The benefits of international diversification with weight constraints: A cross-country examination

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The benefits of international diversification with weight constraints: A cross-country examination Shaun McDowell ∗ Department of Accounting and Finance, The University of Auckland, Auckland, New Zealand

a r t i c l e

i n f o

Article history: Received 22 May 2017 Received in revised form 28 September 2017 Accepted 10 February 2018 Available online xxx JEL classification: G11 G15

a b s t r a c t This paper measures the effect of allocation weight constraints on the potential benefits from international diversification for investors with long investment horizons in 34 countries. Naive international diversification does not provide positive benefits for all investors during the 1993–2014 investment period. Relaxing the market allocation weight constraints applied to in-sample mean-variance optimized portfolios increases the potential for diversification gains. The return-to-risk benefits that these portfolios provide versus the domestic market portfolio are not statistically significant for many investors. There is also an imbalance between the global demand for equity in markets that provide portfolio efficiencies versus the supply of available equity, which is an additional constraint that may limit the efficiency gains that can be captured in equilibrium. © 2018 Board of Trustees of the University of Illinois. Published by Elsevier Inc. All rights reserved.

Keywords: Portfolio choice International financial markets

1. Introduction Quantifying the potential gains from international diversification is useful for assessing the significance of the home bias puzzle. The mutual fund theorem (Lintner, 1965; Sharpe, 1964) and the capital asset pricing model (CAPM) extended to an international setting (Sercu, 1980; Solnik, 1974a) assume risk-sharing investors can improve portfolio efficiency by diversifying into a naive market capitalization weighted (1/M) portfolio. Early literature reports weak correlations between markets and concludes that there are benefits from international diversification (e.g., Grubel, 1968; Lessard, 1973; Levy & Sarnat, 1970). Studies measuring the potential benefits from diversification over long investment horizons available from optimized portfolios with restrictions on short sales report there are benefits from diversification into developed and emerging markets for U.S. investors (De Roon, Nijman, & Werker, 2001; Li, Sarkar, & Wang, 2003), U.K. investors (Fletcher & Marshall, 2005) and investors in other countries (Driessen & Laeven, 2007). These benefits are reported to be reduced for U.S. investors diversifying out of the U.S. market, but not eliminated, when weight constraints on market allocations are considered (Chiou, 2008). McDowell (2017a) extends these results and finds U.S. investors

∗ Corresponding author. E-mail address: [email protected]

do not achieve statistically significant positive return-to-risk (RR) improvements from either naive international diversification or portfolios optimized with relaxed constraints on overseas market allocations and no short sales over the 1988–2014 investment period. This paper addresses a gap in the literature regarding the potential diversification benefits available to global investors with long investment horizons by investigating the following questions: Are investors in different countries likely to achieve significant benefits from diversification into a naive global 1/M portfolio? Does relaxing the weight constraints on market allocations improve the significance of the diversification gains? Do these optimal portfolios share risk across markets and achieve an equilibrium in the global demand for markets that offer efficiency gains and the supply of equity available in those markets? While modern portfolio theory assumes that mean-variance optimizing investors will diversify internationally in order achieve efficiencies in portfolio performance, investors puzzlingly exhibit a bias for local investments.1 An investor must form accurate estimates of future market returns and correlations in order to

1 This bias is identified in the early literature investigating the potential benefits from international diversification (e.g., Levy & Sarnat, 1970; Solnik, 1974b, 1974c). French and Poterba (1991) highlight the extent of this bias across countries. Investors are increasing the size of foreign asset positions over time but the home bias persists (e.g., Stulz, 2005; Tesar & Werner, 1995). For a broader survey of the literature on the equity home bias puzzle refer to Cooper, Sercu, and Vanpee (2013).

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successfully optimize their portfolio. The time-varying nature of market returns and correlations introduces estimation error into ex-ante mean-variance optimization which can result in poor outof-sample performance relative to naive investment strategies (e.g., DeMiguel, Garlappi, & Uppal, 2009; Jorion, 1985). Strategies designed to reduce estimation error through sample covariance matrix shrinkage (Ledoit & Wolf, 2003, 2004a, 2004b) or constraints on the allocation weights in the optimization solution (Behr, Guettler, & Miebs, 2013; DeMiguel, Garlappi, Nogales, & Uppal, 2009; Levy & Levy, 2014) have been reported to provide inconsistent ex-ante performance improvements over naive portfolios of U.S. equities. Constraints on asset weight allocations is equivalent to constructing an unconstrained portfolio optimized using the shrunk covariance matrix derived using Lagrange multipliers from the constraints (Jagannathan & Ma, 2003). Jacobs, Müller, and Weber (2014) find estimation error reduction strategies do not provide significant improvement over naive allocation strategies for European investors diversifying amongst the four regional equity indices of North America, Europe, Asia and emerging markets. McDowell (2017b) reports that a naive global 1/M portfolio provides significant RR gains versus the naive local market portfolio with similar frequency as portfolios optimized out of sample using estimation error reduction strategies for investors in the 34 countries measured. This paper contributes to the literature investigating the potential benefits of international diversification for investors with long investment horizons in several ways. First, this paper follows the in-sample mean-variance optimization with constant correlations methodology presented in McDowell (2017a) to measure the potential benefits from diversification available to investors in 34 countries from a naive global 1/M portfolio, and from maximum return-ro-risk portfolios (MRRPs) and minimum variance portfolios (MVPs) optimized with various levels of market allocation constraints during the 1993–2014 investment period. The cross-country results extend the single country perspective that the related literature presents on this topic (e.g., Chiou, 2008; De Roon et al., 2001; Fletcher & Marshall, 2005; Li et al., 2003; McDowell, 2017a). Measuring the potential benefits from diversifying into the MVP, as well as consideration of market constraints, extends the cross-country results presented in Driessen and Laeven (2007), which only considers short selling restrictions into the MRRP. Next, the Ledoit and Wolf (2008) studentized time series bootstrap confidence interval tests are used to report the significance of the benefits achieved by the optimized portfolios versus the domestic market portfolio. These tests are designed to address the non-normality of returns and fat-tail events that occur with historical financial data. Using a bootstrap technique, inference methods are performed on paired data points of a given block size between the monthly returns of two portfolios to provide a p-value measuring the significance of the hypothesis that the difference between the two portfolios is zero. The in-sample benefits from diversification presented in this paper are likely greater than the benefits that can be captured by most investors forming optimal portfolios ex ante because of estimation error (e.g., DeMiguel, Garlappi, & Uppal, 2009; Jorion, 1985). The Ledoit and Wolf (2008) bootstrap testing methods assist in determining the level of relaxed weight constraints at which an optimized portfolio has the potential to offer an investor significant positive diversification benefits from optimization. The test results find that the 1/M portfolio and the MRRPs with and without positive weight constraints and no short sales do not provide statistically significant RR improvements beyond the domestic market portfolio for a majority of investors. The MVPs with relaxed weight constraints can provide lower volatility levels that are statistically different from the local market. However, these MVPs do not pro-

vide statistically significant positive RR improvements compared to eighteen of the twenty-one developed markets measured. Finally, I report that the global and local market allocations for the various MRRPs and MVPs presented in this paper do not achieve an equilibrium between the global demand for markets that provide potential portfolio efficiencies and the supply of available equity in those markets. This is an additional constraint that may restrict the potential efficiency gains that investors can expect to capture. This paper is divided into four more sections. Sections 2 and 3 present the data and methods used to measure the potential benefits from international diversification. Section 4 presents the results of this study. Section 5 concludes with suggestions for future study. 2. Data Monthly total return MSCI equity index data for 21 developed and 13 emerging markets is used in this study. The MSCI indices are designed to measure 85% of the free float-adjusted market capitalization of equities in a market. The indices are industry benchmarks and are used in previous studies measuring the potential benefits from international diversification (e.g., Driessen & Laeven, 2007; Jacobs et al., 2014; Li et al., 2003). The index data is retrieved from Datastream. The first calendar year that index data for all 34 markets in each of the 34 currencies is available is 1993. The sample period covers December 31, 1992 to December 31, 2014. Annual market capitalization data in U.S. dollars from 1993 to 2012 is from two sources: the World Bank and the World Federation of Exchanges. The World Bank data is available for 33 of the 34 markets. The 1993 Ireland capitalization is not available. This incomplete data is calculated using the annual change to the MSCI index to backward fill the missing 1993 capitalization value from the 1994 Ireland market capitalization data. The Taiwanese market capitalization data is retrieved from the World Federation of Exchanges. Table 1 reports the market capitalization of each market used in this study in U.S. dollars as a percent of all 34 markets combined at the end of 1993 and 2012. The table also presents the geometric annual returns, the standard deviation of returns and the RR ratios of these markets as measured in the domestic currency for the 1993–2014 holding period. The characteristics of the 1/M portfolio, and both the MRRP and the MVP optimized with no short sales and no positive weight constraints in the local currency of each of the 34 countries are also reported. The 1/M portfolio is the most strongly weight constrained portfolio reported in this paper with market allocations restricted to equal the 1993 market capitalization weight of each market.2 The MRRP and MVP optimized with no short sales and no positive weight constraints are referred to as unconstrained portfolios in this study. Should an investor believe that the assumptions underlying the mutual fund theorem hold – that there are no significant transaction costs and markets are perfectly transparent – then an investor might seek to invest in the mutual fund in order to capture the naive diversification benefits available from the less than perfectly correlated markets. Table 1 reports that the volatility of the 1/M portfolio formed using the market capitalization weights at the start of the sample period is lower than the domestic market for most investors. Only the U.S., the U.K. and Suisse markets have a lower

