Global Equity Country Allocation: An Application of Factor Investing Timotheos Angelidis a and Nikolaos Tessaromatis b,*

Global Equity Country Allocation: An Application of Factor Investing Timotheos Angelidis a and Nikolaos Tessaromatis b,* a Department of Economics, University of Peloponnese, Greece. b,* EDHEC Business School and EDHEC Risk Institute, France. This version: 15.1.2016 Abstract Based on the paradigm of factor investing we create global factor portfolios using country indices and robust to estimation error portfolio construction methodologies. Implementable through ETFs or index futures, a portfolio of global factors outperforms significantly, economically and statistically, the world market capitalization portfolio. The out of sample outperformance is robust to transaction costs and alternative portfolio construction methodologies. Including emerging markets in global factor portfolio construction enhances performance further. Country-based factor portfolios returns are spanned by the well-known Fama and French factors and represent a viable alternative to stock based factor portfolios in a world of illiquidity, transactions costs and capacity constraints. JEL classification: G11, G15 * Corresponding author. Tel.: +44 (0)207 871 6744 e-mail addresses: tangel@uop.gr (T. Angelidis), nikolaos.tessaromatis@edhec.edu (N. Tessaromatis) 1

1. Introduction There is now a wealth of evidence suggesting that, in addition to the market equity premium, exposure to value, small capitalization, momentum and low beta stocks is rewarded with long run risk premia. 1 In a world of multiple risk premia an investor should invest, in addition to the world market portfolio, to a multifactor portfolio of diversified risk premia. In a multifactor world the world market portfolio will be an inefficient benchmark for global active equity investment strategies. In this paper we apply factor investing principles, to create a global factor portfolio with targeted exposures to the value, size, momentum and low risk factors constructed from country index funds. The strategy is an application of factor investing to create a global equity portfolio using country funds instead of individual stocks that aims to produce a better return to risk tradeoff than the capitalization weighted world market portfolio. Factor investing represents an alternative and supplementary approach to the existing investment practice. The factor based approach assumes that returns are driven by a small number of investment factors which provide long-term premia to investors. In equities, academic research based on individual stocks supports the view that exposure to small capitalization, value, momentum and low risk factors is compensated with positive risk premia (Fama and French (2012), Ang, Hodrick, Xing and Zhang (2006), Ang, Hodrick, Xing and Zhang (2009) and Frazzini and Pedersen (2014)). Evidence from other asset classes provides further support to the idea of factor investing (Asness, Moskowitz and Pedersen (2013)). The idea of building a globally 1 The academic debate on whether these premia represent compensation to exposure to systematic risks or are the result of market inefficiency due to investor irrationality is not yet settled. The persistence of the value and momentum premia since their discovery years ago supports a rational risk-based explanation or if factor premia are the result of investor irrationality that there must be significant limits to arbitrage. In both cases they are likely to persist in the future. 2

diversified portfolio that combines the world market portfolio with style funds that capture the size, value and momentum premia is consistent with current interest in factor based asset allocation. The current growth of smart beta products suggests strong interest of institutional investors to the idea of factor investing. In the aftermath of the recent credit crisis a growing number of institutional investors including CALPERS and Norway s Global Fund, are reexamining the traditional allocation framework based on asset classes, in favor to asset allocation based on the underlying risk factors within asset classes. In a factor based approach to global equity allocation the investor constructs a global equity portfolio exposed to factors that are believed to carry positive risk premia. We use the factor construction methodology applied to individual stocks, to construct global factor value, small capitalization, high momentum and low risk portfolios from country portfolio indices and compare their performance to the stock based global factor portfolios of Fama and French (2012) and the corresponding MSCI style indices. Using country indices to create factor portfolios has advantages and disadvantages. Country based factor portfolios are easier and simpler to manage. Factors based on countries tend to be more liquid, have more capacity and lower transaction costs. The disadvantage of the use of countries rather than individual stocks is that the significantly smaller number of countries limits factor exposure and hence narrows the latitude in portfolio construction. Individual stocks should offer greater efficiency in harvesting factor returns compared to alternatives including country based factors but in the real world of trading costs, capacity constraints and liquidity issues country based factors might prove to be a viable alternative. Desrosiers, L Her and Plante (2004) examine the benefits of the use of country indices to create relative-value and relative-strength (momentum) global strategies. In a recent paper, 3

