be observed wth some clents and often lead to dscrepances between short- and long-term vews, whch are very dffcult to agree upon. Ths also mples hgher transacton costs, whch have a negatve mpact on the return of the portfolo. 3 The formula for calculatng the asset allocaton effect ( A ) for a specfc asset class s: A (w W ) b, where w s the portfolo weght of asset class, ndex return of asset class. W s the benchmark weght of asset class and b s the The formula for calculatng the stock pckng effect ( S ) for a specfc asset class s: s the portfolo return of asset class and the other varables denote the same as above. S (r b ) W The formula for calculatng the nteracton effect ( I ) for a specfc asset class s: I (w W ) (r b )., where r Another nherent problem of absolute-performance portfolos worthwhle mentonng s the msmatch of the length of the dfferent relevant nvestment horzons. The long-term target return s related to the long-term labltes and therefore mples a long-term nvestment horzon whch may be several years long. On the other hand, the absolute-performance portfolo s drven by short-term market expectatons and therefore has a short-term nvestment horzon. In addton, the asset manager of an absolute-performance portfolo may be forced to trade actvely and may have a daly focus and therefore a daly nvestment horzon. Comparng benchmarks or target returns whch are based on dfferent nvestment horzons s not reasonable and leads to the above-mentoned ssues when evaluatng the qualty of the asset manager and all other decson-makers n the whole nvestment process ncludng the consultant or even the clent. The nvestment horzon of the asset manager may dffer from one day but, for smplcty, we choose a daly nvestment horzon to ds Accordng to other underlyng decsons lke asset allocaton or stock pckng, the return dfferences can be further splt up accordng to, for example, asset classes or sectors. However, ths s not llustrated n ths - Annual n London n The presentaton s avalable from the authors. We assume an expected currency return of 1.6% for CHF/EUR and of -2.8% for CHF/USD n 2002, the realzed currency returns n 2003 beng 7.5% for CHF/EUR and -10.5% for CHF/USD. The rsk expectatons are not shown but correspond to the hstorcal fve year covarance matrx of the underlyng market ndces. Return decomposton of absolute performance mult asset class portfolos Page 13 of 13