In a typical equity tactical country allocation strategy, forecasts of

Research Global Equity Country Allocation: An Application of Factor Investing Timotheos Angelidis and Nikolaos Tessaromatis Timotheos Angelidis is assistant professor of finance, Department of Economics, University of Peloponnese, Tripoli, Greece. Nikolaos Tessaromatis is professor of finance, EDHEC Business School and EDHEC Risk Institute, Nice, France. Under the paradigm of factor investing, we create a global factor allocation strategy using country indexes and portfolio construction methodologies that are robust to estimation error. Implementable through exchange-traded funds or index futures, a portfolio based on country indexes with favorable factor exposures significantly outperforms, both economically and statistically, the world market capitalization portfolio. The outperformance remains significant after taking into account transaction costs, alternative portfolio construction methodologies, and tracking error constraints. From a practical investment perspective, country-based factor portfolios offer a viable alternative implementation of factor investing in a world of illiquidity, transaction costs, and capacity constraints. Disclosure: The authors report no conflicts of interest. CE Credits: 1 In a typical equity tactical country allocation strategy, forecasts of country returns based on financial variables are combined with a portfolio construction rule to create an investment strategy that aims to outperform the world market capitalization portfolio. Such variables as the price-to-earnings ratio, dividend-to-price ratio, shortterm interest rates, term and default premiums, and price momentum are commonly used indicators of future country equity premiums (Hjalmarsson 2010; Rapach and Zhou 2013; Neely, Rapach, Tu, and Zhou 2014). In this article, we apply factor-investing principles to create a global equity portfolio with targeted exposures to four factors value, small capitalization (size), high momentum, and low risk using country index funds instead of individual stocks to produce a better risk return trade-off than the capitalization-weighted world market portfolio. The objectives of our proposed global equity strategy are similar to those of the typical global tactical country equity allocation strategies used by institutional investors. Factor investing represents an alternative and supplementary approach to existing investment practice. The factor-based approach assumes that returns are driven by a small number of investment factors that provide long-term premiums to investors. 1 Academic research based on individual stocks supports the view that exposures to the small-cap, value, high-momentum, and low-risk factors are compensated with positive risk premiums (Ang, Hodrick, Xing, and Zhang 2006, 2009; Fama and French 2012; Frazzini and Pedersen 2014). 2 Evidence on other asset classes provides further support for the idea of factor investing (Asness, Moskowitz, and Pedersen 2013). The idea of building a globally diversified portfolio that combines the world market portfolio with style funds that capture factor premiums is consistent with institutional investors strong interest in smart beta products. 3 Implementing academic research on factor portfolio construction is challenging. Academic factor research pays little attention to the investability of factor portfolios, ignoring such issues as stock liquidity, transaction costs, turnover, and risk constraints all of which portfolio managers face in practice. Implementation constraints are likely to cause Volume 73 Number 4 2017 CFA Institute. All rights reserved. 55

significant performance differences between pure academic factor portfolios and real-life investable stock-based factor portfolios offered by commercial indexes. Creating global factor portfolios using country indexes implemented through country exchangetraded funds (ETFs), stock index futures, or equity swaps is an alternative factor portfolio construction methodology that can produce portfolios that perform on par with stock-based factor portfolios but that are easier to manage and more liquid and have more capacity and lower transaction costs. 4 The disadvantage of using countries instead of individual stocks is that the significantly smaller number of countries reduces the cross-sectional variation in available factor exposures and the ability to fully capture factor premiums. Individual stocks should offer greater efficiency in harvesting factor returns compared with alternatives, including country-based factors. But in the real world of trading costs, capacity constraints, and liquidity issues, country-based factors might prove a viable alternative. There has been some research on the use of country or sector funds to create global investment strategies. Asness, Liew, and Stevens (1997) found that the book-to-price ratio, size, and momentum of country indexes explain the cross section of expected country returns. Keppler and Encinosa (2011) found evidence suggesting that small-cap markets outperform large-cap markets. Desrosiers, L Her, and Plante (2004) examined the performance of relative value and relative strength (momentum) global investment strategies based on country indexes in the 18 largest stock markets. Leclerc, L Her, Mouakhar, and Savaria (2013) used US sector indexes to create alternative equity portfolios that had better performance statistics than the cap-weighted equity benchmark over 1964 2011. Angelidis and Tessaromatis (2014) created cap-weighted factor portfolios on the basis of developed-country indexes and showed the superiority of regime-based portfolio construction methodologies. Li and Pritamani (2015) reported country size and momentum effects for both emerging markets and frontier markets. In this article, we extend the literature on countrybased global factors in several directions. First, we create global equity factors using countries and different portfolio construction (weighting) methodologies and compare their performance with that of the standard cap-weighted schemes used in practice. Using non-market-cap weighting schemes to target exposure to a rewarded factor creates portfolios that are both factor tilted and well diversified (Amenc, Goltz, Lodh, and Martellini 2014). Second, we extend the universe of countries used to create global factor portfolios to include emerging markets. The inclusion of emerging markets increases the number of available assets, allows greater latitude in factor portfolio construction and could potentially improve the risk return performance of factor portfolios. Third, we combine single-factor portfolios to create a global multifactor portfolio using alternative portfolio construction methodologies to control for estimation error. Combining single-factor portfolios in a multifactor portfolio reduces cyclicality in the performance of the single-factor portfolios when correlations between the factors are imperfect and provides opportunities for turnover reduction from the natural crossing effects of rebalancing many portfolios. Our fourth contribution is to compare the performance of stock-based factor portfolios such as the global factor portfolios of Fama and French (2012) and the investable factor indexes used in practice with that of the country-based portfolios that we present in this article. In particular, we assess whether country-based factor premiums are proxies for factor premiums based on individual stocks. If so, country-based portfolios would offer another way to access global factor equity premiums, implemented through fewer and more liquid assets. Alternatively, country-based factor premiums could represent rewards to new factors that improve the investor s mean variance set. The empirical evidence that we present in this article supports a number of conclusions. First, countrybased value, small-cap, high-momentum, and low-risk portfolios have better Sharpe ratios and, in most cases, statistically significant returns in excess of the world market portfolio s. Second, extending the universe of countries used to create global factor portfolios to include emerging markets raises the Sharpe ratios and alphas of all factor portfolios evidence of increased efficiency in harvesting factor returns. Third, the Sharpe ratio of global multifactor portfolios created with various weighting schemes is higher than and statistically significantly different from that of the world market portfolio. Of interest to institutional investors operating under tracking error constraints, the outperformance of the global factor portfolio is preserved for low-tracking-risk portfolios (a tracking error target of 2% a year). The weighting scheme used to combine the four global factors makes little difference to performance. 56 cfapubs.org Fourth Quarter 2017