2 Chiou (2008) uses market weights from the end of the investment period for the weight constraints. As reported in McDowell (2017a), this can introduce a hindsight bias into the results that can increase the measured benefits from diversification. It seems reasonable to this author that the market weights from the beginning of the period must be used to reflect the optimization decision facing an investor at that time.

Please cite this article in press as: McDowell, S. The benefits of international diversification with weight constraints: A cross-country examination. The Quarterly Review of Economics and Finance (2018), https://doi.org/10.1016/j.qref.2018.02.003

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Table 1 The local market portfolio, the 1/M portfolio, the unconstrained MRRP and the unconstrained MVP characteristics for each country for the 1993–2014 investment period. Market (i)

wi (%) 1993

Local

1/M

MRRP

MVP

2012

r

sd

RR

r

sd

RR

r

sd

RR

r

sd

RR

Panel A: Developed markets 1.51 Australia 0.21 Austria 0.58 Belgium Canada 2.41 Denmark 0.31 0.17 Finland 3.37 France 3.43 Germany 2.85 H.K. Ireland 0.14 Italy 1.01 Japan 22.18 1.34 Holland 0.19 N.Z. 0.20 Norway 0.98 Singapore 0.88 Spain 0.79 Sweden Suisse 2.01 8.52 U.K. U.S. 37.98

2.89 0.24 0.67 4.53 0.51 0.36 4.10 3.34 2.49 0.25 1.08 8.28 1.46 0.18 0.57 0.93 2.24 1.26 2.43 6.79 41.99

0.0981 0.0270 0.0830 0.1004 0.1321 0.1428 0.0754 0.0883 0.0933 0.0453 0.0640 0.0186 0.0933 0.0746 0.1034 0.0642 0.1184 0.1363 0.0935 0.0737 0.0956

0.132 0.227 0.192 0.155 0.185 0.311 0.184 0.212 0.257 0.215 0.217 0.186 0.186 0.163 0.224 0.227 0.215 0.223 0.155 0.138 0.149

0.74 0.12 0.43 0.65 0.72 0.46 0.41 0.42 0.36 0.21 0.30 0.10 0.50 0.46 0.46 0.28 0.55 0.61 0.61 0.53 0.64

0.0661 0.0745 0.0748 0.0698 0.0737 0.0714 0.0737 0.0745 0.0746 0.0773 0.0786 0.0726 0.0744 0.0543 0.0785 0.0642 0.0835 0.0796 0.0558 0.0732 0.0746

0.119 0.153 0.153 0.121 0.153 0.152 0.153 0.153 0.152 0.152 0.151 0.180 0.151 0.130 0.147 0.133 0.154 0.137 0.169 0.150 0.152

0.56 0.49 0.49 0.58 0.48 0.47 0.48 0.49 0.49 0.51 0.52 0.40 0.49 0.42 0.53 0.48 0.54 0.58 0.33 0.49 0.49

0.1038 0.1203 0.1205 0.1071 0.1194 0.1175 0.1195 0.1202 0.1133 0.1235 0.1248 0.1209 0.1201 0.0918 0.1248 0.1012 0.1299 0.1254 0.1002 0.1184 0.1134

0.111 0.146 0.145 0.122 0.146 0.145 0.145 0.146 0.151 0.146 0.146 0.193 0.144 0.123 0.142 0.135 0.147 0.130 0.156 0.154 0.152

0.94 0.83 0.83 0.88 0.82 0.81 0.82 0.83 0.75 0.84 0.86 0.63 0.84 0.75 0.88 0.75 0.88 0.97 0.64 0.77 0.75

0.0762 0.0773 0.0782 0.0750 0.0781 0.0737 0.0771 0.0771 0.0803 0.0826 0.0816 0.0639 0.0777 0.0638 0.0847 0.0673 0.0877 0.0900 0.0650 0.0690 0.0804

0.101 0.132 0.132 0.110 0.133 0.131 0.132 0.132 0.137 0.133 0.133 0.162 0.131 0.111 0.129 0.118 0.135 0.118 0.144 0.130 0.137

0.75 0.58 0.59 0.68 0.59 0.56 0.58 0.58 0.59 0.62 0.62 0.40 0.59 0.57 0.66 0.57 0.65 0.76 0.45 0.53 0.59

Panel B: Emerging markets 0.33 Argentina 0.74 Brazil Chile 0.33 0.09 Greece 0.24 Indonesia 1.03 Korea 1.63 Malaysia 1.49 Mexico Philippines 0.30 Portugal 0.09 1.43 Taiwan Thailand 0.97 0.28 Turkey

0.08 2.77 0.70 0.10 0.89 2.66 1.07 1.18 0.59 0.15 1.65 0.86 0.60

0.1340 0.5189 0.1042 0.0322 0.1621 0.0898 0.0750 0.1718 0.0813 0.0490 0.0688 0.0523 0.4481

0.388 0.408 0.193 0.318 0.334 0.293 0.256 0.230 0.268 0.203 0.270 0.352 0.454

0.35 1.27 0.54 0.10 0.48 0.31 0.29 0.75 0.30 0.24 0.26 0.15 0.99

0.1842 0.4366 0.0975 0.0879 0.1659 0.0910 0.0888 0.1531 0.1063 0.0805 0.0853 0.0874 0.3866

0.228 0.329 0.139 0.150 0.260 0.158 0.180 0.159 0.153 0.153 0.135 0.156 0.192

0.81 1.33 0.70 0.59 0.64 0.58 0.49 0.96 0.69 0.53 0.63 0.56 2.02

0.2351 0.5079 0.1329 0.1330 0.2028 0.1298 0.1245 0.1911 0.1414 0.1268 0.1221 0.1240 0.4356

0.235 0.326 0.132 0.143 0.236 0.160 0.176 0.151 0.152 0.146 0.135 0.158 0.183

1.00 1.56 1.01 0.93 0.86 0.81 0.71 1.27 0.93 0.87 0.90 0.79 2.38

0.1827 0.4627 0.1009 0.0919 0.1627 0.0941 0.0899 0.1602 0.1063 0.0847 0.0882 0.0849 0.4092

0.215 0.316 0.123 0.131 0.218 0.143 0.156 0.143 0.138 0.133 0.122 0.139 0.180

0.85 1.47 0.82 0.70 0.75 0.66 0.58 1.12 0.77 0.64 0.72 0.61 2.28

This table reports the 1993–2014 geometric annual returns (r), the standard deviation of returns (sd), and the return-to-risk (RR) ratios for the local portfolio, the 1/M portfolio, and the MRRPs and the MVPs optimized in each country’s local currency with no short positions and no positive weight constraints on market allocations. The weight of each country’s market capitalization (wi (%)) is reported as the percent of market capitalization for all 34 markets combined in U.S. dollars at the end of 1993 and 2012.

