determinants of portfolio performance

by Gary P. Brinson, Brian D. Singer and Gilbert L. Beebower

Determinants ef PortfeHePerfermance n: An Update

This article presents a framework for determining the contributions of different aspects of theinvestment management process—asset allocation policy, active asset allocation, andsecurity selection—to the total return of investment portfolios. Data from 82 large pensionplans indicate that asset allocation policy, however determined, is the overwhelminglydominant contributor to total return. Active investment decisions by plan sponsors andmanagers did little on average to improve performance over the 10-year period December1977 to December 1987. The performance attribution framework is also extended to accountfor actual and synthetic cash holdings within asset classes.

IN "DETERMINANTS of Portfolio Perfor-mance," published in this journal in 1986,we documented the overwhelming contri-

bution of asset allocation policy to the returnperformance of a sample of 91 large pensionplans. ̂ That earlier article developed a system-atic framework for the attribution of returns todifferent types of active investment decisions.

This article, also focusing on return attribu-tion, updates the results of the previous studyand confirms our original conclusions. Specifi-cally, data from 82 large pension plans over the1977-87 period indicate that investment policyexplained, on average, 91.5 per cent of thevariation in quarterly total plan returns. In ad-dition, this article provides an expanded perfor-mance attribution framework that accounts, notonly for security selection and active asset allo-cation, but also for changes in portfolio riskcharacteristics attributable to risk positioningwithin individual asset classes.

Neither this article nor its predecessor at-tempts to evaluate the efficacy of investmentpolicies. Rather, the concentration is on theoverwhelming impact of policy—^however es-tablished—and the incremental effect of activeinvestment sfrategies.^

1. Footnotes appear at end of artide.

FrameworkOur earlier article outlined a framework fordissecting total plan returns into three compo-nents—asset allocation policy, active asset allo-cation, and security selection. The distinctionbetween asset allocation policy and active assetallocation needs to be delineated. Asset alloca-tion policy involves the establishment of normalasset class weights and is an integral part ofinvestment policy. Active asset allocation is theprocess of managing asset class weights relativeto the normal weights over time; its aim is toenhance the managed portfolio's risk/returnfradeoff. This distinction is material to under-standing the importance of investment policyrelative to active management.

Figure A illusfrates the framework for report-ing and analyzing portfolio returns. Quadrant Iindicates the total return provided by the invest-ment policy adopted by the plan sponsor. Thepolicy "portfolio" thus represents a constant,normal allocation to passive asset classes. In-vestment policy, then, identifies the plan's nor-mal portfolio composition. Calculating the pol-icy return involves applying the normal weightsof each investable asset class to the respectivepassive returns.

Quadrants II and in shift the focus to activemanagement. Quadrant II reports the returnattributable to a portfolio reflecting both policyand active asset allocation. Whether active allo-

FINANOAL ANALYSTS JOURNAL / MAY-Jlfl^ 1991 Q 40

GlossaryReturn Attribution: The process of attributing

actual portfolio return to those investment man-agement activities that contribute to the re-turn—investment policy, active asset allocationand security selection.

Investment Policy: Specification of the plan spon-sor's objectives, constraints and requirements,including identification of the normal asset allo-cation mix.

Active Asset Allocation: Temporarily deviatingfrom the policy asset mix in order to benefitfrom a state of capital market disequilibriumwith respect to the investment fundamentalsunderljdng the policy mix.

Coefficients of Determination: The percentage ofvariability in one random variable that is ac-counted for by another random variable. Themore familiar R ,̂ indicating the variability of thedependent variable accounted for by a regres-sion model, is identical to the coefficient ofdetermination for univariate regressions.

Risk Positioning: The active allocation out ofnon-cash assets into cash equivalents at theasset allocation level and the holding of cashwithin an asset class portfolio.

External Risk Positioning: The allocation into andout of cash-equivalent assets. The term "exter-nal" refers to positioning at the asset class level.As segregating the cash component at the assetclass level is a rather common aspect of activeasset allocation performance attribution, "exter-nal risk positioning" is used in a broader senseto mean active asset allocation.

Internal Risk Positioning: The establishment of aposition in actual or synthetic cash, typically tocontrol beta or duration risk, within an assetclass. The term "intemal" refers to positioningwithin an asset class.

