Applying Fundamental Index Methodology to Fixed Income 1. Robert D. Arnott Research Affiliates, LLC

Transcription

1 Applying Fundamental Index Methodology to Fixed Income 1 Robert D. Arnott Research Affiliates, LLC Jason C. Hsu, Ph.D. Research Affiliates, LLC & UCLA Anderson School of Management Feifei Li, Ph.D. Research Affiliates, LLC Shane Shepherd, Ph.D. Research Affiliates, LLC First draft: July, 2007 This draft: March, Rob Arnott is the Chairman and founder of Research Affiliates. Jason Hsu is the Managing Director overseeing the research and investment management group. Feifei Li is an Associate Director in the research group. Shane Shepherd is a senior researcher in the research group. Corresponding author: shepherd@rallc.com. We would like to acknowledge Brett Myers, Vitali Kalensik, Jason Williams, and Michael Brownell for their help in the research process.

2 Abstract The Fundamental Index methodology [Arnott, Hsu & Moore, 2005], applied to U.S. and global equities, has produced statistically significant and economically large outperformance against traditional capitalization-weighted benchmarks in historical testing. Several papers (Treynor, 2005, Hsu, 2006, Arnott, Hsu, 2008, and Arnott, Hsu, Liu, and Markowitz, 2008 draft paper) explore the theoretical rationale for this result, which hinges on a market inefficiency in which pricing error is uncorrelated with value, rather than being uncorrelated with price. In this paper, we apply the methodology to U.S. investment-grade corporate bonds, U.S. high yield bonds, and emerging market bonds (hard currency). We find that fixed income indexes constructed using the Fundamental Index methodology outperform the corresponding capitalization-weighted benchmarks. We also find that the outperformance is higher for markets which practitioners expect to be more inefficient. Both findings are consistent with the empirical evidence found in the equity application of the Fundamental Index.

3 Introduction The Fundamental Index 2 methodology has created significant debates and interests in non-capitalization-weighted indexing since its initial publication (Arnott, Hsu & Moore, 2005). Empirical works by Arnott, Hsu & Moore (2005), Tamura & Shimizu (2005), Hsu & Campollo (2006), and Hsu, Li, Myers & Zhu (2007) have found statistically significant and economically large outperformance against traditional capitalizationweighted indexes when applying the methodology to equities in the U.S., international, and emerging markets. Theoretical works by Treynor (2005) and Hsu (2006) explain why non-priceweighted indexes would be more efficient than price-weighted indexes, when prices are noisy proxies of fair value, as opposed to the Efficient Markets assumption that value is randomly distributed around price. Arnott (2005a,b) posits that size and value premia should be expected in such a world when measured against a price-weighted market index, and observes that the size and value premia are far weaker when measured against a non-price-weighted market index. This suggests that the price component of size, when we measure size based upon market capitalization, helps create the size premium. Arnott & Hsu (2008) and Arnott, Hsu, Liu & Markowitz (2008) explicitly derive the result that mean-reverting noise in prices will result in the value and size effects. Specifically, Arnott & Hsu (2008) show that a non-price-weighted index, like Fundamental Index, could capture equity market premium more efficiently by simultaneously capturing traditional market beta, size and value premium. 2 Research Affiliates holds trademarks on variants of Fundamental Index and has pending patents covering variants of the methodology.

4 Critics argue that the size and value effects are driven by hidden macro risks associated with small cap and value investing rather than pricing noise. Under this interpretation, non-price-weighted schemes, like Fundamental Indexes, are simply strategies which load up on these risk factors. Since value and size are well documented factors common to the U.S. and international equity universes, critics find the Fundamental Indexes universal outperformance in global applications unsurprising. In this paper, we explore this debate by applying Fundamental Index methodology to the fixed income universe. This application is relevant and interesting because size and value are not important risk factors for bonds, and generally, fixed income risk factors are considered distinct from equity risk factors. If the Fundamental Index methodology proves successful in the fixed income space, it would suggest that the size and value equity factors are not drivers of the methodology s success. Instead it supports the opposite conclusion that pricing error may be a key driver in creating the size and value effects. We construct fundamentally weighted investment grade corporate indexes, high yield bond indexes and emerging market bond indexes and compared them to corresponding cap-weighted bond indexes. We find that fundamentally weighted bond indexes outperform their corresponding cap-weighted benchmarks. Additionally, we find that in markets with greater pricing noise, like emerging market bonds and high yield bonds, the Fundamental Index outperformance is also greater. These empirical findings are consistent with the theoretical prediction laid out in Hsu (2006), where expected outperformance against capitalization-weighted indexes is positively related with the size

