Enhancing equity portfolio diversification with fundamentally weighted strategies.

Enhancing equity portfolio diversification with fundamentally weighted strategies.

This is the second update to a paper originally published in October, 2014. In this second revision, we have included fundamental and market capitalization weighted (cap-weighted) performance through September 30, 2017. Overall, our previous suggestions on the optimal asset allocations between fundamentally weighted and cap-weighted indexes for both absolute- investors and benchmark-conscious investors remain the same. On an absolute basis, both Russell RAFI TM Index Series (formerly Russell Index Series) 1 and cap-weighted indexes performed well in 2017. Given the momentum-driven rally in 2017, some outperformance of cap-weighted strategies is expected, relative to their fundamentally weighted counterparts. Historically, a period of cap-weighted indexes outperformance is followed by outperformance of fundamentally weighted strategies. It is extremely difficult to accurately predict when those directional shifts will materialize, therefore combining both strategies may improve a portfolio s risk- characteristics and provide diversification benefits. 1 FTSE Russell changed the Russell Index Series name to Russell RAFI Index Series. The name change was applied to all indexes within the Russell RAFI Index Series, and was effective on December 1, 2016. There are no associated changes to the index constituents or methodology.

Emre Erdogan, Ph.D., CFA, Senior Research Analyst, Charles Schwab Investment Management In this paper we will explore various combinations of traditional market capitalization-weighted ( cap-weighted ) and fundamentally weighted strategies across five distinct equity asset classes. Our goal is to determine whether combining a fundamentally weighted strategy with a cap-weighted strategy in a portfolio would provide any potential diversification benefits and, if so, the optimal allocation among the two. Although our research found slight variations within each asset class with further variation based on whether investors are benchmarkconscious or absolute- inclined our high-level findings include the following: ly weighted strategies can serve as a complement to traditional cap-weighted strategies. Combining fundamentally weighted strategies with cap-weighted strategies may improve a portfolio s risk- characteristics. ly weighted strategies have historically provided the strongest s and the greatest diversification benefits immediately after a stock market bubble bursts. The performance information for the Russell RAFI TM Index Series is back-dated performance based on simulated data (August 1, 1996 February 23, 2011), unless otherwise noted, and actual performance results (February 24, 2011 September 30, 2017) using the strategy of quarterly rebalancing. For the indexes discussed, it is assumed that dividends and capital gains were reinvested. Commissions and other fees were not taken into consideration, and if they had, performance would have been lower. Back tested performance is hypothetical and done with the benefit of hindsight. Past performance of a back tested model is not a guarantee that the model will produce similar results in the future. All of the calculations were produced by Charles Schwab Investment Management, Inc. based on monthly total data from Bloomberg L.P. For Institutional Use Only Enhancing equity portfolio diversification with fundamentally weighted strategies 1

Introduction The broad popularity of traditional capitalization-weighted index strategies those that weight their components based on market capitalization, or number of shares outstanding multiplied by the share price is the result of numerous theoretical models used in academia and industry that posit that the optimal portfolio for a passive investor is a capweighted one 2,3,4. Recent empirical research suggests, however, that cap-weighted indexes are prone to market bubbles, which may expose investors to significant losses when such bubbles burst 5. To help mitigate this potential risk, particularly during bubble periods, investors may want to consider diversifying their cap-weighted equity exposures. Rob Arnott of Research Affiliates, LLC, a pioneer of the Index methodology, along with Jason Hsu and Phillip Moore 6 have proposed a different approach of passive investing that may help diversity equity exposure and potentially create more-robust portfolios that may be less sensitive to the effects of stock market bubbles. In a fundamentally weighted index, security weights are chosen based on fundamental criteria such as revenue, sales, dividends, earnings and/or book value as opposed to market capitalization. We believe that these metrics are a more accurate aggregate measure of the size of a company, because indexes based on market capitalization tend to overweight companies that are richly valued while underweighting those with low valuations. While we believe fundamentally weighted indexing as an investment strategy can stand on its own in an investor s portfolio, we were interested in examining the effects of combining it with the more traditional capitalization-weighted strategy. In this research, we analyzed performance data of fundamentally weighted strategies and their cap-weighted counterparts across five asset classes: U.S. large-cap, U.S. small-cap, international developed large-cap, international developed small-cap, and emerging markets equities. While there are many potential fundamentally weighted and cap-weighted indexes, in this paper, we analyzed data relating to the following indexes: Cap-weighted index ly weighted index 7 S&P 500 Index vs. Russell RAFI US Large Company Index Russell 2000 Index vs. Russell RAFI US Small Company Index MSCI EAFE Index vs. Russell RAFI Dev. ex US Large Company Index MSCI World ex USA Small Cap Index vs. Russell RAFI Dev. ex US Small Company Index MSCI Emerging Markets Index vs. Russell RAFI Emerging Markets Large Company Index 2 Portfolio Selection. Markowitz, Harry. 1, March 1952, Journal of Finance, Vol. 7, pp. 77 91. 3 Markowitz, Harry. Portfolio Selection: Diversification of Investments. New York : John Wiley & Sons., 1959. 4 Risk-Aversion in the Stock Market: Some Emprical Evidence. Sharpe, William. 3, September 1965, Journal of Finance, Vol. 30, pp. 416 422. 5 Arnott, Robert D., Hsu, Jason C. and West, John M. The Index: a better way to invest. Hoboken, New Jersey : John Wiley & Sons, Inc., 2008. 6 Indexation. Arnott, Robert D., Hsu, Jason C. and Moore, Philip. 2, March/April 2005, Financial Analyst Journal, Vol. 61, pp. 83 99. 7 Russell RAFI TM Index Series Construction and Methodology. Russell Investments, August 2017. 2 Enhancing equity portfolio diversification with fundamentally weighted strategies For Institutional Use Only

