Abstract
We introduce Allocation Skew, a novel country allocator. This factor favours countries held with conviction by a small minority of managers. We find that strategies which buy and sell, respectively, the Morgan Stanley Capital International (MSCI) country indices with the highest and lowest scores in terms of this factor generate significant positive returns over a forward annual holding period. We also find that the profitability of this strategy is independent of the momentum effect of Muller and Ward. To build the Allocation Skew factor, we use a dataset that captures fund country allocations, compiled by Emerging Portfolio Fund Research (EPFR Global).
Introduction
A large body of work has been done on country allocation strategies. Keppler (1991) studied dividend yield and cash flow to price (1991) as country allocators, Bhojraj and Swaminathan, (2006), Balvers and Wu (2006) and Muller and Ward (2010) looked at momentum, and Keppler and Traub (1993) and Keppler and Encinosa (2011) documented the size effect. Macedo (1995) showed the benefits of switching country-selection styles between relative value and relative strength depending on volatility while Zaremba looked at a wide variety of country-selection strategies (2015).
We use a dataset that captures fund country allocations, compiled by Emerging Portfolio Fund Research (EPFR Global). Raddatz, Schmukler and Williams (2017) used the EPFR country allocations data to study the effect of benchmarks on the country allocations of mutual funds, Moss, Ramachandran and Standley (2006) used the data to understand why Africa doesn’t get more equity investment and Jotikasthira, Lundbald and Ramadorai (2012) used the data to study financial shocks.
From these allocations, we build allocation skew, a novel country allocator. For a given country, allocation skew is the percentage of managers, tracked by EPFR, in terms of AUM, who hold a smaller position in that country than the average for funds with similar geographic investment mandates. Since the average for funds with similar geographic investment mandates is computed from the same population of managers tracked by EPFR, it follows that whenever a large percentage of managers holds a country at less than average weight, the remaining managers must have large overweights to that same country. Thus, allocation skew causes one to mimic the country overweights of those managers who invest with conviction.
A zero-cost strategy that goes long and short, respectively, the countries in the top and bottom quintiles in terms of allocation skew produces forward annual returns that are statistically significantly above zero. Further this strategy is not subsumed by the momentum effect or Muller and Ward (2010).
Data
Fund assets and country allocations
This paper uses a dataset, compiled by EPFR, of the country allocations of mutual and exchange-traded funds. EPFR classify funds by fund type, whether they are equity funds, bond funds, muni funds, etc. In this paper, given that we are interested in forecasting country equity-market returns, we look at equity funds only.
EPFR also classify funds by geographic investment mandate, global funds, global emerging market funds, US funds, Japan funds, Pacific funds, etc. This paper does not consider single-country funds because the country allocation for these funds always matches the average for funds with the same geographic investment mandate. Thus, we focus exclusively on equity funds with a cross-border focus.
EPFR currently collect monthly country allocations for about 1,300 of these cross-border equity funds (at May 31, 2017). For each of these funds, EPFR also provide the total assets under management (AUM) at the end of each month. In Table 1, we report the number of cross-border equity funds reporting country allocations to EPFR together with their assets under management, expressed in billions of USD, at the end of May, each year, from 2001 to 2017.
Country Allocations
Country Allocations
This table shows the number of cross-border equity funds reporting country allocations to EPFR together with their assets under management (in billions of USD) at the end of May, each year, from 2001 to 2017. These are labelled “Num Funds” and “AUM ($BB)” respectively.
In this paper, we use monthly fund assets provided by EPFR in conjunction with their country allocations. These go back to February 1996 and December 1995, respectively. Monthly assets and country allocations are known, respectively, sometime before midnight, New York time, on the 16th and 23rd day of the following month, provided that that day falls on a weekday. If not, the data are known either on the Friday before or the Monday after.
This research is based on returns of international stock market indices from fifty-two countries. All source data are obtained from the Bloomberg database. Daily time-series are implemented to better study short-term forward-return effects. We follow Zaremba (2015) in adopting Morgan Stanley Capital International (MSCI) indices for all the countries to maintain a consistent return computation methodology.