IVActual

PortfolioReturn

IIIPolicy andSecuritySelectionReturn

11Pblicy and

Active AssetAllocation

Return

IPolicy Return

(PassivePbrtfolio

Benchmark)

Figure A A Simplified Framework forReturn Accountability

Security SelectionActual Passive

3 -< S(2

Active Returns Due to;

Active Asset Allocation II -1Security Selection III -1Other IV-III-n + ITotal IV -1

asset class. This framework specifies that thereturn from policy and security selection isobtained by applying the normal asset classweights to the actual active returns achieved ineach asset class.

Finally, Quadrant IV represents the actualreturn realized by the plan over the period ofperformance evaluation. This is the result of theplan's actual asset class weights interacting withthe actual asset class returns.

Figure B summarizes the calculations requiredto determine the returns for Quadrants I, II and

Figure B Computational Requirements forReturn Accountability*

cation involves anticipating price moves (markettiming) or reacting to market disequilibria (fun-damental analysis), it results in the under oroverweighting of asset classes relative to thenormal weights identified by policy.^ The aim ofactive allocation is to enhance the return and/orreduce the risk of the portfolio relative to itspolicy benchmark. The policy and active assetallocation return is computed by applying theactual asset class weights to their respectivepassive benchmark returns.

Quadrant III presents the returns to a portfo-lio attributable to policy and security selection.Security selection involves active investmentdecisions concerning the securities within each

< l

ActualSecurity Selection

Passive

IV5 (Wai •

IIIX (Wpi •I

Rai)

Rai)

IIX(Wai1

12 (Wpi1

•Rpi)

•Rpi)

'Vlpi = poiicy weight for asset class i; Wai = actual weight for assetclass i; Rpi = passive return for asset class U Rai = actual returnfor asset class i.

FINANCIAL ANALYSTS JOURNAL / MAY-JUNE 1991 D 41

Tabie I Calctilation of Active Contributions to TotalPerfonnance

Return Due to Calculated ByActive Asset

AUocationSecurity Selection

Other

Total

[(Wai * Rpi) - (Wpi * Rpi)](Quadrant II - Quadrant I)[(Wpi * Rai) - (Wpi • Rpi)](Quadrant III - Quadrant I)[Wai - Wpi) (Rai - Rpi)][Quadrant IV - (Quadrant U+ Quadrant HI) -I- Quadrant I][(Wai» Rai) - (Wpi * Rpi)](Quadrant IV - Quadrant I)

in. Table I provides the computational method-ology for determining the sources of activereturns. The active contribution to total perfor-mance is composed of active asset allocation,security selection, and the effects of a cross-product term that measures the interaction ofthe security selection and active asset allocationdecisions.

DataAttributing returns to the various aspects of

the investment process according to this frame-work requires historical data on portfolio com-position (weights), actual investment results,and returns to the appropriate benchmarks. SEICorporation provided 10 years of quarterly data,from December 1977 to December 1987, for 82pension plans in their Large Plan Universe. Theseven series available for each plan were four

asset-class-weight series for equity, bonds, cashequivalents and "other" and three quarterlyrate-of-retum series for the total plan and itsassociated equity and bond components. Thefocus of this artide is on investment perfor-mance, so all returns were expressed gross ofmanagement fees.

An analysis of the asset class weights indi-cates that there was no significant shift in assetclass preferences over the period covered by thesample data. Figure C demonsfrates that theaverage weights of the asset classes for thesample remained remarkably stable over time,despite market frends and volatility. This issomewhat at odds with other surveys showingincreased exposure to equities over similar pe-riods.*

Because the composition of the "other assets"category was unknown, its weight was allocatedto the equity, bond and cash components inproportion to their respective weights. Table IIshows that this component constituted a rela-tively small percentage (less than 15 per cent) oftotal plan assets and did not materially affecttotal plan returns. However, a few plans hadexfraordinarily large allocations to the "other"category over the period; these "outliers" wereomitted from the analysis. None of the samplefunds held non-U.S. bonds, and only two heldnon-U.S. equity. In these cases, the foreignequity was considered part of the equity com-ponent, without a material effect on the results.