Strengths and weaknesses of the two strategies As a result of their different methodologies for weighting securities, fundamentally weighted and cap-weighted strategies offer distinct advantages and considerations, including, but not limited to, those which are summarized below: Cap-weighted strategy Advantages: Captures momentum and market sentiment, favors the segments of the economy expected to experience the greatest future growth Low tracking error relative to a cap-weighted index Generally lower cost Considerations: Markets are not always correct or efficient; frequent pricing errors allocate higher weights to overpriced securities, particularly during market bubbles Large shifts in individual stock and sector allocations may increase exposures to market bubbles When prices of overpriced stocks correct, negative alpha is introduced ly weighted strategy Advantages: Removes price data in portfolio construction, helping to protect against pricing errors in the market Usually has higher exposure to value and lower exposure to momentum factors Considerations: During bubble years and before a bubble bursts, tends to underperform cap-weighted strategies for an extended period Larger tracking error relative to a cap-weighted index Low momentum exposures tend to be more pronounced especially during bubble forming years. The strategy tends to counter the trend of capweighted strategies to overweight high-priced stocks and underweight low-priced ones. Tracking error relative to a cap-weighted strategy tends to be dynamic; tracking error increases during bubble years, potentially helping to protect against overpriced stocks For Institutional Use Only Enhancing equity portfolio diversification with fundamentally weighted strategies 3

Performance differential between the two strategies In this paper, for the five asset classes analyzed, we present detailed performance information for the fundamentally weighted strategies and the capweighted strategies. However, we first examine the risk- characteristics at a high level for the two strategies. To that end, we plotted an efficient frontier (Figure 1) of the cap-weighted and fundamentally weighted strategies for the period from August 1, 1996 through September 30, 2017 (the period for which back-dated and historical data is available) 8 : Figure 1 Efficient frontier of five major cap-weighted strategies and the corresponding fundamentally weighted strategy counterparts: August 1996 September 2017. Efficient frontier (08/1996 09/2017) 14 13 Russell RAFI U.S. Small Co. Index 12 11 Russell RAFI U.S. Large Co. Index Russell RAFI Dev. ex U.S. Small Co. Index Russell RAFI EM Large Co. Index Annualized % 10 9 8 7 6 S&P 500 Index Russell RAFI Dev. ex U.S. Large Co. Index MSCI World ex USA Small Cap Index Russell 2000 Index MSCI Emerging Markets Index 5 MSCI EAFE Index 4 14 15 16 17 18 19 20 21 22 23 24 25 26 Annualized standard deviation % This exercise yielded the following findings: ly weighted strategies would have provided annualized excess s over cap-weighted strategies of 2% to 5% over full market cycles. ly weighted strategies would have had similar risk/volatility as that of the cap-weighted strategies. 8 Return data for the MSCI World ex USA Small Cap Index commenced in December 31, 1998. Therefore, we used the data from the same period for Russell RAFI Developed ex US Small Company Index. 4 Enhancing equity portfolio diversification with fundamentally weighted strategies For Institutional Use Only

Analysis by asset class In this paper, we analyze each of five asset classes separately to evaluate the potential benefits of combining a fundamentally weighted strategy with a cap-weighted strategy in a portfolio and to determine potential allocations between the two. For each asset class, we created 11 sample portfolios comprising various combinations of the cap-weighted strategy and the corresponding fundamentally weighted strategy, starting with a 100% cap-weighted portfolio and increasing the fundamentally weighted allocation by 10% increments up to 100%. Columns in the tables showing the results of these evaluated allocations represent discrete intervals rather than continuous data, and include shading that approximates the allocations that our research suggests as the optimal range for the specified type of investor. As far as our time frame, we initially studied data for the period from August 1996 9 to September 2017, which represents the period for which back-dated and historical data was available. To reduce any potential bias during that period due to market extremes (e.g., the Tech bubble of 2000 and the Credit bubble of 2008), we also broke that period into two sub-periods: August 1, 1996 9 through December 31, 2004, which approximately represents the first half of the available data, and January 1, 2005 through September 30, 2017, which approximately represents the second half of the available data In addition, in our analysis we considered two distinct types of investors: Benchmark-conscious investors who evaluate performance against a cap-weighted index benchmark and are more concerned about excess s and tracking errors relative to that benchmark Because these two types of investors have different investment profiles and sensitivities, we selected different metrics for each. For absolute- investors who are not benchmark-sensitive, we used the following metrics: Annualized Return Annualized Standard Deviation Sharpe Ratio Maximum Drawdown 1-, 3-, and 5-year annualized and calendar-year s For the benchmark-conscious investors, we took a more comparative approach, selecting the following metrics that evaluate excess s and tracking error relative to a cap-weighted index: Annualized Excess Return Annualized Tracking Error Information Ratio 1-, 3-, and 5-year annualized and calendar-year s We present the findings by asset class below, followed by overall potential allocations suggested by the data. Absolute- investors who are not restricted by a specific benchmark 9 See footnote 8. For Institutional Use Only Enhancing equity portfolio diversification with fundamentally weighted strategies 5

U.S. Large-Cap Equities In our analysis of U.S. large-cap equities, we used the S&P 500 Index as a surrogate for the capweighted strategy and the Russell RAFI US Large Company Index as a surrogate for the fundamentally weighted strategy. The tables below present data for each of the 11 portfolio combinations from 100% cap-weighted to 100% fundamentally weighted for the full study period of August 1996 through September 2017. Tables 1 and 2 present the metrics and total s relevant to the absolute- investor; Tables 3 and 4 present comparative data relative to the benchmark-conscious investor. Tables in Appendix A present the data shown in Tables 1 and 3 for the two sub-periods also analyzed. Table 1: U.S. Large-Cap Equities Total analysis (for absolute- investors): August 1996 September 2017 S&P 500 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Annualized 8.6% 8.9% 9.2% 9.4% 9.7% 9.9% 10.1% 10.4% 10.6% 10.8% 11.0% Annualized standard deviation 15.0% 14.9% 14.8% 14.8% 14.7% 14.7% 14.6% 14.6% 14.6% 14.6% 14.6% Sharpe ratio 0.57 0.60 0.62 0.64 0.66 0.68 0.69 0.71 0.73 0.74 0.75 Maximum drawdown -50.9% -50.9% -50.8% -50.7% -50.6% -50.6% -50.5% -50.4% -50.4% -50.4% -50.5% 1 year 18.6% 18.2% 17.9% 17.6% 17.3% 17.0% 16.8% 16.6% 16.4% 16.2% 16.0% 3 year 10.8% 10.6% 10.4% 10.2% 10.0% 9.8% 9.7% 9.5% 9.4% 9.3% 9.2% 5 year 14.2% 14.2% 14.1% 14.1% 14.1% 14.0% 14.0% 14.0% 14.0% 13.9% 13.9% 6 Enhancing equity portfolio diversification with fundamentally weighted strategies For Institutional Use Only

