A Simplified Framework for Return Accountability

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1 Reprnted wth permsson from Fnancal Analysts Journal, May/June Copyrght Assocaton for Investment Management and Research, Charlottesvlle, VA. All rghts reserved. by Gary P. Brnson, Bran D. Snger and Glbert L. Beebower Determnants of Portfolo Performance II: An Update Ths artcle presents a framework for determnng the contrbutons of dfferent aspects of the nvestment management process asset allocaton polcy, actve asset allocaton, and securty selecton to the total return of nvestment portfolos. Data from 82 large penson plans ndcate that asset allocaton polcy, however determned, s the overwhelmngly domnant contrbutor to total return. Actve nvestment decsons by plan sponsors and managers dd lttle on average to mprove performance over the 10-year perod December 1977 to December The performance attrbuton framework s also extended to account for actual and synthetc cash holdngs wthn asset classes. IN DETERMINANTS of Portfolo Performance, publshed n ths journal n 1986, we documented the overwhelmng contrbuton of asset allocaton polcy to the return performance of a sample of 91 large penson plans. 1 That earler artcle developed a systematc framework for the attrbuton of returns to dfferent types of actve nvestment decsons. Ths artcle, also focusng on return attrbuton, updates the results of the prevous study and confrms our orgnal conclusons. Specfcally, data from 82 large penson plans over the perod ndcate that nvestment polcy explaned, on average, 91.5 per cent of the varaton n quarterly total plan returns. In addton, ths artcle provdes an expanded performance attrbuton framework that accounts, not only for securty selecton and actve asset allocaton, but also for changes n portfolo rsk characterstcs attrbutable to rsk postonng wthn ndvdual asset classes. Nether ths artcle nor ts predecessor attempts to evaluate the effcacy of nvestment polces. Rather, the concentraton s on the overwhelmng mpact of polcy however establshed and the ncremental effect of actve nvestment strateges Footnotes appear at end of artcle. Framework Our earler artcle outlned a framework for dssectng total plan returns nto three components asset allocaton polcy, actve asset allocaton, and securty selecton. The dstncton between asset allocaton polcy and actve asset allocaton needs to be delneated. Asset allocaton polcy nvolves the establshment of normal asset class weghts and s an ntegral part of nvestment polcy. Actve asset allocaton s the process of managng asset class weghts relatve to the normal weghts over tme; ts am s to enhance the managed portfolo's rsk/return tradeoff. Ths dstncton s materal to understandng the mportance of nvestment polcy relatve to actve management. Fgure A llustrates the framework for reportng and analyzng portfolo returns. Quadrant I ndcates the total return provded by the nvestment polcy adopted by the plan sponsor. The polcy "portfolo" thus represents a constant, normal allocaton to passve asset classes. Investment polcy, then, dentfes the plan's normal portfolo composton. Calculatng the polcy return nvolves applyng the normal weghts of each nvestable asset class to the respectve passve returns. Quadrants II and III shft the focus to actve management. Quadrant II reports the return attrbutable to a portfolo reflectng both polcy and actve asset allocaton. Whether actve allo- FINANCIAL ANALYSTS JOURNAL/MAY-JUNE

2 Glossary Attrbuton: The process of attrbutng actual portfolo return to those nvestment management actvtes that contrbute to the return nvestment polcy, actve asset allocaton and securty selecton. Investment Polcy: Specfcaton of the plan sponsor's objectves, constrants and requrements, ncludng dentfcaton of the normal asset allocaton mx. Actve Asset Allocaton: Temporarly devatng from the polcy asset mx n order to beneft from a state of captal market dsequlbrum wth respect to the nvestment fundamentals underlyng the polcy mx. Coeffcents of Determnaton: The percentage of varablty n one random varable that s accounted for by another random varable. The more famlar R 2, ndcatng the varablty of the dependent varable accounted for by a regresson model, s dentcal to the