qir 2013q2 us

SECOND QUARTER 2013 | PART TWO

RESEARCH UPDATE

Beginning on page 3

Gerard O’Reilly, PhDHead of Research and Vice PresidentDimensional Fund Advisors

Savina Rizova, PhDVice PresidentDimensional Fund Advisors

Lukas SmartPortfolio ManagerDimensional Fund Advisors

Applying Direct Profitability to Value StocksA value strategy systematically improves expected returns by selecting only firms with low price-to-book ratios, but a value strategy can further increase its expected return by considering market capitalization and direct profitability when selecting low relative price securities.

This paper shows (1) how expected profitability can enhance a value strategy that uses only relative price and company size to select securities, and (2) how security weighting schemas can be used to integrate the three equity dimensions of expected returns into a value strategy’s structure to increase the reliability of expected outperformance vs. conventional benchmarks.

The material in this publication is provided solely as background information for registered investment advisors and institutional investors and is not intended for public use. Unauthorized copying, reproducing, duplicating, or transmitting of this material is prohibited. Dimensional Fund Advisors LP is an investment advisor registered with the Securities and Exchange Commission.

Expressed opinions are subject to change without notice in reaction to shifting market conditions. All materials presented are compiled from sources believed to be reliable and current, but accuracy cannot be guaranteed. This article is distributed for educational purposes, and it is not to be construed as a recommendation of any particular security, strategy, or investment product.

The risk premium E(Rei) [of any asset] is driven by the covariance of returns with the

marginal value of wealth. Given that an asset must do well sometimes and badly at other

times, investors would rather it did well when they are otherwise desperate for a little bit of

extra wealth, and that it did badly when they do not particularly value extra wealth. Thus,

investors want assets whose payoffs have a positive covariance with hunger, and they will

avoid assets with a negative covariance. Investors will drive up the prices and drive down

the average returns of assets that covary positively with hunger, and vice versa, generating

the observed risk premia.

These predictions are surprising to newcomers for what they do not say. More volatile

assets do not necessarily generate a higher risk premium. The variance of the return Rei or

payoff xi is irrelevant per se and does not measure risk or generate a risk premium. Only

the covariance of the return with “hunger” matters.

—John H. Cochrane “Financial Markets and the Real Economy,” in Handbook of the Equity Risk Premium, ed. Rajnish Mehra (Amsterdam: Elsevier, 2007), 237–325.

What drives risk premiums?

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RESEARCH UPDATE

Using the direct profitability measure developed by Dimensional Fund Advisors,1 this is the second in a series of papers that explores the potential value added from incorporating the expected profitability dimension into investment strategies.2 In this paper, we examine how profitability could be applied to small and large cap value strategies in developed markets.

IMPROVING EXPECTED RETURNS: VALUE STRATEGIES

Equity portfolio design can be broadly divided into two steps: (1) finding the dimensions that determine expected returns and (2) structuring portfolios to capture those dimensions. A dimension of expected return identifies differences in expected return. It should be sensible, persistent across time, pervasive across markets, robust to alternative specifications, and cost effective to capture in a well-diversified portfolio. Good portfolio structure should (a) select and/or weight stocks to continually and accurately target the dimensions of expected returns, (b) integrate known dimensions of expected returns to seek to increase the reliability of expected outperformance vs. benchmarks, (c) maintain appropriate diversification to control risk and allow for effective execution, and (d) minimize unnecessary turnover.

Relative price is widely recognized as a dimension of expected return. A lot of academic research shows that average returns on stocks are inversely related to measures of relative price such as price-to-book ratios. For example, from January 1927 to December 2012, US large cap value stocks outperformed US large cap growth stocks by an average of 3.7% per year. The t-statistic of the return difference was 2.1. In Table 1, we present similar outcomes for US small caps and developed market large and small caps.

Motivated by this research, value strategies seek to systematically improve expected returns by selecting firms with low price-to-book ratios. But, within equities, there are two other dimensions of expected returns in addition to relative price—company size and expected profitability. A value strategy could further pursue increased expected returns by considering market capitalization and direct profitability when selecting low relative price securities.3

Value (or any other equity investment) strategies can be designed to focus on selection alone, or on both selection and weighting. In this paper, we show how expected profitability could enhance a value strategy that uses only relative price and company size to select securities. We also show how security weighting schemas could be used to integrate all three dimensions of expected equity returns into a value strategy’s structure to help increase expected outperformance versus conventional benchmarks.

