RESEARCH BRIEF March 2012 In the ten years ending December 2011, the capitalizationweighted MSCI Emerging Markets Index (MSCI EM) provided an annualized total return of 14% with a volatility of 24%. Over the same period, an equal-country-weight portfolio would have had a higher return of 19% with a lower volatility of 22%. Why this extra return and lower volatility? David M. Stein, Ph.D. Chief Investment Officer Vassilii Nemtchinov, Ph.D. Director Applied Research Paul Bouchey, CFA Managing Director Research Peter Dykstra Research Intern Parametric 1918 Eighth Avenue Suite 3100 Seattle, WA 98109 T 206 694 5500 F 206 694 5581 www.parametricportfolio.com
There are numerous possible answers to this question. Past performance can be attributed to many factors: happenstance, higher returns in smaller countries, valuation differences, relative growth opportunities, or tendencies for the overreaction and subsequent reversal of prices. In this paper, we address an alternative explanation. Because of the high country volatility within emerging markets, and without a strong prior expectation of returns, we can mathematically expect higher long-term growth from a rebalanced, equal-weighted portfolio. Such a portfolio is designed to avoid the concentrations that build up in one that is cap-weighted and can exploit variability through volatility harvesting. Figure 1 shows the performance improvement of rebalancing an equal-country-weight strategy versus letting it drift. In each ten-year period, the rebalanced strategy outperforms. Figure 1: TEN-YEAR ROLLING ANNUALIZED RETURNS FOR A REBALANCED VERSUS BUY-AND-HOLD EQUAL-COUNTRY-WEIGHT EMERGING MARKET STRATEGY Source: Parametric Since our ultimate interest is in exploiting this idea in a real, forward-looking portfolio, a purely theoretical outlook is not enough. First, we need to understand in more depth the benefits that can accrue to a carefully structured and rebalanced long-term portfolio, identifying the key drivers of this performance and determining that they are relevant to emerging market countries. Second, we need to examine whether the ideas are implementable in the presence of high transaction costs and other complications. 02
MATHEMATICS OF LONG-TERM GROWTH AND A THEORETICAL MODEL Many articles discuss the importance of rebalancing and its contribution to return. Our observations are based on a well-documented theory of long-term growth in stochastic finance. 1 This theory aims to find the portfolio with the highest final compounded value over multiple periods rather than the one with the highest expected return over any one period. These portfolios differ because (1) there is a difference between an asset s compound return over time and its mean return, and (2) a rebalanced portfolio s compound return is not the same as the weighted average compound returns of the assets in the portfolio. In other words, it is possible to outperform by considering the serial effects of compounding over multiple periods, and it is possible to construct a portfolio with returns greater than the sum of its individual asset returns by implementing a regimen of rebalancing. The primary opportunity for improving compounded returns lies in reducing portfolio volatility. Volatility presents a drag to compounded portfolio returns not captured by expected value because returns accrue geometrically, rather than arithmetically. Hence, a portfolio that is not rebalanced (e.g., a cap-weighted portfolio) can be improved upon through a rebalancing process that aims to reduce portfolio volatility. This process consists of rebalancing each asset to a target weight as its price fluctuates. Not only does this reduce concentration and portfolio volatility, but it establishes an automatic rule for buying assets as their prices fall and selling them as their prices rise, thereby harvesting returns from the natural fluctuations of the market. The mathematical impetus for this growth is shown in the equation below, where g represents the excess growth of a rebalanced portfolio over a buy-and-hold one. g = ½ σ i 2 w i - ½ w i w j σ ij i The first term is the weighted sum of the individual asset variances and the second is the portfolio variance. An increase in asset volatility increases the first term (and so higher asset volatilities are beneficial), but this also increases portfolio variance. The amount by which the second term increases, relative to the first, largely depends on the correlation among the assets. Therefore, a rebalanced portfolio would ideally contain highly volatile, yet uncorrelated assets that individually fluctuate in value but sum to a low total portfolio variance. This relationship can be seen in Figure 2, where excess return of a rebalanced portfolio over a buy-and-hold portfolio increases as asset volatility increases and asset correlation decreases. i, j 1 See Diversifying and Rebalancing Emerging Market Countries in the Journal of Wealth Management (Spring 2009) for a more indepth discussion on this topic. 03
Figure 2: EXCESS RETURN OF AN EQUAL-WEIGHTED REBALANCED PORTFOLIO OVER A BUY-AND- HOLD PORTFOLIO FOR VARIOUS ASSET VOLATILITIES AND CORRELATIONS 5% 4% 3% Rebalancing Premium 2% 1% 0% Source: Parametric Volatility 0.9 0.7 0.5 0.3 0.1 Correlation CHARACTERISTICS OF EMERGING MARKETS WEIGHTS AND RETURNS Emerging markets are well-suited to this multi-period strategy of rebalancing due to their relatively low correlation and high volatility. In considering their potential in a rebalanced strategy, let us first examine a current cap-weighted benchmark, the S&P/IFCI EM Index. The most striking aspect of this benchmark is its high level of concentration and variability in country weights. Over the past 20 years, eight different countries have at one point risen to occupy more than 10% of the index weight, as shown in Figure 3. Though concentration has fallen since 1988 when Malaysia alone accounted for more than half of the index, the level of concentration is still quite high. In December 2011, the top four countries accounted for over 58%, and the top eight countries accounted for over 83% of capitalization. 04
