Equity Performance Attribution Methodology

Transcription

1 Equity erformance Attribution Methodoloy Morninstar Methodoloy aper May 31, Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, in whole or in part, without the prior written consent of Morninstar, Inc., is prohibited.

2 Contents Introduction Overview Effects Versus Components Review of the Classic Approach--rinson, Hood, and eebower Review of Attribution Components--rinson and Fachler Top-Down Versus ottom-up Approach Arithmetic Versus Geometric Attribution Example Note asic Mathematical Expressions Formulas Explanation of Formulas Special Situation I--Groups Without Holdins Special Situation II--Short ositions Top-Down Approach for Sinle eriod Overview Arithmetic Method Geometric Method Example ottom-up Approach for Sinle eriod Overview Arithmetic Method Geometric Method Three-Factor Approach for Sinle eriod Overview Arithmetic Method Geometric Method Multiple-eriod Analysis Overview Multiperiod Geometric Method Multiperiod Arithmetic Method Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 2 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

3 Appendix A: Contribution Overview Sinle eriod Multiple eriod Appendix : Transaction-ased Attribution Overview Sinle eriod Multiple eriod Appendix C: Residual Overview Top-Down Approach, Arithmetic Method Top-Down Approach, Geometric Method Multiperiod Geometric Residual Version History May 2011 Updated for the addition of transaction-based attribution and contribution. March 2009 Updated for the addition of the three-factor model. December 2008 Oriinal version Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 3 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

4 Introduction Overview erformance attribution analysis consists of comparin a portfolio's performance with that of a benchmark and decomposin the excess return into pieces to explain the impact of various portfolio manaement decisions. This excess return is the active return. For a portfolio denominated in the investor's home currency, the investment manaer's active return is decomposed into weihtin effect, selection effect, interaction, transaction effect, and residual. Weihtin effect refers to the portion of an investment manaer's value-add attributable to the manaer's decision on how much to allocate to each market sector, or in other words, a manaer's decision to overweiht and underweiht certain sectors compared with the benchmark. The selection effect represents the portion of performance attributable to the manaer's stock-pickin skill. Interaction, as its name suests, is the interaction between the weihtin and the selection effects and does not represent an explicit decision of the investment manaer. The transaction effect captures the portion of performance attributable to trade execution and can only be calculated if transaction information is provided. A holdinbased attribution analysis is performed when transaction information is not provided, and this type of analysis may produce residuals. Residual is the portion of the return that cannot be explained by the holdins composition at the beinnin of the analysis period, and this ap is usually caused by intraperiod portfolio transactions, security corporate actions, and so on. Attribution analysis focuses primarily on the explicable part of the active return--the weihtin, selection, and interaction. Appendix A is dedicated to contribution, a topic that is often associated with attribution. The transaction effect is presented in Appendix, and residual is discussed in Appendix C Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 4 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

5 Introduction (Continued) This document first reviews the classic attribution approaches of rinson, Hood, and eebower and rinson and Fachler, the principles upon which today's performance attribution methodoloies are founded. The next sections present three attribution approaches: top-down, bottom-up, and three-factor. In addition, each of these three approaches can be implemented usin the arithmetic or the eometric method. These six combinations and their uses are described in the subsequent sections, followed by how these attribution results can be accumulated in a multiperiod analysis. Althouh multiple alternatives are presented in this document, the recommended method of Morninstar is the top-down eometric method. The top-down approach presents a uniform framework for comparin multiple investment manaers, and the eometric method has the merit of theoretical and mathematical soundness. This document focuses on equity attribution performed in the portfolio's base currency, and topics such as fixed income and currency attribution analyses are outside of the scope of this document. Effects Versus Components When performin attribution analysis, it is important to distinuish between effects and components. An effect measures the impact of a particular investment decision. An effect can be broken down into several components that provide insiht on each piece of an overall decision, but each piece in isolation cannot represent the investment manaer's decision. For example, an investment manaer may make an active decision on sector weihtin by overweihtin certain sectors and underweihtin other sectors. As overweihtin certain sectors necessitates underweihtin others and vice versa, the decision is on the entire set of sector weihtins. To better understand the sector-weihtin effect, one may examine the impact of individual sectors as components that provide additional insiht. However, each of these components cannot be used in isolation to measure the impact of a decision, as it is not meaninful to say that an investment manaer made a particular decision to time exposure to the cyclical sector, for example Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 5 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

6 Review of the Classic Approach--rinson, Hood, and eebower Today's approaches to performance attribution are founded on the principles presented in an article 1 written by rinson, Hood, and eebower (H) and published in Therefore, it is important to review the H model even thouh the model in its oriinal form is not adopted. The study is based on the concept that a portfolio's return consists of the combination of roup (for example, asset class) weihtins and returns, and decision-makin is observed when the weihtins or returns of the portfolio vary from those of the benchmark. Thus, notional portfolios can be built by combinin active or passive roup weihtins and returns to illustrate the value-add from each decision. The study deconstructs the value-added return of the portfolio into three parts: tactical asset allocation, stock selection, and interaction. The formulas for these terms are defined below: Tactical Asset Allocation = II - I = ( w j w j ) R j Stock Selection = III - I = w j ( R j R j ) Interaction = IV - III - II + I = ( w j w j ) ( R j R j ) Total Value Added = IV - I = w R w R j j j j These formulas are based on four notional portfolios. These notional portfolios are constructed by combinin different weihtins and returns, and they are illustrated in the chart below: 1 rinson, Gary., L. Randolph Hood, and Gilbert L. eebower, "Determinants of ortfolio erformance," Financial Analysts Journal, July-Auust 1986, pp Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 6 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

7 Introduction (Continued) Where: w j = The benchmark's weihtin for roup j w j = The portfolio's weihtin for roup j R j = The benchmark's return for roup j R = The portfolio's return for roup j j The tactical asset-allocation effect, also known as the weihtin effect, is the difference in returns between notional portfolios II and I. Notional portfolio II represents a hypothetical tactical asset allocator that focuses on how much to allocate to each roup but purchases index products for lack of opinions on which stocks would perform better than others. Notional portfolio I is the benchmark, which, by definition, has passive roup weihtins and returns. These two notional portfolios share the same passive roup returns but have different weihtins; thus, the concept intuitively defines the weihtin effect as the result of active weihtin decisions and passive stock-selection decisions. The stock-selection effect, also known as the selection effect, is the difference in returns between notional portfolios III and I. Notional portfolio III represents a hypothetical securitypicker that focuses on pickin the riht securities within each roup but mimics how much money the benchmark allocates to each roup because the person is anostic on which roups would perform better. As described above, notional portfolio I is the benchmark, which has passive roup weihtins and returns. These two notional portfolios share the same passive roup weihtins but have different roup returns; thus, the concept intuitively defines the selection effect as the result of passive weihtin decisions and active stock-selection decisions Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 7 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

8 Introduction (Continued) While the weihtin and selection effects are intuitive, the interaction portion is not easily understood. The interaction term, as its name suests, is the interaction between the weihtin and the selection effects and does not represent an explicit decision of the investment manaer. Due to its apparent lack of meanin, Morninstar believes that it is a better practice to incorporate it into either the weihtin or the selection effect, whichever of the two represents the secondary decision of the investment manaer. The concept of primary versus secondary decision is discussed in more details in the next section. The Morninstar methodoloy for equity performance attribution is founded on the principles of the H study, but the H model in its oriinal form is not adopted. First, the H model is an asset-class-level model and does not break down attribution effects into roup-level components. The next section presents the rinson and Fachler model; this method addresses roup-level components. Furthermore, much has evolved in the field of performance attribution since the H study. Methodoloies are needed to incorporate the interaction term into the other two effects, accommodate for multiple hierarchical weihtin decisions, perform multiperiod analysis, and so on. These topics are addressed in subsequent sections of this document. Review of Attribution Components--rinson and Fachler The H model presented in the previous section shows how attribution effects are calculated. As discussed in the "Effects versus Components" section of this document, an effect can be broken down into several components. Today's approaches to component-level attribution are based on concepts presented in a study 2 by rinson and Fachler (F) in In this article, the impact of a weihtin decision for a particular roup j is defined as ( w w ) ( R R ), j j j where ( w j w j ) is the same as the equation for the tactical asset-allocation effect in the H study. It is the difference between the portfolio's weihtin in this particular roup and the 2 rinson, Gary., and Nimrod Fachler, "Measurin Non-US Equity ortfolio erformance," Journal of ortfolio Manaement, Sprin 1985, pp Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 8 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

