Frontier Equity Markets: Risk Parity Lessons for Asset Allocation.

Chan-Lau, Jorge A.

The International Finance Corporation (IFC), the World Bank Group, first defined "frontier markets" as small, less-liquid equity markets in developing countries, which despite their investment restrictions are regarded as investable from the perspective of a foreign investor.

The experience of emerging markets suggests that frontier markets offer prospects of higher returns, especially as increased capital flows and infrastructure investment accelerate their economic growth. Indeed, prior to the onset of the subprime crisis in the United States in 2008 and the subsequent sovereign debt crisis in Europe in 2010, frontier markets edged out emerging markets, posting the strongest performance among global equity indexes (Exhibit 1).

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Several factors contribute to the growth potential and long-run strong performance of frontier markets. They include, but are not limited to, fast economic growth, favorable demographics, and abundant natural resources (Howell and Gratsova [20111; Speidell [2011]). There are downside risks, though, as frontier markets are vulnerable to large price corrections during severe distress periods. Investors are more prone to reduce exposure in riskier asset classes, including frontier markets, as observed during the 2008 global financial crisis.

Investing in frontier markets is facilitated by the existence of benchmark investable indexes constructed by Morgan Stanley Capital International (MSCI) and Standard and Poor's (S&P). The MSCI Frontier Markets Index is a free-float adjusted market capitalization index. By mid-November 2013, it included 142 stocks in 25 countries, accounting for 85% of the free-float adjusted' market capitalization in each country. The market capitalization of the index was $130 billion. (1)

The S&P Frontier BMI is a broad benchmark index that tracks the equity return performance of 587 stocks publicly traded in 36 frontier countries. (2) As of mid-November 2013, the mean market capitalization in the index was $1.1 billion, with a median value of $367 million.

The potential diversification benefits of frontier equity markets can be appealing to investors in developed and emerging market countries alike. The argument can be supported informally by examining equity return correlation across different markets, as advanced by Speidell and Krohne [2007]. (3) During the period of May 2002--November 2013, the average weekly return correlation of frontier markets with other global equity indexes ranges between 0.3 and 0.4. In contrast, all other global equity indexes are highly correlated (Exhibit 2, first panel).

Exhibit 2

Global Equity Indexes: Equity Return Correlation

 5/2002-11/2013

 Frontier Europe North EAFE* Emerging
 Markets America Markets

Frontier markets 1.00 0.38 0.34 0.40 0.39
Europe 1.00 0.86 0.98 0.97
North America 1.00 0.85 0.84
East Asia and Far Hast 1.00 1.00
Emerging markets 1.00

 5/2002-12/2007

 Frontier Europe North EAFE* Emerging
 Markets America Markets

Frontier markets 1.00 0.09 0.10 0.11 0.09
Europe 1.00 0.79 0.96 0.94
North America 1.00 0.76 0.76
East Asia and Far Hast 1.00 0.98
Emerging markets 1.00

 5/2008-11/2013

 Frontier Europe North EAFE* Emerging
 Markets America Markets

Frontier markets 1.00 0.49 0.44 0.51 0.51
Europe 1.00 0.88 0.98 0.98
North America 1.00 0.87 0.87
East Asia and Far Hast 1.00 1.00
Emerging markets 1.00

Source: MSCI ami author's calculations.

Frontier markets tend to decouple from other markets when equity prices are increasing (Exhibit 2, second panel) and become more correlated during periods of distress (Exhibit 2, third panel). But even in the latter case, equity price declines in frontier markets are not as correlated as those in other markets.

Although equity return correlations suggest substantial diversification benefits, two factors could reduce them. First, as has been the case with emerging markets, increased integration of frontier market countries with the world economy and the global financial system could lead to diminished diversification. However, a study by Berger et al. [2011] finds no evidence that frontier markets are becoming increasingly integrated over time, even after allowing for structural breaks, and suggests they could help diversify global investors' portfolios.

Second, higher transaction costs, due to lower liquidity and depth, could offset the diversification benefits. Bid--ask spreads in frontier markets can be as high as 10%-12%, as is the case in Kenya and Ukraine (Speidell [2011]), and in general, transaction costs in frontier markets are three times higher than in the United States. Notwithstanding the high transaction costs, investors can benefit from investing in frontier markets. Marshall et al. [2011] find that including frontier market equities in value- and equal-weighted international portfolios can yield higher Sharpe ratios. Frontier markets, therefore, appear better suited as a diversifying asset than emerging markets, as the diversification benefits of the latter could vanish once transaction costs are accounted for (De Roon et al. [2001]).