Figure 3: COUNTRY WEIGHTS OF S&P IFCI EM INDEX FOR 20 YEARS ENDING IN 2011 100.0 CHINA 90.0 80.0 KOREA 70.0 60.0 MEXICO TAIWAN 50.0 BRAZIL 40.0 30.0 MALAYSIA SOUTH AFRICA INDIA RUSSIA 20.0 THAILAND ISRAEL 10.0 ARGENTINA PORTUGAL GREECE OTHER 0.0 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 Source: Parametric, S&P/International Financial Corporation Investable Index and Factset Research Systems. These very high concentrations are even more troubling given the high volatility of countries in the emerging markets, as reflected by the MSCI Emerging Markets Index. For the five years ending December 2011, the volatility of the MSCI EM Index was 29%; over the same period, the S&P500 and MSCI EAFE had volatilities of 19% and 23% respectively. Acting to slightly mitigate these high asset volatilities are relatively low correlations between countries. While the average cross-correlation between developed countries over the past five years has been 0.76, between emerging-market countries it has been only 0.51. With such low correlation, accompanied by high volatility, emerging markets clearly lend themselves to a strategy of rebalancing. In order to judge the actual return potential of the rebalancing strategy when applied to emerging markets, we must turn now to evaluate the practical applicability of our theoretical findings. TARGET WEIGHTS, REBALANCING AND PRAGMATICS The growth premium that we have identified derives from the structure of the target weights and from rebalancing to keep the portfolio on target. The turnover generated by this rebalancing in a real portfolio would come at a cost, particularly in the emerging markets where transaction costs are high. Unconstrained rebalancing could result in transaction costs that outweigh the incremental benefits of rebalancing. How might these costs be reduced, and how much would be given up in performance? 05
One way to reduce transaction costs is to reduce the frequency of rebalancing. It turns out that the realized growth premium benefits very little from rebalancing more often than twice per year. Turnover can also be reduced by rebalancing only when a country exceeds a certain concentration level or deviates too far from a target weight. Figure 4: GROWTH PREMIUM AS A FUNCTION OF BOUND WIDTH AND TRADING COST Source: Parametric In our model, these tolerance bounds can be optimized for any given level of trading costs, as can be seen in Figure 4. When trading costs are low, it is advantageous to leave turnover relatively unconstrained by reducing tolerance bounds in order to harvest as much volatility as possible. When trading costs are high, it is important to maintain a low turnover and thus widen tolerance bounds, despite the loss of potential volatility harvesting. Of course, when the bound is very wide, the portfolio starts to drift from its target and behave more like a cap-weighted portfolio. While a detailed discussion of this topic is beyond the scope of this paper, it is possible to formulate these bounds mathematically and to choose a bound that optimizes long-term growth for the portfolio in the presence of transactions costs. Beyond trading costs, other complexities of the real world intrude as well. The key parameters expected returns, volatilities, correlations, and transactions costs are non-homogeneous, varying by country and over time. There are costs of taxation and custody, and one needs to actively manage portfolio risks and liquidity. These considerations reduce the growth premium. On the other hand, real return sequences are often serially correlated, and it is not uncommon to observe large return reversals; with a careful implementation, these can complement a rebalancing strategy. While we have focused here on country-level rebalancing, the same principles apply to stock-level concentration within countries, and indeed one can add a growth premium to country returns through stock-level rebalancing. 06
CONCLUSION Emerging market countries have high volatility and low correlations. A cap-weighted, indexed portfolio is often highly concentrated in a handful of countries. Its risks are high, and long-term growth expectations are compromised. We provide a mathematical model to show that one can expect to do better with an alternative portfolio structure, one that is rebalanced to relatively equal weights for each country. Of course, real-world implementation complexities and expenses affect practical implementation of theoretical ideas. Fortunately, transactions costs can be managed; it is possible to devise rebalancing approaches that require relatively little turnover yet still maintain the benefits of diversification. In fact, there are aspects of real data such as price reversal and particularly low correlations among the smaller countries that make structured rebalanced portfolios even more attractive in practice. Investments in emerging stock markets are risky due to their high levels of volatility. Our view is that highly diversified, systematically rebalanced portfolios offer an opportunity to achieve compelling growth in the asset class. About Parametric Parametric is an industry-leading provider of structured portfolio management, headquartered in Seattle, Washington. Parametric and its affiliate, Parametric Risk Advisors, offer a variety of structured portfolio solutions, including customized core equity portfolios (U.S., Non-U.S., global), options strategies, and overlay portfolio management. Parametric is a majority-owned subsidiary of Eaton Vance (ticker EV). Disclosure This information is intended solely to report on investment strategies and opportunities identified by Parametric Portfolio Associates. Opinions and estimates offered constitute our judgment and are subject to change without notice, as are statements of financial market trends, which are based on current market conditions. We believe the information provided here is reliable, but do not warrant its accuracy or completeness. This material is not intended as an offer or solicitation for the purchase or sale of any financial instrument. Past performance does not predict future results. The views and strategies described may not be suitable for all investors. Parametric does not provide legal, tax and/or accounting advice. Clients should consult with their own tax or legal advisor, who is familiar with the specifics of their situation, prior to entering into any transaction or strategy described here. Please note that investments in foreign securities and markets pose different and possibly greater risk than those customarily associated with domestic securities, including currency fluctuations, foreign taxes and political and economic instability. 07