9 Introduction (Continued) benchmark's weihtin in the same roup, representin the investment manaer's weihtin decision. In the H model, ( w j w j ) is multiplied by the benchmark's total return. This basic principle is preserved in the F model as the latter also uses the benchmark return. However, in order to ain insiht into each roup's value-add, the term is transformed into the return differential between the roup in question and the total return. Thus, this term intuitively illustrates that a roup is ood if it outperforms the total. This formula is not in conflict with the H model because their results match at the portfolio level; in other words, the sum of F results from all roups equals the H tactical asset-allocation effect. With the two multiplicative terms of the formula combined, the F formula illustrates that it is ood to overweiht a roup that has outperformed and underweiht a roup that has underperformed. This is because overweihtin produces a positive number in the first term of the formula, and outperformance yields a positive number in the second term, leadin to a positive attribution result. Similarly, a neative weihtin differential of an underweihtin combined with a neative return differential of an underperformance produces a positive attribution result. Furthermore, it is bad to overweiht a roup that has underperformed and underweiht a roup that has outperformed because these combinations produce neative results. This concept is illustrated in the chart below 2011 Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 9 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

10 Introduction (Continued) Top-Down Versus ottom-up Approach There are several approaches to performance attribution, and we focus on two of them: topdown and bottom-up. These are two-factor models, decomposin active return into weihtin effect and selection effect. In addition, we present the three-factor model in this document as an alternative to these two approaches. In a three-factor model, the active return is deconstructed into three components, displayin the H Interaction term as the third factor. The choice between the top-down and the bottom-up approaches depends on the investment decision process of the portfolio bein analyzed, and the three-factor model takes an anostic view on the order of the investment decision process. The top-down approach to portfolio attribution is most appropriately used when analyzin an investment manaer with a top-down investment process that focuses on one or multiple weihtin allocation decisions prior to security selection. In this decision-makin process, the weihtin effect is primary and the selection effect is secondary. As discussed in the H section, the interaction term of the H approach is incorporated in the effect of the secondary decision, which is the selection effect in this case. The bottom-up approach is most relevant in analyzin an investment manaer with a bottom-up process that emphasizes security selection. In this decision-makin process, the selection effect is primary, and the weihtin effect is secondary. Unlike the top-down approach, which can measure the effects of multiple weihtin allocation decisions, there is only the weihtin effect in the bottom-up approach. As discussed in the H section above, the interaction term of the H approach is included in the effect of the secondary decision, which is the weihtin effect in this case. oth the top-down and bottom-up approaches involve hierarchical decision. For example, in the case of a top-down analysis, an investment manaer may first decide on reional weihtin, followed by sector weihtin and market-capitalization weihtin, before makin security selections. The analysis is hierarchical because the weihtin at each decision level is anchored upon the weihtin of the prior decision. Similarly, in a bottom-up analysis, an investment manaer first decides on security selection before makin weihtin decisions such as sector weihtin Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 10 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

11 Introduction (Continued) Arithmetic Versus Geometric Attribution As attribution effects are the results of the portfolio's relative weihtin and performance to those of the benchmark, the return comparison can be performed usin an arithmetic or eometric method. The arithmetic method refers to simple subtractions of return terms in formulas and is very intuitive; however, it works best in a sinle-period analysis, and additional "smoothin" is required to apply it in a multiperiod settin. Refer to the "Multiple eriod Analysis" section of this document for details. The eometric method takes a eometric difference by translatin returns into "return relatives" (that is, one plus the return), performin a division of the two return relatives, and subtractin 1 from the result. It is more complicated than the arithmetic method but has the benefit of bein theoretically sound for both sinleperiod and multiperiod analyses when applied to effect statistics. Example As the top-down approach is more complex, as it may involve a hierarchy of weihtin decisions, it is more helpful to provide an example that illustrates this process throuhout the document. Let us assume a simple example in which the investment process consists of decision-makin in the followin order: Decision Level Decision Choice 1 Reional weihtin Asia versus Europe 2 Sector weihtin Cyclical versus defensive 3 Market-cap weihtin Lare cap versus small cap 4 Security selection Note All formulas assume that the individual constituents and the results are expressed in decimal format. For example, the number 0.15 represents 15% Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 11 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

12 asic Mathematical Expressions Formulas As attribution formulas use many mathematical expressions in common, these mathematical expressions and their formulas are defined in this section and are used throuhout the document. [1] w benchmark wt of stock wø = w h h Ω w Ø if if = M < M [2] w portfolio wt of stock wø = w h h Ω w Ø if if = M < M [3] R return on stock = wh Rh h Ω w if if = M < M [4] R return on stock = wh Rh h Ω w if if = M < M 2011 Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 12 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

13 asic Mathematical Expressions (Continued) Where: w = The benchmark's weihtin for roup w = The portfolio's weihtin for roup R = The benchmark's return for roup R = The portfolio's return for roup = The vector that denotes the roup = The number of elements in the vector, representin the hierarchy level of the roup M = The level that represents the security level, that is, the last roupin hierarchy Ω = All of the subroups within the roup that are one hierarchy level below Ø = The total level, which is the equity portion of the portfolio or benchmark Explanation of Formulas A roup represents a basket of securities classified by the end user, such as economic sector, market cap, /E, reion, country, and so on. "Group" is the most eneric term that represents a roup of securities or a sinle security. The symbol represents the vector that denotes the roup. In our example, Europe's cyclical sector's small cap is denoted as (2,1,2) because it is the second reion's first sector's second market-cap bucket. This particular market cap's fifth stock is denoted as (2,1,2,5). When = Ø, it represents the null set that denotes the total level such as the total equity portfolio or the total equity benchmark. The variable is the number of elements in the vector, representin the decision level of the roup in the hierarchy. In our example, = 2 stands for the sector level because it is the second level of decision. Note that = 0 represents the total level such as the total equity benchmark or the total equity portfolio. The variable M denotes the level that represents the security level, that is, the last decision in the hierarchy. In our example, M = 4 because security level is the fourth level of decision Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 13 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

14 asic Mathematical Expressions (Continued) The expression Ω represents all of the subroups within the roup that are one hierarchy level below. Think of a family tree and let each decision level be a eneration of relatives; the Ω symbol represents all of the children of the same parent. In our example, Asia is denoted by = (1). When usin formula [1] to calculate the benchmark weihtin of Asia, Ω (1) represents all of the subroups within Asia. They are cyclical and defensive sectors, denoted by = (1,1 ) and = (1,2 ), correspondinly. The second part of formulas [1] and [2] simply states that the weihtin of Asia is the sum of the weihtins of the Asian cyclical and Asian defensive sectors. Similarly, the second part of formulas [3] and [4] means that the return of Asia is the weihted sum of the returns of Asian cyclical and Asian defensive. Special Situation I: Groups Without Holdins If neither the portfolio nor the benchmark has holdins in a particular roup, this roup should be inored in order to provide a meaninful attribution analysis. If the portfolio does not have holdins in a particular roup but the benchmark does, the roup's portfolio weihtin is zero, and the roup's portfolio return is assumed to be the same as the roup's benchmark return. This rule applies reardless of whether the roup represents lon or short positions. For example, if the sector-weihtin decision is bein evaluated, and the portfolio does not have holdins in the Asian cyclical sector while the benchmark does, the portfolio's return in the Asian cyclical sector is assumed to be the same as the benchmark's return in the Asian cyclical sector. The active return is attributable entirely to the sector weihtin effect and not subsequent decisions such as market-capweihtin and security selection in a top-down model. Similarly, in a bottom-up or threefactor model, the active return is attributable entirely to the sector-weihtin effect and not to the security-selection effect. This makes intuitive sense as the decision to differ from the benchmark's weihtin is a weihtin effect. If the portfolio has holdins in a particular roup but the benchmark does not have holdins in the same roup, the roup's benchmark return is assumed to be the same as the roup's portfolio return. The only exception to this rule is the short position situation described below Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 14 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

15 asic Mathematical Expressions (Continued) Special Situation II: Short ositions When the portfolio or the benchmark has short positions, attribution analysis must be performed on the short positions separately from the lon positions. In other words, short positions and lon positions are in separate roups, and the number of roups is potentially double that of an analysis where only lon positions are present. To ensure that the separation is clear, lon and short positions must be separated at the first level of the decision hierarchy. For example, when the first level of the decision hierarchy is reional allocation, and the reional classifications are Asia and Europe, a portfolio containin short positions should have four reional classifications: Asia lon, Europe lon, Asia short, and Europe short. For levels of the decision hierarchy other than the security level ( < M ), when the benchmark does not have holdins in a particular short position roup, this roup's benchmark's return is assumed to be the same as the benchmark's return of the same roup's lon position counterpart in order to allocate effects correctly. For example, if the benchmark does not have short position holdins in the Asian cyclical sector, the return of this sector is assumed to be the same as the benchmark's return in the lon positions of the Asian cyclical sector Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 15 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