The paper is organized as follows. First, we describe general diversification considerations that should be made when selecting securities to include in a value strategy. Next, we show how the security selection process could be used to integrate direct profitability into developed market small cap value strategies. We follow with developed market large cap value strategies and show how they could be enhanced by applying direct profitability to both security selection and weighting. The different approach between small and large caps used in this paper is primarily caused by differences in trading costs between small and large cap stocks. The last section of the paper presents results.

DIVERSIFICATION CONSIDERATIONS IN SECURITY SELECTION

There are many aspects of diversification: security, sector, and country. A value strategy should use the security selection process to emphasize each aspect. Diversification helps reduce uncertainty and control risk. It also affords portfolio managers and traders flexibility that can be used for effective implementation. For example, portfolio managers could use this flexibility to balance competing premiums while they focus on the dimensions of expected returns. Traders could trade patiently to add value with respect to peers and benchmarks.

For a portfolio to be considered well diversified across securities, it should include both a meaningful percentage of aggregate market capitalization and an appropriate number of firms. For example, value strategies should use price-to-book, market capitalization, and direct profitability slices that are designed to account for this goal. These well-designed slices can be combined with individual security caps to help ensure a value portfolio remains diversified across securities. Security

Table 1Value vs Growth, Annual Returns

Value Growth Difference t-stat

United States Large1927-2012

14.96 11.23 3.73 2.11

United States Small1927-2012

19.13 13.25 5.87 3.37

Developed ex US Large1981-2012

16.69 10.21 6.47 3.18

Developed ex US Small1981-2012

17.14 12.81 4.33 1.90

Past performance is no guarantee of future results. Source: US large and small value and growth indices are the Fama/French research indices. Non-US developed value and growth indices are the Fama/French international indices. Developed ex US small indices are Dimensional indices (Dimensional International Small Cap Value Index and Dimensional International Small Cap High Price-to-Book Index).

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RESEARCH UPDATE

caps can be absolute or relative to a security’s market cap weight in the total eligible market.

To achieve broad sector diversification while preserving the benefits of sector rotation, a security selection process can use dynamic sector caps that are relative to each sector’s weight in the eligible market.4 After sorting eligible stocks on their price-to-book ratios, we can compute the sector weights of the stocks in the lowest price-to-book slice. For sectors that are overweight by more than 10%, their price-to-book breakpoints can be reduced until the weight of each overweight sector is its market weight plus 10%. This approach would decrease the number of securities in the overweight sectors so that only the very lowest price-to-book securities in those sectors are included. Because it also reduces the percentage of market cap included in the value strategy, the price-to-book breakpoints of the underweight sectors should be increased (making additional securities eligible) until the same percentage of market cap as the original price-to-book slice is included. This last step helps preserve security diversification while enforcing broad sector diversification.

Finally, for multi-country value strategies, the price-to-book, market capitalization, and direct profitability slices should target a similar percentage of aggregate market capitalization in each country. Consequently, country weights will naturally be similar to their weights in the total eligible market.

The security selection framework described above acknowledges that the market provides a consensus view of global equilibrium tradeoffs of risk and return. Up-to-the minute news and changes in expectations are reflected in current prices and security, sector, and country weights. By construction, this security selection process for value strategies uses this information to control risk and ensure diversification.

DIRECT PROFITABILITY AND SMALL CAP VALUE

For the purposes of this paper, to integrate direct profitability into a small value strategy, we begin by selecting securities that represent the small cap value universe. We define small cap stocks as those with the smallest market capitalization in the eligible equity universe whose aggregate market capitalization represents 10%–12.5% of the market.5 We then define small cap value stocks as small cap stocks whose price-to-book ratios rank in the lowest 35% of aggregate market cap of the eligible small cap universe. The price-to-book rankings are done separately for each country. This approach seeks to control for country-specific differences in accounting standards. It also promotes country diversification, as the country weights in the value strategy will be similar to their weights in the total eligible universe.

Next, for each country, we exclude firms with the lowest direct profitability. The fraction of market cap excluded is related to the price-to-book ratio. For firms with very low price-to-book ratios (relative to the small value universe in that country), a smaller percentage of low profitability stocks are excluded. For small value firms with higher relative price-to-book ratios (those close to the upper price-to-book breakpoint), larger percentages of low profitability firms are excluded.

Figure 1 illustrates the application of this approach. For firms in the lowest 30% of the price-to-book rankings, those that are also in lowest 10% of the market cap of all small value when ranked by direct profitability are excluded. For firms in the next 5% of the price-to-book ranking (between 30% and 35%), those that are also in the lowest 50% of the market cap of all small value when ranked on direct profitability are excluded.

