Prudential Real Estate Investors

Return Attribution for Commercial Real EstateInvestment Management

David Bradford (973) 683-1698 david.bradford@prudential.com

Youguo Liang, Ph.D. (973) 683-1765 youguo.liang@prudential.com

Robert Hess, Ph.D. (973) 683-1689 robert.hess@prudential.com

Willard McIntosh, Ph.D. (973) 683-1793 willard.mcintosh@prudential.com

March 1999

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h Executive Summary

The practice of evaluating manager performance has gained popularity in recentyears with the development of techniques for decomposing returns intocontributions from various types of manager activities.

Published description of these techniques dates back a little more than a decade.Brinson, Hood and Beebower (1986) pioneered this work, proposing amethodology which separates raw returns into a selection component and anallocation component. Recently, this methodology was applied to Canadiancommercial real estate by Hamilton and Heinkel (1995). The same methodologywas publicized by Lieblich (1995) in The Handbook of Real Estate PortfolioManagement. Brinson, Singer, and Beebower (1991), Higgs and Goode (1993),Singer (1996b), and Dolan (1998) further elaborated this methodology.1

A manager shows superior property selection skills when he/she holds individualproperty investments that outperform the market. Alternatively, the manager mayhold average performing properties in selected sectors of the market,underweighting a property sector when sector return is low and overweighting itwhen return is high, to achieve superior performance. Under these circumstances,this manager is said to have sector allocation skills. A manager may have betterthan average skills in both selection and allocation, or either selection orallocation, or neither of the two.2

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In this paper we offer a refinement to this return attribution approach in cases whereportfolio performance is measured against both an aggregate benchmark and benchmarksfor sub-sectors. We also suggest a modified presentation format to report both single andmulti-period return attributes. This technique may improve the capacity of both managersand investors to assess and improve management skills and manager value added to theportfolio management process. Variations of this methodology are also discussed. Privatecommercial real estate returns are used to illustrate this approach.

Return Attribution

Suppose a portfolio can be fully decomposed into n sectors (typically five sectors forcommercial real estate: apartment, industrial, office, retail, and others) for whichperformance benchmarks exist. Define the following:

ai = (actual) portfolio allocation to sector i, where Σai = 1;bi = benchmark allocation to sector i, where Σbi = 1;Ri = portfolio return for sector i;Bi = benchmark return for sector i;P = portfolio aggregate return, or ΣaiRi; andB = benchmark aggregate return, or ΣbiBi.

Our attribution methodology calls for decomposing returns into the following categories:3

Exhibit 1. Return Attributes for Sector i and the Portfolio

Sector i PortfolioGross Value Added aiRi-biBi R-B, or ΣaiRi-ΣbiBi

Less Neutral Effect (ai-bi)B 0Net Value Added ai(Ri-B)-bi(Bi-B) R-B, or ΣaiRi-ΣbiBi

Selection Contribution ai(Ri-Bi) R-ΣaiBi, or ΣaiRi-ΣaiBi

Allocation Contribution (ai-bi)(Bi-B) ΣaiBi-B, or ΣaiBi-ΣbiBi

Gross value added for the portfolio is simply the difference between the portfolio return(R) and the benchmark return (B). For an individual sector i, however, gross value addedis the proportion of the portfolio return attributable to sector i (aiRi) minus the proportionof the benchmark return attributable to sector i (biBi). This formulation follows theoriginal approach by Brinson, Hood and Beebower (1996) and can be found throughoutthe literature.

The property selection contribution for the portfolio is the portfolio return (R) minus thereturn from an artificial portfolio which has the same allocation to each sector (ai) as theportfolio but whose sector-by-sector returns equal those of the benchmark. That is, afterallowing for allocation differences, any remaining return variation between the portfolioand the benchmark must arise from the manager’s ability to achieve excess returns in eachsector, which come from advantageous investment selections. The corresponding propertyselection contribution for sector i is the difference between portfolio return for the sector

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(Ri) and the benchmark return for the sector (Bi) multiplied by the portfolio allocation to it(ai).