5 of the market mispricing indeed, the square of that mispricing and is independent of the asset class. Fundamental Index methodology: evidence and theory Fundamental Index methodology [Arnott, Hsu and Moore (2005)] proposes an alternative weighting methodology which uses non-price-based metrics of company size to create equity index weights. Empirical evidences demonstrate that this alternative index construction offers statistically significant value-added over traditional capitalizationweighted indexes when applied to developed markets, emerging markets and to both large cap and small cap markets. Arnott, Hsu and Moore (2005) detail outperformance of fundamentally selected and weighted indexes using U.S. data extending back to Tamura & Shimizu (2005) and Hsu & Campollo (2006) show similar outperformance for developed countries using international data extending back to 1988 and 1984, respectively. Hsu, Li, Myers & Zhu (2007) find outperformance when applying the methodology to small cap and emerging markets and confirms that the size of Fundamental Index outperformance is related to the quality of price efficiency for the specific market. Hsu (2006) and Arnott & Hsu (2008) offer theoretical models of noisy prices and argue that price-weighting creates a positive correlation between ex ante pricing error and portfolio weight in the cross-section. Intuitively, if a stock is overvalued, its price will contain a positive pricing error (which reverts back to zero over time, as the market noisily seeks out fair value) and its market capitalization weight will therefore be larger than otherwise. Thus a capitalization-weighted portfolio gives overvalued stocks extra

6 weight, relative to their unknowable fair values, and underweights undervalued stocks. By comparison, non-price-based weighting schemes do not inherently exhibit this positive correlation between portfolio weights and pricing errors. 3 This creates a performance differential between cap-weighted indexes and non-price-weighted indexes and explains the return advantage of Fundamental Indexes. Asness (2006) and Perold (2007) argue that Fundamental Indexes work because they indirectly exploit the small cap and value risk factors, which are risk sources common to global equities. Under this interpretation, the markets are efficient. Traditional cap-weighted indexes offer an efficient and pure capture of the market risk premium. Fundamentally selected and weighted market indexes improve performance against standard benchmarks by loading on risks associated with investing in value oriented and small cap stocks. However, Arnott & Hsu (2008) and Arnott, Hsu, Liu & Markowitz (2008) demonstrate that size and value effects arise naturally whenever market price is defined as fair value plus mean-reverting pricing error. 4 Specifically, Arnott & Hsu (2008) show that in a one factor economy, characterized by this type of noisy price process, the factor premium can be decomposed into excess return from a cap-weighted market portfolio and a size/value portfolio. The derivation further suggests that the Fama-French 3 factor model may be reduced into a one factor model if the market factor is proxied with a non-cap-weighted market portfolio. This result suggests that traditional cap-weighted market indexes are ineffective at capturing the full risk 3 We readily acknowledge that efforts to exploit this inefficiency on sufficient scale will tend to arbitrage away this inefficiency by introducing exactly this sort of link. 4 Jeremy Siegel coined the marvelous expression, Noisy Market Hypothesis, to describe this alternative to the classic EMH worldview. We borrow this expression, with attribution, in our paper.

7 premium associated with the market exposure, and non-price-based market indexes would provide more effective exposure. The models in Hsu (2006) and Arnott & Hsu (2008) are not asset class dependent. Therefore, we can further test the theory underlying the Fundamental Index methodology by examining non-equity asset classes. In this paper, we examine fixed income portfolios constructed using the Fundamental Index strategy laid out in Arnott, Hsu and Moore. Specifically, we construct investment-grade corporate bond indexes, high yield bond indexes and emerging market bonds (hard currency bonds) indexes using alternative size weighting and analyze their performances against traditional cap-weighted bond indexes. Examining the fixed income asset classes also helps assess the validity of the criticism that Fundamental Index methodology is simply a value/small cap equity strategy. Traditionally, the common risk factors for pricing corporate and emerging sovereign bonds are interest rate level, default probability, collateral quality and maturity. These are different risks from common equity risks. Additionally, default pricing models are empirically more successful than equity pricing models. Bond pricing models are not plagued by anomalies, such as value and size effects, found in equity pricing literature. If these default bond Fundamental Indexes outperform the standard cap-weighted default bond benchmarks adjusted for risk, then there is a strong case that the Noisy Market Hypothesis, as detailed in Arnott & Hsu, explains the performance of Fundamental Index for equities. Fixed income Fundamental Indexes: construction