We defined policy weights for each plan (the

Hgnte C Average Asset Class W e i ^ t s , 1977-1^7

1979 mo 1981 1982 1983 1^4 1985 1986 1987

Source: %I Corporatkm


Table n Analysis of Asset Class Weights, 82 Large Pension Plans, 1977-1987

Average

Summary of Holdings

Maximum MinimumStandardDeviation

EquityBondCashOther

53.0%24.5%12.1%10.5%

79.1%53.1%24.1%65.4%

26.0%4.0%3.0%0.1%

10.8%10.4%4.6%

12.0%

Average

Summary of Holdings Excluding "Other"

Maximum MinimumStandardDeviation

EquityBondCash

59.6%26.9%13.6%

83.9%54.0%24.3%

36.5%5.6%3.5%

10.5%10.2%4.9%

normal weights) as the 10-year average of theplan's asset class weights. These funds did notnecessarily favor a "typical" mix of assets (suchas 60/40 stocks/bonds), although, as Table IIshows, the average mix was very close to 60 percent equity and 40 per cent fixed income. FigureD shows that the observed combinations ofequity and bond weights cover almost thewhole range of possibilities.

Some plans showed evidence of a change inpolicy over the 10 years, either by a clear up-ward or downward frend in the weight of anasset class or a sudden and apparently perma-nent shift in the level of the quarterly weights.We attempted to account for this in the analysis.In cases where there appeared to be a policyshift, we divided the 10-year period into twoperiods—prechange and postchange—and cal-

culated returns based on the policy weights ineffect in each period.

ResultsIn addition to the actual reported return for eachplan, we defined three return series—policy,policy and active asset allocation, and policyand security selection. The policy return is thepassive portfolio benchmark return, calculatedas the sum of the policy weighted passive assetclass returns, using the 10-year average assetclass weights (as discussed above) and a suitablepassive index for each asset class. The S&P 500,the Salomon Broad Investment Grade (BIG)bond index and 30-day Treasury bills were usedas the passive indexes for the equity, bond andcash components, respectively.

The poUcy and active asset allocation return is

Figure D Average Equity Weight versus Average Bond Weight, 1977-1987

Big

ht

Bon

dW

60

50

40

30

20

10

0

-

**• • •

. • * •

*• *. "5 *.*' '•.

.'\ •

m • *• • • I I I

20 30 40 50 60Equity Weight

70 80 90

Source: SEI Corporation

FINANCIAL ANALYSTS JOURNAL / MAY-JUNE 1991 D 4 3

Figure E Nfean Armualized Returns by Activity,

82 Large Pension Plans, 1977-1987


IV13.41%

IU13.75%

II13.23%

I13.49%

Active Returns EKie to:

Active Asset AUocation - 0.26%Security Selection + 0.26%Other -0.07%Total -0.08%

calculated using the actual active weights andthe appropriate passive index returns. The pol-icy and security selection return is calculatedusing the policy weights and the actual activereturns. We repeated each analysis using abroader market index than the S&P 500; theresults were virtually identical.

The overall effect of active martagement byplan sponsors or investment managers was neg-ligible. This confirms the findings of our earlierstudy. Figure E and Table in show that theaverage portfolio underperformed its policybenchmark by eight basis points a year.

Individual effects varied widely, from a 3.4per cent per armum underperformance to a 6.7per cent per armum overperformance. The in-cremental return to active management had a

standard deviation of 1.7 per cent. Qearly thecontribution of active management is not statis-tically different from zero (that is, it is mostlikely attributable to chance). While active assetallocation contributed a net underperformanceof 26 basis points, and security selection contrib-uted a gain'of 26 basis points, neither figure isstatisticaUy different from zero.

Active management not only had no measur-able impact on returns, but (in the absence of aproxy for the variability of the respective pen-sion liabilities), it appears to have increased riskby a small margin (Figure F and Table III). Giventhe higher risk level of the policy and securityselection portfolio, it is evident that securityselection contributed to actual plan risk. Activeasset allocation appears to have had a negligibleimpact on risk relative to the benchmark policy.The imperfect correlation between the perfor-mances of the policy amd allocation and thepolicy and security selection portfolios miti-gated some of the increased risk.