In most formulations, including ours, the allocation contribution for the portfolio is thedifference between the return of an artificial portfolio (ΣaiBi) and the aggregatebenchmark return (B or ΣbiBi). The two portfolios have identical sector returns (Bi) butdifferent sector allocations. The return difference, therefore, is properly attributed tosector allocation contribution. Moreover, the sum of the selection contribution and theallocation contribution equals the gross value added for the portfolio.

For individual sectors, however, our allocation contribution formula differs markedly fromthat of Brinson, Hood and Beebower (1986). Intuitively, we want a manager to receive anallocation contribution increment whenever the portfolio manager actively overweightssectors whose benchmarks are outperforming the aggregate and whenever the portfoliounderweights underperforming sectors. Therefore, the allocation contribution for sector iis a product: the incremental allocation (ai-bi) multiplied by the incremental return over theaggregate benchmark (Bi-B). For example, if a portfolio has been allocated 5% more forsector i relative to the benchmark and the benchmark return for sector i is 10% higher thanthe aggregate benchmark return, then the manager receives an allocation contribution of50 basis points associated with sector i. The overweighting of the outperforming sectorgenerates the desired allocation contribution. At the same time, if the portfolio has beenallocated 5% less for sector i and the benchmark for sector i is 10% below the aggregatebenchmark return, the manager also receives an allocation contribution of 50 basis points– a reward for partially avoiding investing in an underperforming sector.

With this change, the selection contribution and the allocation contribution for anindividual sector no longer sum up to the gross value added of that sector. The difference,as shown in Exhibit 1, is properly termed as neutral effect because the sum of these effectsis zero at the portfolio level. In addition, the effect is neutral because it does not captureany value added by the portfolio manager.

An example is the best way to illustrate what the neutral effect captures. Suppose thebenchmark portfolio is comprised of only two sectors: office and retail with 50%allocation to each sector. The actual portfolio has an allocation of 75% to office and 25%to retail. The returns for the benchmark and its two sectors, and the actual portfolio andits two sectors are all identical at 12%. In this case, the property selection contribution forthe office sector (for retail as well) must be zero because the office sector return in theportfolio is the same as the office sector return in the benchmark. The allocationcontribution for the office sector (for retail as well) must be zero because the office sectorreturn is identical to the aggregate benchmark return. That is, there can be no trueselection or allocation advantages because the returns are the same as each other. Yet, thegross value added for the office sector is 0.75*12%-0.5*12% = 3.0% and 0.25*12%-0.5*12% = -3.0% for the retail sector. In this case, the neutral effect for office is (0.75-

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0.5)*12% = 3.0%, and for retail is (0.25-0.5)*12% = -3.0%. Subtracting these terms fromthe respective gross value added figures yields a zero net value added for each sector. The±3.0% are called a neutral effect because they do not capture any net contributions toportfolio performance originated from a manager’s skills. What the neutral effect capturesis the return attributable to a sector when all sectors in the portfolio as well as in thebenchmark are undifferentiated from a return perspective because they all have identicalreturns.

Suppose, now, that the office returns are 14% for both the benchmark and actual portfolioand that the retail returns are 10%, again for both the benchmark and the portfolio. Notethat the aggregate benchmark return is 12% but the portfolio return is 13%, and allselection effects are zero. An overweighting of the better performing office sectorcombined with an underweighting of the poorer performing retail sector generated anexcess return for the portfolio. In this case, the gross value added for the office sector is3.5% and the gross value added for the retail sector is -2.5%. The signs of the two effectsappear correct, but the formula would imply that the office sector contributed the lionsshare of allocation advantages. Now subtract the neutral effect to the office sector of(0.7-0.5)*12% = 3.0% and the retail sector of (0.3-0.5)*12% = -3.0% from the grossvalue added figures. We obtain a net value added of 3.5%-3.0% = 0.5% for the officesector and -2.5%-(-3.0%) = 0.5% for the retail sector. Both contributed a positiveincrement to the allocation contribution. Clearly, this is a more appealing result. Again,the ±3.0% are called a neutral effect because they do not capture any net contributions toportfolio performance originating from a manager’s skills.