coeffcent of determnaton for unvarate regressons. Rsk Postonng:The actve allocaton out of noncash assets nto cash equvalents at the sset a allocaton level and the holdng of cash wthn an asset class portfolo. External Rsk Postonng:The allocaton nto and out of cash-equvalent assets. The term "external" refers to postonng at the asset class level. As segregatng the cash component at the asset class level s a rather common aspect of actve asset allocaton performance attrbuton, "external rsk postonng" s used n a broader sense to mean actve asset allocaton. Internal Rsk Postonng:The establshment of a poston n actual or synthetc cash, typcally to control beta or duraton rsk, wthn an asset class. The term "nternal" refers to postonng wthn an asset class. caton nvolves antcpatng prce moves (market tmng) or reactng to market dsequlbra (fundamental analyss), t results n the under or overweghtng of asset classes relatve to the normal weghts dentfed by polcy. 3 The am of actve allocaton s to enhance the return and/or reduce the rsk of the portfolo relatve to ts polcy benchmark. The polcy and actve asset allocaton return s computed by applyng the actual asset class weghts to ther respectve passve benchmark returns. Quadrant III presents the returns to a portfolo attrbutable to polcy and securty selecton. Securty selecton nvolves actve nvestment decsons concernng the securtes wthn each Fgure A Asset Allocaton Passve A Smplfed Framework for Accountablty Securty Selecton Passve IV Portfolo III Polcy and Securty Selecton Actve s Due to: Actve Asset Allocaton Securty Selecton Other Total II Polcy and Actve Asset Allocaton I Polcy (Passve Portfolo Benchmark) II I III I IV - III - II + I IV I asset class. Ths framework specfes that the return from polcy and securty selecton s obtaned by applyng the normal asset class weghts to the actual actve returns acheved n each asset class. Fnally, Quadrant IV represents the actual return realzed by the plan over the perod of performance evaluaton. Ths s the result of the plan's actual asset class weghts nteractng wth the actual asset class returns. Fgure B summarzes the calculatons requred to determne the returns for Quadrants I, II and Fgure B Asset Allocaton Passve Computatonal Requrements for Accountablty* Securty Selecton Passve IV (Wa Ra) III (Wp Ra) II (Wa Rp) I (Wp Rp) *Wp = polcy weght for asset class ; Wa = actual weght for asset class ; Rp = passve return for asset class ; Ra = actual return for asset class. FINANCIAL ANALYSTS JOURNAL/MAY-JUNE

3 Table I Due to Actve Asset Allocaton Securty Selecton Other Total Calculaton of Actve Contrbutons to Total Performance Calculated By [(Wa * Rp) (Wp * Rp)] (Quadrant II Quadrant I) [(Wp * Ra) (Wp * Rp)] (Quadrant III Quadrant I) [Wa Wp) (Ra Rp)] [Quadrant IV (Quadrant II + Quadrant III) + Quadrant I] [(Wa * Ra) (Wp * Rp)] (Quadrant IV Quadrant I) III. Table I provdes the computatonal methodology for determnng the sources of actve returns. The actve contrbuton to total performance s composed of actve asset allocaton, securty selecton, and the effects of a cross-product term that measures the nteracton of the securty selecton and actve asset allocaton decsons. Data Attrbutng returns to the varous aspects of the nvestment process accordng to ths frame-work requres hstorcal data on portfolo composton (weghts), actual nvestment results, and returns to the approprate benchmarks. SEI Corporaton provded 10 years of quarterly data, from December 1977 to December 1987, for 82 penson plans n ther Large Plan Unverse. The seven seres avalable for each plan were four asset-class-weght seres for equty, bonds, cash equvalents and "other" and three quarterly rate-ofreturn seres for the total plan and ts assocated equty and bond components. The focus of ths artcle s on nvestment performance, so all returns were expressed gross of management fees. An analyss of the asset class weghts ndcates that there was no sgnfcant shft n asset class preferences over the perod covered by the sample data. Fgure C demonstrates that the average weghts of the asset classes for the sample remaned remarkably stable over tme, despte market trends and volatlty. Ths s somewhat at odds wth other surveys showng ncreased exposure to equtes over smlar perods. 