Figure

1

Applying Profitability to

Developed Market Small Cap Value Stocks

Relative Price

Size

LAR

GE

SMA

LL

LOW HIGH

Exp

ecte

d P

rofit

abili

ty

Relative Price

HIG

HLO

W

Stocks below 10%–12.5% market cap limit by common currency

Stocks with lowest 35% of P/B ratios

LOWEST LOW

Conceptual example, provided for informational purposes only.

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RESEARCH UPDATE

Why exclude firms in this way? A value strategy should be structured to target the value premium accurately. The expected value premium is generally largest for the deepest value firms. By applying a graded profitability exclusion, a small value strategy could preserve its deep value focus while incorporating the information in direct profitability about expected returns. This approach can be a very effective way to integrate expected profitability and relative price. Research results indicate this increases expected returns and the reliability of expected outperformance of small value strategies vs. conventional benchmarks.

As mentioned previously, any value strategy should include a meaningful percentage of aggregate market capitalization to ensure diversification. That implies the direct profitability exclusion cannot be too extreme. The methodology described above targets approximately 25%–30% of the market capitalization of eligible small caps in each country.

A small value strategy must continually balance the tradeoffs among competing premiums, diversification, and costs. Because small cap stocks can be costly to trade, in this paper we weight firms in proportion to their market capitalization. Once a basket of stocks has been selected for a small value strategy, this weighting schema generally produces the lowest turnover. By minimizing unnecessary turnover (i.e., turnover that does not increase expected return) and spreading it over all the trading days of the year, those tradeoffs can be effectively managed.

The result is a small value strategy that uses a thoughtful security selection process to balance the dimensions of expected equity returns and help ensure all aspects of diversification are preserved. This approach helps increase the consistency of expected outperformance vs. benchmarks and provides flexibility to efficiently manage costs. Investors are well-positioned to capture the premiums associated with the market, company size, relative price, and expected profitability dimensions in a real-world small value portfolio.

DIRECT PROFITABILITY AND LARGE CAP VALUE

Large cap stocks tend to be more liquid and less expensive to trade than small cap stocks. As a result, we can use both selection and weighting approaches to help improve the expected returns of a large cap value strategy.

For the purposes of this paper, we first select securities that represent the large cap value universe. We define large cap stocks as those with the largest market capitalization in the eligible equity universe whose total market capitalization ranks above the bottom 10%–12.5% of the market.6 Within each country, we define large cap value stocks as large caps whose price-to-book ratios rank in the lowest 30% of the eligible large cap universe.

Next, for each country, we exclude certain firms based on their direct profitability. Sorting large cap value stocks on direct profitability, we identify those with the lowest direct profitability that represent 25% of the aggregate market capitalization of large cap value. Of these, we exclude stocks that have the highest price-to-book ratios and are in the lowest direct profitability quartile. Similar to our approach with small value, the profitability exclusion is based on price-to-book and direct profitability. In this way, the security selection process preserves a deep value focus while incorporating information about expected profitability.

Within this selection of large cap value stocks, we then apply a weighting schema that emphasizes securities with higher profitability, lower market capitalization, and lower relative price. In a well-designed weighting schema, a security’s target weight can deviate from its market cap weight to improve expected strategy returns, but deviations should be measured and controlled to avoid excessive turnover. To achieve those goals, we make a security’s target weight proportional to its market capitalization, with the level of over- or underweight relative to the market weight being a function of direct profitability, market cap, and price-to-book. The strategy overweights securities with higher profitability, lower market capitalization, and lower relative price, and underweights securities with lower profitability, higher market capitalization, and higher relative price.

As an example, let’s look at the US large value index presented in the next section (US Large Low Relative Price with Profitability Index). As a result of the tilt toward companies with lower market capitalization, the average ratio of a firm’s tilted weight to its weight based on market capitalization alone is approximately 0.8 for the largest firms, which represent 50% of the index, and approximately 1.2 for the remaining smaller firms, as of June 2013. Similarly, as a result of the tilt

6

RESEARCH UPDATE

toward companies with higher profitability, the average ratio of target weight to market weight is approximately 1.3 for the most profitable firms, which represent 50% of the index, and approximately 0.7 for remaining lower profitability firms.

Figure 2 summarizes the combination of the selection and weighting approaches in the design of a developed market large cap value strategy.

A large cap value strategy should also continually balance the tradeoffs among competing premiums, diversification, and costs. Large cap value stocks are less costly to trade; therefore, we use a weighting schema that deviates from market cap weights to emphasize company size and expected profitability. This approach helps increase the expected return and the consistency of outcomes. Because a firm’s target weight remains strongly linked to its market capitalization, unnecessary turnover is minimized and risk is controlled by reflecting up-to-the minute news in target weights.

