Dimensions of Expected Return

Transcription

1 Dimensions of Expected Return Research and Implementation October 7, 2014 Eduardo Repetto, Director, Co-Chief Executive Officer and Co-Chief Investment Officer This information is provided for registered investment advisors and institutional investors, and is not intended for public use. Dimensional Fund Advisors LP is an investment advisor registered with the Securities and Exchange Commission. #

2 Agenda 1. Process Design 2. Process Design: Premiums 3. Process Design: Implementation 4. The Process At Work 5. Summary

3 Process Design

4 Prices Incorporate All Available Information Book Equity Book Equity All Available Information News about Cash Flows Expected Cash Flows Price Risk Considerations Discount Rate Investors consider all available information when assessing expected risks in order to demand a rate of return. Investors set the price level in order to satisfy the demanded rate of return. Market prices reflect the discount rate investors applied to future cash flows, plus the company s book equity. 3 #33694

5 Investment Process: Premiums

6 Dimensions of Expected Returns We should minimize the probability of chasing spurious correlations, imprecisely targeting the dimensions of expected returns, or pursuing strategies that may not be profitable after implementation costs. Guiding principles Sensible basis Persistent Pervasive Robust Cost-effective to implement in a diversified strategy 5

7 Evolution of Asset Pricing DIMENSIONS OF RETURNS Company Higher Expected Return Market Company Size Relative Price Profitability Equity premium stocks vs. bonds Small cap premium small vs. large companies Value premium value vs. growth companies Profitability premium high vs. low profitability companies Large Large Large Value Growth Value Growth Small Small Small Advances in research continue to deepen our understanding of expected returns. Relative Price refers to the share price (or market cap) of a firm s stock, divided by a fundamental variable of the firm (e.g., earnings, cash earnings, dividends, net assets). One of the most widely used measures of relative price is the price/book ratio. Profitability is a measure of the expected total future profits of a company divided by its current book equity. 6

8 Stock Valuation Price = Book Equity + (Expected) Future Profits Discount Rate The price market participants are willing to pay depends on What a company owns minus what it owes Plus, the company s ability to produce cash flows in the future Discounted to the present value at the required rate of return. 7 #33694

9 Profitability Relative Price Size Dimensions of Expected Returns Illustrative index performance US STOCKS NON-US DEVELOPED MARKETS STOCKS EMERGING MARKETS STOCKS SMALL LARGE DIFFERENC SMALL LARGE DIFFERENC SMALL LARGE E E DIFFERENC E Dimensional US Small Cap Index S&P 500 Index Dimensional Intl. Small Cap Index MSCI World ex USA Index (gross div.) Dimensional Emerging Markets Small Cap Index MSCI Emerging Markets Index (gross div.) LOW HIGH DIFFERENC E LOW HIGH DIFFERENC LOW HIGH E DIFFERENC E Fama/French US Value Index Fama/French US Growth Index Fama/French International Value Index Fama/French International Growth Index Fama/French Emerging Markets Value Index Fama/French Emerging Markets Growth Index HIGH LOW 8.26 DIFFERENC E 4.72 HIGH LOW DIFFERENC E HIGH LOW 4.23 DIFFERENC E 6.40 Dimensional US High Profitability Index Dimensional US Low Profitability Index Dimensional International High Profitability Index Dimensional International Low Profitability Index Dimensional Emerging Markets High Profitability Index Dimensional Emerging Markets Low Profitability Index Annualized compound returns (%) in US dollars. Profitability is measured as operating income before depreciation and amortization minus interest expense scaled by book. Indices are not available for direct investment. Their performance does not reflect the expenses associated with the management of an actual portfolio. Past performance is not a guarantee of future results. Index returns are not representative of actual portfolios and do not reflect costs and fees associated with an actual investment. Actual returns may be lower. See Index Descriptions in the appendix for descriptions of Dimensional and Fama/French index data. The S&P data are provided by Standard & Poor s Index Services Group. MSCI data MSCI 2014, all rights reserved. 8