Leclerc, L Her, Mouakhar and Savaria (2013) use US sector indices to create alternative equity portfolios and show that they had, for the period from 1964 to 2011, better performance statistics than the capitalization-weighted equity benchmark. We extend the research of Desrosers, L Her and Plante (2004) and Leclerc, L Her, Mouakhar and Savaria (2013) by considering how country indices, for which ETFs and futures contracts exist for all developed and a large number of emerging markets, can be combined using alternative weighting schemes to create a global equity portfolio with targeted factor exposures and examine whether they dominate the capitalization weighted world market portfolio. The performance of global equity factors based on country indices raises the following question: are global factors based on countries really a proxy for global factors based on individual stocks or do they represent rewards to independent global risks? If global equity factors based on countries are simply a combination of stock based factors they will be redundant in the presence of investible stock based funds. However, country based factors might still be useful in the presence of market frictions like liquidity, capacity constraints and transaction costs. We extend the current literature on country based global factors in several directions. First, we create global equity factors using countries and different portfolio construction (weighting) methodologies and compare their performance with the standard capitalization weighted schemes used in practice. Using alternative, to market capitalization, weighting schemes to target exposure to a rewarded factor creates portfolios that are factor-tilted and at the same time well diversified (Amenc, Goltz, Lodh and Martellini (2014)). Second, 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 will reduce the cyclicality in the performance of single factor portfolios when correlations between the factors is 4

not perfect and provide opportunities for turnover reduction due to the natural crossing effects available when rebalancing many portfolios. Third, we extend the universe of countries used to create the global factor portfolios to include emerging markets. The inclusion of emerging markets by increasing the numbers of assets available for factor portfolio construction could improve the return/risk performance of factor portfolios. Fourth, we examine in detail the relationship between the stock based global factor portfolios of Fama and French (2012) and investable indices of factor portfolios used in practice and the country based portfolios we construct in this study. Similarity in the performance of country versus stock based factor portfolios makes country based factor portfolios implementable proxies for factor based portfolio management. The empirical evidence presented in the paper support a number of conclusions. First, country based value, small capitalization, momentum and low risk portfolios outperform the world market capitalization portfolio. Global factor portfolios have better Sharpe ratios than the world market portfolio. Factor portfolios have positive and in most cases statistically significant, returns in excess of the world market portfolio. Capitalization weighted factor portfolios have consistently worst performance (lower Sharpe and information ratios and positive but statistically insignificant alphas) compared to factors based on non-cap weights. Capitalization weighted factors on the other hand have lower turnover and hence lower transaction costs than alternative weighted factors. As in the case of stock based factor portfolios, momentum portfolios require the highest turnover. Using bid-ask spreads from existing country ETFs, we find very reasonable trading costs rising to 0.53% per annum for the highest turnover (780% per annum) momentum factor portfolio. 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 providing evidence for increased efficiency in harvesting factor returns. Despite increased turnover when 5

emerging markets are included in factor construction trading costs are within acceptable institutional practice bounds. Third, global multifactor portfolios created using alternative weighting schemes have higher and statistically significantly different Sharpe ratios than the world market portfolio. The outperformance of the global factor portfolio is preserved for low tracking risk portfolios (2% p.a. tracking error target). The weighted scheme used to combine the four global factors makes little difference to performance. Fourth, the alpha of the global factor portfolio based on factors from countries disappears when returns are adjusted using the Carhart (1997) model, implying that the outperformance of country based factor portfolios represents reward from exposures to the non-market factors used in Carhart s (1997) model. Indeed, the empirical evidence suggests that the Fama and French and momentum factors span the returns of the country based global multifactor portfolio. Country based factor portfolios represent a viable alternative to stock based factor portfolios. In section 2, we describe the dataset and the methodology to create the country factor portfolios and in section 3 we examine the performance of the global single-factor and multifactor portfolios. Section 4 compares the performance of global country portfolios to stock based global factor portfolios. Section 5 concludes the paper. 2. Data and factor portfolio construction methodology We use country dollar total return indices obtained from Thomson Datastream from July 1980 to June 2014 (408 monthly observations) from 23 developed markets: Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Hong Kong, Ireland, Israel, Italy, Japan, Netherlands, New Zealand, Norway, Portugal, Singapore, Spain, Sweden, Switzerland, United Kingdom, and United States. We also use the developed Datastream index (mnemonic: TOTMKDV) to measure the performance of the developed market portfolio. ETFs and futures 6

contracts exist for all developed markets making the creation of the global factor portfolios feasible. We use BlackRock s and Global X s ETFs to estimate trading costs. 2 To construct the global value portfolios we rank at the end of June in year t all countries by a composite valuation indicator that combines a country s price to earnings ratio, price to book ratio, price to cash flow ratio, and dividend yield. Using a composite valuation indicator reduces the measurement error of individual value indicators and could produce value portfolios with superior return to risk trade-offs 3 (see Asness, Frazzini, Israel and Moskowitz (2013) and Israel and Moskowitz (2013)). We form three portfolios containing one third of the 23 countries each and calculate the monthly returns over the next 12 months. The small capitalization portfolio contains a third of all countries with the lowest capitalization and uses also a twelve-month rebalancing rule. We calculate every month the momentum for month t as the cumulative monthly returns for t 2 to t 12 and form three portfolios containing in equal numbers the highest, medium and lowest momentum countries. Finally, we estimate every month the country beta against the world index using a rolling sample of 60 monthly observations and create three portfolios that contains the highest, medium and lowest beta countries. 2 Specifically, we used the following country funds: 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, and United States: ishares Core S&P 500. 3 Novy-Marx (2015) argues that combining indicators could lead to overfitting biases and suggests as a safeguard to also look at the performance of strategies based on individual indicators. In unreported research, available from the authors upon request, we find that the return to risk characteristics of value portfolios based on single value indicators is similar to the performance of value portfolios based on the composite indicator. 7