In addition to transaction costs, there are other risks involved in frontier market investments (Schoen-holz [2010]; Speidell [2011]). Regulatory and trading/execution risk arises from ownership restrictions, domestic registration requirements, custody rules, and the need to use domestic brokers. Foreign exchange risk is ever present, as some of the frontier countries are very volatile; global custodians may require sizable foreign exchange conversion charges; and the ever-present possibility that capital controls could be imposed looms. Investors also have to deal with settlement systems that are more prone to errors, weak corporate governance standards, and political instability.

Despite these obstacles, the case for investing in frontier markets remains valid. The next section analyzes in detail the frontier market allocation in global equity portfolios when risk parity is used.

RISK PARITY ASSET ALLOCATION TO FRONTIER MARKETS

Risk Parity Portfolios

The role of frontier equity markets in a world equity portfolio is discussed in the context of a particular risk-based strategy, risk parity, which equalizes risk contribution across different equity classes.' In other words, risk parity involves assigning the same risk budget to each asset in the portfolio, where the only driving risk factor is the comovement between the asset's return and the return, on the portfolio. (5)

The choice of risk parity is guided by the fact that it is less sensitive to correlation estimates, especially when the number of assets in the portfolio is small (Alvarez et al. [2011]). Risk parity is also supported empirically by the observation that high-beta, high-volatility stocks underperform low-beta, low-volatility stocks, an observation referred to as the low volatility anomaly! (6) Finally, it can be shown that risk parity, while allowing investors to reach their desired risk targets using leverage, is the preferred strategy when investors exhibit leverage aversion (see Frazzini and Pedersen [2010], and Asness et al. [2011]).

In a risk parity strategy, the weights of the different assets are determined in such a way that they contribute equally from a risk perspective. Following Alvarez et al. [2011], in a portfolio P, the risk contribution, CTR, of asset k depends on its portfolio weight, w, and its return correlation with the portfolio returns:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

Risk parity requires equalizing the risk contribution across all assets in the portfolio:

CT[R.sub.k] = CT[R.sub.j], j [not equal to] k, j, k = 1, ... , N (2)

where N is the number of assets in the portfolio. Given the return variance-covariance matrix, Maillard et al. [2010] show that the asset weights in the risk parity portfolio in a long-only portfolio can be calculated as the solution to the problem:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3) s subject to the long-only constraint [[SIGMA].sub.j-1.sup.N] [w.sub.j] = 1, [w.sub.j] > 0[for all]j. Alvarez et al. [2011] describe how the portfolio allocation problem can be extended to alpha risk parity strategies that factor in the investor's priors on expected returns for each asset class: problem (3) is solved replacing the risk contribution per unit of expected return, or alpha, for the absolute risk contributions in Equation (3).

DATA AND RESULTS

The asset allocation exercise assumes that the global equity portfolio comprises five major equity classes: North America equities; European equities, including U.K. equities; East Asia and Far East equities; emerging market equities; and frontier market equities. For the period June 7, 2002, to November 15, 2013, weekly equity returns in U.S. dollars were constructed for each equity class using the corresponding Morgan Stanley Capital Indices (MSCI). The analysis below, therefore,

is relevant for global equity portfolios denominated in U.S. dollars.

Portfolio Weights

The global equity portfolio was constructed by weighting the returns of each equity class by its market capitalization. Exhibit 3 shows the evolution of the weights of each equity class since June 2002 in a market-capitalization-weighted portfolio, in which the frontier market allocation never exceeds 1% of the portfolio.

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Prior to the 2008 financial crisis, the weight of the North America equity allocation declined to about 35%, but it has since recovered. The weight of emerging marking equities in the portfolio has increased steadily to about 10% of the total portfolio allocation.

The calculation of the weights in the risk parity strategy required estimates of the variance-covariance matrix. Rather than relying on forecasts, we calculated the matrix using the standard but backward-looking approach of using past observations over a one-year rolling window. Under risk parity, the asset allocation departs substantially from that suggested by market capitalization weights (Exhibit 4).

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During the period June 2003--November 2013, the frontier market equity allocation ranged from 23% to 48%, with an average value of 35%. North American equities ranked second, with an average weight of 20%. Allocations to equities in Europe, East Asia and Far East, and emerging markets are roughly 15% each.