10 Dimensions of Expected Returns Illustrative index performance Market 9.84% 12.52% Small 12.12% 15.58% Treasury Bill 3.50% 5.00% Large 9.84% 12.34% Standard Deviation 18.77% 15.71% Standard Deviation 12.95% 10.36% Low Relative Price 12.00% 14.22% High Profitability 14.99% High Relative Price 9.44% 11.86% Low Profitability 11.23% Standard Deviation 14.20% 10.92% Standard Deviation 8.94% Annualized compound returns (%) in US dollars. Market is Fama/French Market, Treasury Bill is One-Month T-Bill, Small and Large are Fama/French, Low Relative Price is Fama/French Large Value Research, High Relative Price is Fama/French Large Growth Research, High and Low Profitability are Dimensional Large High and Low Profitability Indexes. The Standard Deviation is the annualized standard deviation of the monthly premium (Market minus T-Bill, for example). Indices are not available for direct investment. Their performance does not reflect the expenses associated with the management of an actual portfolio. Past performance is not a guarantee of future results. Index returns are not representative of actual portfolios and do not reflect costs and fees associated with an actual investment. Actual returns may be lower. See Index Descriptions in the appendix for descriptions of Dimensional and Fama/French index data. Fama/French data provided by Fama/French. US bills from Stocks, Bonds, Bills, and Inflation Yearbook, Ibbotson Associates, Chicago (annually updated work by Roger G. Ibbotson and Rex A. Sinquefield). 9

11 Investment Process: Implementation

12 Considerations for Portfolio Implementation Balancing Expected Premiums with Costs We want to focus on Expected Premiums but must be mindful of... Implementation Costs Effective portfolio implementation requires: Deep understanding of how expected premiums behave: Over time and In an integrated portfolio Consistent focus on managing premiums and costs throughout the investment process 11 #

13 Implications for Portfolio Implementation Efficiently pursuing premiums in a cost-efficient manner Expected Premiums Implementation Costs Expected Days in Portfolio x Expected Daily Premiums Turnover x Cost per Unit of Turnover Portfolio needs to: Be well diversified and consistent Consider multiple premiums Keep implementation costs in mind Make decisions based on rational expectations and current information 12

14 Maintaining Strategy Focus Daily Annual premiums are the accumulation of daily premiums Expected Premiums Implementation Costs Expected Days in Portfolio x Expected Daily Premiums HISTORICAL US DAILY PREMIUMS 3.2 bps Should you treat any day differently? 1.9 bps 1.4 bps 1.5 bps Can we forecast when premiums will show up? If not, daily expected premiums are the same. Equity Premium ( ) Value Premium ( ) Size Premium ( ) Profitability Premium ( ) Please see additional information on Historical US Daily Premiums in the Appendix. Past performance is no guarantee of future results. 13

15 Other Dimensions Targeting the Desired Premiums Selecting and weighting securities designed to increase expected returns Selecting securities When selecting companies, use robust definitions of the asset class. Consider implementation (turnover) implications when deciding definitions (e.g., low-p/b companies in value portfolios). Desired Dimension Weighting selected securities Allocate more than market capitalization weights to securities with higher expected returns. Allocate less than market capitalization weights to companies with not as high expected returns (and achieve desired diversification). A robust and efficient process to select and/or weight securities based on the dimensions of E(R) seeks to: Enhance expected returns Avoid unnecessary turnover Consider implementation implications including competing premiums, turnover, etc. 14

16 Expected Returns Relative Price Security Prices Change Every Day Annual premiums are delivered by different securities Time Time Security prices change; therefore its characteristics change its expected return changes If the E(R) of a security changes, we should consider replacing the security. No need to wait for artificial dates to rebalance. Strategies can be structured to provide continuous exposure to higher expected returns. A dynamic portfolio management process should consider current information (prices) to make rational decision based on expectations. 15

17 Basis Points Maintaining Strategy Focus Daily Annual premiums are the accumulation of daily premiums Expected Premiums Implementation Costs Turnover x Cost per Unit of Turnover MEDIAN PEER TRADING COSTS Typical Spread (bps) Typical Manager Trading Cost (bps) How much should you trade and how often? How do you decide which securities to trade, and how can you avoid paying too much to trade them? US Large Cap US Small Cap All Developed Markets All Emerging Markets Manager trading cost data was provided by Investment Technology Group solely for Dimensional and not for any other third party. These materials are highly confidential and are not to be copied, displayed, or transmitted in any form without the prior written permission of Investment Technology Group. Typical (median) manager trading cost is as of September 30, Typical (average) spread is one year as of December 31, 2013, source: Dimensional Fund Advisors LP. Developed international markets are Dimensional s eligible universe (Canada, Europe, Japan, Asia Pacific, UK). 16