8 The construction of a Fundamental Index portfolio in the fixed income space presents several challenges that do not affect equity index construction. For the corporate arena, most companies have only one issuance of common stock, but many companies issue multiple bond offerings. The emerging market debt space provides a plethora of country data, but the measures of company size explored in the Fundamental Index world (sales, profits, book values, dividends) have no meaning in defining the size of an emerging market economy. Although previous research suggests that any non-price weighting scheme should provide an adequate Fundamental Index, it is important to choose factors that produce a representative index of the underlying securities and thus deliver a broad representation of the particular asset class. We first describe the construction of the corporate investment grade and high yield indexes. Since the only difference between the underlying constituents in these indexes is the credit quality, we utilize the same factors and methodology to construct both indexes. The goal of a fundamental index is to provide a non-price based weighting scheme that maintains a focus on the representativeness of an index to the underlying economy. There is good reason to assume that the same factors that measure importance in the equity markets can also apply to the bond markets. After all, both debt offerings and equity offerings are, at the base level, vehicles for the financing of a corporate enterprise, and both are simple claims upon the future cash flows from these projects. Therefore, the factors that determine the strength of these cash flows and the economic viability of their underlying projects are the basis for the cash distributions and therefore valuations of both corporate equity and debt.

9 Hence we deviate only slightly from the primary factors used in the construction of the equity version of Fundamental Index presented in Arnott, Hsu, and Moore (2005). We examine seven individual factors in the corporate and high yield bond space: total cash flow, free cash flow, total dividends, book value of assets, sales, collateral, and total cash on hand. We gather data on these corporate financials from the Worldscope database. We compute lagged five-year average numbers for all factors except book value of assets, for which we use the most recently reported number. Total dividends includes the aggregate dividends paid, both common and preferred. Collateral is defined as Property, Plant, and Equipment plus Cash and Cash Equivalents. The equity index used shareholders book equity, but here we instead use the book value of assets as that better reflects the claims that bondholders have on the corporate balance sheet. For much the same reason, we explore using a measure of physical collateral. As we shall soon see, these replacements have little effect on the empirical results, but are made because the bond investor s perspective of a company s economic scale differs from the equity investor s perspective. Before applying a Fundamental weight to the individual bond offerings, we first construct fundamental weights for each corporation. This is done in the same manner as that followed by Arnott, Hsu, and Moore (2005). Each company is ranked on each of the four metrics and given a score according to its relative weight on that metric. We compute two composite measures: one including assets, dividends, cash flow, and collateral, and a second that replaces collateral with sales. The overall fundamental weight is assigned by equally weighting all four of the metrics (or, when a company does not pay a dividend, by equally weighting the remaining three metrics).

10 We then turn our attention to the individual bonds. We gather corporate bond constituent data for the years 1997 through 2007 from the Merrill Lynch U.S. Corporate Master Index (for investment grade bonds) and the Merrill Lynch U.S. High Yield Master II Index, BB and B rated (for the high yield universe). The U.S. Corporate Master Index includes all Corporate Investment grade bonds rated AAA to BBB-, and the U.S. Master II Index includes all corporate bonds rated BB+ to B-. Our reason for excluding bonds rated below B- is that the C and D categories have immense bid-ask spreads, so that an investor could not necessarily construct the model portfolio that would be indicated by this work. It goes beyond the scope of this paper, but results improve markedly if we include the C and D range bonds, but we are unsure that this result has any meaning that would be useful to the practitioner community. Our next step is to merge the individual bonds data with the corporate fundamental data. Here we encounter a matching problem: many of the bonds in the Merrill Lynch indexes are not issued by listed corporations for which we have access to accounting data. We encounter difficulty matching privately or employee-owned companies and companies that are based in foreign countries or traded on the OTC exchanges. For example, GMAC is a large issuer of high yield debt. However, the automobile-financing company is 49% owned by General Motors and 51% owned by private equity. Hence, we lack direct corporate financials for which to measure this debt. Another example is Freescale Semiconductor, a company that was taken private in 2006 but whose debt still trades in the index. This matching problem problem is more severe for the high yield index than the corporate index. The month of December 2007 includes 1312 bonds in the high yield index. Of those, 1107 are domiciled in the United States.