standard deviation of returns than the 1/M portfolio. Although the volatility of the 1/M portfolio is generally lower, the returns are not necessarily larger than the local market. As a result, not all investors achieve a higher RR ratio moving from the local portfolio to the naive 1/M portfolio. Several developed markets have RR ratios that are greater than the 1/M portfolio: Australia, Canada, Denmark, the Netherlands, New Zealand, Spain, Sweden, Switzerland, the United Kingdom, and the United States. All emerging markets have higher levels of volatility and lower RR ratios than the 1/M portfolio. While not presented in Table 1, the unconstrained MRRPs and MVPs often hold only a few, heavily weighted markets. Some of the overweighted markets can have small market capitalizations such as Denmark and Switzerland. This paper does not investigate how an optimal unconstrained MRRP or MVP to be held over 22 years is determined successfully ex ante. Strengthening the weight constraints used in optimization solutions can reduce ex-ante estimation error (Jagannathan & Ma, 2003). This paper reports the effect of weight constraints on the potential benefits from diversification. 3. Methods Investors can choose to maximize the RR ratio of their portfolio. Similarly, they can choose to minimize the volatility of their portfolio. They can choose to allocate funds in international markets where the investment opportunities of those markets can be stated

as a vector of multivariate Gaussian stochastic returns of N assets, RT = [r1 , r2 , . . ., rn ]. The mean of asset returns for these markets can be expressed as a vector . The variance–covariance of asset returns can be expressed as a positive definite matrix V. Let S be the set of all real vectors w that define the weights of the assets such that wT 1 = w1 + w2 + · · · + wn = 1, where 1 is an N vector of ones. Using the methods developed by Markowitz (1952), the efficient frontier of global investments can be formed when the objective function and restrictions are combined in order to find the efficient portfolio that minimizes volatility at every level of expected return such that min  =

{w,,}

1 T w Vw + (p − wT ) + (1 − wT 1) 2

(1)

where p is the expected return of the portfolio, and the shadow prices  and  are two positive constants. The quadratic programming solution of assets in a portfolio spanning wp can be obtained by the first-order conditions of Eq. (1). This study reports the potential diversification benefits available from portfolios optimized with no short sales and positive market allocations constrained by the 1993 global market capitalization weights at various weight constraint limits: one times (wx1), two times (wx2), five times (wx5), ten times (wx10) and no weight (nw) constraint. The 1/M portfolio is the most strongly weight constrained portfolio with market allocations restricted to equal the 1993 global market weights at the weight times one limit. A portfolio optimized with no short sales and no positive weight constraints

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Fig. 1. This graph presents the distribution of the difference in annual returns between the naive global portfolio and the local U.S. market for all 60–240 month holding periods between January 1993 and December 2012.

is referred to as an unconstrained portfolio in this study. The gains from diversifying into a portfolio optimized with no positive weight constraints and with short sales (nws) are also reported. An investor may choose to diversify out of the domestic market and into the MRRP optimized in their local currency. The maximum return-to-risk (MRR) ratio achieved by the MRRP is obtained by



MRR = max {wp }



wpT  (wpT Vwp )

1/2

|wpT ∈ S

(2)

where wp is the vector of weights of the assets held in the MRRP.3 The MRR measures the return achieved by the MRRP compared to the standard deviation of the MRRP. For the investor in country i, adjusting the portfolio out of that domestic market and into the internationally diversified portfolio that maximizes the RR ratio, the greatest increment of unit-risk performance is measured as ı=

MRR −1 RRi

(3)

where RRi is the RR ratio of market i. The ı (delta) measure is presented in McDowell (2017a) and represents the percentage change in the RR ratio that can be obtained from moving out of the local portfolio and into the optimally diversified international portfolio. Using a measure implemented in previous literature (e.g., Chiou, 2008; Li et al., 2003; McDowell, 2017a) the reduction in volatility that can result from diversification out of the domestic market and into the MVP is



ε=1−

T wMVP VwMVP

1/2

vi

(4)

where wMVP is the vector of weights of the assets held in the MVP optimized for an investor in country i and vi is the variance of the local market. A positive ε (epsilon) value represents the percentage reduction in portfolio volatility that can be achieved when diversifying out of the domestic market and into the optimal internationally diversified portfolio. A result approaching zero represents diminishing benefits from diversification. 3.1. Testing the statistical significance of the diversification benefits Fig. 1 presents the difference in the annualized returns provided by the naive global time-varying market capitalization weighted portfolio and the local U.S. market portfolio for various holding periods starting from January 1993 and ending in December 2012. The

3 To ensure feasible allocations, the sum of the portfolio weights must equal 1. Setting the condition that market weights must be positive restricts short sales.

global portfolio returns are calculated using the annual 1993–2012 market capitalization weight data against the returns the markets provided each month. From each month, starting at January 1993, the returns for the local and naive global portfolios are calculated for each possible monthly holding period to the end of 2012. Starting from January 1993 there are 240 measurable one month holding periods and a single measurable 240 month holding period. The maximum and minimum difference in outcomes, along with the 75%, 50% and 25% quantiles, are shown in Fig. 1. The graph presents the distribution of the 60–240 month holding period return results to reduce the scale of the graph that occurs from presenting shorter holding periods. Fig. 1 shows that the global portfolio does not always outperform the local U.S. market portfolio. The 50% quantile performance of the naive global portfolio minus the local portfolio is positive for all of the 60–240 month holding periods presented. For holding periods shorter than 10 years, the global portfolio underperformed the local portfolio as much as 25% of the time. The figure shows that there tends to be a larger distribution in the potential difference in annual returns between the global portfolio and local portfolio during shorter holding periods than compared to longer holding periods. These historical results suggest that naive diversification into the global portfolio may provide a U.S. investor with potential excess returns beyond the local portfolio, but the magnitude of these gains are not constant across time. The graphs presented in Fig. 2 report the global time-varying market capitalization weighted portfolio performance versus the local market of 10 countries for all possible 60–240 month holding periods from 1993 to 2012. As with Fig. 1, a positive difference occurs when the naive global portfolio outperforms the local market portfolio. There is no country for which the naive global portfolio always provides superior returns than the local market. While there are countries for which the naive global portfolio can provide greater returns than the local market much of the time, there are also markets that more often outperform the naive global portfolio. The size of the distribution in possible return differences between the naive global portfolio and the domestic portfolio is different for each country. Because the benefits from diversification presented in this paper are determined from finite sample-based estimates rather than from the true population of market returns, one cannot necessarily conclude that an optimized portfolio with a higher sample-based estimate is indeed better than the local portfolio. Furthermore, the measured benefits from diversification presented in this paper are formed using the data in sample and are likely to be greater than the benefits that can be captured by investors forming optimal portfolios ex ante using return and volatility estimates prone to estimation error. For this reason, the Ledoit and Wolf (2008) studentized time series bootstrap confidence interval tests are used

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Fig. 2. Graphs presenting the distribution of the difference in annual returns between the naive global portfolio and various domestic markets in the local currency for all 60–240 month holding periods between January 1993 and December 2012.

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6 Table 2 MRRP delta results. Market

wx1

wx2

wx5

wx10

nw

Panel A: Developed markets −25.01 (0.598) Australia 309.64 (0.140) Austria 13.37 (0.770) Belgium Canada −11.43 (0.920) Denmark −32.59 (0.292) 1.95 (0.996) Finland 17.59 (0.438) France 17.23 (0.570) Germany 35.97 (0.418) H.K. Ireland 141.20 (0.156) Italy 76.88 (0.260) Japan 304.93 (0.070) −1.70 (0.814) Holland −9.22 (0.986) N.Z. 15.66 (0.716) Norway 71.13 (0.292) Singapore −1.18 (0.898) Spain −5.29 (0.998) Sweden Suisse −45.56 (0.216) −8.81 (0.910) U.K. U.S. −23.50 (0.438)

−6.18 (0.960) 421.39 (0.096) 44.34 (0.562) 17.11 (0.530) −13.63 (0.630) 30.37 (0.678) 49.88 (0.182) 49.22 (0.252) 79.68 (0.288) 206.38 (0.048) 122.09 (0.100) 411.71 (0.066) 25.16 (0.402) 20.78 (0.702) 46.86 (0.448) 126.55 (0.140) 23.38 (0.536) 19.64 (0.558) −26.11 (0.428) 17.54 (0.262) 1.19 (0.548)

2.41 (0.792) 451.11 (0.038) 52.55 (0.412) 23.58 (0.378) −8.42 (0.838) 38.46 (0.540) 58.45 (0.068) 57.75 (0.150) 86.57 (0.260) 222.84 (0.046) 134.65 (0.064) 430.19 (0.046) 32.32 (0.208) 30.78 (0.534) 55.26 (0.304) 135.92 (0.156) 29.95 (0.386) 27.33 (0.302) −21.27 (0.526) 21.78 (0.146) 5.05 (0.202)