18 Trading Costs: Meaningful Turnover Translating research into practice requires expertise in balancing premiums and costs STOCKS MIGRATE BALANCING PREMIUMS AND COSTS Mega Caps Mega Caps Days in Portfolio x Expected Daily Premium Cost to Buy and Sell Mid Caps Mid Caps Daily premiums and daily expected return differentials are small: E(R MidBlend R SmallValue ) ~ -0.8 bps 1 Small Value Small Value Buying/selling of securities needs to balance: The expected future premium of a buy candidate vs. a current holding; The cost of the two trades (and any competing premiums) Only consider meaningful turnover by considering the gains in expected returns vs. the cost of executing the trades. 1. Asset class and profitability filters were applied to data retroactively and with the benefit of hindsight. Returns are not representative of indices or actual portfolios and do not reflect costs and fees associated with an actual investment. Please see additional information on Historical US Daily Premiums in the Appendix. Past performance is no guarantee of future results. 17 #

19 Basis Points Trading Costs: Cost per Unit of Turnover Typical trading costs can be high MEDIAN PEER TRADING COSTS 1 Typical Spread US Large Cap Typical Manager Trading Cost (bps) US Small Cap All Developed Markets HISTORICAL US DAILY PREMIUMS All Emerging Markets MINIMIZING COSTS PER UNIT OF TURNOVER Cost per Implementation Costs = Turnover x Unit of Turnover Reduce the cost per trade: Security prices move every day Not all securities leave the desired asset class on the same day There is no need to concentrate turnover due to: arbitrary rebalancing days or predefined holding periods Equity Premium ( ) 3.2 bps Spreading turnover reduces trading costs. Value Premium ( ) Size Premium ( ) Profitability Premium ( ) 1.9 bps 1.4 bps 1.5 bps Many securities have similar characteristics and expected returns. Daily premiums are small compared with immediacy costs. Have many candidate orders when trading and Be willing to trade later to avoid paying for immediacy 1. Manager trading cost data was provided by Investment Technology Group solely for Dimensional and not for any other third party. These materials are highly confidential and are not to be copied, displayed, or transmitted in any form without the prior written permission of Investment Technology Group. Typical (median) manager trading cost is as of September 30, Typical (average) spread is one year as of December 31, 2013, source: Dimensional Fund Advisors LP. Developed international markets are Dimensional s eligible universe (Canada, Europe, Japan, Asia Pacific, UK). 2. Please see additional information on Historical US Daily Premiums in the Appendix. Past performance is no guarantee of future results. 18

20 The Process at Work

21 US Total Market 1

22 SMALL SMALL SIZE SIZE LARGE LARGE Applying Profitability: Index Construction Applying Profitability: US TOTAL MARKET 1 INDEX US TOTAL MARKET 1 WITH PROFITABILITY INDEX LOW RELATIVE PRICE HIGH PROFITABILITY 1 LOW HIGH LOW RELATIVE PRICE HIGH A total market index focused on the dimensions of expected returns Increased emphasis on higher expected return securities: Lower relative price Higher profitability Lower market cap For illustrative purposes only. 1. Profitability is measured as operating income before depreciation and amortization minus interest expense scaled by book. 21 #

23 Applying Profitability: Returns and Characteristics Applying Profitability: Russell 3000 Index Russell 3000 Value Index US Total Market 1 Index 1 US Total Market 1 with Profitability Index 1 RETURNS: Annualized Compound Return Annualized Standard Deviation Annualized Tracking Error (vs. Russell 3000) t-statistic (vs. Russell 3000) CHARACTERISTICS AS OF DECEM BER 31, 2013 Weighted Average Market Cap (millions) $98,844 $104,846 $74,452 $77,812 Median Market Cap (millions) $1,414 $1,227 $1,487 $1,487 Aggregate Price-to-Book Weighted Average Profitability/Book In USD 1. Indices are 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. Source: Dimensional using CRSP and Compustat data. CRSP data provided by the Center for Research in Security Prices. Russell data copyright Russell Investment Group , all rights reserved. 22 #