Global Equity Country Allocation Fourth, country-based factor portfolios have higher returns and volatility but very similar returns to risk (Sharpe ratios) compared with the Fama French stock-based factor portfolios or the MSCI investable indexes. Country-based factor portfolios represent a viable alternative to stock-based factor portfolios. Data and Factor Portfolio Construction Methodology In our study, we used country dollar total return indexes from MSCI for 23 developed markets and 21 emerging markets over July 1980 December 2015 (426 monthly observations). 5 Either ETFs or futures contracts exist for all markets, making the creation of global factor portfolios feasible. For the world market portfolio, we used the MSCI All-Country World Index (ACWI). 6 We used the trading spread of BlackRock s ETFs and Global X s ETFs as an estimate of trading costs (see Appendix A for a list of the country ETFs that we used to estimate trading costs). To construct the global value portfolios, we ranked at the end of June in year t all countries by a composite valuation indicator combining a country s price-toearnings, price-to-book, and price-to-cash-flow ratios along with dividend yield. The valuation metrics that we used are from Datastream and refer to valuation ratios for each of the Datastream country indexes. Using a composite valuation indicator reduces the measurement error of individual value indicators and can produce value portfolios with superior risk return trade-offs (see Asness, Frazzini, Israel, and Moskowitz 2015). 7 We formed three portfolios, each containing one-third of the 44 countries, and calculated the monthly returns over the next 12 months. The small-cap portfolio contained the third of all countries with the lowest capitalization, with country capitalization measured as the total stock market capitalization of the particular Datastream country index. For every month, we calculated the momentum for month t as the cumulative monthly returns for t 2 to t 12 and formed three portfolios containing, in equal numbers, the highest-, medium-, and lowest-momentum countries, respectively. Finally, for every month, we estimated the country beta against the world index, using a rolling sample of 60 monthly observations, and created three portfolios containing the highest-, medium-, and lowest-beta countries. Rebalancing was annual for the value and small-cap portfolios and monthly for the high-momentum and low-beta portfolios. In the first stage of the factor portfolio construction process, we chose the countries with the highest factor exposure. In the second stage, our objective in the single- and multifactor portfolio construction process was to create mean variance-efficient factor portfolios in the presence of estimation risk. In particular, we created factor portfolios using in addition to capitalization weights equal (EW), inverse variance (IV), minimum variance (MinVar), and maximum diversification portfolio (MDP) weights. As discussed in Lee (2011) and Hallerbach (2015), among others, these portfolio construction methodologies used by purveyors of smart beta strategies are equivalent to mean variance-optimal portfolios under very specific assumptions about expected returns, variances, and correlations. Reducing the number of input estimates reduces estimation risk but creates information loss and suboptimal portfolios as compared with mean variance-optimal portfolios free of estimation risk (optimality risk). Alternative portfolio construction methodologies represent different trade-offs between estimation risk and optimality risk (Martellini, Milhau, and Tarelli 2014), but there is little agreement about which portfolio construction methodology is superior. Capitalization weighting (CW) is the most commonly used index construction methodology, despite its well-known shortcomings of excessive concentration and inferior risk-adjusted performance compared with even simple portfolio-weighting rules. From a practical perspective, however, CW indexes represent highly investable strategies, with low turnover and high liquidity capacity. The EW portfolio invests proportionally in each of the countries; because it does not use estimates of return or risk, it is, by definition, free of estimation risk. The EW portfolio is a mean variance-optimal portfolio only if expected returns, variances, and correlations are assumed to be the same for all assets. The IV portfolio rule relies only on variance and assumes that correlations between assets are zero. Kirby and Ostdiek (2012) showed that IV portfolios outperform both equalweighted and cap-weighted portfolios. IV weights are calculated as follows: h 1 2 it wit = σ, i = 1, 2,, N, (1) h N Σ 1 i= 1 2 σit Volume 73 Number 4 cfapubs.org 57