Table 2: U.S. Large-Cap Equities Calendar-year s (for absolute- Investors): August 1996 September 2017 S&P 500 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 1996* 14.4% 14.3% 14.1% 13.9% 13.8% 13.6% 13.4% 13.2% 13.1% 12.9% 12.7% 1997 33.4% 33.2% 33.1% 33.0% 32.9% 32.8% 32.6% 32.5% 32.4% 32.3% 32.2% 1998 28.6% 27.9% 27.2% 26.5% 25.9% 25.2% 24.5% 23.8% 23.1% 22.4% 21.7% 1999 21.0% 19.8% 18.5% 17.2% 15.8% 14.5% 13.1% 11.7% 10.3% 8.8% 7.4% 2000-9.1% -7.4% -5.6% -3.8% -1.9% 0.1% 2.2% 4.3% 6.6% 8.9% 11.4% 2001-11.9% -10.5% -9.0% -7.6% -6.2% -4.8% -3.4% -2.0% -0.6% 0.8% 2.3% 2002-22.1% -21.3% -20.6% -19.9% -19.1% -18.5% -17.8% -17.2% -16.5% -15.9% -15.3% 2003 28.7% 29.4% 30.1% 30.7% 31.3% 31.9% 32.5% 33.0% 33.5% 34.0% 34.5% 2004 10.9% 11.5% 12.1% 12.7% 13.2% 13.7% 14.1% 14.6% 15.0% 15.4% 15.8% 2005 4.9% 5.1% 5.4% 5.5% 5.7% 5.9% 6.1% 6.2% 6.4% 6.5% 6.6% 2006 15.8% 16.3% 16.7% 17.1% 17.5% 17.8% 18.1% 18.4% 18.7% 19.0% 19.2% 2007 5.5% 5.2% 5.0% 4.8% 4.6% 4.4% 4.2% 4.0% 3.9% 3.7% 3.6% 2008-37.0% -36.7% -36.4% -36.1% -35.9% -35.7% -35.4% -35.2% -35.1% -34.9% -34.7% 2009 26.5% 27.4% 28.2% 29.0% 29.7% 30.4% 31.0% 31.6% 32.1% 32.6% 33.0% 2010 15.1% 15.5% 15.9% 16.2% 16.5% 16.8% 17.1% 17.3% 17.5% 17.7% 17.9% 2011 2.1% 2.2% 2.3% 2.4% 2.5% 2.6% 2.7% 2.7% 2.8% 2.9% 2.9% 2012 16.0% 16.1% 16.2% 16.3% 16.4% 16.4% 16.5% 16.5% 16.6% 16.6% 16.7% 2013 32.4% 32.8% 33.1% 33.4% 33.7% 33.9% 34.2% 34.4% 34.6% 34.8% 34.9% 2014 13.7% 13.5% 13.4% 13.3% 13.2% 13.1% 13.0% 12.9% 12.8% 12.7% 12.7% 2015 1.4% 0.8% 0.2% -0.2% -0.7% -1.1% -1.4% -1.7% -2.0% -2.3% -2.6% 2016 12.0% 12.7% 13.3% 13.8% 14.4% 14.8% 15.3% 15.7% 16.0% 16.4% 16.7% 2017* 14.2% 13.5% 12.9% 12.3% 11.8% 11.3% 10.9% 10.5% 10.2% 9.9% 9.6% *Returns for 1996 and 2017 are partial-year s Table 3: U.S. Large-Cap Equities Excess analysis (for benchmark-conscious investors): August 1996 September 2017 Annualized excess S&P 500 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 0.0% 0.3% 0.5% 0.8% 1.0% 1.3% 1.5% 1.7% 1.9% 2.1% 2.3% Tracking error 0.0% 0.5% 1.0% 1.6% 2.1% 2.6% 3.0% 3.5% 4.0% 4.5% 5.1% Information ratio 0.53 0.52 0.52 0.51 0.50 0.49 0.48 0.48 0.47 0.46 1 year excess 3 year excess 5 year excess 0.0% -0.4% -0.7% -1.0% -1.3% -1.6% -1.8% -2.0% -2.2% -2.4% -2.6% 0.0% -0.2% -0.5% -0.7% -0.8% -1.0% -1.1% -1.3% -1.4% -1.5% -1.6% 0.0% 0.0% -0.1% -0.1% -0.2% -0.2% -0.2% -0.2% -0.3% -0.3% -0.3% For Institutional Use Only Enhancing equity portfolio diversification with fundamentally weighted strategies 7