24 US Total Market 2

25 SMALL SMALL SIZE SIZE LARGE LARGE Applying Profitability: Index Construction Applying Profitability: US TOTAL MARKET 2 INDEX US TOTAL MARKET 2 WITH PROFITABILITY INDEX LOW RELATIVE PRICE HIGH PROFITABILITY 1 LOW HIGH LOW RELATIVE PRICE HIGH A total market index focused on the dimensions of expected returns Increased emphasis on higher expected return securities: Lower relative price Higher profitability Lower market cap For illustrative purposes only. 1. Profitability is measured as operating income before depreciation and amortization minus interest expense scaled by book. 24 #

26 Applying Profitability: Returns and Characteristics Applying Profitability: Russell 3000 Index Russell 3000 Value Index US Total Market 2 Index 1 US Total Market 2 with Profitability Index 1 RETURNS: Annualized Compound Return Annualized Standard Deviation Annualized Tracking Error (vs. Russell 3000) t-statistic (vs. Russell 3000) CHARACTERISTICS AS OF DECEM BER 31, 2013 Weighted Average Market Cap (millions) $98,844 $104,846 $66,676 $68,244 Median Market Cap (millions) $1,414 $1,227 $1,487 $1,487 Aggregate Price-to-Book Weighted Average Profitability/Book In USD. 1. Indices are 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. Source: Dimensional using CRSP and Compustat data. CRSP data provided by the Center for Research in Security Prices. Russell data copyright Russell Investment Group , all rights reserved. 25 #

27 US Large Cap Low Relative Price

28 SMALL SMALL SIZE SIZE LARGE LARGE MID MEGA SIZE Applying Profitability: Index Construction Applying Profitability: US LARGE CAP LOW RELATIVE PRICE INDEX US LARGE CAP LOW RELATIVE PRICE WITH PROFITABILITY INDEX RELATIVE PRICE RELATIVE PRICE PROFITABILITY 1 LOW HIGH LOW HIGH LOW HIGH Stocks above 10% market cap limit Stocks above 10% market cap limit Stocks with lowest 20% of P/B ratios Stocks with lowest 30% of P/B ratios LOWEST LOW RELATIVE PRICE Focus on large cap, deep value securities Exclude companies with lowest expected returns: Lowest profitability and high relative price Increased emphasis on higher expected return securities within selected universe: Lower relative price, higher profitability, lower market cap For illustrative purposes only. 1. Profitability is measured as operating income before depreciation and amortization minus interest expense scaled by book. 27 #

29 Applying Profitability: Returns and Characteristics Russell 1000 Index Russell 1000 Value Index US Large Cap Low Relative Price Index 1 US Large Cap Low Relative Price with Profitability Index 1 RETURNS: Annualized Compound Return Annualized Standard Deviation Annualized Tracking Error (vs. Russell 1000) Annualized Tracking Error (vs. Russell 1000 Value) t-statistic (vs. Russell 1000 Value) CHARACTERISTICS AS OF DECEM BER 31, 2013 Weighted Average Market Cap (millions) $107,368 $113,842 $72,192 $76,385 Median Market Cap (millions) $7,522 $6,547 $9,108 $9,109 Aggregate Price-to-Book Weighted Average Profitability/Book In USD. 1. Indices are 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. Source: Dimensional using CRSP and Compustat data. CRSP data provided by the Center for Research in Security Prices. Russell data copyright Russell Investment Group , all rights reserved. 28 #

30 Summary

31 Summary Dimensional was founded on the idea of making compelling academic research investable, and it has consistently sought to add value through portfolio design, management, and implementation. Profitability is another example of Dimensional translating research into application. Adding this dimension enhances our understanding of expected returns and enhances our ability to create better solutions for our clients. 30 #