16 Top-Down Approach for Sinle eriod Overview As discussed in the Introduction, the top-down approach to portfolio attribution is most appropriately used when analyzin an investment manaer with a top-down investment process that focuses on one or multiple weihtin allocation decisions prior to security selection. These decisions are hierarchical. In our example, the investment manaer first decides on reional weihtin, followed by sector weihtin and market-cap weihtin before makin security selections. In this decision-makin process, the weihtin effect is primary, and the selection effect is secondary. This section addresses the top-down approach in a sinle-period attribution analysis. The sinle-period methodoloy serves as a foundation for the multiperiod attribution, and the latter is discussed in the last section of this document. Attribution can be performed usin the arithmetic or eometric method. These methods and their merits are discussed in the Introduction. This section focuses on the presentation and the explanation of the formulas Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 16 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

17 Top-Down Approach for Sinle eriod (Continued) Arithmetic Method w [5] CA = ( w w ) ( R R ) w [6] EA, n h Ω = h Ω CA EA h h, n if n = if n > [7] AAØ = RØ RØ = EA M n= 1 Ø, n Where: CA = Component attributable to roup, calculated based on arithmetic method EA, = Effect attributable to roup at decision level n, based on arithmetic method n AA Ø = The portfolio's active return, based on equity holdins, calculated based on arithmetic method = The roup where roup belons in the prior roupin hierarchy level R Ø = The portfolio's total equity return, calculated based on equity holdins R Ø = The benchmark's total equity return, calculated based on equity holdins The arithmetic method refers to simple subtractions and additions. For example, simple subtractions are used when comparin returns of the portfolio with the benchmark, as shown in the second term of formula [5]. Furthermore, active return in formula [7] is the simple addition of the total effects at various decision levels. These characteristics distinuish the arithmetic method from its eometric counterpart. The arithmetic method also serves as the foundation for the eometric method presented in the next section. In the component calculation in equation [5], there are some terms that are similar to the basic H and F models and many that are not. The H model is at the portfolio level, while formula [5], as its name indicates, is at the components level. In other words, formula [5] calculates how Asia and Europe, as components, each contribute toward the total reional weihtin effect. Thus, it is more appropriate to compare it with the F model Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 17 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

18 Top-Down Approach for Sinle eriod (Continued) To fully understand the component calculation, let us first focus on the first multiplicative term of equation [5]. The F model is founded on the concept of the weihtin effect bein the difference between the portfolio and benchmark weihtins, and the first term of the component formula is essentially that difference. The dissimilarity between the F model and the component formula stems from the latter bein modified for a hierarchical decision-makin structure. For example, an investment manaer may first decide on reional weihtin, followed by sector weihtin and market-cap weihtin, before security selection. The analysis is hierarchical because the weihtin at each decision level is anchored upon the weihtin of the prior decision. For example, let the portfolio's weihtin in Asia be 60% and the benchmark's weihtin in the same reion be 30%, representin a double weihtin. Further assume that there are two sectors in Asia, and the benchmark has half the weihtin in each sector. Thus, each sector has a 15% benchmark weihtin. As the portfolio has 60% in Asia, if it were to mimic the benchmark and place half its weihtin in each of the two sectors, each sector would have a 30% portfolio weihtin and look overweihted even thouh the portfolio mimics the benchmark's allocation. Therefore, one must not compare the portfolio weihtin of the Asia reion's cyclical sector directly with the weihtin of the same sector in the benchmark. The fair comparison is to create an anchorin system like formula [5] where the benchmark's weihtin in the Asia reion's cyclical sector is scaled to the proportion between the portfolio's weihtin in Asia and that of the benchmark. In this example, the benchmark's weihtin in the Asian cyclical sector must be multiplied by 2 before it can be compared with the portfolio's weihtin in the same sector because 2 is the result of 0.6 divided by 0.3. The symbol is the roup that roup belons to in the prior decision level of the hierarchy. Followin the analoy of a family tree, represents the parent of. For example, the term for the Asian cyclical sector represents the Asia reion, as the Asian cyclical sector is part of the Asia reion, and reion is the decision level prior to sector. For simplicity, let us call it the "parent roup" to roup. When = Ø, when the parent roup is the total level, w = w 1. Ø Ø = 2011 Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 18 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

19 Top-Down Approach for Sinle eriod (Continued) Shiftin focus to the second term of equation [5], this term is similar to the F model. In order to adopt a hierarchical structure, the second term is transformed into the return differential between the roup in question and its parent roup. Thus, this term intuitively illustrates that a roup is ood if it outperforms the combined performance of all siblins, and vice versa. For example, if Europe's cyclical sector has a benchmark return of 8.40% while Europe has a benchmark return of 3.53%, the differential is 4.87%, a positive number demonstratin that this reion's cyclical sector has outperformed other sectors in the reion. Formula [5] illustrates the same intuitive concepts in the F article. It is ood to overweiht a roup that has outperformed and underweiht a roup that has underperformed. It is bad to overweiht a roup that has underperformed and underweiht a roup that has outperformed. Formula [6] shows that the effect of a parent roup is the sum of the components of all of its children if the children are components of this decision. For example, when analyzin the sector-weihtin effect, the sectors are components of the decision, so Asia's sector-weihtin effect is the sum of the sector-weihtin components of Asian cyclical and Asian defensive. The effect of a randparent roup is the sum of the effects of all of its children if the children's descendants are components of this decision. For example, when analyzin the selection effect, the securities are components of this decision. Thus, the Asian cyclical sector's selection effect is the sum of the selection effects of Asian cyclical lare cap and Asian cyclical small cap, and these two are in turn sums of the selection components of the underlyin constituent stocks. The formulas for components and effects are universal to all roupin levels. When n < M, the result of the formula is referred to as a weihtin effect. When n = M, the result of the formula is referred to as a selection effect. For example, EA (1,2), 4 is the selection (fourth decision) effect of the first reion's second sector Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 19 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

20 Top-Down Approach for Sinle eriod (Continued) Active return in formula [7] is the value-add of equity securities, and it is the difference between the return of the equity portion of the portfolio and that of the equity portion of the benchmark. Expressed in attribution terms, the active return is the simple addition of the total effects at all decision levels. In other words, it is the sum of the total effects of all four decisions made in the portfolio: reional weihtin, sector weihtin, market-cap weihtin, and security selection. This active return represents the value-add of the equity portion of the portfolio, and it is calculated based on equity holdins as of the beinnin of the analysis period. Refer to the Appendix for the value-add of the total portfolio and residuals that account for the difference between actual and calculated returns. Geometric Method [8] [9] R EA R HL Ø = H ( L 1) Ø,L + R CG CA = 1+ R H if if L = 0 L > 0 [10] EG, n = h Ω h Ω CG EG h h, n if n = if n > M 1+ RØ [11] AG Ø = 1 = (1 + Ø, ) 1 EG n 1+ R Ø n= 1 Where: HL R = Return of the hybrid portfolio at level L CG = Component attributable to roup, calculated based on eometric method EG, = Effect attributable to roup at decision level n, based on eometric method n AG Ø = The portfolio's active return, based on equity holdins, calculated based on eometric method 2011 Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 20 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

21 Top-Down Approach for Sinle eriod (Continued) Equation [5] in the previous section presents the hierarchical anchorin system used in the component formula. The denominator of formula [9] in this section demonstrates another method of hierarchical anchorin, and it is facilitated by the use of the "hybrid" portfolio defined in formula [8]. The hybrid portfolio may look unfamiliar when presented in its concise presentation in formula [8], but it is based on the already familiar hierarchical anchorin system in equation [5]. Recall that in equation [5] the benchmark's weihtin in the Asia reion's cyclical sector is scaled to the proportion between the portfolio's weihtin in Asia and that of the benchmark. The hybrid portfolio is similar to the benchmark portfolio in that the benchmark weihtin in each sector is combined with the benchmark return in the sector, but the scaled benchmark weihtins are used instead of the raw benchmark weihtins. Mathematically the concise form in formula [8] yields the same result as combinin the scaled benchmark weihtins with benchmark returns. The concise form in formula [8] has the benefit of reusin numbers that are already calculated in the arithmetic method. Formula [8] shows that at the total level, no anchorin is required, and the hybrid portfolio is the same as the benchmark portfolio. At levels other than the total level, the hybrid portfolio's return is the sum of the arithmetic total effect of this decision level and the hybrid return of the prior decision level. For example, the sector-level hybrid portfolio is the sum of the arithmetic total sector effect and the return of the reional hybrid portfolio. The effect calculation in formula [10] needs no further explanation as it is similar to its arithmetic counterpart in formula [6]. The active return in formula [11] is also similar to its arithmetic counterpart in formula [7], but eometric operations are used instead of arithmetic operations. The active return is the eometric difference between the returns of the equity portion of the portfolio and the equity portion of the benchmark. Active return can also be computed by eometrically linkin the total effects from all decision levels Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 21 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