where σ it is the estimated volatility of country i based on 60 monthly observations and h 0 is a tuning parameter that adjusts the weights to volatility changes. 8 The IV weighting scheme is mean varianceoptimal if expected returns are equal, correlations between assets are zero, and h = 1. The fourth portfolio construction rule concerns the short sale constrained MinVar portfolio. MinVar portfolios require estimates of variances and covariances but not of expected returns, which are far more difficult to estimate (Merton 1980). Clarke, de Silva, and Thorley (2006) and DeMiguel, Garlappi, and Uppal (2009), among others, showed that the minimum-variance strategy outperforms cap-weighted indexes. The weights of the minimumvariance portfolio are defined as follows: min w w T w, st T Σ.. 1 w = 1 and w i 0, i = 1, 2,, N. (2) MinVar portfolios are mean variance-optimal if expected returns are assumed to be equal. 9 The final weighting scheme that we considered in our study is MDP, proposed by Choueifaty and Coignard (2008), which maximizes the diversification ratio as T w T w Σw and wi 0, i = 1, 2,, N, (3) σ1 where = σ 2. The numerator in Equation 3 is equal σn to portfolio volatility ignoring correlations; the denominator is portfolio volatility with correlations taken into account (diversification). The MDP portfolio is optimal if its assets all have the same Sharpe ratio. Choueifaty and Coignard (2008) showed that the MDP portfolio achieves performance statistics that are consistently better than those of the equal-weighted, minimumvariance, and cap-weighted portfolios. For both the minimum-variance portfolio and the maximum diversification portfolio, the estimates of variances and covariances are based on 60 monthly observations. Table 1 reports the percentage of months that the 44 markets are categorized as small cap, value, high momentum, or low beta over July 1980 December 2015. The data for 11 emerging markets are available since January 1988; for another 10 emerging markets, the database is complete by January 1995. Because some emerging markets have data for a shorter period than the full sample, the percentage of months a country is classified as a particular style covers the period for which data are available for that country. The average and the standard deviation of country returns (columns 1 and 2 of Table 1) are based on return data over January 1995 December 2015, the period for which we have data for all countries. The large-cap markets in the United States, Japan, and the United Kingdom have no participation in small-cap portfolios and almost none in value factor portfolios, but they have significant participation in high-momentum and low-beta portfolios. By definition, the small-cap portfolio consists mainly of emerging markets but also often includes the markets of Austria, Ireland, Israel, New Zealand, and Portugal. Exposure to the momentum factor is more evenly spread across countries; 16 of the 44 countries have an average beta lower than 1 (9 developed and 7 emerging). For equal-weighted portfolios, the average country weight (standard deviation) for the countries in the value, size, momentum, and beta portfolios is 8.11% (2.51%), 9.23% (3.73%), 8.23% (1.52%), and 8.89% (2.37%), respectively. Average weights are similar for the other weighting schemes but are significantly more volatile for the CW, MinVar, and MDP weighting methodologies. Portfolios based on equal and IV weights tend to be better diversified, in terms of country positions, than portfolios based on the other weighting schemes (see Table A3, available online at www.cfapubs.org/doi/ suppl/10.2469/faj.v73.n4.7). Global Single-Factor and Multifactor Portfolios In this section, we report performance statistics of global single-factor portfolios (value, small capitalization, high momentum, and low beta) based on the five alternative weighting schemes (CW, EW, IV, MinVar, MDP) described earlier. We also report performance statistics of global multifactor portfolios created as combinations of global single-factor portfolios using the EW, IV, MinVar, and MDP weighting schemes. The overall sample period is July 1980 December 2015. In our study, we evaluated portfolio performance using various performance criteria. To compare the risk-adjusted performances of two portfolios, we used the Sharpe ratio of portfolio i, SR i, defined as µ i rf SR i = σi, where µ i r f is the average excess 58 cfapubs.org Fourth Quarter 2017

Global Equity Country Allocation Table 1. Markets Descriptive Statistics and Percentage of Time a Market Is Included in Global Factor Portfolios Market Descriptive Statistics Value Size Momentum Beta Average Return Stand. Dev. % of Months % of Months % of Months % of Months Start Date Australia 10.62% 21.03% 17 0 27 27 Jul/80 Austria 5.56 25.79 40 86 46 75 Jul/80 Belgium 9.87 21.27 69 20 29 44 Jul/80 Canada 10.66 20.47 6 0 28 29 Jul/80 Denmark 14.64 19.93 11 31 20 68 Jul/80 Finland 14.77 32.35 32 39 46 1 Jan/88 France 9.21 20.59 49 0 33 8 Jul/80 Germany 9.86 23.17 31 0 30 35 Jul/80 Hong Kong 10.37 24.92 23 0 29 30 Jul/80 Ireland 5.34 22.16 21 75 40 30 Jan/88 Israel 10.80 23.01 52 100 45 60 Jan/93 Italy 7.37 23.95 49 3 46 25 Jul/80 Japan 2.18 18.13 3 0 44 48 Jul/80 Netherlands 9.57 20.45 63 0 19 19 Jul/80 New Zealand 8.72 21.82 18 100 35 58 Jan/88 Norway 10.20 26.65 54 43 30 2 Jul/80 Portugal 5.21 22.66 42 88 42 55 Jan/88 Singapore 7.10 25.43 6 17 32 22 Jul/80 Spain 12.00 24.42 59 0 34 3 Jul/80 Sweden 13.72 25.67 12 18 22 20 Jul/80 Switzerland 10.70 16.75 31 0 28 63 Jul/80 United Kingdom 7.55 15.93 20 0 30 46 Jul/80 United States 10.27 15.16 0 0 33 49 Jul/80 Brazil 12.74 37.06 81 0 37 1 Jan/88 Chile 6.78 23.02 27 50 32 50 Jan/88 China 7.44 34.06 9 13 47 13 Jan/93 Colombia 14.00 31.85 61 96 38 74 Jan/93 Czech Republic 12.73 28.15 81 100 29 47 Jan/95 Egypt 18.02 32.65 68 100 35 69 Jan/95 Greece 6.05 35.04 32 60 48 48 Jan/88 Hungary 16.11 37.11 62 100 43 3 Jan/95 India 11.58 29.97 13 0 34 47 Jan/93 Indonesia 13.84 43.86 4 65 33 31 Jan/88 South Korea 11.73 38.28 61 4 39 13 Jan/88 (continued) Volume 73 Number 4 cfapubs.org 59

Table 1. Markets Descriptive Statistics and Percentage of Time a Market Is Included in Global Factor Portfolios (continued) Market Descriptive Statistics Value Size Momentum Beta Average Return Stand. Dev. % of Months % of Months % of Months % of Months Start Date Malaysia 6.62 28.40 18 0 31 56 Jan/88 Mexico 13.04 27.57 25 11 21 11 Jan/88 Peru 14.84 30.13 55 100 27 52 Jan/93 Philippines 5.83 29.53 11 82 36 58 Jan/88 Poland 10.75 35.50 32 100 33 0 Jan/93 Russia 22.48 52.04 83 22 42 0 Jan/95 South Africa 9.63 26.76 26 0 22 4 Jan/93 Taiwan 5.32 27.60 14 0 40 38 Jan/88 Thailand 7.08 37.78 25 68 35 21 Jan/88 Turkey 20.54 50.61 75 75 43 15 Jan/88 Market 7.97% 15.53% Jul/80 Note: The sample period for factor characteristics is July 1980 December 2015; the sample period for average returns and standard deviations of country indexes is January 1995 December 2015. return of portfolio i and σ i is the standard deviation of portfolio returns. To test the hypothesis that the Sharpe ratios of two portfolios are equal, we used the procedure in Ledoit and Wolf (2008), with 5,000 bootstrap resamples and a block size of b = 5. The portfolio turnover required to not only create but also maintain the factor portfolios could be of critical importance in portfolio performance evaluation. We defined portfolio turnover as 1 T Turnover = 12 = 1 1 Σt Σ N i= 1 1 1 ( wit, + wit, ), T where w it, is the portfolio weight before rebalancing at time t + 1 and w it, +1 is the desired portfolio weight after rebalancing. The turnover measure considers inter-country but not intra-country turnover owing to stock deletions or additions under the assumption that the intra-country turnover of individual country indexes is similar to the turnover required to maintain the world market index. In our study, we proxied transaction costs with current estimates of transaction costs from country ETFs; we estimated portfolio turnover to calculate a portfolio s trading costs (TC), defined as ( ) 1 T TC = 12 = 1 1 Σt Σ N i= 1 wit, + 1 wit, Costi, T 1 where Cost i is half the spread of country i s ETF (obtained from BlackRock and Global X; Appendix A reports trading spreads of developed- and emergingmarket ETFs as of May 2015). TC reflects current estimates of spreads and is thus a good estimate of costs under current trading conditions but probably underestimates past trading costs. Most equity markets ETFs were created only recently, and spread data for most of the ETFs are unavailable for the period we studied. Global Single-Factor Portfolios. Panel A of Table 2 reports performance statistics 10 of value, small-cap, high-momentum, and low-beta portfolios constructed using the five weighting schemes described earlier. Over July 1980 December 2015, the world equity market portfolio had an average return of 10.64%, with a 15.14% standard deviation and a Sharpe ratio of 0.41. Small-cap, value, high-momentum, and low-beta portfolios achieve higher annual returns and have higher volatility than the world market portfolio. The risk return trade-off offered by the factor portfolios is consistently better than the Sharpe ratio of the market portfolio, ranging between 0.48 (high momentum, CW) and 0.84 (high momentum, MinVar), irrespective of the weighting scheme used. 60 cfapubs.org Fourth Quarter 2017