None of these observations defracts from thefinding that the choice of investment policydominates the risk/return posture of the plan. Itis obvious that the overwhelming factor in de-termining the basic, long-term return achievedper unit of risk was investment policy.

Because active asset allocation is the processof managing asset class weights relative to thenormal weights, active management is condi-tional on the investment policy. Thus activereturns are conditionally distributed on the pol-icy return distribution. This domiriance is alsodemonsfrated by the coefficients of determina-tion for policy, policy and active asset alloca-tion, policy and security selection, and activereturns.

The coefficient of determination is the square

Table i n Annualized Returns and Risk by Activity, 1977-1987

PortfolioPolicyPolicy and Active A/APolicy and SelectionActual Portfolio

Active Return ComponentsActive A/A OnlySelection OnlyOther

Total Active Return

AverageReturn

13.4913.2313.7513.41

-0 .26-H0.26-0.07

-0.08

AverageRisk

11.4211.5613.7511.65

ReturnMinimum

12.4311.2610.5210.34

-1.81-3 .32-3 .50

-3 .43

ReturnMaximum

14.5615.0919.3219.95

0.866.121.33

6.73

X-Sec.Std. Dev.

0.490.681.661.75

0.471.520.80

1.67

FINANCIAL ANALYSTS JdnOMAL / MAY-JUNE 1991 D 44

Figure F Policy Risk versus Active Risk, \977-l9«7

16

14

Less RiskThan Pblicy

More RiskThan Policy

10 12Active Risk

14 16


of the correlation coefficient between two jointlydistributed random variables. It is used to de-scribe the amount of variability in one variablethat can be accounted for by another variable. Inthis instance, we are concerned with the per-centage of variability in actual returns that isaccounted for by policy, by policy and activeasset allocation, and by policy and securityselection.

Figure G shows that, on average, policy re-turns accounted for 91.5 per cent of the varianceof actual returns. Being conditionally distrib-uted on the policy returns, active asset alloca-tion and security selection combined could haveaccounted for only a small residual portion ofthe variance of actual returns. In fact, policy andactive asset allocation combined accounted for93.3 per cent and policy and security selectioncombined accounted for about %.l per cent.Again, the dominance of investment policy isdear.^

Although each level of risk was associatedwith a range of plan returns, active returnsgenerally increased with plan risk. Figure Hshows that, for a given risk level, the differencein performance between the best and the worstplans was as much as 3 per cent annually. Thetwo plans with exfraordinarily low risk hadhigher allocations to the "other asset" class—perhaps real estate, given the low volatility.Three other plans had unusuaUy sfrong returns,with each showing exfraordinary returns from

both stock and bond components over the entire10 years.

There are several possible explanations forthese irregularities. First, the arialysis did notaccount for the liability exposure of each plan.The inclusion of a liability proxy might shiftthese perfonnance statistics. Second, the use of10-year average weights for the passive bench-mark may have created an inefficient bench-

Figure G ftrcentage of Variation Explained,1977-1987


rv100.0%

m%.i%

u93.3%

191.5%

Average Minimuin Maximum Std. Dev.

Pblicy 91.5% 67.7% 98.2% 6.6%

Pblicy and Allocation 93.3% 69.4% 98.3% 5.2%

Pblicy and Selection % . 1 % 76.2% 99.8% 5.2%

FINANCIAL ANALYSTS JOURNAL / MAY-JUNE 1991 D 4 5

Hgiue H Average Return versus Average Plan Risk, 1977-1%7


mark. While the impact was probably not great,some bias was infroduced.

It is difficult, given these data, to determineconclusively which asset classes generated goodor bad relative performance. It should be noted,however, that 76 of the 82 equity funds under-performed the S&P 500 on an equity-only basis.

A complete 10-year bond performance was notavfulable for several funds, because their bondweights were zero for several quarters. For the70 cases with complete bond histories, almosttwo-thirds outperformed the passive bondbenchmark. Of those plans that underper-formed their policy benchmarks, over 75 percent underperformed in the bond component.As one would expect, the median cash manageroutperformed the 30-day T-bill index.

