Global Equity Momentum: A Craftsman’s Perspective

GEM has produced attractive absolute and risk-adjusted performance since 1950, both in- and out-of-sample. We replicated the original research using close data proxies. Figure 1 shows that our results tracked the author’s results very closely despite minor differences in how we constructed our index of foreign stocks.

Figure 1. Performance of Global Equity Momentum, 1950 – September 2018. HYPOTHETICAL AND SIMULATED RESULTS

Source: Analysis by ReSolve Asset Management. Data from MSCI, Standard and Poor’s, Barclays, Russell Investments. Benchmark consists of 45% S&P 500, 28% foreign stocks and 27% bond aggregate consistent with original article.

The Original GEM strategy was specified with a 12-month lookback period to measure both trend and momentum, consistent with prior literature on these effects. Many articles have also observed trend and momentum effects for shorter and longer horizons from 1-18 months or longer.

We examined GEM strategies specified with all possible combinations of absolute and relative momentum formed on 1-18 month lookbacks. With 18 possible parameterizations of trend lookbacks and 18 possible momentum lookbacks, there are 324 possible strategy combinations.

Moreover, trend and momentum can be measured in many ways. In addition to total return, investors have used price relative to moving averages, dual and triple MA crosses, breakouts, and risk-adjusted measures. We added a price versus moving average cross strategy to our investigation alongside the original time-series approach. Specifically, we measured momentum as the percentage difference between the current price of the market and a moving average formed on 2-18 month MAs.

The Original GEM applied a trend overlay exclusively on the S&P 500 to signal a move from stocks into bonds. We also examined strategies that required both the S&P 500 and foreign stocks to be in a negative trend before moving into bonds.

When we applied all combinations of lookback horizons on both time-series and moving average specifications, and investigated both S&P 500 and multi-market trend signals we were left with 1226 strategies in total, as described in Figure 2.

Figure 2. 1226 strategies in total derived from four general specifications.

Source: ReSolve Asset Management. For illustrative purposes only.

Nothing special about the original specification

We tested the null hypothesis that there is no statistical difference between the performance of the Original GEM strategy and the other 1225 alternative specifications. Figure 3 plots the wealth trajectory for all 1226 GEM specifications on the same chart. The yellow line at the bottom and the red line at the top trace the 5thand 95th percentile wealth trajectory at each point in time over the sample period from 1950 – 2018. The Original strategy (emphasized dark blue line) was below the 95th percentile at all horizons.

Figure 3. All GEM specifications with Quantile Wealth Bands, 1950 – September 2018. HYPOTHETICAL AND SIMULATED RESULTS.

Source: Analysis by ReSolve Asset Management. Data from MSCI, Standard and Poor’s, Barclays, Russell Investments.

The realized trajectory of performance observed in Figure 3 reflects the exact sequence of events that shaped the performance of markets in the past among an infinite variety of possible alternative paths. It’s important to examine the distribution of possible alternative outcomes to account for the fact that markets will probably take a different path in the future.

We performed a “block bootstrap” to observe other potential paths that returns might have taken while preserving the empirical distribution of the original strategies. We plot 1,000 bootstrapped wealth trajectories as a Quantile Cloud in Figure 4.

Figure 4. GEM Block Bootstrap Cloud with Quantile Wealth Bands, 1950 – September 2018. HYPOTHETICAL AND SIMULATED RESULTS.

Source: Analysis by ReSolve Asset Management. Data from MSCI, Standard and Poor’s, Barclays, Russell Investments.

While the Original specification (traced by emphasized dark blue line) achieved a lucky outcome in-sample, the wealth trajectory is well below the 95th percentile red line, so we have no reason to believe it is “special” from a statistical sense.

When we performed a formal block bootstrap analysis to test if there was a statistically significant difference in annualized returns between the Original strategy and our other 1225 specifications we found that the Original specification only outperformed 61% of the time. In other words, it’s most likely that the outperformance observed from the Original strategy relative to the other specifications in-sample is due to random luck.