Global Equity Country Allocation Table 2. Descriptive Statistics of Country-Based Global Factor Portfolios, July 1980 December 2015 A. Performance statistics Weighting Scheme Average Return Volatility Sharpe Ratio Tracking Error Volatility Turnover Trading Costs Alpha Value portfolios Capitalization weighted 14.77% 19.46% 0.53 10.08% 82.48% 0.03% 4.13%* Equally weighted 16.91 19.85 0.63 11.56 117.38 0.12 6.27** Inverse variance weighted 14.93 18.07 0.58 9.26 113.34 0.10 4.29* Minimum variance weighted 16.05 16.63 0.70** 10.36 196.76 0.18 5.41** weighted 16.63 19.25 0.64 11.97 198.38 0.25 5.99* Growth portfolios Capitalization weighted 10.99% 18.17% 0.36 8.96% 30.01% 0.01% 0.35% Equally weighted 9.00 18.63 0.25 10.24 107.88 0.09 1.64 Inverse variance weighted 10.73 16.47 0.39 7.52 104.52 0.07 0.09 Minimum variance weighted 11.12 15.23 0.44 8.14 153.51 0.07 0.48 weighted 10.50 18.34 0.33 9.85 184.58 0.15 0.14 Small portfolios Capitalization weighted 15.09% 20.23% 0.53 12.78% 43.38% 0.05% 4.45% Equally weighted 16.38 20.04 0.60 13.03 83.50 0.13 5.74* Inverse variance weighted 14.32 17.84 0.56 10.23 81.04 0.11 3.68 Minimum variance weighted 13.86 17.38 0.55 12.03 154.34 0.22 3.22 weighted 16.24 18.74 0.63 12.28 163.30 0.28 5.60* Large portfolios Capitalization weighted 10.58% 15.42% 0.40 1.74% 11.96% 0.03% 0.06% Equally weighted 10.51 16.87 0.36 5.77 56.06 0.01 0.13 Inverse variance weighted 11.29 15.56 0.44 4.26 50.33 0.01 0.65 Minimum variance weighted 11.33 14.06 0.49 5.48 108.35 0.02 0.69 weighted 10.96 16.45 0.40 6.15 127.20 0.03 0.32 High-momentum portfolios Capitalization weighted 13.84% 19.61% 0.48 10.79% 150.25% 0.05% 3.20% Equally weighted 18.14 19.54 0.70* 11.59 496.22 0.39 7.50** Inverse variance weighted 17.50 18.02 0.73** 9.42 570.76 0.36 6.86** Minimum variance weighted 19.06 17.50 0.84** 10.26 778.82 0.46 8.42** weighted 18.50 19.28 0.73* 12.55 682.74 0.49 7.87** (continued) Volume 73 Number 4 cfapubs.org 61

Table 2. Descriptive Statistics of Country-Based Global Factor Portfolios, July 1980 December 2015 (continued) A. Performance statistics Weighting Scheme Average Return Volatility Sharpe Ratio Tracking Error Volatility Turnover Trading Costs Alpha Low-momentum portfolios Capitalization weighted 6.92% 19.92% 0.13 11.61% 142.79% 0.05% 3.72% Equally weighted 9.31 20.64 0.24 12.68 498.32 0.41 1.33 Inverse variance weighted 8.47 18.98 0.22 10.52 576.69 0.38 2.17 Minimum variance weighted 7.94 17.44 0.20 10.83 818.10 0.51 2.70 weighted 8.24 19.45 0.20 12.22 753.84 0.67 2.40 Low-beta portfolios Capitalization weighted 13.81% 16.27% 0.58 9.76% 168.09% 0.02% 3.17% Equally weighted 13.81 16.74 0.56 10.02 170.43 0.12 3.17 Inverse variance weighted 13.46 15.68 0.58 8.82 176.03 0.10 2.82 Minimum variance weighted 13.12 15.33 0.57 9.64 182.11 0.12 2.48 weighted 14.69 17.09 0.60 11.55 203.66 0.15 4.05 High-beta portfolios Capitalization weighted 10.28% 22.25% 0.26 11.23% 48.95% 0.02% 0.36% Equally weighted 12.44 21.72 0.37 11.43 179.42 0.13 1.80 Inverse variance weighted 11.83 20.84 0.36 9.98 206.03 0.14 1.19 Minimum variance weighted 10.74 20.75 0.31 9.77 489.98 0.28 0.10 weighted 13.23 22.71 0.39 13.05 407.83 0.33 2.60 Market portfolio Market 10.64% 15.14% 0.41 B. Correlation analysis Size Value Momentum Beta Size 1.00 Value 0.21 1.00 Momentum 0.04 0.08 1.00 Beta 0.10 0.12 0.18 1.00 *Significant at the 5% level. **Significant at the 1% level. 62 cfapubs.org Fourth Quarter 2017