4 Because the composton of the "other assets" category was unknown, ts weght was allocated to the equty, bond and cash components n proporton to ther respectve weghts. Table II shows that ths component consttuted a relatvely small percentage (less than 15 per cent) of total plan assets and dd not materally affect total plan returns. However, a few plans had extraordnarly large allocatons to the "other" category over the perod; these "outlers" were omtted from the analyss. None of the sample funds held non-u.s. bonds, and only two held non-u.s. equty. In these cases, the foregn equty was consdered part of the equty component, wthout a materal effect on the results. We defned polcy weghts for each plan (the Fgure C Average Asset Class Weghts, Source: SEI Corporaton FINANCIAL ANALYSTS JOURNAL/MAY-JUNE

4 Table II Analyss of Asset Class Weghts, 82 Large Penson Plans, Summary of Holdngs Average Maxmum Mnmum Standard Devaton Equty 53.0% 79.1% 26.0% 10.8% Bond 24.5% 53.1% 4.0% 10.4% Cash 12.1% 24.1% 3.0% 4.6% Other 10.5% 65.4% 0.1% 12.0% Summary of Holdngs Excludng "Other" Average Maxmum Mnmum Standard Devaton Equty 59.6% 83.9% 36.5% 10.5% Bond 26.9% 54.0% 5.6% 10.2% Cash 13.6% 24.3% 3.5% 4.9% normal weghts) as the 10-year average of the plan's asset class weghts. These funds dd not necessarly favor a "typcal" mx of assets (such as 60/40 stocks/bonds), although, as Table II shows, the average mx was very close to 60 per cent equty and 40 per cent fxed ncome. Fgure D shows that the observed combnatons of equty and bond weghts cover almost the whole range of possbltes. Some plans showed evdence of a change n polcy over the 10 years, ether by a clear upward or downward trend n the weght of an asset class or a sudden and apparently permanent shft n the level of the quarterly weghts. We attempted to account for ths n the analyss. In cases where there appeared to be a polcy shft, we dvded the 10-year perod nto two perods prechange and postchange and calculated returns based on the polcy weghts n effect n each perod. Results In addton to the actual reported return for each plan, we defned three return seres polcy, polcy and actve asset allocaton, and polcy and securty selecton. The polcy return s the passve portfolo benchmark return, calculated as the sum of the polcy weghted passve asset class returns, usng the 10- year average asset class weghts (as dscussed above) and a sutable passve ndex for each asset class. The S&P 500, the Salomon Broad Investment Grade (BIG) bond ndex and 30-day Treasury blls were used as the passve ndexes for the equty, bond and cash components, respectvely. The polcy and actve asset allocaton return s Fgure D Average Equty Weght versus Average Bond Weght, Source: SEI Corporaton FINANCIAL ANALYSTS JOURNAL/MAY-JUNE

5 Fgure E Asset Allocaton Passve Mean Annualzed s by Actvty, 82 Large Penson Plans, Securty Selecton Passve IV 13.41% III 13.75% Actve s Due to: II 13.23% I 13.49% Actve Asset Allocaton 0.26% Securty Selecton +0.26% Other 0.07% Total 0.08% calculated usng the actual actve weghts and the approprate passve ndex returns. The polcy and securty selecton return s calculated usng the polcy weghts and the actual actve returns. We repeated each analyss usng a broader market ndex than the S&P 500; the results were vrtually dentcal. The overall effect of actve management by plan sponsors or nvestment managers was neglgble. Ths confrms the fndngs of our earler study. Fgure E and Table III show that the average portfolo underperformed ts polcy benchmark by eght bass ponts a year. Indvdual effects vared wdely, from a 3.4 per cent per annum underperformance to a 6.7 per cent per annum overperformance. The ncremental return to actve management had a standard devaton of 1.7 per cent. Clearly the contrbuton of actve management s not statstcally dfferent from zero (that s, t s most lkely attrbutable to chance). Whle actve asset allocaton contrbuted a net underperformance of 26 bass ponts, and securty selecton contrbuted a gan of 26 bass ponts, nether fgure s statstcally dfferent from zero. Actve management not only had no measurable mpact on returns, but (n the absence of a proxy for the varablty of the respectve penson labltes), t appears to have