We performed the same statistical test to determine if any of the alternative specifications exhibited statistically significant under- or out-performance and found that we can’t reject the hypothesis that they all have the same expected compound means and Sharpe ratios. All specifications have equal merit.

Figure 5. Compound returns across all GEM specifications, in-sample (1974-2011) vs. out-of-sample (1950- 1973 and 2012-2018) periods. HYPOTHETICAL AND SIMULATED RESULTS.

Source: Analysis by ReSolve Asset Management. Data from MSCI, Standard and Poor’s, Barclays, Russell Investments.

Specification risk is a large and uncompensated source of risk

While all 1226 specifications may be expected to produce the same performance in the future, choice of specification introduces an *uncompensated* source of risk. Different specifications will often hold different portfolios through time. Some portfolios may have positions in bonds while others favor stocks. Some portfolios may prefer US stocks over foreign stocks while others signal opposite preferences.

These subtle differences from month to month can produce very significant economic consequences over intermediate horizons. Figure 5 shows the difference in 5-year cumulative returns between lucky (95th percentile) and unlucky (5thpercentile) GEM specifications at each month through time. The average cumulative difference in 5-year returns between lucky and unlucky specifications is 64 percentage points. This represents a surprisingly large potential difference in terminal wealth over a time horizon that most investors would find quite meaningful.

Figure 6. Dispersion of calendar year returns for Global Equity Momentum strategies specified by different absolute and relative momentum lookbacks, 1950 – 2018. HYPOTHETICAL AND SIMULATED RESULTS.

Source: Analysis by ReSolve Asset Management. Data from MSCI, Standard and Poor’s, Barclays, Russell Investments.

Reducing specification risk with an ensemble strategy

A simple way to minimize uncompensated specification risk is to take signals from all specifications at once by building an ensemble strategy. The ensemble takes advantage of a surprising amount of diversity in monthly returns across the different strategy specifications. Figure 7 shows that the pairwise correlations between strategies have ranged from below 0.5 to almost 1. The average correlation between strategy pairs was 0.77 and 25% of strategy pairs had correlations below 0.7.

Figure 7. Pairwise correlations between different GEM strategy specifications ordered from low to high, 1950 – 2018. HYPOTHETICAL AND SIMULATED RESULTS.

Source: Analysis by ReSolve Asset Management. Data from MSCI, Standard and Poor’s, Barclays, Russell Investments.

If the specifications have equal expected performance but offer diversification benefits we should expect an ensemble strategy to preserve the expected performance of the GEM approach, but produce those returns with greater stability. This means that investors with finite investment horizons and random inception and termination dates will probably come closer to realizing their target return, with a much smaller risk of adverse outcomes.

From a financial perspective this translates to greater portfolio sustainability, higher potential withdrawal rates, and a smaller range of terminal wealth. Behaviourally, investors will probably be more likely to stick with an ensemble strategy because there is a smaller chance of large drawdowns and/or long periods of underperformance, which might challenge investors’ resolve.

More consistent returns

We can demonstrate the improved stability of ensemble strategies in a variety of ways by focusing on the expected frequency and magnitude of outcomes that fall well below most investors’ expectations.

For example, the ensemble strategy dominated almost all specifications in terms of drawdowns. Figure 8 plots the average of losses from the 5 worst drawdowns for all 1226 specifications from 1950 – 2018. The median strategy lost an average of 17.4% while the ensemble lost just 13.2%.

Figure 8. Average of 5 worst drawdowns for all specifications of Global Equity Momentum, 1950 – 2018. HYPOTHETICAL AND SIMULATED RESULTS.

Source: Analysis by ReSolve Asset Management. Data from MSCI, Standard and Poor’s, Barclays, Russell Investments.

The Ulcer Ratio expresses the total cumulative amount of pain experienced by an investor accounting for both the length and depth of drawdowns. By dividing the excess return by the Ulcer Ratio, the Martin Ratio captures the amount of “gain” produced per unit of investor “pain”. Per Figure 9 the ensemble strategy produced almost 40% more “gain” relative to “pain” (Martin Ratio) than a typical individual specification.