32 Questions?

33 Appendix

34 Index Descriptions Dimensional US Small Cap Index was created by Dimensional in March 2007 and is compiled by Dimensional. It represents a market-capitalization-weighted index of securities of the smallest US companies whose market capitalization falls in the lowest 8% of the total market capitalization of the Eligible Market. The Eligible Market is composed of securities of US companies traded on the NYSE, NYSE MKT (formerly AMEX), and Nasdaq Global Market. Exclusions: Non-US companies, REITs, UITs, and Investment Companies. From January 1975 to the present, the index also excludes companies with the lowest profitability and highest relative price within the small cap universe. Profitability is measured as Operating Income before Depreciation and Amortization minus Interest Expense scaled by Book. Source: CRSP and Compustat. The index monthly returns are computed as the simple average of the monthly returns of 12 sub-indices, each one reconstituted once a year at the end of a different month of the year. The calculation methodology for the Dimensional US Small Cap Index was amended on January 1, 2014, to include profitability as a factor in selecting securities for inclusion in the index. Dimensional US High Profitability Index was created by Dimensional in January 2014 and represents an index consisting of US companies. It is compiled by Dimensional. Dimensional sorts stocks into three profitability groups from high to low. Each group represents one-third of the market capitalization. Similarly, stocks are sorted into three relative price groups. The intersections of the three profitability groups and the three relative price groups yield nine subgroups formed on profitability and relative price. The index represents the average return of the three highprofitability subgroups. It is rebalanced twice per year. Profitability is measured as Operating Income before Depreciation and Amortization minus Interest Expense scaled by Book. Source: CRSP and Compustat. Dimensional US Low Profitability Index was created by Dimensional in January 2014 and represents an index consisting of US companies. It is compiled by Dimensional. Dimensional sorts stocks into three profitability groups from high to low. Each group represents one-third of the market capitalization. Similarly, stocks are sorted into three relative price groups. The intersections of the three profitability groups and the three relative price groups yield nine subgroups formed on profitability and relative price. The index represents the average return of the three lowprofitability subgroups. It is rebalanced twice per year. Profitability is measured as Operating Income before Depreciation and Amortization minus Interest Expense scaled by Book. Source: CRSP and Compustat. Dimensional International Small Cap Index was created by Dimensional in April 2008 and is compiled by Dimensional. July December 1993: it Includes non- US developed securities in the bottom 10% of market capitalization in each eligible country. All securities are market capitalization weighted. Each country is capped at 50%. Rebalanced semiannually. January Present: Market-capitalizationweighted index of small company securities in the eligible markets excluding those with the lowest profitability and highest relative price within the small cap universe. Profitability is measured as operating income before depreciation and amortization minus interest expense scaled by book. The index monthly returns are computed as the simple average of the monthly returns of four sub-indices, each one reconstituted once a year at the end of a different quarter of the year. Prior to July 1981, the index is 50% UK and 50% Japan. The calculation methodology for the Dimensional International Small Cap Index was amended on January 1, 2014, to include profitability as a factor in selecting securities for inclusion in the index. The Dimensional Indices have been retrospectively calculated by Dimensional Fund Advisors LP and did not exist prior to their index inceptions dates. Accordingly, results shown during the periods prior to each Index s index inception date do not represent actual returns of the Index. Other periods selected may have different results, including losses. Backtested index performance is hypothetical and is provided for informational purposes only to indicate historical performance had the index been calculated over the relevant time periods. Backtested performance results assume the reinvestment of dividends and capital gains. 33