The returns are computed based on capitalization-weighted net total return indices, i.e. the returns are adjusted for corporate actions (splits, reverse splits, issuance rights etc.) and cash distributions to investors (dividends). The “net” technique of computation ensures that the returns account for country-specific dividend tax rates. The sample period for returns runs from December 31, 1999 to May 31, 2017, as available.
The total sample includes the equity markets of the fifty-two countries that were in the MSCI All Country World Index at some point since its launch on Jan 01, 2001 to May 31, 2017, when our return series ends. These countries are Argentina, Australia, Austria, Belgium, Brazil, Canada, Chile, China, Colombia, Czech Republic, Denmark, Egypt, Finland, France, Germany, Greece, Hong Kong, Hungary, India, Indonesia, Ireland, Israel, Italy, Japan, Jordan, Korea, Malaysia, Mexico, Morocco, Netherlands, New Zealand, Norway, Pakistan, Peru, Philippines, Poland, Portugal, Qatar, Russia, Singapore, South Africa, Spain, Sri Lanka, Sweden, Switzerland, Taiwan, Thailand, Turkey, United Arab Emirates, United Kingdom, United States and Venezuela.
In this paper, we back-test using overlapping monthly returns. The month ends are not calendar month ends. Rather they end on the day after allocations data from the previous calendar month become known. That day is the 24th, unless it is a Sunday or Monday. Then, if the 24th is a Sunday or Monday, the month ends on the 26th or 25th respectively. This is done so that the allocation skew signal is traded when it is most fresh.
Index changes
We use a country’s inclusion in the MSCI All Country World Index as a proxy for
investability. Since its launch on Jan 01, 2001, this index has experienced the following
changes: Sri Lanka
was removed after June 2001. Venezuela was removed after May 2006. Jordan was removed after November 2008. Pakistan was removed after December
2008. Argentina was removed after May
2009. Morocco was removed after
November 2013. The United Arab
Emirates came in after May 2014. Qatar came in after May 2014.
A country is considered investable if it was in the MSCI All Country World Index on the trade date. The back-tests in this paper are conducted only on investable countries as defined in this section. This investability restriction causes January 24, 2001 to be the very first trade date in any back-test conducted in this paper.
Allocation skew
Let A denote the dollar ending assets in a fund at the end of a calendar
month, let ω be the percentage allocation of that fund to a given country
at the end of that calendar month, and let
It is important to realize, because the
Suppose one-month allocation skew is large for a given country. A large majority, in terms of assets under management, of funds, by definition, are underweight that country. However, to compensate, the remaining funds must have big over-weights to that country. Thus, allocation skew is a measure of manager conviction.
We sum one-month allocation skew over a lookback window of two, four, six and eight months to yield four additional predictors, namely 2-month, 4-month, 6-month and 8-month allocation skew respectively.
The country-allocations data for a calendar month are known sometime on the 23rd day of the following month, if that day falls on a weekday. Otherwise, the data are known either on the Friday before or the Monday after. To avoid look-ahead bias, we assume that monthly allocations are known on the following Monday if the 23rd falls on a weekend. Since we cannot guarantee that the allocations are known by 4:00 PM on the 23rd of the new month (or the Monday after the 23rd of the new month in the cases where the 23rd falls on a weekend), we trade at the 4:00 PM eastern close on the day after allocations become known.
For this reason, our month ends are not calendar-month ends. Rather our months end on the 24th unless that day is a Sunday or Monday. Then, if the 24th is a Sunday or Monday, the month ends on the 26th or 25th respectively. This is done so that the allocation skew signal is traded when it is most fresh.
Methodology
Quintile portfolios
We use quintile back-tests throughout this paper. Investable countries are ranked in ascending order based on the sorting variable and assigned to one of five quintile portfolios. Recall that a country is considered investable if it was in the MSCI All Country World Index on the trade date. Portfolios are rebalanced monthly to maintain equal weights.
Overlapping forward annual returns
Allocation Skew has a long and uncertain response time. To account for this, all back-tests in this paper use a forward twelve-month return. So as not to throw away data, we choose to use overlapping annual returns.