Modern portfolio theory prescribes the use of mean-variance optimization to create optimal factor portfolios. Optimization requires estimates of expected returns and risks but evidence in DeMiguel, Garlappi and Uppal (2009) suggest that the benefits from optimization based portfolio construction are less than the costs of estimation risk. To reduce estimation risk academics and practitioners proposed alternative portfolio construction rules that use fewer parameter estimates. Lee (2011) and Hallerbach (2015) among others show that the portfolio construction methodologies used in practice by smart beta strategies could be regarded as meanvariance optimal portfolios only under very specific assumptions about expected returns, variances and correlations. Reducing the number of input estimates reduces estimation risk but creates information loss and sub-optimal portfolios compared to mean-variance optimal portfolios free from estimation risk (optimality risk). Alternative portfolio construction methodologies represent different trade-offs between estimation and optimality risk (Martellini, Milhau and Tarelli (2014)) but since there is little agreement at to which portfolio construction methodology is superior we use a number of portfolio construction methodologies as alternatives to the capitalization weighted factor portfolios used in practice. We calculate the monthly return of the four global factor portfolios using capitalization based weights and four alternative portfolio construction methodologies (weighting schemes). Capitalization weighting (CW) represents the most commonly used index construction methodology despite its well-known shortcomings of excessive concentration, arbitrary exposure to non-market factors and inferior risk-adjusted performance compared to even simplistic portfolio weighting rules. However, from a practical perspective, CW indices represent highly investable strategies with low turnover and high liquidity-capacity. 8

Factor portfolios are also calculated using the following alternative portfolio construction rules: equal weighting (EW), inverse variance (IV), minimum variance (MinVar) and the maximum diversification portfolio (MDP). EW invests proportionally in each of the N countries. Since the EW rule does not use estimates of return or risk, is by definition free of estimation risk. EW will be mean-variance optimal only under the assumption that expected returns, variances and correlations are the same for all assets. The second portfolio rule relies only on volatility and assumes that the correlation between assets is zero. Kirby and Ostdiek (2012) show that inverse variance (IV) portfolios outperform both equally and capitalization weighted portfolios. IV weights are calculated according to the following equation: ( 1 h 2) σ w it = it N ( 1 2) σ it i=1 h, i = 1,2,, N (1) 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. 4 The IV weighting scheme is mean-variance optimal if expected returns are equal, correlations between assets are zero and h=1. The third portfolio construction rule we use to construct the global factor portfolios, is the minimum-variance portfolio (MinVar) under no-short sale-constraints. MinVar portfolios require estimates of variances and covariances but not expected returns that are far more difficult to estimate (Merton (1980)). Clarke, de Silva and Thorley (2006) and DeMiguel, Garlappi and Uppal 4 In the empirical part of the paper we set h = 1 following the empirical evidence in Kirby and Ostdiek (2012) that performance is not heavily depended on the choice of the tuning parameter value. As a robustness check, we also set h = 2 and we find that the performance statistics do not differ significantly. 9

(2009) among others show that the minimum-variance strategy outperform capitalization weighted indices. The weights of the minimum-variance portfolio are defined in the following equation: min w w T Σ w, s. t. 1 T w = 1, (2) MinVar portfolios will be mean-variance optimal under the assumption that expected returns are equal. The final weighting scheme we consider is the maximum diversification portfolio (MDP) proposed by Choueifaty and Coignard (2008) that maximizes the diversification ratio defined as: w T σ w T Σ w (3) σ 1 σ 2 where σ = [ ]. The numerator of (3) is equal to portfolio volatility ignoring correlations while σ Ν the denominator is portfolio volatility taking into account correlation (diversification). The MDP portfolio will be optimal if the assets included in the portfolio have the same Sharpe ratio. Choueifaty and Coignard (2008) show that the MDP achieves performance statistics consistently better than those of the equally weighted, the minimum variance and the capitalization weighted portfolios. The alternative weighted methodologies we use to construct factor portfolios reflect various assumptions about the information availability of the inputs required for portfolio optimization. EW portfolios assume no information about returns or risks, IV assumes information about variances while MinVar and MDP assumes information about variances and covariances. 10