Table 4: U.S. Large-Cap Equities Calendar-year excess s (for benchmark-conscious investors): August 1996 September 2017 S&P 500 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 1996* 0.0% -0.2% -0.3% -0.5% -0.7% -0.9% -1.0% -1.2% -1.4% -1.5% -1.7% 1997 0.0% -0.1% -0.2% -0.4% -0.5% -0.6% -0.7% -0.8% -1.0% -1.1% -1.2% 1998 0.0% -0.7% -1.4% -2.0% -2.7% -3.4% -4.1% -4.8% -5.5% -6.2% -6.9% 1999 0.0% -1.3% -2.6% -3.9% -5.2% -6.6% -7.9% -9.3% -10.8% -12.2% -13.7% 2000 0.0% 1.7% 3.5% 5.3% 7.2% 9.2% 11.3% 13.4% 15.7% 18.0% 20.5% 2001 0.0% 1.4% 2.8% 4.3% 5.7% 7.1% 8.5% 9.9% 11.3% 12.7% 14.1% 2002 0.0% 0.8% 1.5% 2.2% 3.0% 3.6% 4.3% 4.9% 5.6% 6.2% 6.8% 2003 0.0% 0.7% 1.4% 2.0% 2.7% 3.2% 3.8% 4.3% 4.8% 5.3% 5.8% 2004 0.0% 0.6% 1.2% 1.8% 2.3% 2.8% 3.3% 3.7% 4.1% 4.5% 4.9% 2005 0.0% 0.2% 0.4% 0.6% 0.8% 1.0% 1.2% 1.3% 1.4% 1.6% 1.7% 2006 0.0% 0.5% 0.9% 1.3% 1.7% 2.0% 2.3% 2.6% 2.9% 3.2% 3.4% 2007 0.0% -0.3% -0.5% -0.7% -0.9% -1.1% -1.3% -1.5% -1.6% -1.8% -1.9% 2008 0.0% 0.3% 0.6% 0.9% 1.1% 1.3% 1.5% 1.7% 1.9% 2.1% 2.3% 2009 0.0% 0.9% 1.8% 2.5% 3.3% 3.9% 4.5% 5.1% 5.6% 6.1% 6.6% 2010 0.0% 0.4% 0.8% 1.1% 1.4% 1.7% 2.0% 2.2% 2.5% 2.7% 2.9% 2011 0.0% 0.1% 0.2% 0.3% 0.4% 0.5% 0.6% 0.6% 0.7% 0.7% 0.8% 2012 0.0% 0.1% 0.2% 0.3% 0.3% 0.4% 0.5% 0.5% 0.6% 0.6% 0.7% 2013 0.0% 0.4% 0.7% 1.0% 1.3% 1.6% 1.8% 2.0% 2.2% 2.4% 2.5% 2014 0.0% -0.2% -0.3% -0.4% -0.5% -0.6% -0.7% -0.8% -0.9% -0.9% -1.0% 2015 0.0% -0.6% -1.1% -1.6% -2.1% -2.4% -2.8% -3.1% -3.4% -3.7% -4.0% 2016 0.0% 0.7% 1.3% 1.9% 2.4% 2.9% 3.3% 3.7% 4.1% 4.4% 4.7% 2017* 0.0% -0.7% -1.4% -1.9% -2.4% -2.9% -3.3% -3.7% -4.1% -4.4% -4.7% *Returns for 1996 and 2017 are partial-year s The following summarizes our findings: Risk: Table 1 shows that volatility would have been similar between the cap-weighted and fundamentally weighted strategies. The data from the sub-periods, however, shows that the fundamentally weighted strategy would have had lower volatility prior to January 2005 (See Tables A1 and A3 in Appendix A). Maximum drawdowns an indicator of risk represented by the peak-to-trough decline of a portfolio presented in those same tables show that the fundamentally weighted strategy would have had significantly better drawdowns during the period ended December 2004, when maximum drawdowns for the capweighted and fundamentally weighted strategies would have been 44.7% and 26%, respectively. For the period beginning January 2005, maximum drawdowns for the two strategies would have been similar. Total and excess s: Table 3 shows that the fundamentally weighted strategy would have outperformed the cap-weighted strategy by 2.3% annually over the full period studied. However, analysis of total and excess calendar year s in Tables 2 and 4 show that the cap-weighted strategy would have outperformed the fundamentally weighted strategy during the bubble years the late 1990s (tech bubble), 2007(housing bubble), as well as in 2014-2015 (low interest rate asset bubble) as well as YTD 2017, which potentially could be a sign of another bubble. This is expected, because performance of cap-weighted strategies are primarily driven by momentum, with momentum stocks performing better as their weights in the 8 Enhancing equity portfolio diversification with fundamentally weighted strategies For Institutional Use Only

strategy increase. A fundamentally weighted strategy a contrarian strategy would be expected to trail its cap-weighted counterpart during periods in which bubbles are developing. Upon the bursting of a bubble, however, the fundamentally weighted strategy would be expected to outperform the cap-weighted one. Tracking error: As shown in Table 3, the tracking error between the two strategies would have been 5.1%. This implies that the two differ notably in their characteristics and exposures to different market styles (betas). Combining the two strategies, therefore, may help investors increase their style diversification. We also noted, as shown in Tables A2 and A4 in Appendix A, that the tracking errors before and after January 2005 would have differed significantly, at 7.4% and 2.5%, respectively. Sharpe and information ratios: As shown in Table 1 and Tables A1 and A3 in Appendix A, the fundamentally weighted strategy would have had a higher Sharpe Ratio an indicator of risk-adjusted performance than the cap-weighted strategy. Table 3 and Tables A2 and A4 in Appendix A show that the fundamentally weighted strategy also would have had a high and positive Information Ratio a measure of outperformance relative to tracking error. Portfolio allocation: U.S. Large-Cap Equities Our analysis of the performance data prior to 2005 in the context of the distinctions between the constructions of the two strategies implies that a fundamentally weighted strategy may provide excess- potential as well as risk-diversification benefits particularly during stock market bubbles. However, we note the cap-weighted strategy s outperformance for four consecutive years (1996 to 1999). Given that the two strategies would have had similar volatilities, for the absolute- U.S. largecap equity investor the data suggests a minimum 50% allocation to a fundamentally weighted strategy. At the other extreme, the data suggests a maximum allocation of 70% so as not to eliminate the diversification benefit gleaned from having exposure to both strategies. For the benchmark-conscious investor concerned with tracking error, however, the data suggests a lower allocation. The important point that these investors should keep in mind when determining their tracking-error tolerance is that, based on our analysis, tracking error between the two strategies tends to change across market cycles. Generally speaking, acceptable tracking-error levels are dependent on a number of factors. For the purposes of this analysis and to determine a rough estimate of the average acceptable tracking error to benchmark-conscious investors, we took the median realized tracking errors of the active funds in Morningstar s U.S. Large Blend Category, which uses the S&P 500 Index as its benchmark; as of September 2017, that median was 3.3%. However, because a fundamentally weighted strategy is passive and does not utilize the investment oversight of a portfolio manager like active funds do, we believe that the acceptable tracking error in this analysis should be significantly lower than 3.3%. For simplicity, then, we assumed that half of this average active-manager tracking error 1.7% is more reasonable. Interpolating the tracking error estimations in Table 3, then, implies that a 1.7% tracking error would have resulted from an approximate fundamentally weighted strategy allocation of 32%. For benchmark-conscious U.S. large-cap equity investors, therefore, the data suggests a maximum 35% allocation to a fundamentally weighted strategy. For Institutional Use Only Enhancing equity portfolio diversification with fundamentally weighted strategies 9