Were the return periods not overlapping, country returns from different periods could be considered independent. Overlapping observations induce autocorrelation so that this is no longer the case. As a result, the ratio between the mean and standard deviation of the returns to each quintile no longer follow a t-distribution and so one can no longer use t-statistics to test for the significance of quintile returns.
Britten-Jones, Neuberger, Nolte (2011) show how to handle regressions with overlapping observations. For any regression where the dependent variable is a time series that is the sum of overlapping sub-periods, their transformation, which preserves the coefficient estimates of the original regression, results in a regression where the dependent variable is the time series of the underlying sub-periods. Although the estimates are preserved, the standard errors of the coefficients and thus the t-statistics are not. These t-statistics of the transformed regression can be interpreted in the standard way.
For this reason, we choose to measure quintile returns in terms of regression coefficients. Our dependent variable is always log country return over a forward year minus the log annual returns of the equal-weight universe of countries. We regress these active annual log country returns against portfolio-membership dummies Q2, Q3, Q4 and Q1–Q5. For any country in the ACWI universe at month t - 1, Q2, Q3 and Q4 are one if that country falls in the second, third or fourth quintile. Otherwise, these columns take on the value zero. The variable Q1–Q5 takes on the value 1/2, 0 or – 1/2 if the country falls in the top quintile, one of the middle quintiles or the bottom quintile respectively. This is done so that the coefficient on this variable measures the return spread between the top and bottom quintiles.
For each country, we use the method laid out in Britten-Jones, Neuberger, Nolte (2011) to transform regressions of overlapping active annual log country returns into regressions of active monthly log country returns which are no longer overlapping.
We then stack observations from each country into a single regression.
Allocation skew and forward returns
Annual forward returns
To see whether this variable can predict forward returns, we look at twelve-month (or annual) forward returns on calendar-time portfolios formed by sorting countries on one, two, four, six and eight-month allocation skew. Countries are ranked in ascending order based on the last-available sorting variable and assigned to one of five quintile portfolios. Portfolios are rebalanced monthly to maintain equal weights.
Months are not calendar months. They end on the 24th unless that day is a Sunday or Monday. Then, if the 24th is a Sunday or Monday, the month ends on the 26th or 25th respectively.
In Panel A of Table 2, we report averages of the sorting variable for each portfolio. The rightmost column shows the difference between the high and low countries in terms of the sorting variable.
Quintile Simulations
Quintile Simulations
This table shows the average past values of the sorting variable and excess return over months t, t + 1,…, and t + 11 for calendar-time portfolios sorted on the sorting variable at month t - 1. The sorting variables used are latest-available allocation skew summed over the past one, two, four, six and eight months. Countries are ranked in ascending order based on the last-available sorting variable as of month t - 1. Months are not calendar months. They end on the 24th unless that day is a Sunday or Monday. Then, if the 24th is a Sunday or Monday, the month ends on the 26th or 25th respectively. Countries are assigned to one of five quintile portfolios. Portfolios are rebalanced monthly to maintain equal weights. In Panel A, we report averages of the sorting variable for each cell. In Panel B, we report coefficients and t-statistics from the regression of log country returns over a forward year minus the log annual returns of the equal-weight universe against portfolio-membership dummies Q2, Q3, Q4 and Q1–Q5. For any country in the ACWI universe at month t - 1, Q2, Q3 and Q4 are one if that country falls in the second, third or fourth quintile. Otherwise, these columns take on the value zero. Q1–Q5 takes on the value 1/2, 0 or – 1/2 if the country falls in the top quintile, one of the middle quintiles or the bottom quintile respectively. Coefficients have been exponentiated and expressed as percentages. t-statistics, shown below in parentheses, use the Britten-Jones et al. adjustment to account for the use of overlapping annual returns.