Figure 9. Excess return divided by Ulcer Ratio (Martin Ratio) for all specifications of Global Equity Momentum, 1950 – 2018. HYPOTHETICAL AND SIMULATED RESULTS.

Source: Analysis by ReSolve Asset Management. Data from MSCI, Standard and Poor’s, Barclays, Russell Investments.

It is instructive to observe the expected loss for a strategy in the event of bad luck. Figure 10 illustrates the average performance of each specification in its worst five calendar years. The ensemble strategy exacted a 4.7% average annualized loss in its worst 5 calendar years while we might expect a typical individual specification to inflict a 7.5% loss.

Figure 10. Average of worst 5 calendar year returns for all specifications of Global Equity Momentum, 1950 – 2018. HYPOTHETICAL AND SIMULATED RESULTS.

Source: Analysis by ReSolve Asset Management. Data from MSCI, Standard and Poor’s, Barclays, Russell Investments.

The paper examined a variety of other methods to quantify the relative stability of the ensemble approach relative to individual specifications. It’s clear from Table 1 that the ensemble dominated in every category.

Table 1. Performance quantiles for GEM strategy specifications on key stability metrics, 1950-2018.

	5th %ile	25th %ile	Median	75th %ile	95th %ile	Original	Ensemble	Original Percent Rank	Ensemble Percent Rank
Compound Return	12.4%	13.4%	14.1%	14.7%	15.7%	14.9%	14.2%	80.8%	54.3%
Sharpe Ratio	0.7	0.78	0.83	0.88	0.95	0.9	0.93	82.7%	93.1%
Avg Max Drawdown	21%	19.1%	17.4%	16.3%	15.3%	16.5%	13.2%	69%	99.9%
Martin Ratio	0.7	0.892	1.103	1.29	1.531	1.351	1.477	82.7%	92.1%
Avg of Worst 5 Years	-10.9%	-8.8%	-7.5%	-6.1%	-4.3%	-7%	-4.7%	59.5%	92%
Worst Decade	35.3%	55%	72%	87.6%	120.4%	55.1%	90.1%	25.1%	78.4%
Without Best Months	7.5%	8.5%	9.1%	9.8%	10.7%	9.8%	9.8%	76%	76.7%
Below Avg Return	7.8%	8.7%	9.3%	9.9%	11%	9.7%	9.8%	66.9%	69.9%

Source: Analysis by ReSolve Asset Management. Data from MSCI, Standard and Poor’s, Barclays, Russell Investments. All performance is gross of taxes and transaction costs.

The ensemble preserves its advantages after accounting for taxes

The ensemble strategy produced many more trades than specifications with longer lookback horizons. The ensemble also produced a larger proportion of short-term gains for tax purposes, resulting in an estimated 0.5% in excess tax costs vs the Original strategy.

We proposed a statistically robust method to drastically reduce trading on short-term noise. This approach reduced trades by over 50 percent and almost completely neutralized the excess tax consequences of deploying the ensemble strategy.

As a result, Figure 11 demonstrates that all of the original benefits of the ensemble were preserved after accounting for taxes.

Figure 11. Percent rank of Global Equity Momentum ensemble strategy relative to all strategy specifications for key performance statistics before and after tax, 1950-2018. HYPOTHETICAL AND SIMULATED RESULTS.

Source: Analysis by ReSolve Asset Management. Data from MSCI, Standard and Poor’s, Barclays, Russell Investments.

Conclusion

When the direct source of an edge is hidden from view, the best we can hope is to capture a portion of the signal with any single specification. Ensembles view an endogenous investment edge from many perspectives. Just as two eyes provide perspective to our visual senses, and Array Radio Telescopes provide an unparalleled view of the universe by combining signals from many small dishes, ensembles provide greater resolution of investment signals to produce a more stable investment experience.

Adam Butler, CFA, CAIA, is co-founder and chief investment officer of ReSolve Asset Management. ReSolve manages funds and accounts in Canada, the United States, and internationally.

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