An examination of Equation (1) and the equity return correlations in Exhibit 2 indicates why risk parity assigns a higher weight to frontier market equities. Compared with other global equities, they exhibit low correlation with the risk parity portfolio. Hence, increasing the risk contribution of frontier market equities requires increasing their weight in the portfolio.

Exhibit 1 shows that market capitalization weights have remained little changed since 2008. This is not the case for risk parity weights calculated using a one-year window, which are especially more volatile for frontier market equities.

It is worth noting that the weight of frontier markets in the risk parity portfolio correlates negatively with those of other global equity markets. Again, Equation (1) and Exhibit 2 explain why this is so. The correlation of frontier market equity returns is countercyclical, declining when global equity prices rise and increasing when they decline. This causes the frontier market risk parity weight to move in sync with global equity prices.

If a longer window is used to calculate the risk contributions, then the risk parity weights are rather stable (Exhibit 5). On average, frontier markets still account for the largest share of the portfolio (30%); followed by North America (20%); East Asia and Far East, and emerging markets (17% each); and Europe (16%).

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For long-only portfolios, there is one practical problem for implementing a risk parity allocation strategy. The small market capitalization of frontier markets may not accommodate the required allocation, especially for asset managers in charge of large portfolios. In addition, many long-only portfolios are managed relatively to a benchmark, restricting the scope for risk parity allocations that could differ substantially from market capitalization weights. Even under these constraints, portfolio managers could increase their chances to beat their benchmarks without increasing the downside risk of the portfolio by modestly overweighting their frontier market allocations.

INVESTMENT PERFORMANCE

Since equity prices in frontier markets can be subject to large swings, especially when investor sentiment deteriorates rapidly, it is necessary to evaluate whether they could effectively contribute to improve the performance of a global equity portfolio. This section first analyzes the performance of frontier markets in isolation and then within a global equity portfolio.

Individual market performance. The individual performance of different equity markets is reported in Exhibit 6, which shows annualized weekly equity returns, standard deviations, and Sharpe ratios. The results are reported for the complete period of study (June 2002-November 2013), the pre-crisis period (June 2002--December 2007), and the crisis/post-crisis period (January 2008-November 2013).

EXHIBIT 6

Annualized Weekly Equity Returns: Mean, Standard Deviation, and
Sharpe Ratio

 Frontier Europe North East Asia Emerging
 Markets America and Far Markets
 East

 Mean Return, in Percent

Periods

6/2002-11/2013 6.8 4.1 4.8 4.1 5.7
672002-12/2007 25.0 12.5 6.7 11.7 13.0
1/2008-11/2013 -10.4 -3.9 3.0 -3.1 -1.2

 Standard Deviation, in Percent

Periods

6/2002-11/2013 15.5 23.2 18.6 20.4 20.7
6/2002-12/2007 12.3 15.5 13.5 14.4 14.9
1/2008-11/2013 17.7 28.7 22.5 24.8 24.9

 Sharpe Ratio

Periods

6/2002-11/2013 0.4 0.2 0.3 0.2 0.3
6/2002-12/2007 2.0 0.8 0.5 0,8 0.9
1/2008-11/2013 -0.6 -0.1 -0.1 -0.1 -0.1

Source: MSCI and author's calculations.

If the complete period is analyzed, frontier and emerging market equities outperform, posting higher returns and higher Sharpe ratios. The performance of frontier markets is especially strong in the pre-crisis period, delivering twice the returns of the other equity classes.

The strong performance of frontier markets was reversed in the crisis/post-crisis period. Returns, on average, declined by 10%, or more than twice the decline of the second-worst-performing market. Frontier markets also underperformed from a risk-adjusted perspective, with a negative Sharpe ratio five times higher than in the other markets.

Portfolio performance. While economic arguments suggest frontier markets should become more integrated over time, so far this has not been the case, as found by Berger et al. [2011]. Moreover, Marshall et al. 120111 show that including frontier market equities leads to higher Sharpe ratios in global equity portfolios.

This section does not repeat or update the results reported by Berger et al. [2011] and Marshall et al. [2011]. Instead, it compares the performance of global equity portfolios, which include frontier markets, under three different weighting schemes. One is the traditional market capitalization weighting. The second is the risk parity weighting scheme, where the risk contributions are calculated using a one-year window. (7)

The third is a simple market capitalization weight that overweights frontier markets in an otherwise market-cap-weighted portfolio by a factor of 10, while reducing the weights of the other equity asset classes. This last scheme facilitates implementing the frontier market allocation and overcomes some of the implementation issues discussed above. The results are presented in Exhibit 7, which shows the results when portfolios are rebalanced continuously (every week) and only at the end of the year.