Seen from this perspective, alternative weighting schemes represent alternative approaches to capitalization weighted portfolios providing different trade-offs between the estimation and optimality risks inherent in portfolio construction. From a theoretical or empirical perspective there is currently very little agreement as to which of the proposed alternative weighted schemes is the best portfolio construction methodology. Table 1 presents descriptive statistics for the 23 developed markets and the world market portfolio. During the 1980:07-2014:06 period the world market portfolio had an average yearly return of 11.70% with 15.26% standard deviation. Of the 23 markets, 20 outperformed the market portfolio and with the exception of the US market all individual markets had higher risk than the world market. The average exposure to the four factors of the 23 markets is presented in table 1. Factor exposures changes from month to month but on average the markets of Japan, US and Denmark are the three highest exposure growth markets while the markets of Belgium, the Netherlands, Spain, Norway, Italy, Israel and France have the most significant exposure to value. In terms of country participation in the value portfolio, Belgium is a constituent for 73% of the months, France for 64% of the months and Spain and Portugal for 63% of the months. Japan and the US markets are never part of the value portfolio. The small capitalization portfolio consists of the markets of Austria, Denmark, Ireland, Israel and Portugal that are part of the portfolio in all months in the sample and Norway (91% of the time), Finland (69%), Singapore (42%), Belgium (21%) and Sweden (19%). Exposure to the momentum factor is more evenly spread across countries while country participation in the momentum portfolio ranges between 45% (Sweden) and 22% (UK) of the months in the sample. Twelve of the twenty-three countries have a beta lower than 1. Israel, Austria, Portugal, Denmark, Switzerland and Belgium are part of the low beta portfolio for more than half the months in the sample. France, Norway, Finland, Sweden and 11

Spain appear in less than 10% of the months. The participation rate of the largest cap markets in the low beta portfolio is significant: US (47%), Japan (42%), UK (37%). 3. Global Single-Factor and Multifactor Portfolios In this section we present performance statistics of the global factor portfolios (value, small capitalization, momentum, and low beta) based on the five alternative weighting schemes (CW, EW, MinVar, IV, MDP) described in the previous section. We also present the performance characteristics of global multifactor portfolios created as combinations of global single factor portfolios using the EW, MinVar, IV and MDP weighting schemes. The sample period for the global single-factor portfolios is from July 1980 to June 2014, while for the global multifactor portfolios starts on July 1985 (we use 60 monthly observations to estimate the variance covariance of countries returns required for some of the alternative weighting methodologies). We evaluate the performance of portfolios using different performance criteria. To compare the risk adjusted performance of two portfolios we use the Sharpe ratio (SR i ) defined as SR i = μ i r f where μ σ i r f is the average portfolio excess return and σ i is the standard deviation of i portfolio returns. We test the hypothesis that the Sharpe ratios of two portfolios are equal using the procedure of Ledoit and Wolf (2008) with 5000 bootstrap resamples and a block size equal to b = 5. To compare the risk adjusted performance of a portfolio against the world equity index we use the information ratio (IR i ) defined as IR i = μ i μ m where μ σ i m and σ ri r m are the average ri rm (raw alpha) and standard deviation (tracking error (TE)) of portfolio s i excess return against the world market portfolio. The portfolio turnover required to create and most importantly maintain the factor portfolios could be a critical factor in portfolio performance evaluation. We firstly calculate the 12

break-even transaction costs (BETC) defined as the fixed transaction cost that makes the excess portfolio return over the market return equal to zero, calculated as μ i μ m. We define portfolio Turnover i turnover as: Turnover = 12 1 T 1 N ( w T 1 i,t+1 w t=1 i=1 i,t ) where w i,t is the portfolio weight before rebalancing at time t + 1 and w i,t+1 is the desired portfolio weight after rebalancing If an investor is faced with transaction costs less than BETC, the portfolio will produce a positive alpha net of transaction costs. The second measure of transaction costs uses current estimates of transaction costs from country ETFs with estimated portfolio turnover to calculate a portfolio s trading cost (TC) defined as TC= 12 1 T 1 N ( w T 1 t=1 i=1 i,t+1 w i,t ) cost i, where cost i is half the spread of country i ETF obtained from BlackRock and Global X. 5 TC reflects current estimates of spreads and hence is a good estimate of costs under present trading conditions but probably underestimates past trading costs. ETFs for most developed markets have been created only recently and spread data for most of the ETFs are not available during the period we study. 3.1. Single global factor portfolios based on developed markets Panel A of table 2 presents performance statistics for value, small capitalization, momentum, and low beta portfolios constructed using the five weighting schemes (CW, EW, MinVar, IV, MDP) described in section 2. During the 1980:07-2014:06 period the world equity market portfolio had an average return of 11.70% with 15.26% standard deviation. The Sharpe ratio of the world market portfolio was 0.47. 5 As of May 2015 half of the trading spread was: 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%, and United States: 0.00421%. 13