12.45 (0.502) 487.55 (0.010) 62.54 (0.330) 29.32 (0.184) −3.01 (0.966) 48.25 (0.388) 68.88 (0.024) 68.17 (0.032) 93.13 (0.190) 242.71 (0.028) 149.73 (0.044) 450.32 (0.042) 41.07 (0.076) 42.42 (0.374) 63.97 (0.272) 147.62 (0.088) 38.25 (0.264) 35.91 (0.170) −15.45 (0.708) 27.11 (0.100) 8.77 (0.218)

26.45 (0.118) 594.30 (0.004) 92.40 (0.100) 35.46 (0.152) 14.64 (0.346) 75.83 (0.252) 100.1 (0.006) 98.68 (0.014) 106.52 (0.162) 300.72 (0.010) 190.38 (0.020) 527.75 (0.044) 66.15 (0.004) 63.14 (0.162) 90.41 (0.096) 166.44 (0.100) 60.67 (0.116) 58.18 (0.076) 5.83 (0.446) 43.78 (0.048) 16.42 (0.324)

Panel B: Emerging markets 133.47 (0.282) Argentina 4.47 (0.894) Brazil Chile 30.39 (0.454) 479.57 (0.104) Greece 31.44 (0.906) Indonesia 88.43 (0.306) Korea 68.63 (0.570) Malaysia 29.04 (0.454) Mexico Philippines 128.37 (0.168) Portugal 117.85 (0.172) 147.16 (0.130) Taiwan Thailand 277.02 (0.224) 104.37 (0.006) Turkey

167.12 (0.230) 14.12 (0.616) 59.87 (0.284) 612.85 (0.056) 50.95 (0.684) 130.56 (0.174) 115.31 (0.376) 49.81 (0.188) 175.95 (0.114) 174.00 (0.096) 206.81 (0.088) 366.34 (0.112) 121.08 (0.002)

171.59 (0.160) 15.89 (0.500) 66.10 (0.230) 650.18 (0.022) 56.16 (0.596) 142.77 (0.112) 123.49 (0.316) 55.95 (0.098) 184.00 (0.084) 188.63 (0.050) 217.46 (0.048) 380.89 (0.110) 126.43 (0.002)

176.30 (0.162) 17.47 (0.412) 73.06 (0.216) 697.37 (0.016) 60.51 (0.494) 153.31 (0.050) 130.92 (0.226) 62.90 (0.032) 193.07 (0.058) 206.90 (0.032) 230.60 (0.060) 397.25 (0.096) 131.79 (0.002)

189.96 (0.114) 22.44 (0.128) 86.82 (0.064) 818.04 (0.006) 77.47 (0.162) 165.30 (0.036) 142.25 (0.210) 69.82 (0.020) 206.09 (0.060) 260.11 (0.006) 253.64 (0.044) 428.17 (0.076) 140.94 (0.002)

nws

% benefit gained wx1

wx2

wx5

wx10

nws

106.87 (0.036) 1093.87 (0.016) 230.09 (0.052) 137.90 (0.014) 98.74 (0.080) 208.53 (0.028) 245.20 (0.018) 241.69 (0.020) 299.20 (0.018) 585.46 (0.010) 394.38 (0.010) 1247.22 (0.008) 185.22 (0.022) 196.97 (0.014) 213.52 (0.038) 393.52 (0.008) 171.78 (0.026) 154.15 (0.020) 117.19 (0.068) 164.18 (0.022) 125.26 (0.038)

−95 52 14 −32 −223 3 18 17 34 47 40 58 −3 −15 17 43 −2 −9 −781 −20 −143

−23 71 48 48 −93 40 50 50 75 69 64 78 38 33 52 76 39 34 −448 40 7

9 76 57 66 −58 51 58 59 81 74 71 82 49 49 61 82 49 47 −365 50 31

47 82 68 83 −21 64 69 69 87 81 79 85 62 67 71 89 63 62 −265 62 53

404 184 249 389 674 275 245 245 281 195 207 236 280 312 236 236 283 265 2009 375 763

391.29 (0.014) 88.84 (0.022) 197.77 (0.022) 1403.09 (0.002) 223.00 (0.014) 368.52 (0.012) 394.17 (0.014) 155.28 (0.004) 421.79 (0.004) 508.07 (0.004) 494.53 (0.006) 874.31 (0.004) 219.96 (0.002)

70 20 35 59 41 53 48 42 62 45 58 65 74

88 63 69 75 66 79 81 71 85 67 82 86 86

90 71 76 79 72 86 87 80 89 73 86 89 90

93 78 84 85 78 93 92 90 94 80 91 93 94

206 396 228 172 288 223 277 222 205 195 195 204 156

This table reports, in percentage form, the delta benefits from diversification out of each domestic market and into MRRPs optimized with no shorts and the 1993 market capitalization weight constraints at the one times (wx1), two times (wx2), five times (wx5), 10 times (wx10) and no weight constraint (nw) level. The results for the MRRPs with no weight constraints and short sales (nws) are also presented. The p-value results from the Ledoit and Wolf (2008) Sharpe ratio tests using a block size of 5 and 499 iterations are presented in parentheses. The percent of the unconstrained benefits captured at each constraint level are reported in the last five columns.

to report the significance of the benefits achieved by an optimized portfolio versus the local market portfolio.4 This assists in determining at what level of relaxed weight constraints an optimized portfolio has the potential to offer statistically significant positive diversification benefits that may justify an investor’s attempt to capture the diversification benefits from optimization. The Ledoit and Wolf (2008) inference methods provide a p-value measuring the significance of the hypothesis that the difference between the RR ratio or the volatility of the paired data points of the monthly returns of two portfolios is zero. The tests are designed to address the non-normality of returns and fat-tail events that occur with historical financial data. The tests are performed using a block length of 5 with 499 iterations. A 10% result is treated as statistically significant in this paper.

4 This paper uses ‘raw’ returns, rather than excess returns, in the optimizations and the reported results. This is done to avoid reducing the size of the measurable sample period because of incomplete risk-free data for some markets. Driessen and Laeven (2007), which also reports cross-country diversification benefits, similarly identifies issues related to incomplete risk-free data. As reported in Wolf and Wunderli (2012), using raw returns rather than excess returns with the Ledoit and Wolf (2008) bootstrapped Sharpe and volatility tests does not tend to change the results qualitatively.

4. Results This section reports the results of examining the potential benefits of international diversification with weight constraints using the data and methods presented in Sections 2 and 3. First, the delta and epsilon results for the 1993–2014 investment period are presented. The benefits of diversification are tested for statistical significance using the Ledoit and Wolf (2008) bootstrap testing methods designed to test whether the difference between two portfolio strategies is significantly different from zero. Analysis of these results seeks to determine whether the naive 1/M portfolio provides positive diversification benefits for all investors and whether optimized portfolios, with or without weight constraints, offer significant efficiency gains beyond the domestic market portfolio. Table 2 reports the delta benefits from diversifying out of an investor’s domestic market and into the no shorts restricted optimal MRRP constrained by the 1993 market capitalization weights at various weight constraint limits: one times (wx1), two times (wx2), five times (wx5), ten times (wx10) and no weight constraints (nw). The portfolio constrained to one times each market’s capitalization weight is the 1/M portfolio. The benefits from diversifying into the MRRP optimized with no positive weight constraints and with short sales (nws) is also reported. The results from the Ledoit and Wolf (2008) Sharpe ratio tests are presented in parentheses. The p-values report the significance of the hypothesis that the difference between the RR ratio of the monthly returns of the domestic

Please cite this article in press as: McDowell, S. The benefits of international diversification with weight constraints: A cross-country examination. The Quarterly Review of Economics and Finance (2018), https://doi.org/10.1016/j.qref.2018.02.003

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7

Table 3 MVP epsilon results. Market

wx1

wx2

wx5

wx10

nw

Panel A: Developed markets 10.17 (0.082) Australia 32.65 (0.002) Austria 20.55 (0.180) Belgium Canada 21.46 (0.004) Denmark 17.28 (0.002) 50.95 (0.002) Finland 16.97 (0.002) France 28.06 (0.002) Germany 41.15 (0.002) H.K. Ireland 29.19 (0.004) Italy 30.50 (0.002) Japan 3.46 (0.358) 18.90 (0.002) Holland 19.91 (0.012) N.Z. 34.34 (0.002) Norway 41.54 (0.002) Singapore 28.67 (0.002) Spain 38.37 (0.002) Sweden Suisse −9.59 (0.100) −8.79 (0.056) U.K. U.S. −1.98 (0.572)