11 We match 852 of those to the corporate accounting data using either a ticker or cusip. Our overall 59.5% match rate removes a large portion of the published index from our analysis. We successfully match 65% of the corporate bonds, and nearly 100% of the emerging markets bonds. To ensure that our results are due to the fundamental selection and weighting and not a sample bias, we compare our fundamental indexes to both the published benchmark as well as a cap-weighted index that we construct from the universe of successfully matched bond issues. Many corporations have multiple bond issues. To avoid overweighting a single company in the index, simply because it parcels its debt amongst a variety of instruments, we do not directly apply the fundamental weight from the corporation to each of its bonds. Instead, when a company issues N bonds, we divide the fundamental score amongst the bonds according to the ratio of each bond s face value to the sum of the face value of debt issued by that corporation. (We also examine a specification of assigning 1/N of the weight to each bond issue; results are similar.) We then rescale the weights to correct for the fact that not all corporations with a fundamental score have debt issues on their books. The resulting list of debt issues and weights comprises our portfolio. We examine two portfolios: one which includes all bonds in the database (as of 2007, that numbered 1312 qualifying issues for the high yield index and 3388 issues for the corporate bond index) and a second which selects and weights the top 500 names by composite fundamental value. A similar procedure, but with different factors, is utilized for the construction of the emerging market bond Fundamental Index. Searching for factors on which to base a fundamental emerging market index leaves many choices. We focus on four factors that

12 signify the importance, both current and potential, of a country in the world economy: total population, land area (as a crude proxy for resources), total gross domestic product, and financial reserves. All factors are computed as smoothed five-year averages. These factors are much less volatile than the ones used in the corporate index; hence the target weights move only gradually. We gather the information on these factors from the CIA World Factbook from 1993 through We also construct a second fundamental index portfolio by substituting face value of debt for the reserves factor. While face value does not provide any specific information about the company issuing the debt obligation, it does meet the requirements for a fundamental factor: it is a relevant measure of size that is uncorrelated with price. We then proceed as before: each country is given a weight on each factor proportional to its representation, and we then compute five-year averages of these weights. A country s aggregate weight is assigned as the equally weighted average of its score on each of the four individual factors. We then gather the constituent issues in the Merrill Lynch Emerging Markets Index, USD-denominated Foreign Sovereign Debt rated BBB+ and lower. As of 2007, this includes 194 separate issues from 33 countries. To avoid the overrepresentation problem created by one country with multiple debt issues, we split the country weight amongst each of its issues according to face value of the debt, in an analogous manner to the procedure used with corporate bonds; this gives the final weighting scheme. We examine two portfolios, one including all bonds and one restricted to the largest fifty bonds selected by face value, as a liquidity screen. Fixed income Fundamental Index: performance and attribution

13 The returns to a fixed income Fundamental Index lend strong support to the Noisy Markets Hypothesis. We show firstly that a non-price weighting scheme can add value over a cap-weighted benchmark in areas where size and value risk factors do not apply; the high yield corporate bond index, the emerging market debt index, and the investment grade corporate bond index all outperform their respective benchmarks. Secondly, we confirm the intuition in Hsu (date?) as the marketplace becomes less efficient, the fundamental index approach adds increasing value. While the value added is small in the relatively efficient corporate investment grade space, the high yield and emerging markets indexes offer a large opportunity for outperformance. Returns to the three Fundamental Indexes and their benchmarks are presented in Table 1. The high yield Fundamental Index outperforms the Merrill Lynch U.S. High Yield Master II (BB-B) Index by 174 basis points per year; the emerging markets debt Fundamental Index outperforms the Merrill Lynch Emerging Markets Debt Index by 396 basis points per year, and the investment grade corporate bond Fundamental Index outperforms the Merrill Lynch U.S. Corporate Master Index by 33 basis points per year. Additionally, all of the individual metrics outperform their respective benchmarks on their own. This strong evidence supports the claim that the Fundamental Index concept works in noisy markets. Furthermore, these out-of-sample tests cast serious doubt upon claims of data mining in the original equity results. We also present results for the entire available universe of bonds in Table 2. The outperformance of the fundamental index strategy is reduced when using the entire index, showing that a portion of the outperformance can be attributed to the sample selection bias. In the high yield space, a cap-weighted index composed of the largest 500 bonds in