An Example

Exhibit 2 shows the performance of a hypothetical commingled real estate portfoliorelative to its benchmark from a property type perspective. It clearly demonstrates thesources of value added by the manager. The benchmark for private real estate is typicallythe National Council of Real Estate Investment Fiduciaries (NCREIF) Property Index,which has four sectors and another category that comprises primarily hotels. As used inthis attribution approach, NCREIF publishes performance benchmarks for thesecategories.

In aggregate, the portfolio return outperformed its benchmark by 5.04%. This excessreturn arose from a positive property selection contribution of 4.48% and a positiveallocation contribution of 0.56%. It is apparent that in this case the property selectioneffects contributed overwhelmingly to the aggregate excess return.

In addition, we can characterize the manager’s contributions by property type. During theevaluation period the manager demonstrated above average property selection skills in theapartment and office sectors. But the property selection skills of the manager were belowaverage in the retail sector and the other category. Note also that the selectioncontribution from the industrial category was zero. This is appropriate as the portfolioreturn for this sector coincided with its benchmark return.

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The manager successfully anticipated the high return of the office sector and the lowreturn of the retail sector and overweighted office and underweighted retail relative to thebenchmark. As a consequence, the allocation contributions from these two sectors werepositive. The manager, however, overweighted both apartments and industrials when theirreturns were low relative to the aggregate return of the benchmark. Their respectiveallocation contributions were negative. Note also that the allocations to the other categorywere identical, resulting in a zero allocation contribution from the category.

Note that the net value added for the industrial sector was slightly negative, an appropriatefinding for a sector whose return (14%) failed to exceed the aggregate benchmark return.The gross value added concept inappropriately assigns a positive value added to thissector, due solely to the fact that it was overweighted in the portfolio relative to thebenchmark. Similarly, the net value added for the retail sector is slightly positive,acknowledging the good judgment of the manager to underweight this category. Thegross value added concept assigns an inappropriately large negative contribution to retail,again reflecting the underweighting of this sector by the manager.

Exhibit 2. An Example of Return Attribution Analysis

Inputs Apartment Industrial Office Retail Other TotalPortfolio Weight 24% 25% 40% 8% 3% 1.00Benchmark Weight 15% 17% 35% 30% 3% 1.00Portfolio Return 17% 14% 30% 6% 10% 20.36%Benchmark Return 12% 14% 20% 12% 18% 15.32%Attribution AnalysisGross Value Added 2.28% 1.12% 5.00% -3.12% -0.24% 5.04% Less Neutral Effect 1.38% 1.23% 0.77% -3.37% 0.00% 0.00%Net Value Added 0.90% -0.11% 4.23% 0.25% -0.24% 5.04% Selection Contribution 1.20% 0.00% 4.00% -0.48% -0.24% 4.48% Allocation Contribution - 0.30% -0.11% 0.23% 0.73% 0.00% 0.56%

Methodological Variations

In their original construct, Brinson, Hood, and Beebower (1986) suggest the followingdecomposition of returns (Exhibit 3):

Exhibit 3. Brinson, Hood and Beebower (1986) Decomposition

Sector i PortfolioTotal Value Added aiRi-biBi R-B Selection Contribution bi(Ri-Bi) ΣbiRi-B Allocation Contribution (ai-bi)Bi ΣaiBi-B Interaction Effect (ai-bi)(Ri-Bi) R+B-ΣaiBi-ΣbiRi

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There are many similarities between this approach and the one we propose here, but thereare two principal differences. First, the allocation contribution is defined totally differentlyfrom the one we propose. Under the formulation presented by Brinson, et. al., a positiveallocation contribution is accorded to a sector whenever the portfolio allocation is largerthan the benchmark, and a negative allocation contribution is accorded whenever thebenchmark allocation is larger than the portfolio allocation, assuming a positive return forthe benchmark. This does not conform to our common sense view of the allocationcontribution because it should be positive only when an outperforming sector isoverweighted or an underperforming sector is underweighted. Nevertheless, as a whole,our net allocation contributions for the portfolio is identical to theirs: the portfolioallocation effect in Exhibit 3 is identical to the one shown in Exhibit 1.