EXHIBIT 7

Annualized Weekly Equity Returns of Global Equity Portfolios:
Mean, Standard Deviation, and Sharpe Ratio

 Continuous Rebalancing

 Risk Parity Market-Cap Constrained
 Portfolio Portfolio Portfolio

 Mean Return, in Percent

6/2003-11/2013 6.0 6.2 6.3
6/2002-12/2007 19.2 14.9 15.4
1/2008-11/2013 -4.4 -0.6 -0.8

 Standard Deviation, in Percent

6/2003-11/2013 16.0 19.5 19.6
6/2002-12/2007 9.5 11.8 11.9
1/2008-11/2013 19.5 23.9 23.9

 Sharpe Ratio

6/2003-11/2013 0.4 0.3 0.3
6/2002-12/2007 2.0 1.3 1.3
1/2008-11/2013 -0.2 0.0 0.0

 End-of-Year Rebalancing

 Risk Parity Market-Cap Constrained
 Portfolio Portfolio Portfolio

6/2003-11/2013 5.6 5.9 6.0
6/2002-12/2007 18.9 14.7 15.2
1/2008-11/2013 -4.7 -0.9 -1.1

6/2003-11/2013 16.1 19.6 19.6
6/2002-12/2007 9.4 11.8 11.8
1/2008-11/2013 19.7 23.9 24.0

6/2003-11/2013 0.3 0.3 0.3
6/2002-12/2007 2.0 1.2 1.3
1/2008-11/2013 -0.2 0.0 0.0

Source: MSCI and author's calculations.

Overall, the results suggest that a risk parity portfolio outperforms the other portfolios during periods of globally rising equity prices and underperforms in the opposite case. Over a long period of time, risk parity portfolios deliver a somewhat better performance as measured by the Sharpe ratio. Since the constrained portfolio is not much different from the market-cap portfolio, given that the frontier market market-cap weights are very small, both portfolios perform similarly. These results together suggest that benefitting from frontier market equities requires adopting an asset allocation heavily tilted toward them, as is the case for risk parity portfolios.

Lessons for Investors

The analysis herein holds some important lessons for global equity investors. Frontier equity markets exhibit low correlation with other equity markets, including emerging markets. Their inclusion in global equity portfolios could enhance diversification. More importantly, an asset allocation strategy based on risk parity shows that deviating from a market capitalization allocation strategy by heavily overweighting frontier markets could help portfolios to outperform when global equity prices are rising.

Frontier market equities, hence, could play a role in tactical asset allocation. Notably, the outperform.ance is not achieved at the expense oflarger losses during downturns relative to market-cap-weighted benchmarks.

There may be some practical roadblocks to adopting a risk parity allocation in long-only global equity portfolios. One is the small market capitalization of frontier markets. Another is that global equity portfolios are managed relative to a benchmark index, which could differ substantially from the risk parity weights. Notwithstanding these roadblocks, the results presented herein suggest frontier market equities can serve as an alternative asset class.

ENDNOTES

The author is thankful to the comments by an anonymous referee. All errors or omissions are the author's sole responsibility. The views in this article represent only those of the author and do not necessarily represent those of the International Monetary Fund (IMF) nor IMF policy.

(1.) Argentina, Bahrain, Bangladesh, Bulgaria, Croatia, Estonia, Jordan, Kazakhstan, Kenya. Kuwait, Lebanon, Lithuania, Mauritius, Nigeria, Oman, Pakistan, Qatar, Romania, Serbia, Slovenia, Sri Lanka, Tunisia, Ukraine, United Arab Emirates, and Vietnam. Calculations reported herein are based on this index.

(2.) The index, in addition to the countries in the MSCI FM index except Serbia, includes Botswana, Cote d'ivoire, Cyprus, Ecuador, Ghana, Jamaica, Latvia, Namibia, Panama, Slovakia, Trinidad and Tobago, and Zambia.

(3.) Cross-market correlation, while helpful to highlight diversification benefits, may not be accurate enough. See, for instance, Carrieri et al. [2007] and Pukthuantong and Roll [2009].