U.S. Small-Cap Equities We applied the same methodology and process described above to the additional four asset classes that we analyzed. For U.S. small-cap equities, we used the Russell 2000 Index as a surrogate for the cap-weighted strategy and the Russell RAFI U.S. Small Company Index as a surrogate for the fundamentally weighted strategy. Tables similar to those presented above for U.S. large-cap equities for the full study period can be found in Appendix B, along with the equivalent tables shown in Appendix A for the two sub-periods. Our findings are summarized as follows: Risk: Table B1 in Appendix B shows that volatility for the cap-weighted strategy would have been slightly higher than that of the fundamentally weighted strategy, at 19.6% and 18.2%, respectively. Further analysis of the volatility during the periods before and after January 2005 (Tables B5 and B7) shows that volatility of the cap-weighted strategy would have been higher prior to January 2005 and lower afterwards. Furthermore, Table B5 shows that during the Tech bubble years (the period prior to January 2005), the cap-weighted strategy would have had a much higher maximum drawdown than that of the fundamentally weighted strategy: 35.1% and 25.1% respectively. Total and excess s: Table B3 in Appendix B shows that the fundamentally weighted strategy would have had an annualized excess of 4.6% relative to the cap-weighted strategy for the full period studied. Tables B6 and B8 show that the fundamentally weighted strategy would have outperformed the cap-weighted strategy in both the period prior to and the one following January 2005, by annualized excess s of 7.6% and 2.6%, respectively. Furthermore, Table B4 shows that the fundamentally weighted strategy would have outperformed the cap-weighted strategy in all calendar years except 1999, 2008, 2015 and YTD 2017. Tracking error: As shown in Table B3, tracking error between the two strategies would have been 7.1%, which is significant. This implies that the two strategies would have had distinctly different styles (betas) and/or industry exposures. Therefore, we believe that having exposures to both strategies may help investors increase their style diversification. Sharpe and information ratios: Table B1 shows that the fundamentally weighted strategy would have had a higher Sharpe Ratio than that of the cap-weighted strategy, at 0.73 and 0.45, respectively. Furthermore, Tables B5 and B7 show that the fundamentally weighted strategy would have had a significantly higher Sharpe Ratio prior to January 2005 than afterwards: 1.07 vs. 0.58. This implies that the fundamentally weighted strategy may have helped reduce the effects of stock market bubbles in this asset class. 10 Enhancing equity portfolio diversification with fundamentally weighted strategies For Institutional Use Only

Portfolio allocation: U.S. Small-Cap Equities Based on our analysis, it appears that in the U.S. small-cap asset class, the fundamentally weighted strategy would have had an advantage over the cap-weighted one. Despite that, however, the data cannot justify an allocation higher than 80%, because as discussed above, the two strategies would have had significantly high tracking error, implying that their style and industry exposures would have been different. As a result, holding both strategies may provide valuable beta diversification. In addition, we observed that the fundamentally weighted strategy would have had slightly higher volatility and slightly worse maximum drawdown after January 2005. For the absolute- U.S. small-cap equity investor, therefore, the data suggests an allocation to a fundamentally weighted strategy of between 50% and 80%. For the benchmark-conscious investor concerned with tracking error, however, the data suggests a lower allocation. Following the rationale and calculation outlined above under U.S. large-cap equities, the median realized tracking error of the active funds in Morningstar s U.S. Small Blend Category, which uses the Russell 2000 Index as its benchmark, as of September 2017 was 5.0%. As before, we applied half that average 2.5%. Interpolating the tracking error estimations in Table B3 implies that a tracking error of 2.5% would have been resulted from an approximate fundamentally weighted strategy allocation of 30%. However, if we look at the sources of the larger tracking error (Table B2 and B4), we notice that it would have been primarily due to the earlier years 1999 2002 and also 2009. As data in Tables B6 and B8 suggests, the most recent tracking error would have been much lower at 3.9% vs. 10.2% prior to January 2005. For benchmark-conscious U.S. small-cap equity investors, therefore, the data suggests a maximum 35% allocation to a fundamentally weighted strategy. For Institutional Use Only Enhancing equity portfolio diversification with fundamentally weighted strategies 11

International Large-Cap Equities We applied the same methodology and process previously described to the international developed ex-u.s. large-cap equity asset class, using the MSCI EAFE Index as a surrogate for the cap-weighted strategy and the Russell RAFI Developed ex-us Large Company Index as a surrogate for the fundamentally weighted strategy. Tables similar to those presented for U.S. small-cap equities can be found in Appendix C. The following summarizes our findings: Risk: Table C1 in Appendix C shows volatility of the two strategies would have been similar. Maximum drawdowns shown in Tables C5 and C7 show that the cap-weighted strategy would have had higher drawdowns. For the period prior to January 2005, maximum drawdowns for the cap-weighted and fundamentally weighted strategies would have been 47.5% and 28.8%, respectively; after January 2005, they would have been 56.4% and 52.4%, respectively. The significantly better maximum drawdown of the fundamentally weighted strategy prior to January 2005 implies that the strategy may have provided investors protection from stock market bubbles. Total and excess s: Table C3 in Appendix C shows that the fundamentally weighted strategy would have had an annualized excess of 3.2% relative to the cap-weighted strategy. Furthermore, Tables C5 and C7 show that the fundamentally weighted strategy would have had higher annualized s than that of the cap-weighted strategy both before and after January 2005. Tables C2 and C4 show that the fundamentally weighted strategy would have outperformed its cap-weighted counterpart in all calendar years shown except 1998, 2011, 2012, 2015 and YTD 2017. Tracking error: As shown in Table C3, the tracking error between the two strategies would have been significant, at 3.8%, implying that the two strategies would have had significantly different styles (betas) and/or industry exposures. Therefore, we believe that having exposures to both strategies may help investors improve their style diversification. Sharpe and information ratios: Table C1 along with Tables C5 and C7 show that the fundamentally weighted strategy would have had a higher Sharpe Ratio than that of the cap-weighted strategy. As shown in Table C3, combining a fundamentally weighted strategy with a cap-weighted strategy in a portfolio would have resulted in an Information Ratio of around 0.84, which we would consider a respectable risk-adjusted excess. 12 Enhancing equity portfolio diversification with fundamentally weighted strategies For Institutional Use Only