Global Equity Country Allocation However, Sharpe ratio differences between the factor portfolios and the world market portfolio are statistically significant 11 only for the value (MinVar weighted) and high-momentum (except CW) portfolios. Nonmarket CW factor portfolio construction rules achieve better risk return trade-offs than cap-based factor portfolios. But when we tested whether there are statistically significant differences between Sharpe ratios across weighting schemes, we found no evidence of a superior factor portfolio weighting methodology (for detailed results, see Table A4, available online at www.cfapubs.org/doi/ suppl/10.2469/faj.v73.n4.7). The difference between factor and world market portfolio returns (alpha) is consistently positive and statistically significantly different from zero for most of the factor portfolios. Average alphas are economically significant, ranging between 2.48% (low beta, MinVar) and 8.42% (high momentum, MinVar). The tracking error of global single-factor portfolios against the world market portfolio is at the high end of active strategies used by institutional investors, ranging between 8.82% (low beta, IV) and 13.03% (small cap, EW). Turnover tends to be lower for the value, small-cap, and low-beta factors but significantly higher for the high-momentum portfolio across all construction methodologies. 12 With respect to the spreads of country ETFs and portfolio turnover, the annual two-way cost of trading is between 2 and 28 bps for the non-momentum portfolios and between 5 and 49 bps for the highmomentum portfolio. Table 2 also reports performance statistics of growth, large-cap, low-momentum, and high-beta portfolios constructed using the five weighting schemes. In all cases, the bottom factor portfolios underperform the top portfolios. On average, the value, small-cap, high-momentum, and low-beta portfolios have 108% higher Sharpe ratios than the corresponding bottom portfolios. With a few exceptions, the market portfolio provides a better risk return trade-off than the bottom factor portfolios. Global Multifactor Portfolios. Given the benefits of single-factor portfolio investing compared with the world market portfolio, it is natural to examine whether combining single-factor portfolios produces further benefits related to diversification. Because all portfolios are exposed to market returns, we can calculate the corresponding correlations of long short factor portfolio returns. The average correlation between portfolios of the various factors and weighting schemes is 0.05 (Panel B of Table 2), suggesting potentially significant diversification benefits if they were combined in a multifactor portfolio. We can create global factor portfolios by combining single-factor portfolios using the four construction methodologies (EW, IV, MinVar, MDP) presented earlier. 13 Assuming monthly rebalancing, each construction methodology combines single-factor portfolios (value, small cap, high momentum, and low beta) based on alternative (CW, EW, IV, MinVar, and MDP) weighting methodologies to deliver the multifactor portfolios (20 altogether). The multifactor portfolios invest in 23 countries at the end of 1990, 33 countries at the end of 2000, and 34 countries at the end of 2015. The average weight of a country in the multifactor portfolio is 3.44%, with a standard deviation of 0.92%. Multifactor portfolios tend to be well diversified with respect to country positions. The total global multifactor portfolio turnover is calculated by adding all the underlying country positions, thus exploiting to the full the natural opportunities available across single-factor portfolios and countries. Global multifactor portfolio turnover considers transactions associated with monthly (1) single-factor portfolio revisions and (2) global multifactor portfolio rebalancing. Performance statistics of the global multifactor portfolios are reported in Table 3, covering July 1980 December 2015, when the average return of the world market portfolio was 10.64%, its volatility 15.14%, and its Sharpe ratio 0.41. Regardless of the weighting scheme, the Sharpe ratios of most of the global multifactor portfolios are higher than and statistically significantly different from the Sharpe ratio of the world market portfolio. This finding is in contrast to the statistically insignificant differences between the Sharpe ratios of single-factor portfolios and the Sharpe ratio of the world market portfolio (Table 2). Combining factors to create a global multifactor portfolio using single-factor portfolios created with CW, EW, IV, MinVar, and MDP improves the Sharpe ratio of the world market portfolio by 40%, 60%, 54%, 73%, and 67%, respectively. The statistical significance of the differences in Sharpe ratios reflects the diversification benefits of investing in a portfolio of global factors: a reduction in portfolio volatility without sacrificing returns. 14 The Sharpe ratio differences of multifactor portfolios based on different weighting schemes, however, are not statistically significant suggesting, as with single-factor portfolios, that the various portfolio construction methodologies produce very similar performances. Volume 73 Number 4 cfapubs.org 63

Table 3. Performance of Global Multifactor Portfolios, July 1980 December 2015 Performance Statistics Multifactor Portfolio Weighting Scheme Average Return Volatility Sharpe Ratio Tracking Error Turnover Trading Costs Alpha A. Single-factor portfolios based on capitalization weights Equally weighted 14.37% 17.11% 0.58* 7.26% 242.61% 0.09% 3.74%** Inverse variance weighted 13.96 16.38 0.58* 6.71 231.66 0.09 3.32** Minimum variance weighted 13.17 15.94 0.55 7.06 243.65 0.10 2.53 weighted 13.90 16.53 0.58* 7.09 245.39 0.10 3.26** B. Single-factor portfolios based on equal weights Equally weighted 16.31% 18.03% 0.66* 9.75% 204.71% 0.18% 5.67%** Inverse variance weighted 16.02 17.73 0.66* 9.59 198.52 0.17 5.38** Minimum variance weighted 15.63 17.42 0.65* 9.73 212.68 0.18 4.99* weighted 16.06 17.78 0.66* 9.40 246.99 0.21 5.42** C. Single-factor portfolios based on inverse-variance weights Equally weighted 15.05% 16.64% 0.64* 7.90% 213.31% 0.15% 4.41%** Inverse variance weighted 14.84 16.45 0.64* 7.85 199.75 0.15 4.21** Minimum variance weighted 13.77 16.03 0.59 7.84 204.53 0.14 3.13* weighted 15.27 16.83 0.65* 7.81 277.38 0.20 4.64** D. Single-factor portfolios based on minimum-variance weights Equally weighted 15.52% 15.49% 0.72** 8.51% 305.23% 0.15% 4.88%** Inverse variance weighted 15.28 15.33 0.71** 8.49 283.55 0.15 4.64** Minimum variance weighted 14.54 15.15 0.67** 8.47 287.96 0.14 3.90* weighted 15.84 15.57 0.74** 8.60 350.46 0.20 5.20** E. Single-factor portfolios based on maximum-diversification-portfolio weights Equally weighted 16.52% 17.44% 0.70* 10.20% 308.20% 0.29% 5.88%** Inverse variance weighted 16.34 17.25 0.69* 10.13 294.08 0.28 5.70** Minimum variance weighted 15.48 16.96 0.65* 10.07 319.60 0.31 4.84* weighted 16.65 17.41 0.70** 10.01 382.36 0.36 6.01** F. Market statistics Market 10.64% 15.14% 0.41 *Significant at the 5% level. **Significant at the 1% level. 64 cfapubs.org Fourth Quarter 2017