Secondly, Brinson, et. al. identify an interaction effect consisting, at the sector level, ofmultiplying the allocation increment (portfolio vs. Benchmark) by the return increment.Other researchers have used the phrase, cross product, to describe terms like this. Wehave chosen to combine this term with the selection contribution. That is, the sum ofinteraction effect and selection contribution in Exhibit 3 is the same as the selectioncontribution in Exhibit 1.

The use of a separate interaction effect avoids the problem of trying to assign it to either aselection contribution or an allocation contribution. In truth, it has characteristics of both,consisting of the product of a return increment (a selection effect) and an allocationincrement. There is really no logical way to determine the superiority of one approachover another in this regard. Therefore, for completeness we present three variations of thisreturn attribution construction in Exhibit 4. All are logical, rational and make commonsense.

Exhibit 4. Variations of Return Decomposition for Sector i

Method I Method II Method IIIGross Value Added aiRi-biBi aiRi-biBi aiRi-biBi

Less Neutral Effect (ai-bi)B (ai-bi)B (ai-bi)BNet Value Added ai(Ri-B)-bi(Bi-B) ai(Ri-B)-bi(Bi-B) ai(Ri-B)-bi(Bi-B) Selection Contribution ai(Ri-Bi) bi(Ri-Bi) bi(Ri-Bi) Allocation Contribution (ai-bi)(Bi-B) (ai-bi)(Ri-B) (ai-bi)(Bi-B) Interaction Effect (ai-bi)(Ri-Bi)

Method I assigns all of the interaction effect to the selection contribution. That is, anycontributions arising from portfolio sector returns that vary from the sector benchmarkreturns appear in the selection contribution. Method II assigns all of the interaction effectto the allocation contribution. Therefore, any contribution arising from portfolio sectorshares that vary from the benchmark allocation shares appear in the allocationcontribution. Method III makes no assignment of the interaction effect; it appears as aseparate line in the report.

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One should select one of the methodologies and apply it consistently. We recommendMethod I on the basis of simplicity and ease of interpretation. After all, it is very difficultto explain an interaction effect to a portfolio manager or a pension fund client.4

Further Considerations

Strategic versus Tactical Allocation

Allocation contributions can be further decomposed into strategic and tactical allocationcontributions with the introduction of portfolio allocation strategic targets for each sector(pi). If a portfolio has a policy allocation target of pi to sector i, then for any particularperiod the strategic allocation contribution is (pi-bi)(Bi-B) and the tactical allocationcontribution is (ai-pi)(Bi-B).5 The two add up to the allocation contribution of (ai-bi)(Bi-B)as shown in Exhibit 1.

Multiple Periods

There are many ways to approximately aggregate period-specific return attributes to asingle, multi-period selection and allocation contributions but no entirely satisfactory wayexists to generate an exact aggregation.

One method is to treat averages of sub-period selection and allocation contributions asmulti-period attributes. While this methodology does not introduce additional terms in themulti-period attribution presentation, it also does not capture the cumulative effect of amanager’s selection and attribution skills.6

Another method is to compound the individual period selection contributions into themulti-period selection contribution (doing the same for allocation contributions). Thismethod is sound in reasoning but complicated in implementation because of many errorterms that appear in the calculations.7

We prefer the methodology shown in Exhibit 5. This methodology calls for creating a setof multiple-interval sector weights and sector returns, then computing the attributionmeasures from these multi-period performance measures; averaging the single periodsector weights to produce the multi-period sector weights; calculating compounded,annualized sector returns for the multi-period sector returns. Follow the same for theaggregate returns. Finally, calculate portfolio and benchmark weighted average returnsfrom the multi-period sector returns and weights.