Portfolio allocation: International Large-Cap Equities In our analysis of the international developed ex-u.s. large-cap equities asset class, we observed that whereas the two strategies would have had similar volatilities, the fundamentally weighted strategy would have had a clear maximum drawdown advantage. Because of the similar volatilities, then, for the absolute- international large-cap equity investor the data suggests a minimum 50% allocation to a fundamentally weighted strategy. At the other extreme, due to the drawdown and excess advantages of the fundamentally weighted strategy, the data suggests a maximum allocation of 75%. For the benchmark-conscious investor concerned with tracking error, however, data suggests a lower allocation. Following the rationale and calculation outlined under U.S. large-cap equities, the median realized tracking error of the active funds in Morningstar s Foreign Large Blend Category, which uses the MSCI EAFE Index as its benchmark, as of September 2017 was 3.8%. As before, we applied half that average 1.9%. Interpolating the tracking error estimations in Table C3 implies that a tracking error of 1.9% would have resulted from an approximate fundamentally weighted strategy allocation of 42%. However, given the nature of fundamental index performance and relatively low tracking error we think keeping a maximum 50% allocation to a fundamentally weighted strategy for benchmark-conscious international large-cap equity investors makes the most sense. For Institutional Use Only Enhancing equity portfolio diversification with fundamentally weighted strategies 13

International Small-Cap Equities We applied the same methodology and process previously described to the international developed ex-u.s. small-cap equity asset class, using the MSCI World ex-usa Small Cap Index as a surrogate for the cap-weighted strategy and the Russell RAFI Developed ex-us Small Company Index as a surrogate for the fundamentally weighted strategy. Tables similar to those presented for the previous two asset classes can be found in Appendix D. Note that the analysis period for this asset class differs from the others discussed in this paper because data was not available for the cap-weighted strategy prior to December 1998. The following summarizes our findings: Risk: Table D1 shows volatility of the fundamentally weighted strategy would have been lower than that of the cap-weighted strategy. The same table shows that maximum drawdown would have been better in the fundamentally weighted strategy. As shown in Tables D5 and D7, prior to January 2005, maximum drawdowns for the cap-weighted and fundamentally weighted strategies would have been 28.8% and 20.1%, respectively; after January 2005, they would have been much higher, at 60.2% and 53.3%, respectively. Total and excess s: Table D3 shows an annualized excess of 2.1% for the fundamentally weighted strategy smaller than the other asset classes discussed thus far. Tables D2 and D4 show that the fundamentally weighted strategy would have outperformed the cap-weighted strategy in all calendar years except 2005, 2009, 2010 and YTD 2017 with the underperformance roughly 5% for two consecutive years 2009 and 2010. Such underperformance would be a concern for most investors, particularly benchmark-sensitive ones. Tracking error: As shown in Table D3, the tracking error between the two strategies would have been approximately 3.8%. This implies that the two would have differed notably in their characteristics and exposures to different market styles (betas). As with previously discussed asset classes, therefore, we believe that combining these two strategies in a portfolio may help investors improve their style diversification. Sharpe and information ratios: As shown in Table D1, along with Tables D5 and D7, the fundamentally weighted strategy would have had a higher Sharpe Ratio than that of the cap-weighted strategy both before and after January 2005. As shown in Table D3, combining a fundamentally weighted strategy with a cap-weighted strategy in a portfolio for purposes of this analysis would have resulted in an Information Ratio of 0.54. 14 Enhancing equity portfolio diversification with fundamentally weighted strategies For Institutional Use Only

Portfolio allocation: International Small-Cap Equities Based on our analysis, it appears that in the international small-cap equities asset class, combining a fundamentally weighted strategy with a cap-weighted strategy in a portfolio would have benefited investors through both a better maximum drawdown and lower volatility. In terms of performance, the fundamentally weighted strategy would have outperformed the cap-weighted one, although its excess s would have been lower than in other asset classes previously discussed. For an absolute investor, the slightly higher s and lower volatility suggest that a large allocation to a fundamentally weighted strategy may provide a valuable risk-reduction benefit. Therefore, for the absolute- international small-cap equity investor, the data suggests an allocation to a fundamentally weighted strategy of between 50% and 80%. For the benchmark-conscious investor concerned with tracking error, however, the data suggests a lower allocation, keeping two things in mind: (1) that alpha would not have been as large as with the other asset classes discussed, and (2) that the fundamentally weighted strategy would have significantly underperformed the cap-weighted one for two consecutive years. We note that for these two years (2009 and 2010), both strategies would have been up significantly (Table D2), and the cap-weighted strategy s outperformance might suggest that momentum would have been a meaningful driver. A similar story can be seen YTD 2017: both cap-weighted and fundamentally weighted strategies would have been up significantly at 24.7% and 22.7% respectively. We expect that, by its design, a fundamentally weighted strategy will underperform a cap-weighted strategy in momentum-driven markets.an absolute- investor is likely to be more accepting of this given the potential diversification benefit that the fundamentally weighted strategy provides when a momentum-driven bubble ultimately bursts. Benchmark-conscious investors would likely be less tolerant in general. As far as tracking error, we followed the same rationale and calculation outlined under U.S. large-cap equities. The median realized tracking error of the active funds in Morningstar s Foreign Small Blend Category, which uses the MSCI World ex USA Small Cap Index as its benchmark, as of September 2017 was 3.8%. As before, we applied half that average 1.9%. Interpolating the tracking error estimations in Table D3 implies that such a tracking error would have resulted from an approximate fundamentally weighted strategy allocation of 45%. However, given our argument above and information ratio of roughly 0.54, for benchmark-conscious international smallcap equity investors, the data suggests a maximum 30% allocation to a fundamentally weighted strategy. For Institutional Use Only Enhancing equity portfolio diversification with fundamentally weighted strategies 15