Panel B shows the basic results of this paper. We report coefficients and t-statistics from the regression of log country returns over a forward year minus the log annual returns of the equal-weight universe against portfolio-membership dummies Q2, Q3, Q4 and Q1–Q5. For any country in the ACWI universe at month t - 1, Q2, Q3 and Q4 are one if that country falls in the second, third or fourth quintile. Otherwise, these columns take on the value zero. Q1–Q5 takes on the value 1/2, 0 or – 1/2 if the country falls in the top quintile, one of the middle quintiles or the bottom quintile respectively. Coefficients have been exponentiated and expressed as percentages. t-statistics are shown below in parentheses.
For each country, we use the method laid out in Britten-Jones, Neuberger, Nolte (2011) to transform regressions of overlapping active annual log country returns into regressions of active monthly log country returns which are no longer overlapping. We then stack observations from each country into a single regression.
We measure the size and significance of the average return of the zero-cost portfolio that holds the top fifth and sells short the bottom fifth by the coefficient and t-statistic on the “Q1 – Q5” variable.
As you can see from the column “Q1 – Q5” in the table, there are statistically significant profits associated with the zero-cost long/short strategy, no matter whether the lookback horizon is one, two, four, six or eight months.
We now give an overview of how allocation skew predicts returns at various forward time horizons.
Countries are ranked in ascending order based on the last-available four-month allocation skew as of month t – k and assigned to one of five quintile portfolios. Portfolios are rebalanced monthly to maintain equal weights.
We regress log country returns over months t, t + 1,…, and t + 11 minus the log annual returns of the equal-weight universe over the same period against portfolio-membership dummies Q2, Q3, Q4 and Q1–Q5. For any country in the ACWI universe at month t - k, Q2, Q3 and Q4 are one if that country falls in the second, third or fourth quintile. Otherwise, these columns take on the value zero. Q1–Q5 takes on the value 1/2, 0 or – 1/2 if the country falls in the top quintile, one of the middle quintiles or the bottom quintile respectively.
Months are not calendar months. They end on the 24th unless that day is a Sunday or Monday. Then, if the 24th is a Sunday or Monday, the month ends on the 26th or 25th respectively.
As before, we measure the size and significance of the average return of the zero-cost portfolio that holds the top fifth and sells short the bottom fifth by the coefficient and t-statistic on the “Q1 – Q5” variable.
Table 3 shows the coefficients and t-statistics associated with the Q1–Q5 variable from the regression of log country returns over months t, t + 1,…, and t + 11 minus the log annual returns of the equal-weight universe over the same period against portfolio-membership dummies Q2, Q3, Q4 and Q1–Q5 formed at month t – k. Coefficients have been exponentiated and expressed as percentages. t-statistics are shown below in parentheses.
Four-month Allocation Skew lagged k - 1 months
Four-month Allocation Skew lagged k - 1 months
This table shows the average return over month t, t + 1,…, and t + 11 the average return over months t, t + 1,…, and t + 11 to the zero-cost portfolio that holds the top fifth and sells short the bottom fifth of asset classes in terms of the latest-available four- month Allocation Skew as of month t - k. Countries are ranked in ascending order based on the last-available sorting variable as of month t - k. Months are not calendar months. They end on the 24th unless that day is a Sunday or Monday. Then, if the 24th is a Sunday or Monday, the month ends on the 26th or 25th respectively. Countries are assigned to one of five quintile portfolios. Portfolios are rebalanced monthly to maintain equal weights. We report coefficients and t-statistics associated with the Q1–Q5 variable from the regression of log country returns over a forward year minus the log annual returns of the equal-weight universe against portfolio-membership dummies Q2, Q3, Q4 and Q1–Q5. For any country in the ACWI universe at month t - k, Q2, Q3 and Q4 are one if that country falls in the second, third or fourth quintile. Otherwise, these columns take on the value zero. Q1–Q5 takes on the value 1/2, 0 or – 1/2 if the country falls in the top quintile, one of the middle quintiles or the bottom quintile respectively. Coefficients have been exponentiated and expressed as percentages. t-statistics, shown below in parentheses, use the Britten-Jones et al. adjustment to account for the use of overlapping annual returns.
For each country, we use the method laid out in Britten-Jones, Neuberger, Nolte (2011) to transform regressions of overlapping active annual log country returns into regressions of active monthly log country returns which are no longer overlapping. We then stack observations from each country into a single regression.