We also cap security weights in our large cap value strategies. Security caps build additional diversification considerations into the weighting schema. They limit any single security’s representation. A small cap value strategy tends to hold many more names than a large cap value strategy; consequently, while security caps can be applied in small value strategies, they are generally less important.

The result is a large value strategy that uses a thoughtful security selection and weighting process to balance the dimensions of expected equity returns and help ensure all aspects of diversification are preserved. Investors are well-positioned to capture the premiums associated with the market, company size, relative price, and expected profitability dimensions in a real-world large value portfolio.

Figure

2

Applying Profitability to

Developed Market Large Cap Value Stocks

Relative Price

Size

LAR

GE

SMA

LL

LOW HIGH

Stocks above 10%–12.5% market cap limit

Stocks with lowest 30% of P/B ratios

ExpectedProfitability

Size

Relative Price

ME

GA

MID

LOWEST LOW

LOW

HIGH

Conceptual example, provided for informational purposes only.

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RESEARCH UPDATE

EMPIRICAL RESEARCH

In this section, we explore the potential value added from focusing on all three dimensions of expected equity returns in value strategies. We begin with US small and large value. Tables 2A and 2B report the performance of US value indices constructed based on the methodology described above (US Small Low Relative Price with Profitability Index and US Large Low Relative Price with Profitability Index), as well as

the performance of market-cap weighted small and large cap value indices that include all stocks with price-to-book ratios in the bottom 25% of the eligible size universe (US Small Low Relative Price Index and US Large Low Relative Price Index). The low relative price indices in Tables 2A and 2B are rebalanced annually. For comparison purposes, we also report the historical performance of the Russell indices.7

Table 2AUS Small Cap Value Indices with and without Profitability, 1979-2012

1979-2012

US Small Low Relative

Price Index

US Small Low Relative Price with Profitability Index

Russell 2000 Value Index

Russell 2000 Index

Annualized Compound Return 17.47 17.90 13.18 11.35

Relative Premium (vs. Russell 2000 Value)

4.30 4.72 — —

Annualized Average Return 18.35 18.48 14.05 12.84

Annualized Standard Deviation 20.63 19.41 17.67 19.93

t-Stat of Monthly Return Difference (vs. Russell 2000 Value)

3.55 4.63 — —

Annualized Tracking Error (vs. Russell 2000)

8.73 8.30 5.96

Annualized Tracking Error (vs. Russell 2000 Value)

7.06 5.59 — —

Past performance is no guarantee of future results. Source: Compiled by Dimensional using CRSP and Compustat data. CRSP data provided by the Center for Research in Security Prices. See appendix for additional information on the Dimensional indices.

Table 2BUS Large Cap Value Indices with and without Profitability, 1979-2012

1979-2012US Large Low

Relative Price Index

US Large Low Relative Price with Profitability Index

Russell 1000 Value Index

Russell 1000 Index


Relative Premium (vs. Russell 1000 Value)

1.53 2.16 — —



t-Stat of Monthly Return Difference (vs. Russell 1000 Value)

2.27 2.94 — —

Annualized Tracking Error (vs. Russell 1000)

6.76 7.02 4.86

Annualized Tracking Error (vs. Russell 1000 Value)

4.49 4.57 — —

Past performance is no guarantee of future results. Source: Compiled by Dimensional using CRSP and Compustat data. CRSP data provided by the Center for Research in Security Prices. See appendix for additional information on the Dimensional indices.

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RESEARCH UPDATE

From 1979 to 2012, the Russell 2000 earned an annualized compound return of 11.4% vs. 13.2% for the Russell 2000 Value, 17.5% for the US Small Low Relative Price Index, and 17.9% for the US Small Low Relative Price with Profitability Index. By incorporating direct profitability in the security selection process, the US Small Low Relative Price with Profitability Index outperformed the US Small Low Relative Price Index by approximately 0.4% per year. The standard deviation of the US Small Low Relative Price with Profitability Index was more than 1% lower than the US Small Low Relative Price Index.

Looking at annual returns, the US Small Low Relative Price with Profitability Index outperformed the Russell 2000 Value Index in 27 of the 34 years from 1979 to 2012, while the US Small Low Relative Price Index outperformed the Russell 2000 Value Index in 23 of the 34 years. Further, the t-statistic of the US Small Low Relative Price with Profitability Index’s monthly premium vs. the Russell 2000 Value was 4.63, compared with 3.55 for the US Small Low Relative Price Index. This increase in the reliability of outperformance vs. the Russell 2000 Value is attributed to adding expected profitability to the security selection process. The market, size, and value coefficients from a Fama/French three-factor regression are similar for the US Small Cap Value Indices with and without Profitability.8 The HML coefficient was approximately 0.7 for the US Small Cap Value Indices with and without Profitability. Hence, both indices provide a similar focus on the size and value premiums.