22 Top-Down Approach for Sinle eriod (Continued) Example Followin the example described earlier, below is a top-down investment process that consists of decision-makin in the followin order: reional weihtin, sector weihtin, market-cap weihtin, and security selection. Hierarchical Structure Illustration Total Ø, 1 Asia (1) Reion Wt Sector Wt Market Cap Wt Sec Selection Active Ret EG EG Ø, 2 EG Ø, 3 EG Ø, 4 AG CG EG (1), 2 EG (1), 3 EG (1), 4 CG EG (1,1), 3 EG (1,1), 4 CG EG (1,1,1), 4 CG EG (1,1,2), 4 CG EG (1,2), 3 EG (1,2), 4 CG EG (1,2,1), 4 CG EG (1,2,2), 4 CG EG (2), 2 EG (2), 3 EG (2), 4 CG EG (2,1), 3 EG (2,1), 4 CG EG (2,1,1), 4 CG EG (2,1,2), 4 CG EG (2,2), 3 EG (2,2), 4 CG EG (2,2,1), 4 CG EG (2,2,2), 4 Cyclical (1,1) Lare Cap (1,1,1 ) Small Cap (1,1,2 ) Defensive (1,2 ) Lare Cap (1,2,1) Small Cap (1,2,2 ) Europe (2) Cyclical (2,1) Lare Cap (2,1,1) Small Cap (2,1,2 ) Defensive (2,2) Lare Cap (2,2,1) Small Cap (2,2,2) 2011 Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 22 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

23 Top-Down Approach for Sinle eriod (Continued) Attribution Weihtins Returns Attribution ortfolio ench ortfolio ench Reion Sector Mkt Cap Selection Active Return Total Asia Cyclical Lare Cap Small Cap Defensive Lare Cap Small Cap Europe Cyclical Lare Cap Small Cap Defensive Lare Cap Small Cap First Decision: Reional Weihtin H,0 R = RØ = ( w(1) R(1) + w(2) R(2) ) / wø = ( ) /1.00 = H,0 CG (1) = ( w(1) wø / wø w(1) ) ( R(1) RØ ) /(1 + R ) = ( / ) ( ) /( ) = H,0 CG (2) = ( w(2) wø / wø w(2) ) ( R(2) RØ ) /(1 + R ) = ( / ) ( ) /( ) = Total reional weihtin effect: EG = CG + CG = Ø,1 (1) (2) = 2011 Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 23 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

24 Top-Down Approach for Sinle eriod (Continued) Second Decision: Sector Weihtin H,1 H,0 H,0 H,0 R = EAØ,1 + R = EGØ,1 (1 + R ) + R = ( ) = H,1 CG (1,1) = ( w(1,1) w(1) / w(1) w(1,1) ) ( R(1,1) R(1) ) /(1 + R ) = ( / ) ( ) /( ) = H,1 CG (1,2) = ( w(1,2) w(1) / w(1) w(1,2) ) ( R(1,2) R(1) ) /(1 + R ) = ( / ) ( ) /( ) = EG ( 1),2 = CG(1,1) + CG(1,2) = = H,1 CG (2,1) = ( w(2,1) w(2) / w(2) w(2,1) ) ( R(2,1) R(2) ) /(1 + R ) = ( / ) ( ) /( ) = H,1 CG (2,2) = ( w(2,2) w(2) / w(2) w(2,2) ) ( R(2,2) R(2) ) /(1 + R ) = ( / ) ( ) /( ) = EG ( 2),2 = CG(2,1) + CG(2,2) = ( ) + ( ) = Total sector weihtin effect: EG = EG + EG = ( ) = Ø,2 (1),2 (2),2 Third Decision: Market-Cap Weihtin H,2 H,1 H,1 H,1 R = EAØ,2 + R = EGØ,2 (1 + R ) + R = ( ) ( ) = H,2 CG (1,1,1) = ( w(1,1,1) w(1,1) / w(1,1) w(1,1,1) ) ( R(1,1,1) R(1,1) ) /(1 + R ) = ( / ) ( ) /( ) = H,2 CG (1,1,2) = ( w(1,1,2) w(1,1) / w(1,1) w(1,1,2) ) ( R(1,1,2) R(1,1) ) /(1 + R ) = ( / ) ( ) /( ) = EG ( 1,1),3 = CG(1,1,1) + CG(1,1,2) = ( ) + ( ) = H,2 CG (1,2,1) = ( w(1,2,1) w(1,2) / w(1,2) w(1,2,1) ) ( R(1,2,1) R(1,2) ) /(1 + R ) = ( / ) ( ) /( ) = H,2 CG (1,2,2) = ( w(1,2,2) w(1,2) / w(1,2) w(1,2,2) ) ( R(1,2,2) R(1,2) ) /(1 + R ) = ( / ) ( ) /( ) = EG ( 1,2),3 = CG(1,2,1) + CG(1,2,2) = ( ) + ( ) = EG = EG + EG = ( ) + ( ) = ( 1),3 (1,1),3 (1,2), Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 24 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

25 Top-Down Approach for Sinle eriod (Continued) H,2 CG (2,1,1) = ( w(2,1,1) w(2,1) / w(2,1) w(2,1,1) ) ( R(2,1,1) R(2,1) ) /(1 + R ) = ( / ) ( ) /( ) = H,2 CG (2,1,2) = ( w(2,1,2) w(2,1) / w(2,1) w(2,1,2) ) ( R(2,1,2) R(2,1) ) /(1 + R ) = ( / ) ( ) /( ) = EG ( 2,1),3 = CG(2,1,1) + CG(2,1,2) = ( ) + ( ) = H,2 CG (2,2,1) = ( w(2,2,1) w(2,2) / w(2,2) w(2,2,1) ) ( R(2,2,1) R(2,2) ) /(1 + R ) = ( / ) ( ( ))/( ) = H,2 CG (2,2,2) = ( w(2,2,2) w(2,2) / w(2,2) w(2,2,2) ) ( R(2,2,2) R(2,2) ) /(1 + R ) = ( / ) ( ( )) /( ) = 0 EG ( 2,2),3 = CG(2,2,1) + CG(2,2,2) = = EG ( 2),3 = EG(2,1),3 + EG(2,2),3 = ( ) = Total market-cap-weihtin effect: EG = EG + EG = ( ) = Ø,3 (1),3 (2),3 Fourth Decision: Security Selection H,3 H,2 H,2 H R = EAØ,3 + R = EGØ,3 (1 + R ) + R = ( ) ( ) = Instead of showin every stock in the portfolio and benchmark, let us show just one example and assume w 0. 15, w 0, and R = R ( 1,1,1,1) = ( 1,1,1,1) =,2 ( 1,1,1,1) (1,1,1,1) = CG (1,1,1,1) = ( w(1,1,1,1) w(1,1,1) / w(1,1,1) w(1,1,1,1) ) ( R(1,1,1,1) R(1,1,1) ) /(1 + R = ( / ) ( ( ) /( ) = Further, assume that the total security-selection effect: EG Ø,4 = Active Return AG Ø = ( 1+ EGØ,1) (1 + EGØ,2 ) (1 + EGØ,3) (1 + EGØ, 4) 1 = ( ) ( ) ( ) ( ) 1 = H,3 ) 2011 Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 25 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

26 ottom-up Approach for Sinle eriod Overview As discussed in the Introduction, the bottom-up approach to portfolio attribution is most appropriately used when analyzin an investment manaer with a bottom-up investment process that focuses on security selection. The weihtin effect is secondary to the decisionmakin process. Unlike the top-down process, which may involve a series of weihtin decisions, there is only one weihtin effect in the bottom-up process. This section addresses the bottom-up approach in a sinle-period attribution analysis. Multiperiod attribution is discussed in the last section of this document. Arithmetic Method w [12] CA = ( w w ) ( R R ) w [13] EA, n h Ω = h Ω CA EA h h, n if n = + 1 if n > + 1 [14] AA Ø = RØ RØ = EAØ,1 + EAØ, 2 Where: CA = Component attributable to roup, calculated based on arithmetic method EA, = Effect attributable to roup at decision level n, based on arithmetic method n AA Ø = The equity portfolio's active return, based on equity holdins, calculated based on arithmetic method = The roup where roup belons in the prior roupin hierarchy level n = Decision level, where n = 1 is the weihtin decision and = 2 Ø = The total level, which is the total equity n is the security-selection decision 2011 Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 26 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