14 our matched subsample outperforms the published index by 100 basis points per year. Apparently there is great value in excluding foreign-based corporations and those not listed on the major exchanges. Still, the fundamental index strategy shows sizeable outperformance even over this substitute cap-weighted benchmark. As we will see more evidence of later, the fixed income Fundamental Indexes are in general less volatile and less risky than their benchmarks; they all boast a superior average credit rating and a shorter duration, and they in general have lower standard deviations around their returns and hence higher Sharpe ratios. Much like the equity version of Fundamental Index, these provide superior performance with lower volatility and risk. The investment grade and high yield space provide an excellent opportunity to test the proposition that the efficacy of a Fundamental Index is correlated with the level of noise in a marketplace. The direct comparison between the investment grade Fundamental Index and the high yield Fundamental Index shows that much greater outperformance is realized in the noisier high yield space, while the more efficient investment grade marketplace has less volatility and, presumably, pricing error. One common criticism of the Fundamental Index is that it merely serves as a value play in disguise. If the well-documented excess returns to value stocks are a payment for the assumption of systematic risk, then the value tilt of the Fundamental Index means that its outperformance comes about simply due to added risk. Since the value and size factors are of primary importance in the equity markets, we cannot expect them to adequately explain the returns on a fixed income portfolio. Instead, we follow the footsteps of Fama and French (1993) and Fama and French (1996) and examine a three-

15 factor model augmented by two factors of primary importance to the fixed income markets: duration and credit risk. We present a formal analysis of the risk factors in Table 3. Panel A shows the basic CAPM regression. None of the benchmarks have significant alphas, while all of the Fundamental Indexes show significantly positive risk-adjusted alphas. Panel B shows that the three-factor model of Fama and French (1992) does have some explanatory power on the fixed income Fundamental Index. While the alphas remain positive, adding in additional sources of risk mitigate the strength of the t-stats. It is interesting to note that the three-factor model does a reasonable job of explaining the returns in the benchmarks. This is not entirely surprising, as Fama French (1993) suggest that the size and value factors proxy for unknown risk sources that are common to stocks and bonds, even though these risk factors may be difficult to measure in the fixed income space. Panel C details results to the full regression detailed in Fama French (1993). We augment the well known three factor model with a duration risk factor and a default risk factor. We construct the term spread as the difference in returns between a portfolio of year Treasury notes and the 3-month T-bill. The default risk factor is constructed as the difference between the returns given by a portfolio of investment grade corporate debt and the 10-year T-bill. Our results are robust to these risk adjustments. We see first that all three portfolios have lower risk loadings than their cap-weighted counterparts. Thus, their outperformance comes despite lower duration and credit risk. The alphas far exceed those of the benchmarks, and the high yield alpha is strongly significantly different from zero. These results make it clear that the outperformance of the

16 fundamental index strategy in fixed income markets is not due to excess exposure to known risk factors. Of course, these models all attempt to explain the returns of a portfolio above the risk-free rate. Since the Fundamental Index is so closely related to its capitalizationweighted counterpart, it is of great interest to compare and attribute differences in performance between these two portfolios. Accordingly, we carry out a Brinson attribution analysis (Brinson and Fachler, 1985), including a dynamic version (Hsu, Kalensik and Myers, working paper) between the Fundamental Index portfolios and their benchmarks. This compares the portfolio holdings on a security-by-security basis and determines how much of the outperformance of the Fundamental Index is due to stock selection and how much due to either a static or dynamic allocation to risk factors. For this analysis, we examine duration risk and credit risk. We attribute the fundamental portfolios against our matched-group benchmarks rather than the published indexes; due to the difference in selection universe, this benchmark gives a better appraisal of the risk assumed by the portfolio. Of course, this alternative benchmark outperforms the published benchmark and is thus a higher standard. Results are robust to the use of the published benchmarks. The results are presented in Table 4. Because the Fundamental Indexes provide superior performance despite generally lower duration and better credit ratings, these results are quite illuminating. For all three fixed income portfolios, the bulk of the outperformance is due to security selection component. The second largest component is the dynamic exposure to the risk factors, and the static exposure accounts for a very small (or even negative) amount of the outperformance. For the high yield index, a lower