Four-month allocation skew at month t - 7 has residual predictive power over month t, t + 1,…, and t + 11. Thus, in a sense, allocation skew has predictive power out to almost 18 months.
Controlling for momentum
The momentum effect has been well-documented in the literature. Muller and Ward (2010) found that strategies which buy the best performing, and sell the worst performing, MSCI country indices over the previous 11 months generate significant positive returns over a forward one month holding period. To ensure our new variable is not just a proxy for momentum, we control for the momentum effect by regressing it out of our variable.
We do this, for each period, by taking the residual obtained by regressing prior allocation skew against prior eleven-month return. We do this for one, two, four, six and eight-month allocation skew. For each sorting variable thus generated, countries are ranked in ascending order based on the last-available sorting variable as of month t – 1 and assigned to one of five quintile portfolios. Portfolios are rebalanced monthly to maintain equal weights.
Months are not calendar months. They end on the 24th unless that day is a Sunday or Monday. Then, if the 24th is a Sunday or Monday, the month ends on the 26th or 25th respectively.
As before, we measure the size and significance of the average return of the zero-cost portfolio that holds the top fifth and sells short the bottom fifth by the coefficient and t-statistic on the “Q1 – Q5” variable.
In Table 4, we report coefficients and t-statistics from the regression of log country returns over a forward year minus the log annual returns of the equal-weight universe against portfolio-membership dummies Q2, Q3, Q4 and Q1–Q5. For any country in the ACWI universe at month t - 1, Q2, Q3 and Q4 are one if that country falls in the second, third or fourth quintile. Otherwise, these columns take on the value zero. Q1–Q5 takes on the value 1/2, 0 or – 1/2 if the country falls in the top quintile, one of the middle quintiles or the bottom quintile respectively. Coefficients have been exponentiated and expressed as percentages. t-statistics are shown below in parentheses.
Controlling for Momentum
Controlling for Momentum
This table shows the average excess return over months t, t + 1,…, and t + 11 for calendar-time portfolios sorted on the sorting variable at month t - 1. The sorting variable is the residual obtained by regressing the latest-available allocation skew summed over the past one, two, four, six and eight months on eleven-month past return. Countries are ranked in ascending order based on the last- available sorting variable as of month t - 1. Months are not calendar months. They end on the 24th unless that day is a Sunday or Monday. Then, if the 24th is a Sunday or Monday, the month ends on the 26th or 25th respectively. Countries are assigned to one of five quintile portfolios. Portfolios are rebalanced monthly to maintain equal weights. We report coefficients and t-statistics from the regression of log country returns over a forward year minus the log annual returns of the equal-weight universe against portfolio-membership dummies Q2, Q3, Q4 and Q1–Q5. For any country in the ACWI universe at month t - 1, Q2, Q3 and Q4 are one if that country falls in the second, third or fourth quintile. Otherwise, these columns take on the value zero. Q1–Q5 takes on the value 1/2, 0 or – 1/2 if the country falls in the top quintile, one of the middle quintiles or the bottom quintile respectively. Coefficients have been exponentiated and expressed as percentages. t-statistics, shown below in parentheses, use the Britten-Jones et al. adjustment to account for the use of overlapping annual returns.
For each country, we use the method laid out in Britten-Jones, Neuberger, Nolte (2011) to transform regressions of overlapping active annual log country returns into regressions of active monthly log country returns which are no longer overlapping. We then stack observations from each country into a single regression.
The performance of the zero-cost long/short strategy remains statistically significant, no matter whether the lookback horizon is one, two, four, six or eight months. In short, the effect associated with allocation skew is not subsumed by that of momentum.
Allocation skew turns out to be predictive of forward return. A zero-cost strategy that goes long and short the countries in the top and bottom quintiles of allocation skew produces returns that are statistically significantly different from zero. Further this strategy is not subsumed by the momentum effect of Muller and Ward (2010). When prior eleven-month return is regressed out, the zero-cost strategy, produces returns that remain significantly above zero. All this remains true when allocation skew is summed over the trailing two, four, six and eight months.