Global Equity Country Allocation Global multifactor portfolios strongly outperform the world market portfolio, producing annual alphas of between 2.53% (for CW single-factor portfolios combined using MinVar) and 6.01% (for MDP single-factor portfolios combined using MDP) all statistically different from zero except for the MinVar multifactor portfolio based on CW single-factor portfolios. The annual average alphas of multifactor portfolios based on CW, EW, IV, MinVar, and MDP single-factor portfolios are 3.21%, 5.37%, 4.10%, 4.66%, and 5.61%, respectively. All portfolios have significant tracking errors against the world market portfolio, which, when combined with the high alphas, produce information ratios (defined as the ratio of alpha to tracking error) of between 0.36 (CW single-factor portfolios combined using MinVar) and 0.60 (MinVar or MDP single-factor portfolios combined using MDP). Yearly average turnover is 263%, mainly owing to the high turnover of the momentumstyle portfolios, implying an average breakeven cost (the fixed transaction cost that makes the excess portfolio return over the market return equal to zero) of 1.78% and annual trading costs of 0.18%. Globally diversified factor portfolios generate substantial excess returns net of transaction costs. 15 Global multifactor portfolios under tracking error constraints. The global multifactor portfolios created by combining global single-factor portfolios have significant relative risk (tracking error) against the world market portfolio. Reflecting the current institutional practice of managing portfolios against benchmarks, we also constructed global multifactor portfolios under a 2% tracking error constraint against the world market portfolio. The tracking error constraint results in a less-than-optimal portfolio, with the performance difference between unconstrained and constrained portfolio returns reflecting the cost of the constraint. Table 4 reports statistics of the five global factor portfolios under a 2% tracking error constraint. As expected, benefits are reduced across portfolioweighting schemes but remain significant under the typical tracking error constraints imposed on investment portfolios in practice by institutional investors. Sharpe ratios of constrained multifactor portfolios are considerably lower than their unconstrained counterparts but remain statistically significantly different from the world market portfolio s Sharpe ratio for the majority of weighting schemes. There is a similar reduction in the active return to tracking error (information ratio) under the active risk constraint, but on average, the information ratio remains economically significant (0.43). The tracking error constraint drastically reduces portfolio turnover to an average of 76.66% across all weighting schemes, compared with the annual turnover without constraints of 262.63%. Transaction costs are also lower (an annual average of 0.05%), ranging between 0.03% and 0.08%. The combination of superior absolute risk-adjusted performance, strong active returns, low tracking error, and reasonable turnover makes global factor portfolios very attractive to institutional investors. Global multifactor portfolios based on developed markets only. Country ETFs and stock index futures in developed markets are more liquid and can be traded at larger volumes than their counterparts in some emerging markets. Creating factor portfolios using ETFs and equity index futures in developed markets should be easier and more cost effective. But the question is, Will excluding emerging markets from the investor s menu preserve the benefits of country-based factor portfolio construction? Table 5 reports performance statistics of global equally weighted value, small-cap, high-momentum, and low-beta factor portfolios based on various weighting schemes that combine countries from all countries and from developed countries. 16 We also combined the single-factor portfolios using alternative weighting schemes, but the results, consistent with Table 3, are very similar to those obtained using equal weights. The sample period for both datasets is July 1980 December 2015. Global multifactor portfolios based on factors for developed markets achieve higher returns (and volatility) than the world market portfolio. Their Sharpe ratios are consistently higher than the Sharpe ratio of the world market portfolio but are statistically significantly different only when minimum-variance weights are used to create the single-factor portfolios. Global factor portfolios based on developed countries outperform the world market portfolio consistently and statistically significantly, achieving an annual average alpha of 3.05% across all weighting schemes. The addition of emerging markets improves the performance of global multifactor portfolios. Return and risk are generally higher when all countries are used in the creation of the factor portfolios. The Sharpe ratios of all-country portfolios are higher than the Sharpe ratios of portfolios based on developed Volume 73 Number 4 cfapubs.org 65

Table 4. Performance of Global Multifactor Portfolios under a 2% Tracking Error Constraint, July 1980 December 2015 Performance Statistics Multifactor Portfolio Weighting Scheme Average Return Volatility Sharpe Ratio Tracking Error Turnover Trading Costs Alpha A. Single-factor portfolios based on capitalization weights Equally weighted 11.63% 15.49% 0.47* 2.03% 82.41% 0.03% 1.00%** Inverse variance weighted 11.59 15.33 0.47* 2.01 93.59 0.03 0.95* Minimum variance weighted 11.10 14.57 0.46 1.87 83.32 0.03 0.46 weighted 11.55 15.19 0.47* 2.04 102.15 0.04 0.91* B. Single-factor portfolios based on equal weights Equally weighted 11.65% 15.34% 0.47* 2.07% 53.47% 0.04% 1.01%* Inverse variance weighted 11.61 15.29 0.47* 2.08 53.94 0.04 0.97* Minimum variance weighted 11.41 14.99 0.47 2.07 55.52 0.04 0.77 weighted 11.58 15.26 0.47* 2.05 66.87 0.05 0.94* C. Single-factor portfolios based on inverse-variance weights Equally weighted 11.60% 15.20% 0.47* 2.03% 67.54% 0.05% 0.96%* Inverse variance weighted 11.54 15.15 0.47* 2.04 66.09 0.04 0.90* Minimum variance weighted 11.17 14.77 0.46 2.03 58.27 0.04 0.53 weighted 11.64 15.21 0.48* 2.02 90.17 0.06 1.00* D. Single-factor portfolios based on minimum-variance weights Equally weighted 11.53% 14.74% 0.48** 2.03% 88.40% 0.05% 0.89%* Inverse variance weighted 11.48 14.69 0.48** 2.05 85.61 0.04 0.85* Minimum variance weighted 11.22 14.50 0.47* 2.09 72.29 0.04 0.58 weighted 11.59 14.81 0.49** 2.07 97.86 0.06 0.96* E. Single-factor portfolios based on maximum-diversification-portfolio weights Equally weighted 11.63% 15.10% 0.48* 2.06% 72.73% 0.06% 0.99%* Inverse variance weighted 11.61 15.06 0.48* 2.08 70.57 0.06 0.97* Minimum variance weighted 11.65 14.90 0.49* 2.16 78.14 0.06 1.01* weighted 11.71 15.10 0.49* 2.05 94.32 0.08 1.07** F. Market statistics Market 10.64% 15.14% 0.41 *Significant at the 5% level. **Significant at the 1% level. 66 cfapubs.org Fourth Quarter 2017