17 exposure to duration risk hurts the returns. We see that this is actually a result of poor timing; the dynamic attribution on duration hurts performance by 38 basis points. The credit exposure helps slightly (8 basis points), and security selection leads to 94 basis points of outperformance. For the investment grade corporate bonds, both duration and credit risk is negligibly different from the benchmark. However, superior security selection delivers 22 basis points of outperformance. And for emerging markets, the portfolio shows a significant allocation to the risk factors. The fundamental portfolio owes 115 and 82 basis points of its outperformance to the duration and credit risk factors, respectively. However, the majority of this allocation comes from the dynamic timing element, and this still leaves 156 basis points of outperformance to security selection. Overall, the outperformance of the fundamental indexes in the fixed income space cannot be explained away by exposure to risk factors; rather, it comes from superior security selection and, to the extent that risk plays a role, it does so in a generally dynamic way. We also examine the performance of the portfolios under various macroeconomic conditions. Table 5 shows the performance figures split into bull and bear markets in the relevant benchmark index, and split into rising and falling Fed Funds rate regimes. In the equity space, previous research has shown a pattern where the Fundamental Index matches the benchmark performance in good markets, but outperforms significantly in flat or down markets. That trend is, to a large extent, repeated in the fixed income space. For high yield bonds, we show underperformance performance with the benchmark in bull markets and during periods of rising Fed Funds rates, and strong outperformance of 5.6% and 5.0%, respectively, during bear markets and falling rates. The story is similar for corporate investment grade debt outperformance in falling rate regimes,

18 underperformance during rising rates, and slight outperformance in both bull and bear markets. On the other hand, the emerging markets index shows the opposite pattern very strong outperformance in bull markets but severe underperformance during bear markets, along with strong outperformance during rising rate regimes. At least for the corporate bonds, applying a fundamental index strategy is less prone to macroeconomic events than the cap-weighted benchmarks. These countercyclical trends show that it is unlikely that hidden macroeconomic risk factors may be behind the returns. Future research and conclusion In this paper, we apply the methodology to U.S. investment-grade corporate bonds, U.S. high yield bonds, and emerging market bonds (hard currency). We find that fixed income indexes constructed using the Fundamental Index methodology outperform the corresponding capitalization-weighted benchmarks. We also find that the outperformance is higher for markets which practitioners expect to be more inefficient. Both findings are consistent with the empirical evidence found in the equity application of the Fundamental Index.

19 References Arnott, Robert D., Editor s Corner: What Cost Noise? Financial Analysts Journal, v. 61, No. 2, Arnott, Robert D., Editor s Corner: Disentangling Size and Value, Financial Analysts Journal, v. 61, No. 5, Arnott, Robert D. and Jason C. Hsu, Noise, CAPM and the Size and Value Effects, Journal of Investment Management, v. 6, No. 1, Arnott, Robert D., Jason C. Hsu, Jun Liu and Harry Markowitz, Can Noise Create the Size and Value Effects, UCSD and Research Affiliates working paper, Arnott, Robert D., Jason C. Hsu and Philip Moore, Fundamental Indexation, Financial Analysts Journal, v. 61, No. 2, Asness, Clifford, The Value of Fundamental Indexing. Institutional Investor, vol. 40, no. 10 (October):94-99, Hsu, Jason C., Cap-Weighted Portfolios Are Sub-optimal Portfolios, Journal of Investment Management, 3 rd Quarter, Hsu, Jason C. and Carmen Campollo, An Examination of Fundamental Indexation, Journal of Indexes, Jan/Feb, Hsu, Jason C., Feifei Li, Brett W. Myers and Julia Zhu, Accounting-Based Index ETFs and Inefficient Markets, Exchange Traded Funds Guide, Fall, Perold, André F., Fundamentally Flawed Indexing. Financial Analysts Journal, vol. 63, no. 6 (November/December):31-37, Shimizu, Y. and H. Tamura, Fundamental Indices, Do they outperform market-cap weighted indices on a global basis? Security Analysts Journal, v. 43, No. 10, Oct, Treynor, Jack, Why Market-Valuation-Indifferent Indexing Works, Financial Analysts Journal, v. 61, No. 5, 2005.