We find similar results for US large caps. From 1979 to 2012, the Russell 1000 earned an annualized compound return of 11.5% vs. 12.0% for the Russell 1000 Value, 13.5% for the US Large Low Relative Price Index, and 14.1% for the US Large Low Relative Price with Profitability Index. By focusing on all three dimensions of expected equity returns when selecting and weighting stocks, the US Large Low Relative Price with Profitability Index outperformed the US Large Low Relative Price Index by more than 0.6% per year. The higher average returns were achieved with a very similar standard deviation. The inclusion of direct profitability and market cap in the index design also results in more reliable outperformance relative to the Russell 1000 Value Index. The t-statistic of the monthly premium increases from 2.27 to 2.94 when we move from the US Large Low Relative Price Index to the US Large Low Relative Price with Profitability Index. The Fama/French three factor coefficients are very similar for the low relative price indices with and without profitability (approximately 0.6 for both).

Overall, Table 2 suggests that by consistently focusing on all three dimensions of expected equity returns, we could (1) improve the expected performance of a small or large cap value strategy, (2) increase the consistency of their expected outperformance relative to benchmarks, and (3) maintain broad diversification.

Tables 3A and 3B illustrate that broad diversification. We present the characteristics of the low relative price indices along with the Russell indices as of June 2013. The value indices that use direct profitability in their construction are well diversified across securities and sectors. The aggregate index characteristics illustrate how the low relative price indices with profitability balance market cap, price-to-book, and direct profitability.

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RESEARCH UPDATE

Table 3ACharacteristics for US Small Cap Value Indices with and without Profitability

Data in USD as of 6/30/2013US Small Low


US Small Low Relative Price Index

with Profitability IndexRussell 2000

ValueRussell

2000

Weighted Average Market Cap 1,121 1,181 1,385 1,603

Aggregate Price-to-Book 0.92 1.03 1.33 1.85

Weighted Average Direct Profitability 0.15 0.18 0.16 0.22

Number of Securities 672 691 1,392 1,934

Consumer Discretionary 10.6 11.3 13.1 14.8

Consumer Staples 3.0 3.8 2.8 3.8

Energy 14.1 12.1 6.1 5.7

Financials 27.0 27.1 24.8 14.6

Health Care 5.4 4.9 4.5 12.6

Industrials 14.2 17.3 12.3 14.9

Information Technology 15.9 14.7 12.1 16.6

Materials 7.8 7.4 5.1 4.8

REITs 0.0 0.0 12.8 8.3

Telecommunication Services 1.1 1.1 0.5 0.7

Utilities 0.8 0.3 5.9 3.2

Total 100.0 100.0 100.0 100.0

Source: Compiled by Dimensional using CRSP and Compustat data. CRSP data provided by the Center for Research in Security Prices. See appendix for additional information on the Dimensional indices.

Table 3BCharacteristics for US Large Cap Value Indices with and without Profitability

Data in USD as of 6/30/2013US Large Low


US Large Low Relative Price with Profitability Index

Russell 1000 Value

Russell 1000

Weighted Average Market Cap 76,543 66,341 97,398 95,057

Aggregate Price-to-Book 1.16 1.25 1.49 2.09

Weighted Average Direct Profitability 0.19 0.22 0.24 0.35

Number of Securities 206 226 696 989

Consumer Discretionary 10.5 10.6 8.6 13.0

Consumer Staples 5.8 5.0 7.1 9.8

Energy 20.7 20.6 15.3 9.9

Financials 25.7 24.3 24.7 14.2

Health Care 9.3 10.7 11.8 12.4

Industrials 11.7 11.5 9.0 10.9

Information Technology 6.2 6.8 7.0 17.2

Materials 3.9 5.0 3.3 3.6

REITs 0.0 0.0 4.0 3.1

Telecommunication Services 5.6 5.1 3.0 2.7

Utilities 0.6 0.4 6.3 3.4

Total 100.0 100.0 100.0 100.0

Source: Compiled by Dimensional using CRSP and Compustat data. CRSP data provided by the Center for Research in Security Prices. See appendix for additional information on the Dimensional indices.

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RESEARCH UPDATE

Next, we analyze non-US developed market value indices. Can we draw similar conclusions? Tables 4A and 4B say we can. We compare the performance of non-US developed market value indices that include direct profitability in their security selection and/or weighting schemas (Non-US Developed Small Low Relative Price with Profitability Index and Non-US Developed Large Low Relative Price with Profitability Index) to the performance of market-cap weighted value indices that include all stocks whose price-to-book ratios rank in the bottom 25% of the eligible size universe in each developed market outside the US (Non-US Developed Small Low Relative Price Index and Non-US Developed Large Low Relative Price Index). For reference, we also report the historical performance of the MSCI World ex US Small and Small Value Indices and the MSCI World ex US Standard and Standard Value Indices.