Unavoidably, there is one variance: the total value added is different from the gross valueadded because compounded component returns do not add up to the compounded totalreturn. In the example below, the total value added of 4.29% per annum is the differencebetween the portfolio return and the benchmark return. Gross value added of 3.62% is thedifference between the portfolio and benchmark weighted average returns. We call the

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difference the compounding effect. The rest of attribution analysis for a multi-period isstraightforward, decomposing the gross value added into the attribution categories.

In the example below, over multiple periods, the portfolio manager has outperformed thebenchmark by 4.29% per year, of which 3.56% is due to the manager’s property selectionskills and only 0.06% is due to the manager’s sector allocation skills (returns areannualized). It is apparent that the policy allocation targets would not have worked wellover the whole period, but tactical divergence from the targets in the actual sectorallocations during this period by the manager offset their detrimental potential.

Selection and allocation contributions of the sectors over the whole period can also beclearly interpreted. For example, the office investments had a large, positive selectioncontribution but a marginally positive allocation contribution. The retail investments,however, had a marginally negative selection contribution but a large, positive allocationcontribution. Therefore, superior property selection skills contributed most of the valueadded in the office sector whereas superior allocation skills provided the value added inthe retail sector.

Exhibit 5. Multiple-Period Return Attribution

Muti-Period Inputs Apartment Industrial Office Retail Other TotalPortfolio Weight a 20.5% 23.5% 36.0% 14.0% 6.0% 1.00Policy Weight a 20.0% 20.0% 27.5% 27.5% 5.0% 1.00Benchmark Weight a 16.0% 16.5% 35.5% 29.0% 3.0% 1.00Portfolio Return b 12.93% 11.45% 25.94% 11.36% 12.47% 17.68%Benchmark Return b 10.49% 11.98% 16.96% 11.50% 12.89% 13.39%Portfolio Weighted Average Return c 17.02%Benchmark Weighted Ave Return c 13.40%Multi-Period Attribution AnalysisTotal Value Added 4.29% Less Compounding Effect 0.68%Gross Value Added 0.97% 0.71% 3.32% -1.74% 0.36% 3.62% Less Neutral Effect 0.60% 0.94% 0.07% -2.01% 0.40% 0.00%Net Value Added 0.37% -0.23% 3.25% 0.27% -0.04% 3.62% Selection Contribution 0.50% -0.13% 3.23% -0.02% -0.03% 3.56% Allocation Contribution -0.13% -0.10% 0.02% 0.28% -0.02% 0.06% Strategic Allocation Contr. -0.12% -0.05% -0.29% 0.03% -0.01% -0.43% Tactical Allocation Contr. -0.01% -0.05% 0.30% 0.26% -0.01% 0.49%a Simple average of subperiod weightsb Subperiod returns are compounded to arrive to the multi-period return; annualizing returns if necessaryc Weighted average returns using multi-period sector weights and returns

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Summary

In this paper we offer a refinement to a return attribution method proposed by thepioneers of return attribution analysis. Returns for the aggregate portfolio are decomposedinto selection and allocation contributions as originally presented. We introduce the use ofa neutral effect, which aggregates to zero at the portfolio level, that insures properinterpretation of the decomposition of the sector returns of the portfolio into selection andallocation contributions. The allocation contribution can be further separated into strategicallocation and tactical allocation contributions if policy weights for the portfolio areknown.

For multi-period attribution analysis, we recommend first compounding returns,annualizing them if necessary, and averaging portfolio weights, then performing regularattribution analysis on these returns and weights.

Knowledge of a portfolio manager’s property selection skills and sector allocation skills isimportant to investors, consultants and the managers themselves. While the nature andfocus of these skills may change over time, it is our hope that this paper helps to advancethe development and acceptance of a unified approach to measure them.

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Notes

1 In broad terms there are two attribution methodologies. The first is an attributionanalysis with no consideration given to risk, termed by us as return attribution,exemplified by the Brinson, Hood, and Beebower (1986) methodology. Return attributionanalysis relates a money manager’s skills such as selection and allocation to returns earnedby the manager, but without an explicit analysis of incremental risk relative to abenchmark. The second is an attribution analysis which incorporates the risk dimension.We term this methodology risk-adjusted return attribution. Fama (1972) was the firstperson to decompose returns into a component that measures a manager’s skill level and acomponent that is attributable to the underlying risk in the portfolio. Ankrim (1992)presents an extension to Fama’s method. Please see Singer (1996a) for a review of risk-adjusted return attribution methods.