LimitationsOur analysis lacks some precision because of

perfonnance data limitations. First, as noted,the composition of the "other asset" categorywas unknown; in many cases, however, thiscategory constituted only a small percentage ofthe total portfolio. Second, policy portfolioswere inferred from the long-term average assetclass weights, and there is no assurance thatthey reliably represent the actual benchmarks.In terms of assessing the importance of thebenchmark to investment returns, however,this is probably not a serious proUem. Adjust-ing for apparent shifts in policy weights hadvery little effect on the analysis. In fact, using a

simple 60/40 stock/bond mix as a passive bench-mark for all the funds resulted in virtually thesame average results as indicated in Figure G.Given the average portfolio composition in Ta-ble II, this is not too surprising.

Finally, we do not know the actual number ofdifferent money managers used by these 82pension plans. While it is highly unlikely thatthe data represent only a few managers, thestudy does refiect the performance of individualmanagers, not necessarily pension fund perfor-mance in general. Furthermore, we know noth-ing about the styles of the managers or their useof futures and options. Some almost certsiinlyaltered intemal risk positions by hedging duringthe last quarter of 1987; this is indicated by thepositive equity returns at a time when themarket as a whole was down by almost 25 percent. The issue of hedging, and the broaderissue of risk positioning, is treated in moredepth below.

Internal versus External Risk PositioningBesides shifting asset class weights—^i.e., exter-nal risk p(»itioiiii^—a manager or sponsor canchange exposure to an asset class within aportfolio component-—intemal risk position-ing. Intemal methods include altering tiie com-ponent's beta or duration by using long or shorffutures positions, carrying cash or hedging thecurrency component. Looking at any single risk-positioning activity, external or internal, will not

FINANCIAL ANALYSTS K>U8NAL / MAY-JUNE 1991 D 4 6

Table IV Attribution of Intemal and External Risk Positioning

Equation (1) Equation (3)Security SelectionRisk Positioning

ExternalInternalCross Product

Cross Product

(Ra - Rp)Wp(Wa - Wp){Rp - R)(Wa - Wp)(Rp - R)

00

(Wa - Wp)(Ra - Rp)

(Rs - Rp)Wp(Wa - Wp)(Rp - R) + c(Rh - Rp)Wa

(Wa - Wp)(Rp - R)c(Rh - Rp)Wp

c(Wa - WpXRh - Rp)[(1 - c)Wa - Wp](Rs - Rp)

give a complete or accurate measure of theactive portfolio management effect.

The performance-attribution framework out-lined above defines the exfra return, E, to amulti-asset porffolio attributable to a particularasset class as:

E = (Ra - Rp)Wp

E = (Rs - Rp)Wp - Wp)(Rp - R)

Wa - Wp)(Rp - R)

- Wp)(Ra - Rp), (1)

where

Wp = the normtd weight of the asset class,Wa = the actual weight,Rp = the total passive return on the asset

class index,Ra = the total active return on the asset

class, andR = the total portfolio benchmark retum.

The first term on the right-hand side of Equation(1) defines the contribution of security selectionand the second gives the portion attributable toexternal risk positioning (active asset alloca-tion). The third term isolates the interaction ofsecurity selection and allocation. Within thisdefinition of retum, the contribution of riskpositioning is limited to changes in the weightsof asset classes.

This is an unnecessary consfraint. We cansubdivide the actual active retum on each assetclass into a pure selection component, Rs—indicating the equity-only retum—and a com-ponent that isolates the effect of intemal riskpositioning, Rj,—vindicating the actual orthetic cash retum:

= (1 - c)Rs + (2)

where c equals the proportion of the fund heldin cash. Inserting Equation (2) into Equation (1)provides a framework for determining the effectof asset class performance, in terms of bothsecurity selection and explicit intemal risk activ-ity, on the extra retum of the entire portfolio:

[(1 -

(3)

Table IV compares Equations (1) and (3),showing the contribution to the exfra retum of amulti-asset portfolio from security selection, ac-tive asset allocation (extemal risk positioning)and intemal risk positioning. The effect of inter-nal risk positioning indicated in the table isequal to the difference between the return onthe cash position and the retum on the assetclass index (R^ — Rp), adjusted by the impliedweight of the risk-adjusted position in the totalindex (cWp).