ncreased rsk by a small margn (Fgure F and Table III). Gven the hgher rsk level of the polcy and securty selecton portfolo, t s evdent that securty selecton contrbuted to actual plan rsk. Actve asset allocaton appears to have had a neglgble mpact on rsk relatve to the benchmark polcy. The mperfect correlaton between the performances of the polcy and allocaton and the polcy and securty selecton portfolos mtgated some of the ncreased rsk. None of these observatons detracts from the fndng that the choce of nvestment polcy domnates the rsk/return posture of the plan. It s obvous that the overwhelmng factor n determnng the basc, long-term return acheved per unt of rsk was nvestment polcy. Because actve asset allocaton s the process of managng asset class weghts relatve to the normal weghts, actve management s condtonal on the nvestment polcy. Thus actve returns are condtonally dstrbuted on the polcy return dstrbuton. Ths domnance s also demonstrated by the coeffcents of determnaton for polcy, polcy and actve asset allocaton, polcy and securty selecton, and actve returns. The coeffcent of determnaton s the square Table III Annualzed s and Rsk by Actvty, Average Average Rsk Mnmum Maxmum X-Sec. Std. Dev. Portfolo Polcy Polcy and Actve A/A Polcy and Selecton Portfolo Actve Components Actve A/A Only Selecton Only Other Total Actve FINANCIAL ANALYSTS JOURNAL/MAY-JUNE

6 Fgure F Polcy Rsk versus Actve Rsk, Source: SEI Corporaton of the correlaton coeffcent between two jontly dstrbuted random varables. It s used to descrbe the amount of varablty n one varable that can be accounted for by another varable. In ths nstance, we are concerned wth the percentage of varablty n actual returns that s accounted for by polcy, by polcy and actve asset allocaton, and by polcy and securty selecton. Fgure G shows that, on average, polcy returns accounted for 91.5 per cent of the varance of actual returns. Beng condtonally dstrbuted on the polcy returns, actve asset allocaton and securty selecton combned could have accounted for only a small resdual porton of the varance of actual returns. In fact, polcy and actve asset allocaton combned accounted for 93.3 per cent and polcy and securty selecton combned accounted for about 96.1 per cent. Agan, the domnance of nvestment polcy s clear. 5 Although each level of rsk was assocated wth a range of plan returns, actve returns generally ncreased wth plan rsk. Fgure H shows that, for a gven rsk level, the dfference n performance between the best and the worst plans was as much as 3 per cent annually. The two plans wth extraordnarly low rsk had hgher allocatons to the "other asset" class perhaps real estate, gven the low volatlty. Three other plans had unusually strong returns, wth each showng extraordnary returns from both stock and bond components over the entre 10 years. There are several possble explanatons for these rregulartes. Frst, the analyss dd not account for the lablty exposure of each plan. The ncluson of a lablty proxy mght shft these performance statstcs. Second, the use of 10-year average weghts for the passve benchmark may have created an neffcent bench- Fgure G Asset Allocaton Passve Percentage of Varaton Explaned, IV 100.0% III 96.1% Securty Selecton Passve II 93.3% I 91.5% Average Mnmum Maxmum Std. Dev. Polcy 91.5% 67.7% 98.2% 6.6% Polcy and Allocaton 93.3% 69.4% 98.3% 5.2% Polcy and Selecton 96.1% 76.2% 99.8% 5.2% FINANCIAL ANALYSTS JOURNAL/MAY-JUNE

7 Fgure H Average versus Average Plan Rsk, Source: SEI Corporaton mark. Whle the mpact was probably not great, some bas was ntroduced. It s dffcult, gven these data, to determne conclusvely whch asset classes generated good or bad relatve performance. It should be noted, however, that 76 of the 82 equty funds underperformed the S&P 500 on an equty-only bass. A complete 10-year bond performance was not avalable for several funds, because ther bond weghts were zero for several quarters. For the 70 cases wth complete bond hstores, almost two-thrds outperformed the passve bond benchmark. Of those plans that underperformed ther polcy benchmarks, over 75 per cent underperformed n the bond component. As one would expect, the medan cash manager outperformed the 30-day T-bll ndex. Lmtatons Our analyss