Emerging Markets Equities We applied the same methodology and process previously described to the emerging markets equity asset class, using the MSCI Emerging Markets Index as a surrogate for the cap-weighted strategy and the Russell RAFI Emerging Markets Large Company Index as a surrogate for the fundamentally weighted strategy. Tables similar to those presented for the previous three asset classes can be found in Appendix E. The following summarizes our findings: Risk: Table E1 along with Tables E5 and E7 in Appendix E show that volatilities for the two strategies would have been a bit higher for the fundamentally weighted strategy, both for the full period and for the two sub-periods. Maximum drawdown numbers in these tables show that the fundamentally weighted strategy would have had slightly better drawdown numbers: Prior to January 2005, maximum drawdowns for the cap-weighted and fundamentally weighted strategies would have been 56% and -49.8%, respectively; after January 2005, they would have been 61.4% and -58.6%, respectively. Total and excess s: Table E3 shows that over the full period studied, the fundamentally weighted strategy would have outperformed the cap-weighted strategy by 5.0%. However, as shown in Tables E6 and E8 representing the two subperiods, we see that most of this outperformance would have occurred during the earlier period, during which the excess would have been 9.2%. Tracking error: As shown in Table E3, the tracking error between the two strategies would have been 7.2% larger than with other asset classes previously discussed. We note, however, that most of it would have occurred primarily in four years 1998, 1999, 2003 and 2016 when the fundamentally weighted strategy would have significantly outperformed the cap-weighted one: by 28.6%, 16%, 27.9% and 22%, respectively (as shown in Table E4). Sharpe ratio: As shown in Table E1 as well as in Tables E5 and E7, the Sharpe Ratio for the fundamentally weighted strategy would have been higher than that of the cap-weighted strategy, particularly prior to 2005. 16 Enhancing equity portfolio diversification with fundamentally weighted strategies For Institutional Use Only

Portfolio allocation: Emerging Markets Equities Based on our analysis in the tables shown in Appendix E, it appears that in the emerging markets equities asset class, combining a fundamentally weighted strategy with a capweighted strategy in a portfolio may benefit investors. Given the similar total risk profiles of the two strategies, along with the fundamentally weighted strategy s slightly better maximum drawdown and its outperformance, for the absolute- emerging markets equity investor, the data suggests an allocation to a fundamentally weighted strategy of between 50% and 80%. For the benchmark-conscious investor concerned with tracking error, however, the data suggests a lower allocation. Following the rationale and calculation outlined under U.S. large-cap equities, the median realized tracking error of the active funds in Morningstar s Emerging Markets Blend Category, which uses the MSCI Emerging Markets Index as its benchmark, as of September 2017 was 4.5%. As before, we applied half that average 2.3%. Interpolating the tracking error estimations in Table E3 implies that such a tracking error would have resulted from an approximate fundamentally weighted strategy allocation of 23%. However, data suggests a slightly higher allocation for two reasons: (1) as explained above, the large tracking error would have been primarily due to significant outperformance in a few years, and (2) the Information Ratio of around 0.7 provided by the addition of the fundamentally weighted strategy is favorable difficult even for actively managed funds to achieve. For benchmark-conscious emerging markets equity investors, therefore, data suggests a maximum 40% allocation to a fundamentally weighted strategy. For Institutional Use Only Enhancing equity portfolio diversification with fundamentally weighted strategies 17

Next steps and further research Since the initial paper was written, we explored some drivers behind the performance of fundamentally weighted and cap-weighted strategies, focusing on U.S. large-cap and U.S. small-cap equities. The research shows that value is not the only driver of performance, other factors have clear influence on performance as well.* Conclusion In this paper, we analyzed and presented an asset allocation framework designed to help diversify equity allocation using fundamentally weighted strategies in conjunction with cap-weighted strategies across five asset classes. Generally speaking, our results suggest the following: ly weighted strategies can serve as a complement to traditional capitalizationweighted strategies. Combining fundamentally weighted strategies with cap-weighted strategies may improve a portfolio s risk- characteristics. ly weighted strategies have historically provided the strongest s and the greatest diversification benefits immediately after a stock market bubble bursts. Our quantitative and qualitative analysis concludes that allocation to a fundamentally weighted strategy might differ for each of the five asset classes we analyzed, as summarized below. As a rule of thumb, however, the data offers the following guidelines: For absolute- investors who are not concerned about comparison against a benchmark, an allocation to a fundamentally weighted strategy of between 50% and 80%. For benchmark-conscious investors who are concerned with tracking error, an allocation to a fundamentally weighted strategy of up to 50%. Summary of allocations by asset class Asset class U.S. Large-Cap Equities U.S. Small-Cap Equities International Large-Cap Equities International Small-Cap Equities Emerging Markets Equities ly weighted strategy allocation ranges For absolute investors For benchmarkconscious investors 50% to 70% 0% to 35% 50% to 80% 0% to 35% 50% to 75% 0% to 50% 50% to 80% 0% to 30% 50% to 80% 0% to 40% The allocation ranges presented herein are based on our interpretations of the metrics provided in the body of this paper and in the Appendices under various market conditions, as well as our acknowledgement of the advantages and considerations of the two strategies as presented at the beginning of this paper. Although performance does not guarantee future performance, the disciplined and well-defined portfolio construction methodologies for both cap-weighted and fundamentally weighted strategies give us greater confidence that the diversification benefits of adding exposure to fundamentally weighted strategies may be particularly valuable immediately prior to and after the bursting of stock market bubbles. *See Understanding the Performance Drivers Behind ly Weighted Strategies at https://www.schwabfunds.com/public/file/p-8299708. 18 Enhancing equity portfolio diversification with fundamentally weighted strategies For Institutional Use Only

Appendix A: Supplemental tables for U.S. Large-Cap Equities analysis Period from August 1996 December 2004 Table A1: U.S. Large-Cap Equities Total analysis (for absolute- investors): August 1996 December 2004 S&P 500 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Annualized 9.4% 9.9% 10.4% 10.8% 11.3% 11.7% 12.1% 12.6% 13.0% 13.3% 13.7% Annualized standard deviation 16.8% 16.5% 16.2% 15.9% 15.6% 15.4% 15.2% 15.0% 14.9% 14.8% 14.7% Sharpe ratio 0.56 0.60 0.64 0.68 0.72 0.76 0.80 0.84 0.87 0.90 0.93 Maximum drawdown -44.7% -42.2% -39.6% -36.9% -34.1% -31.2% -28.4% -26.7% -26.4% -26.2% -26.0% Table A2: U.S. Large-Cap Equities Excess analysis (for benchmark-conscious investors): August 1996 December 2004 Annualized excess S&P 500 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 0.0% 0.5% 1.0% 1.4% 1.9% 2.3% 2.7% 3.1% 3.5% 3.9% 4.3% Tracking error 0.0% 0.7% 1.4% 2.1% 2.9% 3.6% 4.3% 5.1% 5.8% 6.6% 7.4% Information ratio 0.69 0.68 0.67 0.66 0.64 0.63 0.62 0.61 0.60 0.58 For Institutional Use Only Enhancing equity portfolio diversification with fundamentally weighted strategies 19