20 Table 1: Performance of Fixed Income Fundamental Indexes vs. Benchmarks -- Top 500 names (top 50 for EMD) Top 500 names selected by fundamental weight for the High Yield and Investment Grade indexes Top 50 names selected by face value for the Emerging Markets index For the corporate indexes, combined A includes assets, dividends, cash flow, and collateral Combined B includes assets, dividends, cash flow, and sales For the emerging markets, Combined A includes population, area, GDP, and reserves Combined B includes population, area, GDP, and face value "Published Index" is the index return for the relevant Merrill Lynch benchmark return provided by Bloomberg "Benchmark" is the cap-weighted benchmark constructed from our particular matched subsample Excess returns and tracking error are computed against the published index Panel A: High Yield Corporate Bonds Std Excess Return Dev Sharpe Credit Rating Duration Ret t stat Track Error Assets BB2/BB Dividends BB Cash Flow BB Free Cash Flow BB2/BB Collateral BB Cash BB Sales BB Combined A BB2/BB Combined B BB2/BB Benchmark BB3/B Published Index Panel B: Investment Grade Corporate Bonds Std Excess Inf. Return Dev Sharpe Credit Rating Duration Ret t stat Track Error Ratio Assets AA3/A Dividends AA2/AA Cash Flow AA Free Cash Flow AA3/A Collateral AA3/A Cash AA3/A Sales AA3/A Combined A AA Combined B AA Benchmark A Published Index Panel C: Emerging Market Bonds (top 50, sorted by face value) Std Excess Inf. Return Dev Sharpe Credit Rating Duration Ret t stat Track Error Ratio Population BB1/BB Area BB2/BB GDP BB Reserves BB1/BB Face Value BB2/BB Combined A BB Combined B BB2/BB Benchmark BB2/BB Published Index Inf. Ratio

21 Table 2: Performance of Fixed Income Fundamental Indexes vs. Benchmarks -- Entire Index (no selection component) For the corporate indexes, combined A includes assets, dividends, cash flow, and collateral Combined B includes assets, dividends, cash flow, and sales For the emerging markets, Combined A includes population, area, GDP, and reserves Combined B includes population, area, GDP, and face value "Published Index" is the index return for the relevant Merrill Lynch benchmark return provided by Bloomberg "Benchmark" is the cap-weighted benchmark constructed from our particular matched subsample Excess returns and tracking error are computed against the published index Panel A: High Yield Corporate Bonds Return Std Dev Sharpe Credit Rating Duration Excess Ret t stat Track Error Inf. Ratio Assets BB3/B Dividends BB3/B Cash Flow BB Free Cash Flow BB Collateral BB3/B Cash BB3/B Sales BB3/B Combined A BB2/BB Combined B BB2/BB Benchmark BB3/B Published Index Panel B: Investment Grade Corporate Bonds Std Excess Inf. Return Dev Sharpe Credit Rating Duration Ret t stat Track Error Ratio Assets A Dividends AA3/A Cash Flow AA3/A Free Cash Flow A Collateral A Cash A Sales A Combined A AA3/A Combined B AA3/A Benchmark A1/A Published Index Panel C: Emerging Market Bonds Return Std Dev Sharpe Credit Rating Duration Excess Ret t stat Track Error Inf. Ratio Population BB Area BB1/BB GDP BB Reserves BB Face Value BB2/BB Combined A BB Combined B BB1/BB Benchmark BB2/BB Published Index

22 Table 3: CAPM, Three-Factor, and Five-Factor regressions for Benchmark and fundamental portfolios Monthly regressions of portfolio and benchmark returns upon risk factors. Results for alphas are presented as return percent per month. The Beta, SMB, and HML regressors are the three Fama-French factors and taken from Ken French s web site; the TERM regressor is the return on a portfolio of year US Treasury bills minus the risk free rate; and the DEFAULT regressor is the return on the Merrill Lynch Corporate Master (Investment Grade) Index minus the risk free rate. Panel A: CAPM model Benchmark alpha beta alpha t-stat High Yield Investment Grade Emerging Markets Fundamental Index alpha beta alpha t-stat High Yield Investment Grade Emerging Markets Panel B: Three-Factor Benchmark alpha beta SMB HML alpha t- stat High Yield Investment Grade Emerging Markets Fundamental Index alpha t- alpha beta SMB HML stat High Yield Investment Grade Emerging Markets Benchmark Panel C: Five-Factors alpha beta SMB HML TERM DEF alpha t-stat High Yield Investment Grade #DIV/0! Emerging Markets Fundamental Index alpha beta SMB HML TERM DEF alpha t-stat High Yield Investment Grade Emerging Markets