35 Index Descriptions Dimensional International Low Profitability Index was created by Dimensional in January 2013 and represents an index consisting of non-us Developed companies. It is compiled by Dimensional. Dimensional sorts stocks into three profitability groups from high to low. Each group represents one-third of the market capitalization of each eligible country. Similarly, stocks are sorted into three relative price groups. The intersections of the three profitability groups and the three relative price groups yield nine subgroups formed on profitability and relative price. The index represents the average return of the three low-profitability subgroups. The index is rebalanced twice per year. Profitability is measured as Operating Income before Depreciation and Amortization minus Interest Expense scaled by Book. Source: Bloomberg. Dimensional International High Profitability Index was created by Dimensional in January 2013 and represents an index consisting of non-us Developed companies. It is compiled by Dimensional. Dimensional sorts stocks into three profitability groups from high to low. Each group represents one-third of the market capitalization of each eligible country. Similarly, stocks are sorted into three relative price groups. The intersections of the three profitability groups and the three relative price groups yield nine subgroups formed on profitability and relative price. The index represents the average return of the three high-profitability subgroups. The index is rebalanced twice per year. Profitability is measured as Operating Income before Depreciation and Amortization minus Interest Expense scaled by Book. Source: Bloomberg. Dimensional Emerging Markets Low Profitability Index was created by Dimensional in April 2013 and represents an index consisting of emerging markets companies and is compiled by Dimensional. Dimensional sorts stocks into three profitability groups from high to low. Each group represents one-third of the market capitalization of each eligible country. Similarly, stocks are sorted into three relative price groups. The intersections of the three profitability groups and the three relative price groups yield nine subgroups formed on profitability and relative price. The index represents the average return of the three low-profitability subgroups. The index is rebalanced twice per year. Profitability is measured as Operating Income before Depreciation and Amortization minus Interest Expense scaled by Book. Source: Bloomberg. Dimensional in April 2013 and represents an index consisting of emerging markets companies and is compiled by Dimensional. Dimensional sorts stocks into three profitability groups from high to low. Each group represents one-third of the market capitalization of each eligible country. Similarly, stocks are sorted into three relative price groups. The intersections of the three profitability groups and the three relative price groups yield nine subgroups formed on profitability and relative price. The index represents the average return of the three high-profitability subgroups. The index is rebalanced twice per year. Profitability is measured as Operating Income before Depreciation and Amortization minus Interest Expense scaled by Book. Source: Bloomberg. Dimensional Emerging Markets Small Cap Index was created by Dimensional in April 2008 and is compiled by Dimensional. January December 1993: Fama/French Emerging Markets Small Cap Index. January Present: Dimensional Emerging Markets Small Index Composition: Market-capitalizationweighted index of small company securities in the eligible markets excluding those with the lowest profitability and highest relative price within the small cap universe. Profitability is measured as operating income before depreciation and amortization minus interest expense scaled by book. The index monthly returns are computed as the simple average of the monthly returns of four sub-indices, each one reconstituted once a year at the end of a different quarter of the year. Source: Bloomberg. The calculation methodology for the Dimensional Emerging Markets Small Cap Index was amended on January 1, 2014, to include profitability as a factor in selecting securities for inclusion in the index. Dimensional Emerging Markets High Profitability Index was created by The Dimensional Indices have been retrospectively calculated by Dimensional Fund Advisors LP and did not exist prior to their index inceptions dates. Accordingly, results shown during the periods prior to each Index s index inception date do not represent actual returns of the Index. Other periods selected may have different results, including losses. Backtested index performance is hypothetical and is provided for informational purposes only to indicate historical performance had the index been calculated over the relevant time periods. Backtested performance results assume the reinvestment of dividends and capital gains. 34

36 Index Descriptions Fama/French US Value Index Provided by Fama/French from CRSP securities data. Includes the lower 30% in price-to-book of NYSE securities (plus NYSE Amex equivalents since July 1962 and Nasdaq equivalents since 1973). Fama/French US Growth Index Provided by Fama/French from CRSP securities data. Includes the higher 30% in price-to-book of NYSE securities (plus NYSE Amex equivalents since July 1962 and Nasdaq equivalents since 1973). Fama/French International Value Index: 2008 present: Provided by Fama/French from Bloomberg securities data. Simulated strategy of MSCI EAFE countries in the lower 30% price-to-book range : Provided by Fama/French from MSCI securities data. Fama/French International Growth Index: 2008 present: Provided by Fama/French from Bloomberg securities data. Simulated strategy of MSCI EAFE countries in the higher 30% price-to-book range : Provided by Fama/French from MSCI securities data. Fama/French Emerging Markets Value Index: 2009 present: Provided by Fama/French from Bloomberg securities data. Simulated strategy using IFC investable universe countries. Companies in the lower 30% price-to-book range; companies weighted by float-adjusted market cap; countries weighted by country float-adjusted market cap; rebalanced monthly : Provided by Fama/French from IFC securities data. IFC data provided by International Finance Corporation. Fama/French Emerging Markets Growth Index : 2009 present: Provided by Fama/French from Bloomberg securities data. Simulated strategy using IFC investable universe countries. Companies in the higher 30% price-to-book range; companies weighted by float-adjusted market cap; countries weighted by country float-adjusted market cap; rebalanced monthly : Provided by Fama/French from IFC securities data. IFC data provided by International Finance Corporation. Results shown during periods prior to each Index s index inception date do not represent actual returns of the respective index. Other periods selected may have different results, including losses. Backtested index performance is hypothetical and is provided for informational purposes only to indicate historical performance had the index been calculated over the relevant time periods. Backtested performance results assume the reinvestment of dividends and capital gains. 35