Period from January 2005 September 2017 Table A3: U.S. Large-Cap Equities Total analysis (for absolute- investors): January 2005 September 2017 S&P 500 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Annualized 8.4% 8.5% 8.6% 8.7% 8.8% 8.9% 9.0% 9.1% 9.2% 9.3% 9.4% Annualized standard deviation 13.8% 13.9% 14.0% 14.0% 14.1% 14.2% 14.2% 14.3% 14.4% 14.5% 14.6% Sharpe ratio 0.61 0.61 0.62 0.62 0.63 0.63 0.63 0.64 0.64 0.64 0.65 Maximum drawdown -50.9% -50.9% -50.8% -50.7% -50.7% -50.6% -50.5% -50.5% -50.4% -50.4% -50.5% Table A4: U.S. Large-Cap Equities Excess analysis (for benchmark-conscious investors): January 2005 September 2017 Annualized excess S&P 500 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 0.0% 0.1% 0.2% 0.3% 0.4% 0.5% 0.6% 0.7% 0.8% 0.9% 1.0% Tracking error 0.0% 0.3% 0.5% 0.8% 1.1% 1.3% 1.6% 1.8% 2.1% 2.3% 2.5% Information ratio 0.38 0.39 0.39 0.39 0.39 0.39 0.39 0.39 0.40 0.40 20 Enhancing equity portfolio diversification with fundamentally weighted strategies For Institutional Use Only

Appendix B: Tables for U.S. Small-Cap Equities analysis Period from August 1996 September 2017 Table B1: U.S. Small-Cap Equities Total analysis (for absolute- Investors): August 1996 September 2017 Annualized Annualized standard deviation R2K 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 8.8% 9.5% 10.1% 10.6% 11.1% 11.5% 12.0% 12.3% 12.7% 13.1% 13.4% 19.6% 19.4% 19.1% 18.9% 18.7% 18.6% 18.5% 18.4% 18.3% 18.2% 18.2% Sharpe ratio 0.45 0.49 0.53 0.56 0.59 0.62 0.65 0.67 0.70 0.72 0.73 Maximum drawdown -52.9% -53.1% -53.3% -53.4% -53.6% -53.7% -53.8% -53.9% -54.0% -54.0% -54.1% 1 year 20.7% 20.3% 19.9% 19.6% 19.3% 19.1% 18.9% 18.8% 18.7% 18.5% 18.4% 3 year 12.2% 12.0% 11.8% 11.6% 11.5% 11.4% 11.4% 11.3% 11.2% 11.2% 11.1% 5 year 13.8% 14.0% 14.2% 14.3% 14.4% 14.5% 14.6% 14.6% 14.7% 14.7% 14.8% Table B2: U.S. Small-Cap Equities Calendar-year total s (for absolute- investors): August 1996 September 2017 R2K 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 1996* 9.3% 9.6% 9.9% 10.2% 10.5% 10.8% 11.0% 11.3% 11.6% 11.9% 12.2% 1997 22.4% 23.0% 23.7% 24.3% 24.9% 25.6% 26.2% 26.8% 27.5% 28.1% 28.7% 1998-2.5% -2.2% -1.9% -1.5% -1.2% -0.9% -0.6% -0.3% 0.0% 0.3% 0.6% 1999 21.3% 19.8% 18.4% 17.0% 15.6% 14.2% 12.9% 11.6% 10.4% 9.1% 7.9% 2000-3.0% -0.8% 1.5% 3.8% 6.1% 8.4% 10.7% 12.9% 15.2% 17.5% 19.8% 2001 2.5% 4.7% 6.9% 8.9% 10.9% 12.8% 14.6% 16.3% 18.0% 19.6% 21.1% 2002-20.5% -18.8% -17.3% -15.9% -14.6% -13.4% -12.3% -11.3% -10.3% -9.4% -8.6% 2003 47.3% 47.5% 47.7% 47.9% 48.1% 48.2% 48.4% 48.5% 48.6% 48.7% 48.8% 2004 18.3% 19.1% 19.8% 20.4% 20.9% 21.4% 21.8% 22.2% 22.5% 22.9% 23.2% 2005 4.6% 5.5% 6.3% 7.0% 7.7% 8.2% 8.7% 9.2% 9.6% 10.0% 10.3% 2006 18.4% 18.5% 18.6% 18.7% 18.7% 18.8% 18.9% 18.9% 19.0% 19.0% 19.0% 2007-1.6% -1.4% -1.3% -1.1% -1.0% -0.9% -0.8% -0.8% -0.7% -0.6% -0.6% 2008-33.8% -33.9% -34.1% -34.2% -34.3% -34.4% -34.4% -34.5% -34.6% -34.6% -34.7% 2009 27.2% 31.2% 34.6% 37.5% 40.1% 42.3% 44.3% 46.1% 47.7% 49.2% 50.5% 2010 26.9% 27.8% 28.5% 29.1% 29.6% 30.0% 30.4% 30.7% 31.0% 31.3% 31.5% 2011-4.2% -4.1% -4.0% -3.9% -3.8% -3.8% -3.7% -3.7% -3.7% -3.6% -3.6% 2012 16.4% 16.9% 17.3% 17.6% 17.9% 18.1% 18.3% 18.5% 18.6% 18.8% 18.9% 2013 38.8% 38.9% 39.0% 39.1% 39.2% 39.2% 39.3% 39.3% 39.4% 39.4% 39.4% 2014 4.9% 5.6% 6.1% 6.5% 6.9% 7.2% 7.4% 7.7% 7.9% 8.0% 8.2% 2015-4.4% -4.5% -4.6% -4.6% -4.7% -4.7% -4.7% -4.8% -4.8% -4.8% -4.8% 2016 21.3% 21.8% 22.2% 22.6% 22.9% 23.1% 23.3% 23.4% 23.6% 23.7% 23.8% 2017* 10.9% 10.2% 9.6% 9.2% 8.8% 8.5% 8.2% 8.0% 7.8% 7.6% 7.5% * Returns for 1996 and 2017 are partial-year s For Institutional Use Only Enhancing equity portfolio diversification with fundamentally weighted strategies 21