The global capitalization weighted value portfolio achieved an annual return of 14.30% and annualized volatility of 18.61%. The Sharpe ratio is higher (0.52) but statistically insignificantly different from the Sharpe ratio of the world market portfolio (0.47). Alternative weighting portfolio construction methodologies improve the performance of global value portfolios relative to the capitalization weighted portfolio, achieving higher returns and Sharpe ratios. The best performing alternative weighting scheme is the MDP with a Sharpe ratio of 0.63 albeit not statistically different from the Sharpe ratio of the world market portfolio. The outperformance of the global value portfolios relative to the world market is statistically significant for all weighting schemes except when portfolios are based on capitalization weights and ranges between 2.60% for the capitalization weighted portfolios and 4.18% for MDP weighted portfolios. The tracking error of global value portfolios against the world market portfolio are at the high end of active portfolio strategies and range between 9.54% and 10.93%. Portfolio turnover is between 75.35% (CW) and 151.16% (MinVar) and our estimate of trading costs between 0.03% (CW) and 0.11% (MinVar). Given the strong outperformance of the global value portfolios, an investor who faces transaction costs less than 3.45% (CW) or 2.33% (MinVar) will find all portfolios strategies profitable net of costs. We do not observe statistically significant differences between the Sharpe ratios of the various weighting schemes 6, suggesting that the choice of the weighting scheme does not affect the performance statistics of the global value portfolios. However, portfolios based on the four weighting schemes outperform CW portfolios by on average 1.12% (ranging between 0.89% for the EW and 1.57% for the MDP). 6 We test for the statistical significance of the Sharpe ratios of each weighting scheme against the other but do not report the estimates p-values due to space limitations. Detailed results are available upon request. 14

Small capitalization factor portfolios perform better than the world market portfolio. The CW size portfolio achieves a Sharpe ratio of 0.52 versus a Sharpe ratio of 0.61of the IV portfolio. The Sharpe ratio differences and the raw alphas are positive across all weighting schemes but do not differ statistically from zero. The average turnover across all weighting schemes is 61.30% and the average trading cost 0.07%. Although, as in the case of global value portfolios, the differences between the Sharpe ratios of the various weighting schemes are not statistically significantly different, we note that the CW portfolio underperformed size portfolios based on alternative weighted schemes by, on average, 0.84% per annum. Global momentum portfolios outperform strongly the world market portfolio. With the exception of the CW portfolio, all other weighting schemes (EW (0.68), MinVar (0.82), IV (0.75) and MDP (0.78)) achieve higher and statistically significantly different Sharpe ratios against the world market portfolio (0.47). Raw alpha is uniformly positive across all weighting schemes and strongly statistically significantly different from zero (with the exception of CW). Portfolio tracking errors against the world market portfolio are high by active management standards and information ratios range between 0.22 (CW) and 0.69 (MDP). The underperformance of the CW portfolio relative to the other four portfolios is statistically significant and ranges from 3.44% (EW) to 5.53% (MDP). As in the case of stock based momentum strategies, turnover is high for all portfolio construction strategies. The EW portfolio has annual turnover 484.72% but rises to 614.50% for the IV portfolio, 695.37% for the CW portfolio, 780.62% for the MDP portfolio, and 886.24% for the MinVar portfolio. The high turnover of the global momentum portfolios results in annual 15

average trading costs of 0.37%, as much as three times higher than the costs of the value and size portfolios. Despite the higher costs, raw alphas net of transaction costs remain strongly positive. 7 A capitalization weighted portfolio of low-beta countries achieved an annualized return of 14.82% with 16.56% volatility, a Sharpe ratio of 0.62 and a raw alpha of 3.13% per annum. Alternative weight schemes achieve similar performance but as with the value and small cap portfolios their Sharpe ratios are not statistically significantly different than the Sharpe ratio of the world market portfolio. However, as with the other factors, all weighting schemes outperform significantly the world market portfolio. The turnover of low beta portfolios is higher than the turnover of size or value but lower than momentum portfolios. For the capitalization weighted low-beta portfolio annual turnover is 216.63%, implying a break-even cost of 1.44%. Based on the current spreads of country ETFs and turnover, we estimate annual transaction costs of 0.06% for CW that rises to 0.18% for MDP, substantially lower than the estimated break-even costs. The best performing portfolio is based on the minimum variance weighting scheme which outperformed significantly the word portfolio by 3.65% with a tracking error of 10.38% and information ratio of 0.35. The evidence on the performance of global single factor country-based portfolios suggests that value, small capitalization, momentum and low beta portfolios have better return/risk characteristics (higher Sharpe ratios) than the world market portfolio. Although the differences in Sharpe ratios between the factor portfolios and the world market portfolio are statistically 7 Turnover is reduced when we use a 6 month instead of the 1 month rebalancing rule. Average turnover across all weighting schemes falls from 692% to 261%. However, the lower turnover is accompanied by a significant reduction in the return to risk ratio of the momentum factor portfolio (the average Sharpe ratio across all weighting schemes is reduced from 0.71 for 1 month rebalancing to 0.52 for 6 month rebalancing). 16