These tables present data over the longest available common time periods for the indices (for example, the MSCI World ex USA Small Cap Index begins in 1999).

Compared with the US, we observe the same general pattern of higher returns and higher t-statistics of the monthly return difference vs. benchmarks for the low relative price indices with profitability vs. those without profitability. Comparing the low relative price indices with and without profitability, we observe similar or lower standard deviations and similar market, size, and value coefficients using Fama/French developed ex US factors. The HML coefficient was approximately 0.7 for the non-US developed small low relative price indices with and without profitability and approximately 0.5 for the US large low relative price indices with and without profitability.

Tables 4A and 4B suggest that, by focusing on company size, relative price, and expected profitability when selecting and weighting securities for developed market small and large cap value strategies, we can improve their expected returns and the reliability of their expected outperformance vs. conventional benchmarks.

Table 4ANon-US Developed Small Cap Value Indices with and without Profitability

1999-2012

Non-US Developed Small Low Relative

Price Index

Non-US Developed Small Low Relative Price with

Profitability Index

MSCI World ex USA Small Cap Value

Index (gross div.)

MSCI World ex USA Small Cap Index

(gross div.)


Relative Premium (vs. MSCI Value)

2.40 2.71 — —



t-Stat of Monthly Return Difference (vs. MSCI Value)

2.32 2.84 — —

Annualized Tracking Error (vs. MSCI)

6.01 5.72 3.71 —

Annualized Tracking Error (vs. MSCI Value)

3.93 3.46 — —

Past performance is no guarantee of future results. Source: Compiled by Dimensional using Bloomberg data. See appendix for additional information on the Dimensional indices. MSCI data copyright MSCI 2013, all rights reserved.

11

RESEARCH UPDATE

CONCLUSION

When designing investment solutions, it is important to remember that prices are a reliable source of information, and structure and implementation drive performance. Our analysis illustrates how an investor might use direct profitability to enhance expected returns when selecting securities for small or large value strategies. Further, our analysis shows how to integrate company size and expected profitability when weighting securities in large value strategies. These examples show how portfolio structure can be used to accurately target the dimensions of higher expected returns.

In this paper, our analysis also considers implementation. The security selection process helps ensure broad diversification across securities, sectors, and countries. To reduce expected costs, we choose to market-cap weight the small cap value strategies. For large cap value strategies, we deviate from market weights to increase expected returns, but we use a measured, controlled, low-turnover weighting schema that incorporates current price. Low turnover combined with broad diversification allow for disciplined yet flexible and patient portfolio management and trading processes that control implementation costs.

Such solutions would seek to add value for investors across all aspects of the investment process.

Table 4BNon-US Developed Large Cap Value Indices with and without Profitability

July 1991 - Dec 2012

Non-US Developed Large Low Relative

Price Index

Non-US Developed Large Low Relative Price with

Profitability Index

MSCI World ex USA Value Index (gross div.)

MSCI World ex USA Index (gross div.)


Relative Premium (vs. MSCI Value)

0.60 1.32 — —



t-Stat of Monthly Return Difference (vs. MSCI Value)

1.05 1.73 — —

Annualized Tracking Error (vs. MSCI)

6.76 6.28 3.40 —

Annualized Tracking Error (vs. MSCI Value)

4.70 4.32 — —

Past performance is no guarantee of future results. Source: Compiled by Dimensional using Bloomberg data. See appendix for additional information on the Dimensional indices. MSCI data copyright MSCI 2013, all rights reserved.

APPENDIX

12

APPENDIX

US Large Low Relative Price Index: This index was created by Dimensional in July 2013 and is compiled by Dimensional from CRSP and Compustat. It focuses on large cap value companies. Large cap companies are generally defined as the top 90% of the eligible market. Large cap value companies are defined as large cap companies whose relative price is in the bottom 25% of the large cap market after the exclusion of utilities, companies lacking financial data, and companies with negative relative price. The eligible market is composed of securities of US companies traded on the NYSE, AMEX, and Nasdaq Global Market. Exclusions: Non-US companies, REITs, UITs, and investment companies. The index is rebalanced annually and backtested performance results assume reinvestment of dividends and capital gains. Filters were applied to data retroactively and with the benefit of hindsight. Returns are not representative of actual portfolios and do not reflect costs and fees associated with an actual investment. Actual returns may be lower. It is not possible to invest directly in an index, which is unmanaged.