Global Equity Country Allocation Table 5. Global Multifactor Portfolios Based on All vs. Developed Countries, July 1980 December 2015 Performance Statistics Country Universe Average Return Volatility Sharpe Ratio Tracking Error Turnover Trading Costs Alpha A. Single-factor portfolios based on capitalization weights Developed countries 12.55% 16.40% 0.50 6.46% 228.12% 0.07% All countries 14.37% 17.11% 0.58* 7.26% 242.61% 0.09% 1.82%* B. Single-factor portfolios based on equal weights Developed countries 13.45% 16.73% 0.54 7.73% 189.65% 0.12% All countries 16.31% 18.03% 0.66* 9.75% 204.71% 0.18% 2.86%* C. Single-factor portfolios based on inverse-variance weights Developed countries 13.86% 16.24% 0.58 7.49% 202.41% 0.12% All countries 15.05% 16.64% 0.64* 7.90% 213.31% 0.15% 1.20% D. Single-factor portfolios based on minimum-variance weights Developed countries 14.33% 15.52% 0.64* 8.04% 294.00% 0.12% All countries 15.52% 15.49% 0.72** 8.51% 305.23% 0.15% 1.19% E. Single-factor portfolios based on maximum-diversification-portfolio weights Developed countries 14.25% 16.51% 0.60 8.50% 285.92% 0.20% All countries 16.52% 17.44% 0.70* 10.20% 308.20% 0.29% 2.27% F. Market statistics Market 10.64% 15.14% 0.41 *Significant at the 5% level. **Significant at the 1% level. countries only, by an average of 15% across all weighting schemes. All-country-based multifactor portfolios outperform developed-country-based multifactor portfolios by an average of 1.87%. Turnover is slightly higher (6%, on average, across weighting schemes) when emerging markets are part of the investment set. Higher turnover combined with higher bid ask spreads for emergingmarket ETFs results in marginally higher trading costs. Across all weighting schemes, rebalancing global factor portfolios costs, on average, 17.2 bps a year for emerging markets and 12.6 bps for developed markets. The results reported in Table 5 suggest that the superior performance of country-based factor portfolios vis-à-vis the cap-weighted global market portfolio is robust to restricting the universe of countries to developed countries only. Adding emerging markets to the investor s opportunity set further improves the risk return trade-off offered by developed-country multifactor portfolios. Country-Based vs. Stock-Based Global Factor Portfolios In this section, we examine the performance differences between the country-based factor portfolios and the Fama French and momentum stock-based factor portfolios widely used in academic research. We also compare the performances of country-based factor portfolios and the investable factor indexes Volume 73 Number 4 cfapubs.org 67

used as benchmarks for the creation of factor portfolios in practice. Fama French Factor Portfolios. Global multifactor portfolios outperform the world market portfolio, achieving positive and statistically significant alphas. These results are consistent with positive alphas being either (1) compensation for exposure to global equity factors different from the nonmarket factors traditionally based on stock-level data or (2) proxies for the Fama French and momentum stock-based factors. In the first case, the new factor portfolios would enhance the investor s opportunity set. If country-based factor portfolios are spanned by the Fama French and momentum stock-based (FF) factors, country-based factors could offer an alternative way to access global factor premiums implemented through fewer and more liquid assets, compared with the thousands of positions in illiquid stocks required by the FF factors. Comparing country-based factors with the global factors of Fama and French (2012) over the common sample period, November 1990 December 2015 (see Table A8, available online at www.cfapubs.org/doi/ suppl/10.2469/faj.v73.n4.7), we found that the differences in the alphas of country- versus FF-based factor portfolios 17 are consistently positive and economically, but not statistically, significantly different from zero, except for the small-cap factor portfolio. Equally weighted factor portfolio combinations based on country and FF factors produce insignificantly different Sharpe ratios, suggesting that country-based factor portfolios are a good substitute for FF factor portfolios. 18 Risk-adjusted alphas based on Carhart s (1997) four-factor model are also not statistically significantly different from zero, though they are economically significant. Overall, the evidence suggests that global country-based factor portfolios are a linear combination of the well-known Fama French factors. 19 Investable Stock-Based Factor Portfolios: MSCI Global Factor Indexes. The FF factor portfolios are not investable; they do not address issues of illiquidity, transaction costs, or the capacity constraints faced by investors when investing in large numbers of stocks to create factor portfolios. For practical factor-based investing, investors can use a number of investable indexes that deal with illiquidity, turnover, and capacity constraints. It is important to compare the performance of countrybased factor portfolios created with country ETFs or stock index futures with the performance of investable stock-based portfolios. In our study, we used the MSCI global factor indexes, which have the longest history of all available indexes, as an investable alternative to country-based factor portfolios. We used the following MSCI global indexes: MSCI ACWI Enhanced Value Index, MSCI ACWI Equal Weighted Index, MSCI ACWI Momentum Index, and MSCI ACWI Minimum Volatility Index. Table A11 (available online at www.cfapubs.org/doi/ suppl/10.2469/faj.v73.n4.7) reports the empirical results for December 1997 December 2015. The country-based value portfolio, constructed with equal weights, has higher returns and volatility than the MSCI ACWI Enhanced Value Index portfolio but offers the same risk return trade-off (Sharpe ratio of 0.47). The country-based value portfolio outperforms the MSCI value portfolio but has a zero risk-adjusted alpha. A different picture emerges when we examine the size portfolio. The country-based small-cap portfolio achieves a better risk return trade-off (Sharpe ratio of 0.53) than the MSCI ACWI Equal Weighted Index (Sharpe ratio of 0.40). The country-based size portfolio achieves a higher return than the MSCI ACWI Equal Weighted Index and a risk-adjusted alpha of 2.22%. The country-based high-momentum portfolio has a higher return, risk, and Sharpe ratio than the MSCI ACWI Momentum Index. The momentum index is rebalanced semi-annually and uses buffer rules to reduce turnover, which, however, also tends to reduce returns. Country-based momentum portfolios achieve a statistically insignificant but economically positive alpha and risk-adjusted alpha relative to the MSCI ACWI Momentum Index. Finally, the MSCI ACWI minimum-volatility portfolio has a lower return and volatility and a better return to risk than the country-based low-risk portfolio but it also has a risk-adjusted alpha close to zero. MSCI-based portfolios generally have lower volatilities than country-based portfolios, reflecting better diversification, but their average returns tend to be lower. An equally weighted global multifactor country-based portfolio outperforms the MSCI equally weighted combined multifactor portfolio by 2.85% (1.33% on a risk-adjusted basis). Both alpha and risk-adjusted alpha are not statistically significantly different from zero. Conclusion Factor investing the idea that allocation decisions should be based on factors instead of the usual asset 68 cfapubs.org Fourth Quarter 2017