27 ottom-up Approach for Sinle eriod (continued) These formulas are similar to their counterparts in the "Top-Down Approach" section of this document. The component formula in equation [12] demonstrates a hierarchical anchorin structure that is similar to that of its top-down counterpart in equation [5]. In the case of formula [12], it is the portfolio weihtin of a roup that is scaled to the proportion between the benchmark's weihtin and the portfolio's weihtin in the parent roup. Once scaled, the portfolio weihtin can be fairly compared with the benchmark weihtin. In other words, when evaluatin the stock-selection component of a particular stock, one should not compare the portfolio's weihtin in the stock directly with the benchmark's weihtin in the same stock. One must scale the portfolio's weihtin in this stock by the proportion between the benchmark's weihtin in the sector and the portfolio's weihtin in the sector, assumin the investment manaer roups stocks by sector. To accompany this anchorin system, it is the portfolio's return in the security that is compared with the benchmark's return in the sector in the second term of formula [12]. Similarly, when evaluatin a sector, it is the portfolio's return in the sector that is compared with the benchmark's total return, and this is consistent with incorporatin the interaction term of the H model into the weihtin effect in a bottom-up approach. The effect formula in equation [13] is intentionally written to be the same as its top-down counterpart in equation [6], a concept that is already familiar. In order to achieve this, n = 1 is set to denote the weihtin decision and n = 2 the security-selection decision, even thouh security selection is the primary decision. This order is more intuitive as it matches the roupin hierarchy structure where = 1 represents the sector and = 2 the security. Formula [13] shows that the effect of a parent roup is the sum of the components of all of its children if the children are components of this decision. For example, when analyzin the selection effect, the securities are components of the decision, so the cyclical sector's selection effect is the sum of the selection components of all stocks in the sector. The effect of a randparent roup is the sum of the effects of all of its children. For example, the total equity portfolio's selection effect is the sum of the selection effects of cyclical and defensive sectors, and these two are in turn sums of selection components of the underlyin constituent stocks Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 27 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

28 ottom-up Approach for Sinle eriod (continued) Active return in formula [14] is the same as its top-down counterpart in equation [7], but only two decisions are involved: weihtin and selection. Active return is the value-add of the portfolio above the benchmark, and it is the difference between the return of the equity portion of the portfolio and that of the equity portion of the benchmark. Expressed in attribution terms, active return is the simple addition of the total weihtin effect and the total selection effect. This active return represents the value-add of the equity portion of the portfolio. Refer to the Appendix for the value-add of the total portfolio. Geometric Method CA 1+ EAØ,2 + R [15] CG = CA 1+ RØ [16] EG, n h Ω = h Ω CG EG h h, n Ø if if if = 1 if = 2 n = + 1 n > RØ [17] AG Ø = 1 = (1 + EGØ,1) (1 + EGØ,2 ) 1 1+ R Ø Where: CG = Component attributable to roup, calculated based on eometric method EG, = Effect attributable to roup at decision level n, based on eometric method n AG Ø = The equity portfolio's active return, based on equity holdins, calculated based on eometric method 2011 Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 28 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

29 ottom-up Approach for Sinle eriod (continued) The eometric component formula in equation [15] is similar to its top-down counterpart in formulas [8] and [9]. While the top-down approach allows multiple decisions and is better presented with two formulas, the bottom-up approach only requires one formula as there are only two decisions. Similar to equation [9], the component formula in equation [15] shows the use of the "hybrid" portfolio in the denominator to facilitate hierarchical anchorin. This anchorin system is similar to the one used in equation [12] for the arithmetic component calculation. Recall that in equation [12] the portfolio's weihtin in a stock is scaled to the proportion between the benchmark's weihtin in the sector and that of the portfolio. The hybrid portfolio is similar to the actual portfolio in that the portfolio's weihtin in each stock is combined with the portfolio return in each stock, but the scaled portfolio weihtins are used instead of the raw portfolio weihtins. Mathematically the concise form in the denominator of equation [15] yields the same result as combinin the scaled portfolio weihtins with portfolio returns, and the concise form has the benefit of reusin numbers that are already calculated in the arithmetic method. The effect formula in equation [16] is the same as its arithmetic counterpart in formula [13] and its top-down counterpart in formula [10]. Formula [16] shows that the effect of a parent roup is the sum of the components of all of its children if the children are components of this decision. The effect of a randparent roup is the sum of the effects of all of its children if the children's descendants are components of this decision. The active return calculation in formula [17] is essentially the same as its top-down counterpart in formula [11], demonstratin that active return is achieved by takin the eometric difference between the portfolio's equity return and the benchmark's equity return or by eometrically linkin the total weihtin and selection effects Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 29 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

30 Three-Factor Approach for Sinle eriod Overview The three-factor approach decomposes the active return into weihtin effect, selection effect, and interaction. Unlike the top-down and bottom-up approaches presented in the previous sections, the three-factor model takes an anostic view reardin the order of decision-makin in the investment process. Thus, there is no distinction between primary and secondary effects. This approach to performance attribution is most appropriately used when one seeks purity in both weihtin and selection effects and isolates the interaction between these two decisions into its own term. As stated in the Introduction, the interaction term does not represent an explicit decision of the investment manaer, and Morninstar believes that it is a better practice to use the top-down and bottom-up approaches where the interaction term is embedded into the secondary effect of the investment process. This section addresses the three-factor approach in a sinle-period attribution analysis. Multiperiod attribution is discussed in the last section of this document Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 30 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

31 Three-Factor Approach for Sinle eriod (Continued) Arithmetic Method [18] CA w ( w w = w CAh h Ω ) ( R R ) if if n = n > [19] EA Ø, n = CA h Ω Ø h [20] IA ( w = w IAh h Ω ) ( R R ) if if = 1 = 0 [21] AA Ø = RØ RØ = EAØ,1 + EAØ,2 + IAØ Where: CA = Component attributable to roup, calculated based on arithmetic method EA Ø, n = Effect attributable to the total equity portfolio at decision level n, based on arithmetic method IA = Interaction attributable to roup, based on arithmetic method AA Ø = The equity portfolio's active return, based on equity holdins, calculated based on arithmetic method = The roup where roup belons in the prior roupin hierarchy level n = Decision level, where n = 1 is the weihtin decision, and = 2 Ø = The total level, which is the total equity n is the security-selection decision 2011 Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 31 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

32 Three-Factor Approach for Sinle eriod (Continued) These formulas are similar to their counterparts in the "ottom-up Approach" section of this document. The component formula in equation [18] demonstrates a hierarchical anchorin structure similar to that of its bottom-up counterpart in equation [12]. In formula [18], the portfolio weihtin of a roup is scaled to the proportion between the benchmark's weihtin and the portfolio's weihtin in the parent roup. Once scaled, the portfolio weihtin can be compared fairly with the benchmark weihtin. In other words, when evaluatin the stockselection component of a particular stock, one should not compare the portfolio's weihtin in the stock directly with the benchmark's weihtin in the same stock. One must scale the portfolio's weihtin in this stock by the proportion between the benchmark's weihtin in the sector and the portfolio's weihtin in the sector, assumin the investment manaer roups stocks by sector. To accompany this anchorin system, it is the benchmark's return in the security that is compared with the benchmark's return in the sector in the second term of formula [18]. Similarly, when evaluatin a sector, it is the benchmark's return in the sector that is compared with the benchmark's total return. Formula [18] has a different form when n >. These symbols are intentionally written to be similar to their counterparts in the top-down and bottom-up approaches. In order to achieve this, n = 1 is set to denote the weihtin decision and n = 2 the security-selection decision, even thouh there is not a distinction between primary and secondary effects in the threefactor approach. This order is more intuitive as it matches the roupin hierarchy structure where = 1 represents the sector and = 2 the security. However, there is a sinificant difference between the three-factor model and its top-down and bottom-up counterparts when it comes to the determination of an effect versus a component. In the top-down and bottom-up approaches, a term is an effect when n >. However, in the three-factor model only the total equity level is considered an effect. Thus, the second portion of formula [18] is for subtotals where n >. For example, the cyclical sector's selection component effect is the sum of selection components of all stocks in the sector. Formula [19] shows that the effect of the total equity level is the sum of the components of all of its children. For example, the total equity portfolio's selection effect is the sum of the selection effects of the cyclical and defensive sectors, and these two are in turn sums of the selection components of the underlyin constituent stocks Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 32 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