significant 8 only for the momentum factor, the return difference (portfolio alpha) is economically and statistically significant. To maintain the factor portfolios requires some turnover but our estimates of transaction costs based on the spreads of country ETFs suggest that even the high turnover momentum portfolio is profitable net of costs. Alternatively, it requires unrealistically high transactions costs to make the excess return produced by all factors zero. Non-market capitalization weighted factor portfolio construction rules achieve better return to risk tradeoffs compared to capitalization based factor portfolios but the differences in Sharpe ratios are not statistically significant. 3.2. Global multi-factor portfolios based on developed markets Given the benefits of single-factor portfolio investing compared to the world market portfolio it is natural to examine whether combining single factor portfolios will produce further benefits due to diversification. Panel B of table 2 presents the correlation matrix of single factor portfolios for each of the weighting schemes. Correlations are high given that these are long only portfolios where the market factor drives most of their returns but less than one. The lowest correlation is between the low beta and value CW portfolios (76.16%) and the highest between small cap and low beta portfolios for EW portfolios (92.22%). Correlations in general are lower for CW factor portfolios. 8 The test statistic of the differences between Sharpe ratios depends on the number of observations used in testing (34 years in our case). How many years of data are required for the differences in Sharpe ratios to become statistically significant? To answer this question we generate simulated returns using a bootstrap approach. Specifically, we draw randomly with replacement from the sample returns to generate artificial samples with the same mean and standard deviation. Then we perform the Sharpe ratio test and we repeat this procedure 500 times. The Sharpe ratios of the global value and low beta portfolios are statistically significantly different from the Sharpe ratios of the world market portfolio with an extra 16 years of data. The small capitalization portfolio requires 30 more years. Our calculations suggest that long investments periods are required before factor based portfolio returns outperform statistically reliably the world market portfolio and highlight the long-term nature and risks of factor investing. 17

To study the benefits of factor combination, we create global factor portfolios using the four portfolio construction methodologies (EW, MinVar, IV, MDP) presented earlier and in addition mean-variance optimization (MV). In the absence of estimation risk when generating forecasts of risk and return mean-variance portfolios are optimal and therefore better than nonoptimization based portfolio construction rules. In an influential study, DeMiguel, Garlappi and Uppal (2009) show that mean-variance portfolios using return and risk inputs based on historical returns lead to very poor out-of-sample performance, inferior to other much simpler portfolio construction methodologies. However, Kan and Zhou (2007) show theoretically and empirically that the loss that arises from the estimation error of unknown parameters is smaller when the number of assets is small and the periods of observed returns data are sufficient large. In our study we look at the out of sample performance of portfolios of four assets over relatively long samples, conditions under which mean-variance optimization is likely to be less affected by estimation error. We therefore use, in addition to the four weighting schemes mentioned earlier, meanvariance optimization to combine the four factors by maximizing the Sharpe ratio (MV): max( w μ r f ) where w is 1x4 matrix of the weights, μ w w is a 4x1 mean matrix based on an expanding sample window, and Σ is a 4x4 variance-covariance matrix based on a rolling 60 month window. Each portfolio construction methodology combines the single-factor portfolios (value, small capitalization, momentum and low beta portfolios) to deliver a multifactor portfolio. The total global multifactor portfolio turnover is calculated by adding all the underlying country positions and therefore exploits to the full the natural crossing opportunities available across single factor portfolios and countries. Global multifactor portfolio turnover takes into account 18

transactions associated with monthly (a) single-factor portfolio revisions and (b) global factor portfolio rebalancing. Table 3 shows the performance characteristics of the global multifactor portfolios for the period from July 1985 to June 2015. During this period the average return of the world market portfolio is 11.22%, its volatility 15.71% and its Sharpe ratio 0.48. Panel A of table 3 presents for the capitalization weighted global single factor portfolios performance statistics of the five alternative factor portfolio combinations. Irrespective of the weighting scheme used to create the global multifactor portfolio, the Sharpe ratios are higher and statistically significantly different from the Sharpe ratio of the world market portfolio. This finding is in contrast with the statistically insignificant differences in the Sharpe ratios of single factor portfolios compared with the Sharpe ratio of the world market portfolio presented in table 2. The significance of the differences in Sharpe ratios reflect the benefits from diversification gained when investing to a portfolio of global factors. The Sharpe ratios for different weighting methodologies are very similar. Combining factors to create a global multifactor portfolio improves the Sharpe ratio of the world market portfolio by, on average, 40%. On average the raw alpha of global multifactor portfolios against the world market portfolio is 3.26% and differs statistically from zero for all portfolio construction methodologies. The active return to tracking error (information) ratios ranges between 0.34 (MV) and 0.50 (IV). The average annual portfolio turnover across all weighting schemes is 248.01% 9 implying a break-even cost of 1.32% and trading costs of 0.08%. Globally diversified factor portfolios generate substantial returns to investors net of transaction costs. 9 The high turnover of the combined portfolios is due to the high turnover of the momentum style portfolios. For example, the turnover of the CW momentum portfolio is close to 174.29% (see table 2). 19