lacks some precson because of performance data lmtatons. Frst, as noted, the composton of the "other asset" category was unknown; n many cases, however, ths category consttuted only a small percentage of the total portfolo. Second, polcy portfolos were nferred from the long-term average asset class weghts, and there s no assurance that they relably represent the actual benchmarks. In terms of assessng the mportance of the benchmark to nvestment returns, however, ths s probably not a serous problem. Adjustng for apparent shfts n polcy weghts had very lttle effect on the analyss. In fact, usng a smple 60/40 stock/bond mx as a passve benchmark for all the funds resulted n vrtually the same average results as ndcated n Fgure G. Gven the average portfolo composton n Table II, ths s not too surprsng. Fnally, we do not know the actual number of dfferent money managers used by these 82 penson plans. Whle t s hghly unlkely that the data represent only a few managers, the study does reflect the performance of ndvdual managers, not necessarly penson fund performance n general. Furthermore, we know nothng about the styles of the managers or ther use of futures and optons. Some almost certanly altered nternal rsk postons by hedgng durng the last quarter of 1987; ths s ndcated by the postve equty returns at a tme when the market as a whole was down by almost 25 per cent. The ssue of hedgng, and the broader ssue of rsk postonng, s treated n more depth below. Internal versus External Rsk Postonng Besdes shftng asset class weghts.e., external rsk postonng a manager or sponsor can change exposure to an asset class wthn a portfolo component nternal rsk postonng. Internal methods nclude alterng the component's beta or duraton by usng long or short futures postons, carryng cash or hedgng the currency component. Lookng at any sngle rskpostonng actvty, external or nternal, wll not FINANCIAL ANALYSTS JOURNAL/MAY-JUNE

8 Table IV Attrbuton of Internal and External Rsk Postonng Equaton (1) Equaton (3) Securty Selecton (Ra Rp)Wp (Rs Rp)Wp Rsk Postonng (Wa Wp)(Rp R) (Wa Wp)(Rp R) + c(rh Rp)Wa External (Wa Wp)(Rp R) (Wa Wp)(Rp R) Internal 0 c(rh Rp)Wp Cross Product 0 c(wa Wp)(Rh Rp) Cross Product (Wa Wp)(Ra Rp) [(1 c)wa Wp](Rs Rp) gve a complete or accurate measure of the actve portfolo management effect. The performance-attrbuton framework outlned above defnes the extra return, E, to a mult-asset portfolo attrbutable to a partcular asset class as: E = (R a R p )W p + (W a W p )(R p R) + (W a W p )(R a R p ), (1) where W P = the normal weght of the asset class, W a = the actual weght, R p = the total passve return on the asset class ndex, R a = the total actve return on the asset class, and R = the total portfolo benchmark return. The frst term on the rght-hand sde of Equaton (1) defnes the contrbuton of securty selecton and the second gves the porton attrbutable to external rsk postonng (actve asset allocaton). The thrd term solates the nteracton of securty selecton and allocaton. Wthn ths defnton of return, the contrbuton of rsk postonng s lmted to changes n the weghts of asset classes. Ths s an unnecessary constrant. We can subdvde the actual actve return on each asset class nto a pure selecton component, R s ndcatng the equty-only return and a component that solates the effect of nternal rsk postonng, R h ndcatng the actual or synthetc cash return: R a = (1 c)r s + cr h, (2) where c equals the proporton of the fund held n cash. Insertng Equaton (2) nto Equaton (1) provdes a framework for determnng the effect of asset class performance, n terms of both securty selecton and explct nternal rsk actvty, on the extra return of the entre portfolo: E = (R s R p )W p + [(W a W p )(R p R) + c(r h R p )W a ] + [(1 c)w a W p ] (R s R p ). (3) Table IV compares Equatons (1) and (3), showng the contrbuton to the extra return of a mult-asset portfolo from securty selecton, actve asset allocaton (external rsk postonng) and nternal rsk postonng. The effect of nternal rsk postonng ndcated n the table s equal to the dfference between the return on the cash poston and the return on the asset class ndex (R h - R p ), adjusted by the mpled weght of the rsk-adjusted poston n the total ndex (cw p ). Wth nether nternal