Global Equity Country Allocation classes has attracted both theoretical and practical interest. Under the paradigm of factor investing, we created global factor portfolios using country indexes and portfolio construction methodologies that are robust to estimation error. Value, small-cap, high-momentum, and low-risk global factor portfolios, implemented through ETFs or index futures, outperform the world market capitalization portfolio. A portfolio of country index funds tilted toward smallcap, value, high-momentum, and low-beta countries provides a significantly better, both economically and statistically, combination of return and risk than the world market portfolio. An equally weighted multifactor country-based portfolio with a 2% tracking error constraint against the world market portfolio delivers an annual alpha of 1% an active risk return trade-off that competes favorably with the promises of typical tactical asset allocation institutional mandates. The empirical evidence suggests that (1) choosing the right factor exposure is more important than the weighting schemes used to construct the factor portfolios; (2) all factor portfolio construction methodologies generate better performance than the market portfolio, with the minimum-risk and maximum-diversification methodologies among the best; and (3) inclusion of emerging markets in a developed-markets-only universe provides greater latitude in factor portfolio construction and significantly improves the performance of factor portfolios. Our empirical evidence suggests that country-based factor portfolios provide a risk-and-return performance similar to that of stock-based factor portfolios. However, country ETFs are cheaper to trade than stock-based factor ETFs, because country ETFs that track cap-weighted country indexes (1) overweight large-cap stocks and thus are more liquid than nonmarket-cap stock-based factor portfolios, which tend to put more weight on smaller-cap stocks, and (2) are easier, cheaper, and more effectively hedged by market makers and other liquidity providers in ETFs than in stock-based factor ETFs. 20 Ratcliffe, Miranda, and Ang (2017, p. 3) defined capacity as the breakeven hypothetical AUM at which the associated turnover transactions exactly offset the historically observed premium, arguing that the capacity of factor strategies depends on the expected factor premium, turnover, and trading costs. The turnover of countrybased factor and multifactor portfolios is lower than the turnover of stock-based international factor strategies (Frazzini, Israel, and Moskowitz 2015, Table IV). 21 The lower turnover and transaction costs associated with country-based factor portfolios suggest that the capacity of country-based portfolios is as good as or better than that of stock-based strategies. From a practical investment perspective, country-based factor portfolios offer a viable alternative implementation of factor investing in a world of illiquidity, transaction costs, and capacity constraints. Appendix A. Developed- and Emerging-Market ETFs Used to Estimate Trading Costs We used the following country/location funds for developed markets: Australia: ishares MSCI Australia; Austria: ishares MSCI Austria Capped; Belgium: ishares MSCI Belgium Capped; Canada: ishares MSCI Canada; Denmark: ishares MSCI Denmark Capped; Finland: ishares MSCI Finland Capped; France: ishares MSCI France; Germany: ishares MSCI Germany; Hong Kong: ishares MSCI Hong Kong; Ireland: ishares MSCI Ireland Capped; Israel: ishares MSCI Israel Capped; Italy: ishares MSCI Italy Capped; Japan: ishares MSCI Japan; Netherlands: ishares MSCI Netherlands; New Zealand: ishares MSCI New Zealand Capped; Norway: Global X MSCI Norway; Portugal: Global X FTSE Portugal 20; Singapore: ishares MSCI Singapore; Spain: ishares MSCI Spain Capped; Sweden: ishares MSCI Sweden; Switzerland: ishares MSCI Switzerland Capped; United Kingdom: ishares MSCI United Kingdom; United States: ishares Core S&P 500. As of May 2015, half the trading spread was as follows: Australia: 0.0215%; Austria: 0.1306%; Belgium: 0.0537%; Canada: 0.0182%; Denmark: 0.08%; Finland: 0.1226%; France: 0.0195%; Germany: 0.0168%; Hong Kong: 0.0227%; Ireland: 0.162%; Israel: 0.1682%; Italy: 0.0336%; Japan: 0.0434%; Netherlands: 0.0339%; New Zealand: 0.1542%; Norway: 0.1201%; Portugal: 0.1689%; Singapore: 0.0388%; Spain: 0.0152%; Sweden: 0.0359%; Switzerland: 0.0251%; United Kingdom: 0.0268%; United States: 0.00421%. We used the following country/location funds for emerging markets: Brazil: ishares MSCI Brazil Capped; Chile: ishares MSCI Chile Capped; China: ishares MSCI China; Colombia: ishares MSCI Colombia Capped; Greece: Global X FTSE Greece 20; India: ishares MSCI India; Volume 73 Number 4 cfapubs.org 69