The first return attribution methodology was published in 1986 by Brinson, Hood, andBeebower. Return attribution for private commercial real estate is particularly relevantbecause risk measures such as volatility and beta are not universally accepted as truemeasures of risk when applied to private real estate. The major reasons cited areinfrequent trading and valuation of commercial real estate and appraisal smoothing.

2 Market timing skills in a broad sense are equivalent to allocation skills because markettiming is accomplished through changing allocations. Market timing means increasing ordecreasing allocation to a sector when the return is anticipated to rise or fall relative to abenchmark. Both market timing and allocation have been used to describe the same set ofskills. We choose to use the term allocation for the sake of consistency.

3 This is in line with the one proposed by Singer (1996b).

4 Another way to view the variations is that selection contribution cannot be totallyseparate from allocation contribution. The gray area between the two suggests that thereare different ways of decomposing returns into selection and allocation components.Methods I and II may have delineated the upper and lower limits (or lower and upperlimits) of selection contribution as well as allocation contribution.

5 Methods II and III may have similar adjustments.

6 While we do not recommend this method of aggregation, this does not imply that it isuseless. A perfect analogy would be arithmetic average and geometric average of return.While the arithmetic average is not cumulative, it is certainly a useful metric in abstractinginformation from a series of period returns.

7 Many error terms need to be introduced when contributions are compounded. Althoughthese error terms are generally small in magnitude, they can be large if more periods areinvolved or more volatile performance relative to the benchmark is analyzed (see thefollowing).

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Sector i PortfolioTotal Value Added x Less Error 1 xGross Valued Added x x Less Neutral Effect x x Less Error 2 x xNet Value Added x x Error 3 x x Selection Contribution x x Allocation Contribution x x Strategic Allocation Contr. x x Tactical Allocation Contr. x x Error 4 x x

x = applicable to the cell.

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References

Ankrim, Ernest M., “Risk-Adjusted Performance Attribution,” Financial AnalystsJournal, April 1992, 75-82.

Brinson, Gary P., L. Randolph Hood and Gilbert L. Beebower, “Determinants of PortfolioPerformance,” Financial Analysts Journal, July-August 1986, 39-44.

Brinson, Gary P., Brian D. Singer and Gilbert L. Beebower, “Determinants of PortfolioPerformance II: An Update,” Financial Analysts Journal, May-June 1991, 40-48.

Dolan, Phillip M., “Assessing the Value in Asset Allocation,” The Journal of PerformanceMeasurement, Spring 1998, 5-16.

Fama, Eugene F., “Components of Investment Performance,” The Journal of Finance,June 1972, 551-567.

Hamilton, Stanley W. and Robert L. Heikel, “Sources of Value-Added in Canadian RealEstate Investment Management,” Real Estate Finance, Summer 1995, 57-70.

Higgs, Peter J. and Stephen Goode, “Target Active Returns and Attribution Analysis,”Financial Analysts Journal, June 1993, 77-80.

Lieblich, Fred, “The Real Estate Portfolio Management Process,” The Handbook of RealEstate Portfolio Management, Joseph L. Pagliari Editor, Irwin, Chicago, 1995, 998-1058.

Singer, Brian, “Evaluation of Portfolio Performance: Aggregate Return and RiskAnalysis,” The Journal of Performance Measurement, Fall 1996a, 6-16.

Singer, Brian, “Evaluation of Portfolio Performance: Attribution Analysis,” The Journalof Performance Measurement, Winter 1996b, 45-55.

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Information contained herein is based on data obtained from recognized statisticalservices, issuer reports or communications, or other sources, believed to be reliable.However, such information has not been verified by us, and we do not make anyrepresentations as to its accuracy or completeness. Any statements nonfactual in natureconstitute current opinions, which are subject to change.