15.14 (0.016) 37.04 (0.006) 25.67 (0.092) 27.53 (0.002) 22.63 (0.002) 54.14 (0.002) 22.37 (0.002) 32.74 (0.002) 46.39 (0.002) 33.69 (0.002) 35.03 (0.002) 12.20 (0.010) 24.27 (0.002) 23.76 (0.002) 38.37 (0.002) 46.32 (0.002) 33.17 (0.002) 42.53 (0.002) −2.61 (0.666) 0.07 (1.000) 7.13 (0.004)

19.18 (0.004) 39.69 (0.002) 28.85 (0.038) 28.71 (0.002) 25.73 (0.002) 56.35 (0.002) 25.67 (0.002) 35.55 (0.002) 46.69 (0.002) 36.48 (0.002) 37.56 (0.002) 12.70 (0.004) 27.46 (0.002) 26.77 (0.002) 41.40 (0.002) 47.44 (0.002) 35.72 (0.002) 45.28 (0.002) 1.60 (0.766) 4.88 (0.118) 7.65 (0.008)

21.45 (0.002) 40.73 (0.002) 30.12 (0.026) 28.74 (0.002) 26.96 (0.002) 57.21 (0.002) 26.96 (0.002) 36.67 (0.002) 46.86 (0.002) 37.42 (0.002) 38.38 (0.002) 13.19 (0.006) 28.66 (0.002) 28.41 (0.002) 42.23 (0.002) 47.83 (0.002) 36.70 (0.002) 46.38 (0.002) 3.83 (0.466) 5.65 (0.062) 7.92 (0.004)

23.48 (0.002) 41.60 (0.002) 31.20 (0.022) 28.74 (0.002) 27.97 (0.002) 57.81 (0.002) 27.96 (0.002) 37.64 (0.002) 46.86 (0.002) 37.96 (0.002) 38.85 (0.002) 13.30 (0.004) 29.57 (0.002) 31.41 (0.002) 42.47 (0.002) 47.85 (0.002) 37.44 (0.002) 46.97 (0.002) 6.94 (0.024) 5.65 (0.038) 7.92 (0.004)

Panel B: Emerging markets 41.13 (0.322) Argentina 19.45 (0.116) Brazil Chile 28.25 (0.004) 52.90 (0.002) Greece 22.12 (0.760) Indonesia 46.21 (0.076) Korea 29.77 (0.372) Malaysia 30.93 (0.406) Mexico Philippines 42.73 (0.002) Portugal 24.63 (0.002) 49.87 (0.002) Taiwan Thailand 55.65 (0.002) 57.78 (0.002) Turkey

43.49 (0.354) 21.30 (0.142) 31.96 (0.002) 55.92 (0.002) 24.43 (0.706) 48.62 (0.070) 33.69 (0.336) 33.74 (0.340) 46.18 (0.002) 29.45 (0.002) 53.73 (0.002) 58.19 (0.002) 58.82 (0.002)

43.84 (0.294) 21.92 (0.104) 33.06 (0.002) 57.55 (0.002) 26.70 (0.632) 49.80 (0.074) 35.71 (0.306) 35.67 (0.308) 47.26 (0.002) 32.37 (0.002) 54.46 (0.002) 59.39 (0.002) 59.25 (0.002)

44.11 (0.296) 22.27 (0.092) 33.67 (0.002) 58.26 (0.002) 28.13 (0.600) 50.88 (0.020) 38.03 (0.254) 37.26 (0.266) 47.84 (0.002) 33.51 (0.002) 54.76 (0.002) 60.21 (0.002) 59.65 (0.002)

44.58 (0.282) 22.70 (0.022) 36.64 (0.002) 58.87 (0.002) 34.68 (0.362) 51.13 (0.010) 39.16 (0.142) 37.89 (0.148) 48.47 (0.002) 34.39 (0.002) 54.78 (0.002) 60.36 (0.002) 60.38 (0.002)

nws

% benefit gained wx1

wx2

wx5

wx10

nws

36.44 (0.002) 53.54 (0.002) 45.10 (0.006) 45.21 (0.002) 42.21 (0.002) 65.70 (0.002) 42.45 (0.002) 50.35 (0.002) 62.54 (0.002) 50.00 (0.002) 51.29 (0.002) 33.06 (0.002) 43.94 (0.002) 41.58 (0.002) 51.89 (0.002) 59.80 (0.002) 49.81 (0.002) 56.07 (0.002) 26.97 (0.004) 31.34 (0.002) 35.03 (0.002)

43 78 66 75 62 88 61 75 88 77 79 26 64 63 81 87 77 82 −138 −156 −25

64 89 82 96 81 94 80 87 99 89 90 92 82 76 90 97 89 91 −38 1 90

82 95 92 100 92 97 92 94 100 96 97 96 93 85 97 99 95 96 23 86 97

91 98 97 100 96 99 96 97 100 99 99 99 97 90 99 100 98 99 55 100 100

155 129 145 157 151 114 152 134 133 132 132 249 149 132 122 125 133 119 389 555 442

55.01 (0.218) 28.31 (0.004) 48.66 (0.002) 67.27 (0.002) 43.90 (0.026) 58.69 (0.002) 52.46 (0.002) 48.76 (0.006) 60.30 (0.002) 47.46 (0.002) 65.41 (0.002) 67.89 (0.002) 64.32 (0.002)

92 86 77 90 64 90 76 82 88 72 91 92 96

98 94 87 95 70 95 86 89 95 86 98 96 97

98 97 90 98 77 97 91 94 97 94 99 98 98

99 98 92 99 81 100 97 98 99 97 100 100 99

123 125 133 114 127 115 134 129 124 138 119 112 107

This table reports, in percentage form, the epsilon benefits from diversification out of each domestic market and into MVPs optimized with no shorts and the 1993 market capitalization weight constraints at the one times (wx1), two times (wx2), five times (wx5), 10 times (wx10) and no weight constraint (nw) level. The results for the MVPs with no weight constraints and short sales (nws) are also presented. The p-value results from the Ledoit and Wolf (2008) volatility tests using a block size of 5 and 499 iterations are presented in parentheses. The percent of the unconstrained benefits captured at each constraint level are reported in the last five columns.

portfolio and the optimized portfolio is zero. A 10% result is treated as statistically significant in this paper. The last five columns report the portion of the potential gains achieved by the unconstrained MRRP captured by the different MRRPs. The results presented in Table 2 report that the 1/M portfolio does not provide improved RR performance over all domestic market portfolios. Investors in 10 of the 21 developed markets have reduced RR performance with the 1/M portfolio. Diversification out of emerging markets and into the 1/M portfolio provides benefits. In the case of Brazil, the RR ratio only improves by 4.47%. Of the 24 countries reported to have positive potential diversification benefits with the 1/M portfolio, only Japan and Turkey have gains that are significantly different than the domestic portfolio. Investors in three countries do not benefit from optimization at the two times weight constraint level: Australia, Denmark and Switzerland. The United States only achieves a 1.19% improvement of the RR ratio. For 22 countries the two times weight constraint level captures a majority of the potential gains from diversification offered by the unconstrained MRRP. For example, an Argentinian investor can capture 88% of the potential unconstrained MRRP delta benefits with the wx2 MRRP. Only Austria, Ireland, Japan, Greece, Portugal and Turkey have positive potential benefits from diversification into the wx2 MRRP that are significantly different than the domestic portfolio. The unconstrained MRRP provides positive diversification benefits for investors in all

countries. The RR gains are significant versus 10 developed markets and 9 emerging markets. The U.S. results reported in Table 2 for MRRPs with no short sales are consistent with the insignificant positive RR gains reported in McDowell (2017a) for similarly constrained portfolios held during the 1988–2014 investment period. When short sales are considered the MRRPs offer statistically significant diversification gains for all investors, which is similar to the significant positive Sharpe ratio improvements reported in Driessen and Laeven (2007). Table 3 reports the epsilon benefits of diversification into the MVP. The results from the Ledoit and Wolf (2008) volatility tests are presented in parentheses. Diversification into the 1/M portfolio does not provide volatility reducing benefits for all investors. The domestic Suisse, U.K., and U.S. markets have lower levels of volatility than the 1/M portfolio. The 1/M portfolio’s volatility reduction benefits are significant for 17 developed countries and 8 emerging markets. The smallest gains from weakening the weight constraints on the MVP come from diversifying out of the U.S., U.K., and Switzerland. For investors in most countries, the majority of the unconstrained MVP epsilon benefits are captured by the 1/M portfolio. The nw MVPs and the nws MVPs provide significant volatility reducing benefits for investors in 30 countries and 33 countries, respectively. Table 4 reports the delta performance of the MVPs. An investor might choose to diversify into the MVP in order to reduce the