Panels B, C, D, and E of table 3 present performance statistics for the EW, MinVar, IV, MDP and MV based single factor portfolio combinations. The main findings presented in panel A of table 3 do not alter significantly. The Sharpe ratios of global factor portfolios are statistically higher than the Sharpe ratio of the world market portfolio and generally higher but not statistically significant than the return to risk offered by capitalization weighted single factor portfolios. Global factor portfolios outperform strongly the world market portfolio producing annual raw alphas of between 3.42% (for MinVar single factors combined using MinVar) and 6.44% (for MV single factor portfolios combined using MinVar), all statistically different form zero. Average yearly turnover is 327.41%%, consistent with 0.21% per annum trading costs and a break-even cost of 1.69%. Global factor portfolios based on single factors constructed using the minimum variance portfolio construction methodology seems to produce the best performance compared to the other portfolio construction methodologies: the average Sharpe ratio is 0.80 and the yearly average raw alpha 6.29%. When we test whether Sharpe ratio across different global multifactor portfolio construction methodologies (EW, IV, and MDP) are different we find no evidence of statistically significant differences suggesting that different global multifactor portfolio construction methodologies produce very similar performance statistics. The similarity in performance between MV and the other portfolio construction rules may be attributed to the small number of assets and to the expanding sample window we use to estimate expected returns and risks (see Kan and Zhou (2007)). However, the portfolio turnover of the MV multifactor portfolio for all weighting methodologies, except for CW portfolios, is at least two times greater than the average turnover and the trading costs of the other weighting schemes a (EW, MinVar, IV, and MDP). This finding is in line with the presented evidence in DeMiguel, 20

Garlappi, Nogales and Uppal (2009). MV portfolios also tend to have higher tracking error against the market portfolio. It is beyond the scope of this paper to explore turnover reduction techniques (such as those used for example by Novy-Marx and Velikov (2015)) but we look at the next section the effect of tracking error constraints on the turnover of MV portfolios. 3.2.1. Global factor portfolios under tracking error constraints Reflecting current institutional practice of managing portfolios against benchmarks we also construct global multifactor portfolios under a 2% tracking error constraint. The tracking error constraint will result in a less than optimal portfolio with the difference in performance between unconstrained and constrained portfolios returns reflecting the cost of the tracking error constraints. Table 4 shows statistics for the five global factor portfolios under the assumption of a 2% tracking error constraint. As expected benefits are reduced across portfolio weighting schemes but remain significant under the typical tracking error constraints imposed in practice on investment portfolios by institutional investors. Sharpe ratios of constrained multifactor portfolios are considerably lower than their unconstrained counterpart but remain statistically significantly different from the Sharpe ratio of the world market portfolio when we use the MinVar, IV, and MDP weighting scheme. There is 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 (0.41). The tracking error constraint reduces drastically portfolio turnover to an average of 109.35% across all weighting schemes compared to the annual turnover when there are no constrains of 311.53%%. Excluding MV portfolios, annual turnover is less than 100% for most other portfolio construction methodologies. Transaction costs are also lower (average 0.06% per annum) and range between 0.03% and 0.13% per annum. The combination of good absolute risk 21

adjusted performance, strong active returns, low tracking error and reasonable turnover make global factor portfolios very attractive to institutional investors. The imposition of tracking error constraints does not change the conclusion about the performance of MV portfolios. MV portfolios produce performance statistics that are similar to the statistics of the other four weighting schemes. However, it tends to have higher ex-post tracking error (2.56% per annum) than the other four portfolio construction methodologies (2.08%). Turnover continues to be almost two times greater than the average turnover of the four methods as are implementation costs. The evidence presented in tables 3 and 4 suggests that the MV weighting scheme produces performance statistics that are similar to the other methods with significantly higher trading costs making this methodology less attractive that the other portfolio construction rules. For this reason we do not analyze further the performance of MV based global multifactor portfolios. 3.3. Extending the investable universe: inclusion of emerging markets Cakici, Fabozzi and Tan (2013) provide robust evidence of value and momentum premia for 18 emerging markets for the period from January 1990 to December 2011. For all emerging markets they show that the monthly value and momentum premia are 1.15% and 0.86% respectively, significantly higher than value (0.40%) and momentum (0.63%) premia based on stocks from developed markets. If factor premia are higher for emerging markets, expanding the developed markets universe to include emerging country indices might improve the performance of country based portfolios. We use country dollar total return indices from Thomson Datastream from 21 emerging markets: Brazil, Chile, China, Colombia, Czech Republic, Egypt, Greece, Hungary, India, 22