33 Three-Factor Approach for Sinle eriod (Continued) The interaction term in formula [20] confirms that it is indeed the interaction between the weihtin and selection decisions, as it is the cross-product of active weihtin manaement and active selection decision. The formula is the same as the one in the H article, but it is deconstructed into two equations here for applications at the sector and total equity portfolio levels. At the sector level, the interaction term is the product between a particular sector's weihtin relative to the benchmark and its relative return. A positive interaction term in a particular sector demonstrates that the investment manaer is successful in overweihtin the sector when active manaement added value, or underweihtin a sector when active manaement subtracted value. In contrast, a neative interaction term in a particular sector implies that the investment manaer has made an unsuccessful decision in overweihtin the sector when active manaement subtracted value, or underweihtin the sector when active manaement added value. Note that when calculatin the interaction term, it does not matter how the sector performs compared with the overall benchmark; what matters is whether the portfolio's return in the sector is better than that of the benchmark in the same sector. Thus, counterintuitively, it is possible for the interaction term to be positive even if the sector has poor weihtin and selection attribution results. This happens when the portfolio is underweiht in a sector where active manaement is poor but the sector still outperforms the overall benchmark. For example, let us assume that the portfolio returns 5% in the cyclical sector while the benchmark returns 8%, and the benchmark's overall return is 2%. In this case, if the portfolio is underweiht in the cyclical sector, the cyclical sector's component of the weihtin effect would be neative for havin an underweihtin in a sector that outperforms the benchmark (8% versus 2%). The sector's selection effect is neative as the portfolio underperforms the benchmark in the sector (5% versus 8%). However, the sector's interaction term is positive even thouh weihtin and selection are both poor, as the portfolio is underweiht in a sector where active manaement underperforms (5% versus 8%) Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 33 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

34 Three-Factor Approach for Sinle eriod (Continued) Active return in formula [21] is similar to its top-down and bottom-up counterparts in equations [7] and [14], but the interaction term must be included. Active return is the portfolio's value-add above the benchmark, and it is the difference between the return of the equity portion of the portfolio and that of the equity portion of the benchmark. Expressed in attribution terms, the active return is the simple addition of the total weihtin effect, the total selection effect, and the interaction term. This active return represents the value-add of the equity portion of the portfolio. Refer to the Appendix for the value-add of the total portfolio Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 34 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

35 Three-Factor Approach for Sinle eriod (Continued) Geometric Method CA [22] CG = 1+ R Ø [23] EG Ø, n = CG h Ω Ø h [24] IG IA 1+ R = IA Ø 1+ R IGh h Ω Ø Ø (1 + EG Ø,1 1 ) (1 + EG Ø,2 1 ) 1+ RØ [25] AG Ø = 1 = (1 + EGØ,1) (1 + EGØ,2 ) (1 + IGØ ) 1 1+ R Ø if if = 1 = 0 Where: CG = Component attributable to roup, calculated based on eometric method EG Ø,n = Effect attributable to the total equity portfolio at decision level n, based on eometric method IG = Interaction attributable to roup, based on eometric method AG Ø = The equity portfolio's active return, based on equity holdins, calculated based on eometric method The eometric component formula in equation [22] is a simplified version of its top-down and bottom-up counterparts in formulas [9] and [15]. Similar to equations [9] and [15], the component formula in equation [22] shows the use of the "hybrid" portfolio in the denominator to facilitate anchorin. However, as the three-factor model is anostic on the order of decisionmakin, both weihtin and selection are anchored on the total equity benchmark just as primary decisions are anchored in the top-down and bottom-up eometric calculations Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 35 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

36 Three-Factor Approach for Sinle eriod (Continued) The effect formula in equation [23] is the same as its arithmetic counterpart in formula [19]. Formula [23] shows that the effect of the total equity is the sum of the components of all of its children. As stated in the "Multiple eriod Analysis" section, only effects can be eometrically compounded over time. Therefore, when runnin a three-factor eometric model in a multiperiod settin, only the attribution results at the total equity level will be presented, and no details will be provided at levels below the total equity such as sector or security level. The interaction term in formula [24] is not immediately intuitive. There is not an intuitive explanation for the anchorin process used in transformin the arithmetic interaction term to its eometric format. Therefore, the anchor is obtained throuh backward enineerin, knowin that the excess return is the result of eometrically linkin the eometric weihtin effect, the eometric selection effect, and the eometric interaction term. Thus, one can infer the eometric interaction term and solve for the multiplier needed in convertin the arithmetic interaction term into its eometric format. The active return calculation in formula [25] is essentially the same as its top-down and bottom-up counterparts in formulas [11] and [17], but the equation has been expanded to accommodate the interaction term. The formula demonstrates that active return is achieved by takin the eometric difference between the portfolio's equity return and the benchmark's equity return, or by eometrically linkin the total weihtin effect, the total selection effect, and the interaction term Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 36 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

37 Multiple-eriod Analysis Overview The previous sections of this document demonstrate how effects and components are calculated for each sinle holdin period. A holdin period is determined by portfolio holdins update, benchmark holdins update, and month-end. For example, if portfolio holdins are available on Jan. 31, 2008, March 15, 2008, and April 30, 2008, and assumin that benchmark holdins are available at quarter-ends, the period between Feb. 1, 2008, and Feb. 28, 2008, represents the first holdin period, the period between March 1, 2008, and March 15, 2008, is the second holdin period, the period between March 16, 2008, and March 31, 2008, is the third period, and the period between April 1, 2008, and April 30, 2008, is the fourth period. When applyin the formulas in the previous sections, weihtins are taken from the beinnin of the period, and returns are based on the entire holdin period. For example, when analyzin the first holdin period, weihtins are based on Jan. 31, 2008, and returns are from Feb. 1, 2008, to March 31, It is often desirable to perform an analysis that spans over several portfolio holdin dates, for example, from Feb. 1, 2008, to June 30, Althouh one miht think of treatin this as a sinle period, that is, takin the weihtins as of Jan. 31, 2008, and applyin them to returns from Feb. 1, 2008, to June 30, 2008, valuable information could be lost. ortfolio constituents and their weihtins miht have chaned between Jan. 31, 2008, and March 31, 2008, due to buys, sells, adds, trims, corporate actions, and so on. For the most meaninful analysis, portfolio holdins should be updated frequently, especially for hiher-turnover portfolios. Frequent portfolio holdin updates create multiple sinle periods, and the followin sections demonstrate how these sinle-period attribution results can be accumulated into an overall multiperiod outcome. Multiperiod attribution effects consist of accumulatin sinle-period results. Similar to a sinleperiod analysis, results can be calculated usin the arithmetic method or the eometric method. Use the multiperiod arithmetic method to accumulate sinle-period arithmetic attribution results, and use the multiperiod eometric method to link sinle-period eometric results. These multiperiod methods apply to attribution results from both the top-down and the bottom-up approaches Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 37 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

38 Multiple-eriod Analysis (Continued) Multiperiod Geometric Method The eometric method is the method recommended by Morninstar. The eometric method has the merit of bein theoretically and mathematically sound. As stated in the Introduction, it is important to distinuish between effects and components when performin an attribution analysis. An effect measures the impact of a particular investment decision. An effect can be broken down into several components (for example, individual sectors such as cyclical) that provide insiht on each piece of an overall decision, but each piece in isolation cannot represent the impact of decision-makin. Therefore, theoretically, multiperiod linkin is only applicable to an effect and not a component. From a mathematical viewpoint, accumulatin components over time either by addin or compoundin, and addin them back toether either by simple summation or eometric linkin, does not equal the active return. Use the followin formulas to link sinle-period eometric attribution effects into multiperiod results: T [26] EG, n, T, Cum = ( 1+ EG, n, t ) 1 t= 1 T M 1+ RØ,T,Cum [27] AGØ, T, Cum = 1 = (1 + AG t = Ø, ) 1 EGØ, n, T, Cum 1+ R Ø,T,Cum t= 1 Where: EG, n, T, Cum = Cumulative effect for roup decision level n, calculated based on eometric method, cumulative from sinle holdin periods 1 to T AG Ø, T, Cum = Cumulative active return of the portfolio, calculated based on eometric method, cumulative from sinle holdin periods 1 to T EG,, = Effect attributable to roup at decision level n, calculated based on eometric method, for n t sinle period t R Ø,T,Cum = The portfolio's return for the total level (total equity portfolio), cumulative from sinle holdin period from 1 to T R Ø,T,Cum = The benchmark's return for the total level (total equity portfolio), cumulative from sinle holdin period from 1 to T AG Ø, = Active return of the portfolio, calculated based on eometric method, for sinle period t t M = The level that represents the security level, that is, the last roupin hierarchy n= Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 38 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