Please cite this article in press as: McDowell, S. The benefits of international diversification with weight constraints: A cross-country examination. The Quarterly Review of Economics and Finance (2018), https://doi.org/10.1016/j.qref.2018.02.003

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8 Table 4 MVP delta results. Market

wx1

wx2

wx5

wx10

nw

Panel A: Developed markets −25.01 (0.582) Australia 309.64 (0.136) Austria 13.37 (0.768) Belgium Canada −11.43 (0.912) Denmark −32.59 (0.292) 1.95 (0.992) Finland 17.59 (0.440) France 17.23 (0.574) Germany 35.97 (0.440) H.K. Ireland 141.20 (0.174) Italy 76.88 (0.212) Japan 304.93 (0.060) −1.70 (0.832) Holland −9.22 (0.978) N.Z. 15.66 (0.716) Norway 71.13 (0.292) Singapore −1.18 (0.900) Spain −5.29 (1.000) Sweden Suisse −45.56 (0.208) −8.81 (0.874) U.K. U.S. −23.50 (0.434)

−26.68 (0.588) 311.05 (0.154) 13.93 (0.806) 1.44 (0.858) −31.93 (0.272) 1.22 (0.928) 17.39 (0.484) 17.63 (0.648) 49.10 (0.452) 147.57 (0.138) 79.76 (0.280) 245.32 (0.084) −0.69 (0.922) −14.64 (0.926) 21.68 (0.746) 78.87 (0.336) 0.94 (0.912) −2.02 (0.986) −51.59 (0.122) −6.21 (0.986) −15.94 (0.458)

−19.06 (0.702) 334.31 (0.092) 20.99 (0.710) 4.46 (0.708) −26.94 (0.328) 6.76 (0.986) 24.90 (0.368) 24.24 (0.554) 53.58 (0.358) 161.46 (0.146) 84.92 (0.234) 251.69 (0.044) 4.73 (0.746) −6.82 (0.988) 27.73 (0.604) 84.77 (0.248) 6.16 (0.832) 3.66 (0.858) −48.12 (0.110) −1.29 (0.722) −13.39 (0.608)

−10.59 (0.896) 372.51 (0.080) 31.08 (0.614) 4.86 (0.698) −22.21 (0.446) 16.24 (0.884) 34.87 (0.248) 35.22 (0.408) 61.93 (0.296) 180.19 (0.088) 98.56 (0.216) 277.95 (0.034) 13.40 (0.574) 9.29 (0.708) 37.27 (0.558) 97.37 (0.208) 13.75 (0.644) 12.59 (0.684) −43.45 (0.104) −0.87 (0.734) −8.72 (0.830)

1.52 (0.698) 390.25 (0.062) 36.98 (0.552) 4.85 (0.702) −17.88 (0.610) 22.28 (0.754) 41.80 (0.154) 39.99 (0.332) 61.93 (0.328) 194.14 (0.076) 108.63 (0.180) 296.84 (0.026) 18.20 (0.388) 24.70 (0.410) 42.32 (0.494) 101.23 (0.164) 18.34 (0.508) 24.54 (0.466) −25.37 (0.260) −0.87 (0.744) −8.72 (0.862)

Panel B: Emerging markets 133.47 (0.294) Argentina 4.47 (0.898) Brazil Chile 30.39 (0.552) 479.57 (0.094) Greece 31.44 (0.910) Indonesia 88.43 (0.342) Korea 68.63 (0.556) Malaysia 29.04 (0.444) Mexico Philippines 128.37 (0.260) Portugal 117.85 (0.188) 147.16 (0.138) Taiwan Thailand 277.02 (0.210) 104.37 (0.002) Turkey

142.66 (0.278) 13.21 (0.666) 39.85 (0.484) 487.92 (0.110) 32.37 (0.888) 88.15 (0.340) 81.85 (0.576) 38.61 (0.318) 138.10 (0.214) 122.24 (0.192) 156.68 (0.138) 274.81 (0.250) 114.96 (0.002)

145.34 (0.308) 12.61 (0.638) 43.31 (0.412) 516.20 (0.088) 38.54 (0.782) 96.20 (0.246) 91.25 (0.460) 42.82 (0.196) 146.45 (0.142) 135.10 (0.158) 164.45 (0.112) 294.55 (0.186) 119.04 (0.002)

147.05 (0.262) 13.03 (0.566) 49.69 (0.354) 562.97 (0.062) 41.52 (0.640) 112.04 (0.108) 96.24 (0.362) 47.96 (0.092) 157.32 (0.122) 152.24 (0.114) 179.00 (0.138) 310.96 (0.126) 124.16 (0.002)

145.87 (0.210) 15.36 (0.438) 52.73 (0.198) 593.45 (0.058) 53.73 (0.232) 114.50 (0.078) 97.02 (0.198) 50.13 (0.044) 153.91 (0.056) 163.39 (0.092) 183.54 (0.124) 309.82 (0.150) 130.53 (0.002)

nws

% benefit gained wx1

wx2

wx5

wx10

nws

19.90 (0.720) 450.03 (0.194) 53.64 (0.872) 38.53 (0.704) −7.97 (0.316) 42.44 (0.956) 58.05 (0.720) 57.38 (0.784) 95.27 (0.732) 230.36 (0.262) 145.31 (0.260) 369.16 (0.364) 35.64 (0.988) 24.78 (0.972) 52.61 (0.752) 119.09 (0.510) 42.64 (0.838) 47.11 (0.664) −27.48 (0.026) 19.68 (0.734) 10.07 (0.422)

−1640 79 36 −236 182 9 42 43 58 73 71 103 −9 −37 37 70 −6 −22 180 1013 269

−1750 80 38 30 179 5 42 44 79 76 73 83 −4 −59 51 78 5 −8 203 715 183

−1250 86 57 92 151 30 60 61 87 83 78 85 26 −28 66 84 34 15 190 149 153

−694 95 84 100 124 73 83 88 100 93 91 94 74 38 88 96 75 51 171 100 100

1305 115 145 794 45 191 139 143 154 119 134 124 196 100 124 118 232 192 108 −2263 −115

182.37 (0.164) 34.21 (0.224) 77.61 (0.368) 715.01 (0.112) 57.01 (0.524) 111.28 (0.226) 130.92 (0.454) 79.97 (0.058) 198.78 (0.124) 205.57 (0.182) 222.94 (0.140) 360.41 (0.188) 173.77 (0.002)

91 29 58 81 59 77 71 58 83 72 80 89 80

98 86 76 82 60 77 84 77 90 75 85 89 88

100 82 82 87 72 84 94 85 95 83 90 95 91

101 85 94 95 77 98 99 96 102 93 98 100 95

125 223 147 120 106 97 135 160 129 126 121 116 133

This table reports, in percentage form, the delta benefits from diversification out of each domestic market and into MVPs optimized with no shorts and the 1993 market capitalization weight constraints at the one times (wx1), two times (wx2), five times (wx5), 10 times (wx10) and no weight constraint (nw) level. The results for the MVPs with no weight constraints and short sales (nws) are also presented. The p-value results from the Ledoit and Wolf (2008) Sharpe ratio tests using a block size of 5 and 499 iterations are presented in parentheses. The percent of the unconstrained benefits captured at each constraint level are reported in the last five columns.