Indonesia, South Korea, Malaysia, Mexico, Peru, Philippine, Poland, Russia, South Africa, Taiwan, Thailand, and Turkey. We construct the factor and the multifactor portfolios following the procedure we describe in sections 2 and 3.1. ETFs and futures contracts exist for most of the emerging markets making the creation of the global factor portfolios quite feasible. We use BlackRock s and Global X s ETFs to estimate trading costs. 10, 11 Table 5 presents for the various weighting schemes Sharpe ratios, turnover and trading costs for the value, small capitalization, momentum, and low beta portfolios based on developed and the extended (developed and emerging) dataset. It also shows the return difference (raw alpha) of global factor portfolios based on developed and developed plus emerging markets with corresponding t-statistics. The sample for both datasets starts in January 1990. Extending the developed markets dataset to include emerging markets improves consistently the return to risk tradeoff of country based value, small capitalization, momentum and low beta factors portfolios. Sharpe ratios improve on average by 25% (from 0.56 to 0.70) for the value portfolio, by 41% (from 0.50 to 0.70) for the small capitalization portfolio and by 14% (from 0.64 to 0.73) for the momentum portfolio. The small improvement for the low beta factor portfolio (from 0.59 to 0.63) is due to the fact that emerging markets have higher betas compared to developed markets and the low beta factor portfolio is therefore dominated by developed markets. With the exception of the value (for the MinVar weighting scheme) and small capitalization (for 10 Specifically, we used the following country funds: 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, Indonesia: ishares MSCI Indonesia, South Korea: ishares MSCI South Korea Capped, Malaysia: ishares MSCI Malaysia, Mexico: ishares MSCI Mexico Capped, Peru: ishares MSCI All Peru Capped, Philippine: ishares MSCI Philippines, Russia: ishares MSCI Russia Capped, South Africa: ishares MSCI South Africa, Taiwan: ishares MSCI Taiwan, Thailand: ishares MSCI Thailand Capped, and Turkey: ishares MSCI Turkey. 11 As of May half the trading spread was: Brazil: 0.0149%, Chile: 0.0621%, China: 0.0248%, Colombia: 0.4312%, Greece: 0.0746%, India: 0.0159%, Indonesia: 0.0421%, South Korea: 0.0087%, Malaysia: 0.0380%, Mexico: 0.0122%, Peru: 0.1269%, Philippine: 0.0614%, Russia: 0.0681%, South Africa: 0.0592%, Taiwan: 0.0315%, Thailand: 0.0673%, and Turkey: 0.0657%. 23

the CW, EW, IV and MDP weighting schemes) factors, the differences in the Sharpe ratios of factor portfolios based on the developed and extended samples are not statistically significant. Global value portfolios based on developed and emerging markets outperforms global value portfolios based only on developed markets by 2.58% per annum. The addition of emerging markets improves considerably the performance of the global small capitalization factor portfolio. The average raw alpha is 4.56% per annum and statistically significantly from zero for the CW, EW, IV and MDP portfolio construction rules. For momentum portfolios the benefits of emerging markets are smaller. On average broadly based factor portfolios outperform by 2.04% per annum. Given the dominance of larger countries in the low beta portfolio there is a much smaller (0.66% per annum) benefit from the inclusion of emerging markets in the creation of global factor portfolios. Turnover is higher when emerging markets are part of the investment set. Higher turnover combined with higher bid-ask spreads for emerging market ETFs result in higher trading costs. Rebalancing value portfolios cost, on average across all weighting schemes, 15 basis points per annum with emerging markets and 8 basis points per annum with developed markets only. For momentum portfolios adding emerging markets increases costs from 40 basis points to 61 basis points per annum. For small capitalization and low beta portfolios the increases are from 8 to 17 and from 11 to 14 basis points per annum respectively. Expanding the developed markets dataset to include emerging markets improves the performance of country based factor portfolios, increasing consistently factor portfolio Sharpe ratios across all weighting schemes. Excess returns are economically significant and for the value and size global factors in many cases statistically significant. Despite increases in turnover when 24

emerging markets are included, trading costs remain low and within acceptable bounds from a practical point of view. In summary, the evidence presented support the view that country based factor portfolios outperform the world market portfolio. Global factor portfolios created on the basis of market capitalization weights underperform consistently global factors based on alternative weighting methodologies. Alternative country weighting methodologies to create the four global factor portfolios or the multifactor portfolio do not seem to lead to significant economic or statistical differences in factor portfolio returns. Given the similarities in performance we only report from now on results based on the EW weighting scheme (performance factor portfolios based on the other weighting schemes are available upon request). 4. Country versus stock based global factors 4.1. Fama and French factor portfolios Global multifactor portfolios outperform the world market portfolio, achieving positive and statistically significant raw alphas. Is it possible that the estimated alpha is compensation for exposure to the non-market factors traditionally based on stock level data? The evidence in Fama and French (1992 and 1993), Frazzini and Pedersen (2014) and Fama and French (2012) among many others suggests that exposure to size, value, momentum and beta factors is associated with compensation in the form of risk premia both at a single country and global stock level. Alternatively, is it possible that the return of the global factor portfolio based on countries represents simply a mapping to the Fama and French stock based factors? Table 6 compares country based factors with the global factors of Fama and French (2012) over the common sample period November 1990 to June 2014. We use the capitalization weighted 25