(4.) Risk-based strategies require forecasting only the variance-covariance matrix of returns and avoid the need to forecast expected returns. In addition to risk parity, risk-based strategies include minimum variance portfolio theory and maximum diversification. Minimum variance portfolios tend to deliver corner solutions (Black and Litterman [1992]; Litterman and Quantitative Resources Group [2003]; and Meucci [2009]) while maximum diversification is not as robust as risk parity to changes in correlation estimates.

(5.) For textbook treatments of risk budgeting, see Pearson [2002] and Scherer [2002].

(6) As noted in Alvarez et al. [2011]. For recent references on the low volatility anomaly, see Baker et al. [2011], and Frazzini and Pedersen [2010].

(7.) Results for the five-year window are not reported since they would only cover the period June 2007--November 2013.

REFERENCES

Alvarez, M.A., Y. Luo, R. Cahan, J. Jussa, and Z. Chen. "Risk Parity and Risk-Based Allocation." Portfolios under Construction, Deutsche Bank, New York, 2011.

Asness, C., A. Frazzini, and LH. Pedersen. "Leverage Aversion and Risk Parity." AQR Capital Management, Connecticut, and New York University, New York, 2011. Forthcoming in. Fithnicial Analysts Journal.

Baker, M., B. Bradley, and J, Wurgler. "Benchmarks as Limits to Arbitrage: Understanding the Low-Volatility Anomaly."

Financial Analysts Journal. 67 (2011), pp. 40-54. Berger, D., K. Pukthuanthong, and J.J. Yang. "International Diversification with Frontier Markets."

Journal of Financial Economics, 101 (2011), pp. 227-242.

Black, F., and R. Litterman. "Global Portfolio Optimizatio." Financial Analysts Journal (1992), pp. 28-43.

Carrieri, F., V. Errunza, and K. Hogan. "Characterizing World Market Integration through Time." Journal of and Quantitative Analysis, 42 (2007), pp. 915-94.0.

De Roon, F.A., T.E. Nijman, and 13J.M. Werker. "Testing for Mean-Variance Spanning with Short-Sale Constraints and Transaction Costs: The Case of Emerging Markets." Journal of Finance, 56: (2001), pp, 721-742.

Forbes, K., and R. Rigobon. "No Contagion, Only Interdependence: Measuring Stock Market Comovements." Journal qf Finance, 57 (2002). pp. 2223-2261.

Frazzini, A., and L.H. Pedersen. "Betting Against Beta." AQR Asset Management and New York University, 2010.

Howell, A., and M. Gratsova. "Call of the Frontier: The Search for a New Generation of Emerging Markets." Ceti Global Perspectives and Solutions. New York: Citigroup, 2011.

Litterman, R., and Quantitative Resources Group. Modern Investment Management: An Equilibrium Approach. New York: Wiley Finance, 2003.

Maillard, S., T. Roncalli, and J. Teiletche. "On the Property of Equally-Weighted Risk Contribution Portfolios." The Journal of Portfolio Ma nagement , 36 (Summer, 2010), pp. 60-70.

Marshall, B., N.H. Nguyen, and N. Visaltanachoti. "Frontier Market Diversification and Transaction Costs." Massey University, 2011.

Meucci, A. Risk and Asset Allocation. New York: Springer Finance, 2009.

Pearson, N.D. Risk Budgeting: Portfolio Problem Solving with Value-at-Risk. New York: Wiley Finance, 2002.

Pukthuanthong, K., and R. Roll. "Global Market Integration: An Alternative Measure and Its Application "Journal of Financial Economics, 94 (2009), pp. 214-232.

Scherer, B. Portfolio Construction and Risk Budgeting. London: Risk Books, 2002.

Schoenholz, D. "The New Frontier: Understanding the Opportunities, Knowing the Risks." Financial Services. New York: Ernst and Young, 2010.

Speidell, L. Frontier Market Equity Investing: Finding the Winners of the Future. Research Foundation of CFA Institute, 2011.

Speidell, L., and A. Krohne. "The Case for Frontier Equity Markets." The Journal of Investing, 16 (2007), pp. 12-22.

Jo order reprints of this article, please contact Dewey Palmieri at dpalmieri@iijournals.com or 212-224-3'675.

JORGE A. CHAN-LAU is a senior economist at the International Monetary Fund and a senior fellow at the Center for Emerging Market Enterprises at the Fletcher School, Tufts University in Washington, DC.

jchanlau@imf.org