US Large Low Relative Price with Profitability Index: This index was created by Dimensional in July 2013 and is compiled by Dimensional from CRSP and Compustat. It focuses on large cap value companies and overweights higher expected return securities (higher profitability, lower relative price, and lower market cap). Large cap companies are generally defined as the top 90% of the eligible market. Large cap value companies are defined as large cap companies whose relative price is in the bottom 30% of the large cap market after the exclusion of utilities, companies lacking financial data, and companies with negative relative price. Profitability is measured as operating income before depreciation and amortization minus interest expense scaled by book. The eligible market is composed of securities of US companies traded on the NYSE, AMEX, and Nasdaq Global Market. Exclusions: Non-US companies, REITs, UITs, and investment companies. The index is rebalanced annually and backtested performance results assume reinvestment of dividends and capital gains. Filters were applied to data retroactively and with the benefit of hindsight. Returns are not representative of actual portfolios and do not reflect costs and fees associated with an actual investment. Actual returns may be lower. It is not possible to invest directly in an index, which is unmanaged.

US Small Low Relative Price Index: This index was created by Dimensional in July 2013 and is compiled by Dimensional from CRSP and Compustat. It focuses on small cap value companies. Small cap companies are generally defined as the bottom 10% of the eligible market. Small cap value companies

are defined as small cap companies whose relative price is in the bottom 25% of the small cap market after the exclusion of utilities, companies lacking financial data, and companies with negative relative price. The eligible market is composed of securities of US companies traded on the NYSE, AMEX, and Nasdaq Global Market. Exclusions: Non-US companies, REITs, UITs, and investment companies. The index is rebalanced annually and backtested performance results assume reinvestment of dividends and capital gains. Filters were applied to data retroactively and with the benefit of hindsight. Returns are not representative of actual portfolios and do not reflect costs and fees associated with an actual investment. Actual returns may be lower. It is not possible to invest directly in an index, which is unmanaged.

US Small Low Relative Price with Profitability Index: This index was created by Dimensional in July 2013 and is compiled by Dimensional from CRSP and Compustat. It focuses on small cap value companies and excludes companies with low profitability. Small cap companies are generally defined as the bottom 10% of the eligible market. Small cap value companies are defined as small cap companies whose relative price is in the bottom 35% of the small cap market after the exclusion of utilities, companies lacking financial data, and companies with negative relative price. Profitability is measured as operating income before depreciation and amortization minus interest expense scaled by book. The eligible market is composed of securities of US companies traded on the NYSE, AMEX, and Nasdaq Global Market. Exclusions: Non-US companies, REITs, UITs, and investment companies. The index is rebalanced annually and backtested performance results assume reinvestment of dividends and capital gains. Filters were applied to data retroactively and with the benefit of hindsight. Returns are not representative of actual portfolios and do not reflect costs and fees associated with an actual investment. Actual returns may be lower. It is not possible to invest directly in an index, which is unmanaged.

Non-US Developed Large Low Relative Price Index: This index was created by Dimensional in July 2013 and is compiled by Dimensional from Bloomberg securities data. It focuses on large cap value companies in non-US developed markets. Large cap companies are generally defined as the top 87.5% of the eligible market in each country. Value breaks are formed by country on the bottom 25% of large companies ranked on relative price after the exclusion of utilities, companies lacking financial data, and companies with negative relative price. Maximum index weight of any one company is capped at 5%. Countries included are Australia, Austria, Belgium, Canada, Denmark, Finland,

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France, Germany, Greece, Hong Kong, Ireland, Italy, Japan, Netherlands, New Zealand, Norway, Portugal, Singapore, Spain, Switzerland, Sweden, and United Kingdom. The index excludes REITs. The index is rebalanced semiannually and backtested performance results assume reinvestment of dividends and capital gains. Filters were applied to data retroactively and with the benefit of hindsight. Returns are not representative of actual portfolios and do not reflect costs and fees associated with an actual investment. Actual returns may be lower. It is not possible to invest directly in an index, which is unmanaged.

Non-US Developed Large Low Relative Price with Profitability Index: This index was created by Dimensional in July 2013 and is compiled by Dimensional from Bloomberg securities data. It focuses on large cap value companies in non-US developed markets and overweights higher expected return securities (higher profitability, lower relative price, and lower market cap). Large cap companies are generally defined as the top 87.5% of the eligible market in each country. Value breaks are formed by country on the bottom 30% of large companies ranked on relative price after the exclusion of utilities, companies lacking financial data, and companies with negative relative price. Profitability is measured as operating income before depreciation and amortization minus interest expense scaled by book. Maximum index weight of any one company is capped at 5%. Countries included are Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Hong Kong, Ireland, Italy, Japan, Netherlands, New Zealand, Norway, Portugal, Singapore, Spain, Switzerland, Sweden, and United Kingdom. The index excludes REITs. The index is rebalanced semiannually and backtested performance results assume reinvestment of dividends and capital gains. Filters were applied to data retroactively and with the benefit of hindsight. Returns are not representative of actual portfolios and do not reflect costs and fees associated with an actual investment. Actual returns may be lower. It is not possible to invest directly in an index, which is unmanaged.