39 Multiple-eriod Analysis (Continued) Use the followin formulas to annualize multiperiod results: y, n, T, Ann (, n, T, Cum m [28] EG = 1+ EG ) 1, y Ø, T, Ann ( Ø, T, Cum m [29] AG = 1+ AG ) 1, where EG, n, T, Ann = Annualized effect for roup decision level n, calculated based on eometric method, over the time period from 1 to T AG Ø, T, Ann = Annualized active return of the portfolio, calculated based on eometric method, over the time period from 1 to T EG, n, T, Cum = Cumulative effect for roup decision level n, calculated based on eometric method, cumulative from sinle holdin periods 1 to T AG Ø, T, Cum = Cumulative active return of the portfolio, calculated based on eometric method, cumulative from sinle holdin periods 1 to T y = The number of periods in a year; for example, it is 12 when data are in monthly frequency m = The total number of periods; for example, it is 40 when the entire time period spans over 40 months 2011 Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 39 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

40 Multiple-eriod Analysis (Continued) Multiperiod Arithmetic Method As stated in the previous section, the eometric method is the one recommended by Morninstar for its theoretical and mathematical soundness. Multiperiod linkin is only applicable to an effect and not a component. As components provide additional insiht, several methodoloies have emered to accumulate components over multiple time periods. The word "accumulate" is a more appropriate term than the word "link" as components and effects are added over time rather than eometrically compounded. These alternative methodoloies are commonly called triple-sum, as the cumulative active return (excess return over benchmark) over multiple periods is the sum of components in all roups (for example, sectors), decisions (weihtin versus selection), and time periods. As addin components over time does not equal the cumulative active return, additional mathematical "smoothin" is applied to make them match. Mathematical smoothin is where formulas and philosophies differ amon various alternative methodoloies. It is important to make sure the choice of method does not sinificantly distort the reality--for example, alterin the relative results of components and effects or causin a detractor to appear as a contributor or vice versa. This document presents one of several arithmetic methodoloies, the Modified Fronello methodoloy. 3 The use of the arithmetic method in the Modified Fronello methodoloy should not be interpreted as an endorsement from Morninstar. 3 Fronello, Andrew Scott ay, "Readers' Reflections," Journal of erformance Measurement, Winter 2002/2003, pp This methodoloy is a modified version of the authors' oriinal work in "Linkin Sinle eriod Attribution Results," Journal of erformance Measurement, Sprin 2002, pp Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 40 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

41 Multiple-eriod Analysis (Continued) Use the followin formulas to accumulate sinle-period arithmetic attribution components and effects into multiperiod results: [30] CA,T,Cum 2 2 ) CA,T [31] EA,n,T,Cum ( 2 + RØ,T + RØ,T ) ( 2 + RØ,T- 1,Cum + RØ,T- 1,Cum = CA,T 1,Cum + ( 2 + RØ,T + RØ,T ) ( 2 + RØ,T- 1,Cum + RØ,T- 1,Cum = EA,n,T 1,Cum ) EA,n,T [32] AAØ, T,Cum = RØ, T, Cum RØ, T, Cum = EA M n= 1 Ø,n,T, Cum Where: CA T, from sinle holdin periods 1 to T EA, n, T, Cum = Cumulative effect attributable to roup at decision level n, calculated based on arithmetic method, cumulative from sinle holdin periods 1 to T AA, T R Ø,T = The benchmark's return for the total level (total equity portfolio), at sinle holdin period T R Ø,T = The portfolio's return for the total level (total equity portfolio), at sinle holdin period T R Ø,T, Cum = The benchmark's return for the total level (total equity portfolio), cumulative from periods 1 to T R Ø,T, Cum = The portfolio's return for the total level (total equity portfolio), cumulative from periods 1 to T CA, T = Component at sinle holdin period T for roup, based on arithmetic method EA, n, T = Effect at sinle holdin period T for roup decision level n, based on arithmetic method, Cum = Cumulative component attributable to roup, calculated based on arithmetic method, cumulative Ø, T Cum = The portfolio's cumulative active return, based on arithmetic method, cumulative from periods 1 to M = The level that represents the security level, that is, the last roupin hierarchy 2011 Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 41 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

42 Multiple-eriod Analysis (Continued) Note: At period T=1, CA, T, Cum = CA and EA, n, T, Cum = EA, n, and these terms are defined in the "Sinle-eriod" sections. Use the followin formulas to annualize multiperiod results: [33] CA, T, Ann CA =, T, Cum y m [34] EA, n, T, Ann EA =, n, T, Cum y m [35] AA AA Ø, T, Ann = Ø, T, Cum y m Where: CA, T, Ann = Annualized component attributable to roup, calculated based on arithmetic method, over the time period from 1 to T EA, n, T, Ann = Annualized effect attributable to roup at decision level n, calculated based on arithmetic method, over the time period from 1 to T AA Ø, T, Ann = The portfolio's annualized active return, calculated based on arithmetic method, over the time period from 1 to T CA, T, Cum = Cumulative component attributable to roup, calculated based on arithmetic method, cumulative from sinle holdin periods 1 to T EA, n, T, Cum = Cumulative effect attributable to roup at decision level n, calculated based on arithmetic method, cumulative from sinle holdin periods 1 to T AA Ø, T, Cum = The portfolio's cumulative active return, based on arithmetic method, cumulative from periods 1 to T y = The number of periods in a year; for example, it is 12 when data are in monthly frequency m = The total number of periods; for example, it is 40 when the entire time period spans over 40 months 2011 Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 42 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

43 Multiple-eriod Analysis (Continued) Unlike the eometric method, in which frequency conversion such as annualizin is clearly defined, there is not a defined formula for annualizin an arithmetic method; therefore, ( y / m) is adopted with the end oal of preservin the arithmetic method's additive property across roups and types of attribution effects Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 43 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

44 Appendix A: Contribution Overview Contribution is a topic that is often associated with attribution. Contribution is an absolute analysis that multiplies the absolute weihtin in a sector or security by the absolute return, so an investment with mediocre performance may have a lare contribution simply because a lare amount of money is invested in it. Attribution, on the other hand, shows relative weihtin and relative returns. A ood result can come only from overweihtin an outperformin investment or underweihtin an underperformin one, a better measure of an investment manaer's skill. As contribution is an absolute analysis and attribution a relative analysis, they complement each other. Sinle eriod In a sinle-period analysis, the contribution is defined as [36] [37] C C w = R Ch h Ω w = R Ch h Ω if if if if = M < M = M < M where C = Contribution toward the portfolio associated with roup C = Contribution toward the benchmark is associated with roup M = The level that represents the security level; that is, the last roupin hierarchy 2011 Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 44 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

45 Appendix A: Contribution (Continued) Multiple eriod Use the followin formulas to link sinle-period contribution into multiperiod results: T T [38] C, T, Cum = ( 1+ R, t 1, Cum) w, t R, t = (1 + R, t 1, Cum) C, t t= 1 t= 1 T T [39] C, T, Cum = ( 1+ R, t 1, Cum) w, t R, t = (1 + R, t 1, Cum) C, t t= 1 t= 1 y, T, Ann (, T, Cum m [40] C = 1+ C ) 1 y, T, Ann (, T, Cum m [41] C = 1+ C ) 1 Where: C, T, Cum = Cumulative contribution toward the portfolio associated with roup, cumulative from sinle holdin periods 1 to T C, T, Cum = Cumulative contribution toward the benchmark associated with roup, cumulative from sinle holdin periods 1 to T C, T, Ann = Annualized contribution toward the portfolio associated with roup, cumulative from sinle holdin periods 1 to T C, T, Ann = Annualized contribution toward the portfolio associated with roup, cumulative from sinle holdin periods 1 to T = The portfolio's return for the total level, cumulative from periods 1 to t 1 = The benchmark's return for the total level, cumulative from periods 1 to t 1 R Ø,t 1, Cum R Ø,t 1, Cum 2011 Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 45 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

46 Appendix A: Contribution (Continued) At sement levels--for example, a particular sector or stock--the multiperiod contribution is not the eometric compoundin of sinle-period contribution fiures. Weihtin chanes may be due to transactions that cause the capital base for the sement to chane. Therefore, at the beinnin of each period it is necessary to compute the sement's capital base by multiplyin the total portfolio's wealth by the sement's weihtin, before applyin the base to the period's contribution. The total portfolio's wealth at the beinnin of the period is represented by 1 plus the cumulative portfolio return up to that time; in other words, it is the rowth of $1. Expressed another way, a sement's multiperiod contribution is the sum of this sement's dollar contributions from every period, assumin a $1 initial investment in the total portfolio. When contributions are expressed in cumulative terms, sement contributions sum to that of the total portfolio. However, once annualized, these numbers no loner add up Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 46 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