With neither intemal nor extemal risk posi-tioning, the confribution of the asset class man-ager to the exfra retum on the total portfolio isgiven by the exfra retum from selection only.That is, setting Ra equal to R ,̂ Wa equal to Wpand c equal to zero in Equation (3) gives:

The decision to risk-position internally withinthe asset class alters this result, and the contri-bution to relative performance becomes:

Eh = Wp(Ra - Rp). (5)

Subfracting Equation (4) from Equation (5)gives the total effect of the intemal hedgingdecision being imposed on preexisting selectionperformance:

Eh - Es = Wp(Ra - Rs) = c(Rh - Rp)Wp

- c(Rs - Rp)Wp. (6)

The second term is the portion of the cross-product term infroduced by the explicit decisionto hedge the asset holdings. That is, the firstterm isolates the pure effect of the hedge andthe second measures the effect of the interaction


of the hedge and the results of the selectionsfrategy.

Equation (6) shows that, even if the hedgedoes protect the fund from an adverse retum onthe asset class (i.e., R^ > Rp), the net effectmight be negative. If selection within the fund isalso successful (i.e., R̂ > Rp), the second termin Equation (6) could be larger than the first. Themore effective the selection process, the lessatfractive internal hedging is.

Rearranging terms in Equation (6) shows thatthe total effect of the hedge on the perfonnanceof the total portfolio is equal to:

c(Rh - Rs)Wp.

If Rs exceeds Rj,, an intemal hedge will defractfrom performance of both the fund and a multi-asset porffolio, even when the retum on cashexceeds the retum on the index (R^ > Rp).

Our data do not allow us to go into a detailedanalysis of performance attribution. A generalproxy for the amount of intemal risk position-ing, however, could be the beta of the activeretxuns with respect to a passive benchmark. Asdata become available, it would be useful toexplore further the impact of intemal risk posi-tioning on performance attribution.

ConclusionFor our sample of pension plans, active invest-ment decisions by plan sponsors and managers,both in terms of selection and timing, did littleto improve performance over the 10-year periodfrom December 1977 to December 1987. Al-though individual results varied widely, in gen-eral it was difficult to find positive explanatoryrelations between performance and investmentbehavior. For example, exfra returns seemed tobe unrelated to the level of active management.Moreover, it seemed to be harder for managers

to outperform equity benchmarks than bondand cash benchmarks; many more plans hadpositive contributions from the bond and cashportions of their portfolios.

A more detailed history of portfolio composi-tions would help to specify better the contribu-tions of investment decisions to overaU perfor-mance. In particular, the extent of intemal riskpositioning used by managers could signifi-cantly alter attributions.* •

Footnotes1. G. P. Brinson, L. R. Hood and G. L. Beetxjwer,

"Deternunants of Portfolio Performance," Finan-cial Analysts Journal, July/August 1986.

2. C. R. Hensel, D. D. Ezra and J. H. Ilkiw ("TheValue of Asset Allocation Decisions," Russell Re-search Commentaries, March 1990) provide alterna-tive support for the conclusion that the policydecision dominates other aspects of the invest-ment process. They offer a useful extension of thismethodology for evaluating policy allocations.

3. G. P. Brinson, "Asset Allocation vs. Market Tim-ing," Investment Management Review, Septemt)er-October 1988.

4. D. Gallagher, "The Sixty-four Billion Dollar Ques-tion," Global Investor, June 1988.

5. One potential drawback to the use of correlationcoefficients arises from the fact that the retumseries may not be normally distributed. In fact, anactively managed portfolio is likely to have achi-square component. This arises from the factthat the retum to an actively managed portfolio isthe product of normally distributed weights andnormally distributed returns. The product of twonormally distributed random variables follows thechi-square distribution. A discussion of this phe-nomenon appears in P. H. Dybvig and S. A. Ross,"Differential Information and Performance Mea-surement using a Security Market Line," Journal ofFinance, June 1985.

6. We thank Matthew R. Smith for his valuableassistance in the preparation of this article.

FINANOAL ANALYSTS JOURNAL / MAY-JUNE 1991 D 48

determinants of portfolio performance

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