estimation error associated with market return estimates used in ex-ante mean-variance optimization (e.g., Jagannathan & Ma, 2003; Jorion, 1985). This is likely to reduce the economic gains that can be achieved from optimization into the MVP versus a similarly weight constrained mean-variance optimized MRRP. As previously presented in Table 2, investors in 10 of the 21 developed markets have reduced RR performance with the 1/M portfolio. As the weight constraints on the MVP are relaxed, the number of countries that achieve positive RR improvements increases. Although the volatility reducing benefits of diversification are significant for many investors, the low RR ratios of some portfolios, relative to the domestic market portfolio, do not necessarily support the argument for diversification. For example, in the case of a U.S. investor diversifying into the MVP with market allocations constrained to two times a market’s capitalization weight, volatility is reduced by 7.13% and is reported to be statistically significant. However, the RR ratio of this MVP is 15.94% lower than the domestic market’s RR ratio. Following the principles of the separation theorem, a U.S. investor could form a portfolio that obtains the same volatility as the 1/M portfolio with a larger RR ratio by investing in the U.S. market and holding a portion of their portfolio in a risk-free asset. At the two times market capitalization constraint level, investors in 8 developed countries do not achieve higher RR ratios than the domestic market. The unconstrained MVP does not have higher RR ratios than the domestic market for investors in Denmark, Switzerland, the United Kingdom and the United States. Investors

in three developed countries and six emerging markets have positive RR benefits from diversification into the unconstrained MVP that are statistically different from their domestic market portfolio. While not presented here, the use of short sales has the potential to affect relatively large marginal reductions in volatility, which improves RR ratios versus the nw MVP, with relatively small changes to portfolio returns compared to the domestic market portfolio. As a result, the significance of the RR gains for some countries weaken compared to the nw MVPs, and only Mexican and Turkish investors realize significant positive RR benefits from diversification into the nws MVP. While investors may have the potential to achieve significant volatility reducing benefits from international diversification into an MVP optimized with or without short sales and weight constraints, it is not evident from these empirical results that there will also be significant positive economic benefits. These results extend Li et al. (2003) to report that MVPs optimized with or without short sales do not provide significant positive RR improvements to portfolio efficiency for U.S. investors. The negative MVP delta benefits presented for U.S. investors diversifying into weight constrained portfolios are also consistent with the results reported in McDowell (2017a). Reporting the potential volatility reducing benefits and RR gains from diversifying into MVPs with various levels of market constraints for investors in 34 countries also extends the cross-country results presented in Driessen and Laeven (2007), which only reports the effect of short selling restrictions into the MRRP.

Please cite this article in press as: McDowell, S. The benefits of international diversification with weight constraints: A cross-country examination. The Quarterly Review of Economics and Finance (2018), https://doi.org/10.1016/j.qref.2018.02.003

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Table 5 MRRP global and local market allocations. Market (i)

wx2

wx5

wx10

nw

nws

Panel A: Developed markets 1.51 Australia Austria 0.21 Belgium 0.58 2.41 Canada 0.31 Denmark 0.17 Finland 3.37 France Germany 3.43 H.K. 2.85 Ireland 0.14 1.01 Italy 22.18 Japan 1.34 Holland 0.19 N.Z. 0.20 Norway 0.98 Singapore 0.88 Spain 0.79 Sweden 2.01 Suisse U.K. 8.52 37.98 U.S.

wi (%)

3.03 – 0.19 4.83 0.62 0.35 – – 1.68 – – – 0.55 0.38 0.07 – 1.75 1.59 4.02 5.96 73.78

[3.03] [–] [1.15] [4.83] [0.62] [0.35] [–] [–] [–] [–] [–] [–] [2.69] [0.38] [0.40] [–] [1.76] [1.59] [4.02] [16.91] [75.96]

7.18 – 0.36 4.60 1.54 0.49 – – 0.13 – – – 0.02 0.92 0.02 0.01 0.96 2.11 10.05 1.26 69.48

[7.57] [–] [2.89] [12.07] [1.54] [0.87] [–] [–] [–] [–] [–] [–] [–] [0.95] [1.01] [–] [4.41] [3.97] [10.05] [12.03] [80.87]

7.89 – 0.01 2.75 3.09 0.88 – – 0.06 – – – – 1.83 – 0.02 1.21 1.37 20.09 0.37 59.36

[15.15] [–] [–] [23.11] [3.09] [1.74] [–] [–] [–] [–] [–] [–] [–] [1.89] [2.02] [–] [8.82] [7.94] [20.09] [4.31] [72.27]

1.88 – – 0.45 34.41 0.96 – – 0.02 – – – – 0.05 – – – – 45.03 – 15.87

[46.57] [–] [–] [17.19] [38.32] [2.27] [–] [–] [–] [–] [–] [–] [–] [16.67] [–] [–] [–] [–] [66.12] [–] [31.05]

69.44 −43.93 27.12 28.05 106.40 15.11 −48.85 −25.49 −0.01 −55.75 −21.85 −44.89 −5.18 −22.49 −14.27 −6.95 62.52 −20.29 99.77 −16.15 48.48

[83.82] [−32.62] [32.38] [43.64] [100.99] [19.23] [−39.29] [−19.94] [−0.38] [−50.26] [−6.46] [−64.17] [−0.61] [41.54] [7.73] [1.39] [66.39] [0.65] [169.50] [34.52] [66.60]

Panel B: Emerging markets 0.33 Argentina Brazil 0.74 0.33 Chile Greece 0.09 0.24 Indonesia 1.03 Korea 1.63 Malaysia 1.49 Mexico Philippines 0.30 0.09 Portugal Taiwan 1.43 0.97 Thailand 0.28 Turkey

– 0.49 0.36 – 0.01 0.04 0.27 0.04 – – – – 0.01

[0.23] [1.47] [0.66] [–] [0.49] [2.06] [3.25] [2.97] [–] [–] [–] [–] [0.55]

– 0.17 0.13 – 0.02 0.05 0.36 0.11 – – – – 0.01

[–] [3.67] [1.65] [–] [1.22] [5.14] [8.13] [7.43] [–] [–] [–] [–] [1.39]

– 0.08 0.12 – 0.03 0.11 0.46 0.22 0.01 – – – 0.02

[–] [7.35] [3.30] [–] [2.44] [10.28] [16.27] [14.86] [–] [–] [–] [–] [2.77]

– 0.19 0.05 – 0.08 0.12 0.47 0.37 0.01 – – – 0.03

[–] [26.06] [16.18] [–] [27.93] [11.46] [16.11] [24.75] [–] [–] [–] [–] [11.76]

−8.24 1.22 −1.01 −23.03 −2.05 2.86 16.45 −5.02 −9.40 −39.57 2.52 −21.42 0.56

[13.26] [37.95] [24.84] [−20.84] [39.85] [24.17] [45.24] [34.71] [9.87] [−29.78] [8.46] [−17.22] [16.27]

This table reports the aggregate global allocation and local allocation for each market for the MRRPs optimized with no shorts and the 1993 market capitalization weight constraints at the two times (wx2), five times (wx5), 10 times (wx10) and no weight constraint (nw) level. The results for the MRRPs optimized with no positive weight constraints and with short sales (nws) are also presented. The domestic allocation is presented in brackets. The weight of each country’s market capitalization (wi (%)) is reported as the percent of market capitalization for all 34 markets combined in U.S. dollars at the end of 1993.

The empirical results presented in this paper suggest that not all investors with long investment horizons are certain to benefit from naive diversification. Nor do optimized portfolios with weakened weight constraints necessarily achieve RR ratios that are greater than the domestic market. Furthermore, optimized portfolios that achieve positive RR gains may not be significantly different than the local market portfolio. Considering the documented difficulties of outperforming naively diversified portfolios because of estimation error in ex-ante optimization (e.g., DeMiguel, Garlappi, & Uppal, 2009; Jagannathan & Ma, 2003; Jorion, 1985), these results suggest that for investors that enforce weight constraints on overseas market allocations the benefits from international diversification may not be as significant as previously reported (e.g., Chiou, 2008; Driessen & Laeven, 2007; Li et al., 2003).

4.1. A disequilibrium in market allocations This subsection reports the global and local market allocations for the various MRRPs and MVPs presented in this paper. The global demand is calculated as the sum of all countries’ market capitalization weight adjusted allocation to each market. The local demand is the domestic investor’s optimal allocation for the local market. The results show that an imbalance can occur between the global demand for markets that provide potential portfolio efficiencies versus the supply of available equity in those markets.