Non-US Developed Small Low Relative Price Index: This index was created by Dimensional in July 2013 and is compiled by Dimensional from Bloomberg securities data. It focuses on small cap value companies in non-US developed markets. Small cap companies are generally defined as the bottom 12.5% of the eligible market in each country. Value breaks are formed by country on the bottom 25% of small companies ranked on relative price after the exclusion of utilities, companies lacking financial data, and companies with negative relative price. Maximum index weight of any one company is capped at 5%. Countries included are

Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Hong Kong, Ireland, Italy, Japan, Netherlands, New Zealand, Norway, Portugal, Singapore, Spain, Switzerland, Sweden, and United Kingdom. The index excludes REITs. The index is rebalanced semiannually and backtested performance results assume reinvestment of dividends and capital gains. Filters were applied to data retroactively and with the benefit of hindsight. Returns are not representative of actual portfolios and do not reflect costs and fees associated with an actual investment. Actual returns may be lower. It is not possible to invest directly in an index, which is unmanaged.

Non-US Developed Small Low Relative Price with Profitability Index: This index was created by Dimensional in July 2013 and is compiled by Dimensional from Bloomberg securities data. It focuses on small cap value companies and excludes companies with low profitability. Small cap companies are generally defined as the bottom 12.5% of the eligible market in each country. Value breaks are formed by country on the bottom 35% of small companies ranked on relative price after the exclusion of utilities, companies lacking financial data, and companies with negative relative price. Profitability is measured as operating income before depreciation and amortization minus interest expense scaled by book. Maximum index weight of any one company is capped at 5%. Countries included are Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Hong Kong, Ireland, Italy, Japan, Netherlands, New Zealand, Norway, Portugal, Singapore, Spain, Switzerland, Sweden, and United Kingdom. The index excludes REITs. The index is rebalanced semiannually and backtested performance results assume reinvestment of dividends and capital gains. Filters were applied to data retroactively and with the benefit of hindsight. Returns are not representative of actual portfolios and do not reflect costs and fees associated with an actual investment. Actual returns may be lower. It is not possible to invest directly in an index, which is unmanaged.

APPENDIX

14

REFERENCES

1. See Gerard O’Reilly and Savina Rizova, “Expected Profitability: A New Dimension of Expected Returns,” Dimensional Fund Advisors’ Quarterly Institutional Review 9, no. 1 (2013a): 4–7.

2. The first paper examined how the expected profitability dimension could be applied to a universe of US large cap stocks. See Gerard O’Reilly and Savina Rizova, “Applying Direct Profitability to US Large Caps,” Dimensional Fund Advisors’ Quarterly Institutional Review 9, no. 1 (2013b): 8–11.

3. Direct profitability is defined as operating income before amortization and depreciation minus interest expense scaled by book equity. It is a reliable proxy for expected profitability. For more information on direct profitability, see O’Reilly and Rizova (2013a).

4. For more information on this issue, see Savina Rizova, “Dimensional’s Approach to Sector Representation in Value Strategies,” a Dimensional Fund Advisors white paper of November 8, 2012, available at https://my.dimensional.com/insight/papers_library/95021/.

5. In this paper, we exclude utilities and REITs from the eligible universe, as they do not fully capture the equity premium and have market-like expected returns. In the US, we target stocks in the lowest 10% of aggregate market capitalization. For developed countries outside the US, we target the lowest 12.5%.

6. In this paper, we exclude utilities and REITs from the eligible universe, as they do not fully capture the equity premium and have market-like expected returns. In the US, we target stocks above the bottom 10% of aggregate market capitalization. For developed countries outside the US, we target stocks above the bottom 12.5%.

7. Because the Russell Indexes start in 1979, our analysis focuses on 1979–2012.

8. For more information on the Fama-French three-factor model, see Eugene F. Fama and Kenneth R. French, “Common risk factors in the returns on stocks and bonds,” Journal of Financial Economics 33 (1993): 3-56.

DISCLOSURES

Dimensional Fund Advisors LP is an investment advisorregistered with the Securities and Exchange Commission.

Past performance is no guarantee of future success. Indices are not available for direct investment. There is no guarantee strategies will be successful.

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