nor external rsk postonng, the contrbuton of the asset class manager to the extra return on the total portfolo s gven by the extra return from selecton only. That s, settng R a equal to Rs, Wa equal to Wp and c equal to zero n Equaton (3) gves: E s = W p (R s R p ). (4) The decson to rsk-poston nternally wthn the asset class alters ths result, and the contrbuton to relatve performance becomes: E h = W p (R a R p ). (5) Subtractng Equaton (4) from Equaton (5) gves the total effect of the nternal hedgng decson beng mposed on preexstng selecton performance: E h E s = W p (R a R s ) = c(r h R p )W p c(r s R p )W p. (6) The second term s the porton of the crossproduct term ntroduced by the explct decson to hedge the asset holdngs. That s, the frst term solates the pure effect of the hedge and the second measures the effect of the nteracton FINANCIAL ANALYSTS JOURNAL/MAY-JUNE

9 of the hedge and the results of the selecton strategy. Equaton (6) shows that, even f the hedge does protect the fund from an adverse return on the asset class (.e., R h > R p ), the net effect mght be negatve. If selecton wthn the fund s also successful (.e., R s > R p ), the second term n Equaton (6) could be larger than the frst. The more effectve the selecton process, the less attractve nternal hedgng s. Rearrangng terms n Equaton (6) shows that the total effect of the hedge on the performance of the total portfolo s equal to: c(r h R s )W p. If R s exceeds R h, an nternal hedge wll detract from performance of both the fund and a mult-asset portfolo, even when the return on cash exceeds the return on the ndex (R h > R p). Our data do not allow us to go nto a detaled analyss of performance attrbuton. A general proxy for the amount of nternal rsk postonng, however, could be the beta of the actve returns wth respect to a passve benchmark. As data become avalable, t would be useful to explore further the mpact of nternal rsk postonng on performance attrbuton. Concluson For our sample of penson plans, actve nvestment decsons by plan sponsors and managers, both n terms of selecton and tmng, dd lttle to mprove performance over the 10-year perod from December 1977 to December Although ndvdual results vared wdely, n general t was dffcult to fnd postve explanatory relatons between performance and nvestment behavor. For example, extra returns seemed to be unrelated to the level of actve management. Moreover, t seemed to be harder for managers to outperform equty benchmarks than bond and cash benchmarks; many more plans had postve contrbutons from the bond and cash portons of ther portfolos. A more detaled hstory of portfolo compostons would help to specfy better the contrbutons of nvestment decsons to overall performance. In partcular, the extent of nternal rsk postonng used by managers could sgnfcantly alter attrbutons. 6 Footnotes 1. G. P. Brnson, L. R. Hood and G. L. Beebower, "Determnants of Portfolo Performance," Fnancal Analysts Journal, July/August C. R. Hensel, D. D. Ezra and J. H. Ilkw ("The Value of Asset Allocaton Decsons," Russell Research Commentares, March 1990) provde alternatve support for the concluson that the polcy decson domnates other aspects of the nvestment process. They offer a useful extenson of ths methodology for evaluatng polcy allocatons. 3. G. P. Brnson, "Asset Allocaton vs. Market Tmng,'' Investment Management Revew, September-October D. Gallagher, "The Sxty-four Bllon Dollar Queston,'' Global Investor, June One potental drawback to the use of correlaton coeffcents arses from the fact that the return seres may not be normally dstrbuted. In fact, an actvely managed portfolo s lkely to have a ch-square component. Ths arses from the fact that the return to an actvely managed portfolo s the product of normally dstrbuted weghts and normally dstrbuted returns. The product of two normally dstrbuted random varables follows the ch-square dstrbuton. A dscusson of ths phenomenon appears n P. H. Dybvg and S. A. Ross, "Dfferental Informaton and Performance Measurement usng a Securty Market Lne," Journal of Fnance, June We thank Matthew R. Smth for hs valuable assstance n the preparaton of ths artcle. FINANCIAL ANALYSTS JOURNAL/MAY-JUNE

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