47 Appendix : Transaction-ased Attribution Overview A conventional performance attribution analysis is holdin-based. This is based on the assumption that portfolio holdins at the beinnin of a sinle period are held until the end of the period with no transactions in between. In reality, transactions occur, and the closest a holdin-based attribution analysis can reflect reality is by updatin portfolio holdins at a daily frequency. However, a daily holdin-based attribution analysis inores intraday trades and may lead to an unexplained residual in the analysis--in other words, a ap between the actual return of the portfolio and the portfolio return computed by the weihted averae of individual security returns. A transaction-based attribution analysis has the advantae of capturin the impact of these intraday trades and minimizin the unexplained residual. Althouh the impact of intraday tradin can be implied by the residual in a daily holdins-based analysis, a transaction-based analysis has the added benefit of itemizin every trade's value-add. In a transaction-based attribution analysis, the transaction effect captures the portion of performance attributable to trade execution and can only be calculated if transaction information is provided. Althouh traders may use other measures to evaluate their execution, in an attribution analysis the value-add of trade execution is defined as the difference between the transaction price and the end-of-day price. This is because the latter is the pricin used in performance measurement. Securities may be deposited or withdrawn in kind from a portfolio, and in such cases the transaction effect is calculated based on the deposit or withdrawal price instead of the trade price Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 47 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

48 Appendix : Transaction-ased Attribution (Continued) Sinle eriod One more rule is required in definin a sinle period for transaction-based attribution, in addition to the sinle-period rules applicable to holdin-based attribution stated in the "Multiple-eriod Analysis" section of this document. The day of the transaction must be its own sinle period. For example, if there is a transaction on Jan. 5, the previous sinle period ends on Jan. 4, Jan. 5 is its own sinle period, and the next sinle period starts on Jan. 6. The formulas for transaction-based weihtin, return, and contribution are [42] MV + TC = MV w~ h h Ω w~ Ø if = M if 0 < < M R [43] EMV TC + TW MV MV + TC ~ ~ = ~ R w R h h h Ω w~ ~ ~ wh Rh h Ω [44] ~ C w~ ~ R = ~ Ch h Ω if = M if < M if if = M and TC = TW = 0 = M and ( TC 0 or TW if 0 < < M if = 0 0) 2011 Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 48 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

49 Appendix : Transaction-ased Attribution (Continued) where w ~ = ortfolio's effective weihtin for the purpose of transaction-based attribution calculation, for roup R ~ = ortfolio's transaction-based return for roup C ~ = ortfolio's transaction-based contribution to return for roup MV ortfolio's beinnin market value for roup, where = Ø represents the total portfolio TC ortfolio's total deposit/contribution (sum of all purchases and transfers in) for roup EMV ortfolio's endin market value for roup TW ortfolio's total withdrawal (sum of all sells and transfers out) for roup Note: The portfolio's effective weihtin, displayed. w ~, is for calculation purposes only and is not 2011 Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 49 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

50 Appendix : Transaction-ased Attribution (Continued) The formulas for transaction-based attribution measures are [45] TA w~ ~ = R w TAh h Ω R if = M if < M M ~ [46] AAØ = RØ RØ = EAØ,n + IAØ + TAØ [47] TG n= 1 ~ TA 1+ R = TA Ø 1+ R TGh h Ω ~ 1+ RØ = 1 = 1+ R Ø Ø 1 if = M if < M M Ø 1 Ø n= 1 [48] AG ( 1+ EGØ,n ) ( 1+ IGØ ) ( 1+ TGØ ) where TA = Transaction effect attributable to roup, based on arithmetic method AA Ø = Active return, calculated based on arithmetic method TG = Transaction effect attributable to roup, based on eometric method AG Ø = Active return, calculated based on eometric method Multiple eriod The methodoloy for transaction-based multiperiod attribution is the same as that of holdinbased attribution, except that transaction-based portfolio returns are used in place of their holdin-based counterparts. To calculate the transaction-based multiple period contribution, please substitute the holdin-based contribution with the transaction-based contribution in the multiperiod holdin-based contribution formula Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 50 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

51 Appendix C: Residual Overview The residual, also known as the return ap, is the portion of the return that cannot be explained. In a holdin-based attribution analysis, it is the return that cannot be explained by the holdins composition at the beinnin of the analysis period and is usually caused by intraperiod portfolio transactions, security corporate actions, and so on. In order to measure the residual, returns must be available for all securities in the portfolio and benchmark, includin nonequity securities such as cash-equivalent securities. erformance attribution analysis also must be performed on the total portfolio and not just the equity portion of the portfolio. The main portion of this document focuses only on the equity portion of the portfolio. This section addresses full portfolio top-down attribution analysis, as bottom-up attribution analysis is meaninful only for the equity portion of a portfolio Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 51 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

52 Appendix C: Residual (Continued) Top-Down Approach, Arithmetic Method In a top-down arithmetic attribution, residuals are defined in the formulas below. A residual is the difference between the actual return and the calculated return, the latter is based on the holdins as of the beinnin of the period. This is intuitive, as the actual return only differs from its counterpart if transactions or corporate actions have occurred durin the holdin period. [49] GA = R RØ + EX [50] GA = R R Ø [51] AA where M = R R = AAØ + GA GA EX = n=1 EA GA = The portfolio's residual, calculated based on arithmetic method GA = The benchmark's residual, calculated based on arithmetic method Ø, n AA = The portfolio's active return, calculated based on arithmetic method + GA GA EX R = The portfolio's actual return, when performin attribution analysis on the total portfolio R Ø = The portfolio's calculated return, based on formula [4] EX = The portfolio's net prospectus expense ratio R = The benchmark's actual return, when performin attribution analysis on the total portfolio R Ø = The benchmark's calculated return, based on formula [3] AA Ø = The portfolio's calculated active return, based on equity holdins, calculated based on arithmetic method EA Ø,n = Effect attributable to the total equity portfolio at decision level n, based on arithmetic method 2011 Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 52 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

53 Appendix C: Residual (Continued) Top-Down Approach, Geometric Method In a top-down eometric attribution, residuals are defined in the formulas below. Similar to their arithmetic counterparts, a eometric residual is the eometric difference between the actual return and the calculated return. 1+ R [52] GG = ( 1+ EX ) 1 1+ R Ø 1+ R [53] GG = 1 1+ R Ø 1+ R M 1+ AG + + EG Ø 1 GG 1 Ø, [54] AG = 1 = 1 = 1+ R 1+ EX 1+ GG 1+ EX n= 1 n 1+ GG 1+ GG 1 here GG = The portfolio's residual, calculated based on eometric method GG = The benchmark's residual, calculated based on eometric method AG = The portfolio's active return, calculated based on eometric method R = The portfolio's actual return, when performin attribution analysis on the total portfolio R Ø = The portfolio's calculated return, based on formula [4] EX = The portfolio's net prospectus expense ratio R = The benchmark's actual return, when performin attribution analysis on the total portfolio R Ø = The benchmark's calculated return, based on formula [3] AG Ø = The portfolio's calculated active return, based on equity holdins, calculated based on eometric method EG Ø,n = Effect attributable to the total equity portfolio at decision level n, based on eometric method 2011 Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 53 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.

54 Appendix C: Residual (Continued) Multiperiod Geometric Residuals Residuals from sinle-period eometric attribution analysis can be linked over multiple periods to form an overall result. These formulas are not applicable to residuals calculated usin the arithmetic method. T, ) 1 t= 1 [55] GG T Cum = ( 1+ GGt y T, Ann ( T, Cum m [56] GG = 1+ GG ) 1 T, ) 1 t= 1 [57] GG T Cum = ( 1+ GGt y T, Ann ( T, Cum m [58] GG = 1+ GG ) 1 where GG T, Cum = Cumulative residual of the portfolio, calculated based on eometric method, cumulative from sinle holdin periods 1 to T GG T, Ann = Annualized residual of the portfolio, calculated based on eometric method, over the time period from 1 to T GG T, Cum = Cumulative residual of the benchmark, calculated based on eometric method, cumulative from sinle holdin periods 1 to T GG T, Ann = Annualized residual of the benchmark, calculated based on eometric method, over the time period from 1 to T y = The number of periods in a year; for example, it is 12 when data are in monthly frequency m = The total number of periods; for example, it is 40 when the entire time period spans over 40 months 2011 Morninstar, Inc. All rihts reserved. The information in this document is the property of Morninstar, Inc. Reproduction or transcription by any means, 54 in whole or part, without the prior written consent of Morninstar, Inc., is prohibited.