Table 5 presents the global and local market allocations for the MRRPs with relaxed weight constraints. It is evident from the global weights presented for each portfolio that there can be a disequilibrium in the demand and supply of equity in some markets. For example, the wx2 MRRP global allocation for the U.S. market is 73.78%. The market capitalization of the U.S. market is only 37.98% of global market capitalization in 1993. The global allocation includes the local U.S. investor’s optimal allocation for the U.S. market of 75.96%, which is presented in brackets. Subtracting the U.S. investor’s local allocation from the reported global allocation makes the non-U.S. investors’ aggregate market-capitalization adjusted global allocation to the U.S. market 44.93%. There is a disequilibrium between the U.S. investor’s optimal allocation to the U.S. market and the non-U.S. investors’ demand for the same market capital. As weight constraints are relaxed, the demand and supply disequilibrium can become more extreme. For example, the nw MRRP global allocation for the Suisse market is 45.03%. This exceeds the Suisse market’s global capitalization of 2.01% by more than 22 times. The Suisse investor’s MRRP allocation alone is 66.12% of this market’s capitalization. The global demand for the Danish market is more than 100 times that market’s capitalization. The aggregate global market-capitalization adjusted allocation to the Danish and Suisse markets is 79.44%. Combined, Denmark and Switzerland represent only 2.32% of global capitalization.

Please cite this article in press as: McDowell, S. The benefits of international diversification with weight constraints: A cross-country examination. The Quarterly Review of Economics and Finance (2018), https://doi.org/10.1016/j.qref.2018.02.003

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10 Table 6 MVP global and local market allocations. Market (i)

wx2

wx5

wx10

nw

nws

Panel A: Developed markets 1.51 Australia Austria 0.21 Belgium 0.58 2.41 Canada 0.31 Denmark 0.17 Finland 3.37 France Germany 3.43 H.K. 2.85 Ireland 0.14 1.01 Italy 22.18 Japan 1.34 Holland 0.19 N.Z. 0.20 Norway 0.98 Singapore 0.88 Spain 0.79 Sweden 2.01 Suisse U.K. 8.52 37.98 U.S.

wi (%)

0.35 0.08 0.30 0.24 0.20 – 0.87 – 0.06 0.01 0.32 22.28 0.03 0.13 0.01 0.03 0.11 – 4.02 16.93 43.93

[3.03] [0.42] [1.15] [4.83] [0.62] [–] [6.75] [–] [–] [0.27] [2.01] [44.36] [–] [0.38] [0.40] [–] [1.76] [1.59] [4.02] [17.03] [52.71]

0.14 0.03 0.42 0.35 0.39 – – – 0.03 – 0.18 26.24 0.01 0.21 – 0.03 – – 9.97 22.04 34.02

[7.57] [0.56] [2.89] [9.00] [1.54] [–] [–] [–] [–] [–] [5.03] [45.54] [–] [0.95] [1.01] [–] [0.30] [3.97] [10.05] [42.58] [48.20]

0.27 – 0.31 0.27 0.45 – – – 0.04 – 0.06 24.62 – 0.27 – 0.02 – – 18.73 18.96 29.49

[15.15] [–] [3.00] [8.70] [3.09] [–] [–] [–] [–] [–] [5.74] [44.24] [–] [1.89] [0.18] [–] [–] [7.94] [20.09] [57.59] [45.53]

0.54 – – 0.21 0.20 – – – 0.01 – 0.03 23.93 – 0.11 – 0.02 – – 23.14 15.65 28.27

[33.97] [–] [–] [8.69] [1.04] [–] [–] [–] [–] [–] [3.00] [43.27] [–] [24.50] [–] [–] [–] [–] [54.07] [57.59] [45.53]

11.88 −5.70 0.94 −1.63 16.11 −6.45 −1.92 −8.59 −2.94 −10.42 5.78 22.25 −15.70 7.12 −13.23 −1.45 −9.16 −15.90 20.56 46.99 45.92

[52.30] [3.39] [8.01] [27.35] [15.47] [−1.26] [5.39] [−2.00] [−2.73] [−9.16] [17.22] [40.37] [−19.35] [26.96] [8.68] [6.07] [8.14] [3.44] [52.53] [89.14] [64.60]

Panel B: Emerging markets 0.33 Argentina Brazil 0.74 0.33 Chile Greece 0.09 0.24 Indonesia 1.03 Korea 1.63 Malaysia 1.49 Mexico Philippines 0.30 0.09 Portugal Taiwan 1.43 0.97 Thailand 0.28 Turkey

0.01 0.01 0.39 0.02 0.01 0.02 3.23 0.05 0.07 0.11 0.12 0.05 –

[0.65] [1.47] [0.66] [–] [0.49] [2.06] [3.25] [2.97] [0.60] [0.18] [2.86] [1.89] [0.55]

0.01 0.03 0.23 – 0.03 0.05 5.17 0.11 0.08 0.13 0.04 0.02 –

[1.63] [3.67] [1.65] [–] [1.22] [5.14] [8.13] [7.43] [1.49] [0.46] [1.05] [–] [1.39]

0.01 0.05 0.36 0.01 0.03 0.11 5.45 0.22 0.10 0.15 0.02 – –

[3.25] [7.35] [3.30] [–] [2.44] [10.28] [16.27] [14.86] [2.98] [0.92] [0.73] [–] [2.77]

0.04 0.13 0.38 0.01 0.12 0.15 5.59 0.34 0.12 0.96 0.01 – –

[11.13] [17.96] [23.57] [–] [31.94] [14.51] [27.58] [22.75] [11.84] [8.13] [0.77] [–] [10.58]

−0.36 −6.12 10.84 −3.09 −2.92 −0.53 11.05 −3.48 1.98 17.14 2.42 −8.73 −2.64

[22.34] [28.91] [32.18] [−5.91] [38.40] [20.40] [39.46] [35.57] [17.92] [18.53] [8.40] [−4.81] [15.03]

This table reports the aggregate global allocation and local allocation for each market for the MVPs optimized for the 1993–2014 investment period with no shorts and the 1993 market capitalization weight constraints at the two times (wx2), five times (wx5), 10 times (wx10) and no weight constraint (nw) level. The results for the MVPs optimized with no positive weight constraints and with short sales (nws) are also presented. The domestic allocation is presented in brackets. The weight of each country’s market capitalization (wi (%)) is reported as the percent of market capitalization for all 34 markets combined in U.S. dollars at the end of 1993.

Table 6 presents the global and local market allocations for the MVPs. As with the MRRP allocations, there can be an imbalance between the global demand for a market and the local supply of available equity in excess of the domestic investor’s optimal allocation. For example, the wx2 MVP global allocation for the U.K. market is 16.93%. This exceeds the U.K. market’s 8.52% portion of global capitalization. In the case of the nw MVP, the global marketcapitalization adjusted demand for the Suisse market is 23.14%. This is 11 times the Suisse market’s capitalization. Given the difficulties of forming mean-variance optimized portfolios that outperform naive investment strategies out of sample (e.g., DeMiguel, Garlappi, & Uppal, 2009; Jacobs et al., 2014), the benefits from diversification presented in this paper are only theoretical gains that investors may have the potential to capture. The portfolio allocations presented in Tables 5 and 6 suggest that, should universally accessible methods eventually be presented in the literature that significantly reduce estimation error in optimal portfolios formed for long investment horizons, there may be an imbalance between the demand for markets that provide potential portfolio efficiencies and the supply of available equity in those markets. Following basic economic principles of supply and demand, market prices would be expected to adjust if there is excess demand for a market’s equity. If markets are efficient, then this dynamic adjustment would continue until the measured benefit from diversification into the market is reduced and an equilibrium between market supply and demand is achieved. In such

a scenario, the potential benefits from diversification into these markets would likely only be captured by early participants in the trade. 5. Conclusion This paper reports the potential benefits from international diversification available to investors in 34 countries diversifying into weight constrained MRRPs and MVPs optimized in their local currency during the 1993–2014 investment period. The naive 1/M portfolio is not found to provide improved return-to-risk performance or lower volatility than the domestic market portfolio for all investors. While weakening the weight constraints imposed on the MRRP and the MVP increases the potential gains from diversification, the improved RR performance is not reported to be significantly different than the domestic market portfolio for many investors. Furthermore, there can be a disequilibrium between the global demand for equity in markets that provide portfolio efficiencies versus the supply of available equity, which is likely to constrain the potential gains that can be captured by investors. These results suggest that, for investors that enforce weight constraints on global market allocations in static optimized portfolios to be held over long investment horizons, the benefits from international diversification may not be as significant as reported in previous literature (e.g., Chiou, 2008; Driessen & Laeven, 2007; Li et al., 2003).

Please cite this article in press as: McDowell, S. The benefits of international diversification with weight constraints: A cross-country examination. The Quarterly Review of Economics and Finance (2018), https://doi.org/10.1016/j.qref.2018.02.003

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