37 Index Descriptions US Total Market 1 Index was created by Dimensional in July 2013 and represents a portfolio consisting of US companies with an emphasis on companies with smaller capitalization and lower relative price and is compiled by Dimensional from CRSP and Compustat. The index excludes REITs, non- US companies, UITs, and investment companies. US Total Market 1 with Profitability Index was created by Dimensional in July 2013 and represents an index consisting of the US Total Market 1 Index with the addition of a profitability overlay, which overweights companies with higher profitability and underweights companies with lower profitability. Profitability is measured as operating income before depreciation and amortization minus interest expense scaled by book. US Total Market 2 Index was created by Dimensional in July 2013 and represents a portfolio similar to US Total Market 1 Index, but with a stronger emphasis on companies with smaller capitalization and lower relative price and is compiled by Dimensional from CRSP and Compustat. The index excludes REITs, non-us companies, UITs, and investment companies. US Total Market 2 with Profitability Index was created by Dimensional in July 2013 and represents an index consisting of the US Total Market 2 Index with the addition of a profitability overlay, which overweights companies with higher profitability and underweights companies with lower profitability. Profitability is measured as operating income before depreciation and amortization minus interest expense scaled by book. US Large Cap Low Relative Price Index was created by Dimensional in July 2013 and represents a portfolio of large cap US companies with low relative price and is compiled by Dimensional from CRSP and Compustat. 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 20% of the large-cap market after the exclusion of utilities, companies lacking financial data, and companies with negative relative price. The index excludes REITs, non-us companies, UITs, investment companies, and utilities. US Large Cap Low Relative Price with Profitability Index was created by Dimensional in July 2013 and represents an index similar to the US Large Cap Low Relative Price Index, but it emphasizes companies with higher profitability, lower relative price, and lower capitalization. Profitability is measured as operating income before depreciation and amortization minus interest expense scaled by book. 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. The indices are 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. 36 #

38 Historical US Daily Premiums The Annual Equity Premium is the average annual Fama/French Total US Market Research Factor. The Annual Size Premium is the average annual Fama/French US SmB Research Factor. The Annual Value Premium is the average annual Fama/French US HmL Research Factor. The Annual Profitability Premium is the Average Annual Return on six Dimensional High Profitability Indexes (Small/Low Relative Price, Small/ Medium Relative Price, and Small/High relative Price, Large/Low Relative Price, Large/ Medium Relative Price, and Large/High Relative Price) minus the average annual return on the equivalent six Dimensional Low Profitability Indexes. Dimensional indexes used data from the Center for Research in Security Prices (University of Chicago) and Compustat. Index descriptions available upon request. The Dimensional Indices have been retrospectively calculated by Dimensional Fund Advisors LP and did not exist prior to their index inceptions dates. Accordingly, the results shown during the periods prior to each Index s index inception date do not represent actual returns of the Index. Other periods selected may have different results, including losses. Backtested index performance is hypothetical and is provided for informational purposes only to indicate historical performance had the index been calculated over the relevant time periods. Backtested performance results assume the reinvestment of dividends and capital gains. Returns do not represent actual portfolios and do not reflect costs and fees associated with an actual investment. Daily premiums are calculated by dividing the annual premiums by 264, the approximate number of trading days in one year, back to Profitability is calculated by dividing the annual premiums by 252, the approximate number of trading days in one year, back to Past performance is no guarantee of future results. Diversification does not protect against loss in declining markets. 37