23 Table 4: Dynamic Brinson Performance Attribution This table shows the risk attribution due to static and dynamic loadings on duration and credit risk factors Returns RAFI Benchmark Diffference High Yield 7.84% 7.10% 0.74% Investment Grade 6.71% 6.38% 0.33% Emerging Markets 15.29% 11.75% 3.53% Duration Total Static Dynamic High Yield -0.29% 0.10% -0.38% Investment Grade 0.02% -0.03% 0.05% Emerging Markets 1.15% 0.33% 0.82% Credit Total Static Dynamic High Yield 0.08% -0.02% 0.10% Investment Grade 0.09% 0.05% 0.04% Emerging Markets 0.82% -0.71% 1.52% Security Selection High Yield 0.94% Investment Grade 0.22% Emerging Markets 1.56%

24 Table 5: Performance of the Fundamental Index strategy in Macroeconomic Cycles This table shows the performance of the Fixed Income fundamental index strategies during Bull and Bear markets (based upon the relevant benchmark index returns) and during rising and falling Fed Fund rate regimes. Rising High Yield Bonds Bull Bear Fed Fund Rate Falling Fed Fund Rate RAFI HY Bond 8.5% 7.6% 6.7% 9.2% Merril Lynch HY Master II Index 10.4% 2.0% 8.0% 4.2% US 3-Month T-Bill 3.0% 4.5% 3.6% 3.9% RAFI HY Bond Volatility 4.3% 5.8% 3.7% 6.2% Merril Lynch HY Master II Volatility 5.2% 7.5% 4.1% 8.2% RAFI HY Bond Sharpe Ratio Merril Lynch HY Master II Sharpe Ratio RAFI HY Bond Excess Return Over Merril Lynch HY Master II -1.9% 5.6% -1.3% 5.0% RAFI HY Bond Tracking Error wrt Merril Lynch HY Master II 2.2% 5.5% 1.9% 5.7% RAFI HY Bond Information Ratio Investment Grade Bonds Bull Bear Rising Fed Fund Rate Falling Fed Fund Rate RAFI Corporate Bond 7.8% 3.7% 3.6% 9.9% Merril Lynch Corporate Master Index 7.4% 3.4% 4.0% 8.9% US 3-Month T-Bill 3.4% 4.8% 3.6% 3.9% RAFI Corporate Bond Volatility 4.8% 3.6% 4.7% 4.3% Merril Lynch Corporate Master Volatility 4.7% 3.4% 4.6% 4.2% RAFI Corporate Bond Sharpe Ratio Merril Lynch Corporate Master Sharpe Ratio RAFI Corporate Bond Excess Return Over Merril Lynch Corporate Master 0.4% 0.3% -0.4% 1.1% RAFI Corporate Bond Tracking Error wrt Merril Lynch Corporate Master 1.1% 0.6% 0.5% 1.3% RAFI Corporate Bond Information Ratio

25 Emerging Market Bonds Bull Bear Rising Fed Fund Rate Falling Fed Fund Rate RAFI EMD 22.5% -21.0% 26.5% 4.5% Merril Lynch IGOV Index 15.4% -11.5% 17.2% 5.3% US 3-Month T-Bill 3.5% 5.0% 3.6% 3.9% RAFI EMD Volatility 13.1% 31.7% 13.8% 20.3% Merril Lynch IGOV Volatility 9.6% 26.3% 8.6% 17.0% RAFI EMD Sharpe Ratio Merril Lynch IGOV Sharpe Ratio RAFI EMD Excess Return Over Merril Lynch IGOV 7.0% -9.5% 9.3% -0.8% RAFI EMD Tracking Error wrt Merril Lynch IGOV 7.5% 7.7% 8.7% 6.4% RAFI EMD Information Ratio