The Impact of Crowding in Alternative Risk Premia Investing

Figures & data

Figure 1. Divergence Premia: Cross-Sectional Momentum Strategy

^aWinners are not formulaically more expensive than losers, even though they have generally been so historically.

Figure 2. Momentum Performance vs. Turnover, December 2005–April 2018

Notes: This figure shows annual turnover of an equity momentum strategy (top versus bottom decile) and its rolling one-year performance. The strategy is a combination of three quarterly rebalanced strategies that rebalanced in different months of a quarter. The universe is a global developed market equity universe.

Figure 3. Convergence Premia: Cross-Sectional Value Strategy

Note: τ denotes the time to convergence of the valuation spread and is a function of investor flows.

Figure 4. Value Performance vs. Turnover, December 2005–April 2018

Notes: This figure shows the annual turnover of an equity value strategy (cheap versus expensive decile) and its rolling one-year performance. The strategy is a combination of three quarterly rebalance strategies that rebalanced in different months of a quarter. The universe is a global developed market equity universe.

Table 1. Overview of Asset Class Data and Strategies

Equities
Universe	Global developed markets
Period	September 2004–May 2018
Factor model	Four-factor model: MSCI World Index, size, value, momentum
Test portfolios	Top decile/bottom decile, equally weighted
Convergence	Value: book-to-price ratioSize: market capitalization
Divergence	Momentum: residual of cross-sectional regression of past 12-month return (ex most recent month) against stock volatility (estimated over the same period)Quality: return on assetsLow risk: beta to MSCI World Index
Source	Worldscope, Axioma
Commodities
Universe	24 S&P GSCI (Goldman Sachs Commodity Index) commodities:Chicago wheat, Kansas wheat, corn, soybeans, coffee, sugar, cocoa, cotton, live cattle, feeder cattle, lean hogs, WTI (West Texas Intermediate) crude oil, Brent crude oil, gas oil, heating oil, RBOB (reformulated blendstock for oxygenate blending) gasoline, natural gas, aluminum, LME (London Metal Exchange) copper, lead, nickel, zinc, gold, silver
Period	January 1999–May 2018
Factor model	Two-factor model: GSCI Commodity Index, carry
Test portfolios	Top third/bottom third, equally weighted
Divergence	Momentum: past 12-month return
Source	Bloomberg
Foreign exchange (FX)
Universe	26 developed and emerging market currencies:Australian dollar, Brazilian real, Canadian dollar, Swiss franc, Chilean peso, Chinese yuan in the offshore market, Czech koruna, euro, British pound, Hungarian forint, Israeli new shekel, Indian rupee, Japanese yen, South Korean won, Mexican peso, Malaysian ringgit, Norwegian krone, New Zealand dollar, Philippine peso, Polish zloty, Russian ruble, Swedish krona, Singapore dollar, Turkish lira, new Taiwan dollar, South African rand
Period	January 2000–May 2018
Factor model	Three-factor model: US dollar index, carry, momentum
Test portfolios	Top third/bottom third, equally weighted
Convergence	Value: purchasing power parity
Divergence	Momentum: past 12-month return
Source	Bloomberg

Figure 5. CoMetric for Equity Momentum and Value, September 2004–May 2018

Notes: The figure presents the average pairwise excess correlation for the winners and losers (Panel A) and for the cheap and expensive stocks (Panel B) of a global equities universe. The estimation is weekly, and the past 52 weekly returns (or 5 × 52 weekly returns for value) of each stock were used for the estimation. The returns of the assets in the momentum (value) baskets are factor adjusted for the market, size, and value (momentum) factors. The sample period is September 2004 (first estimates become available 52 or 5 × 52 weeks later, accordingly) to May 2018.

Figure 6. Equity Momentum Event Study

Notes: This figure shows average buy-and-hold performance of a long–short equity momentum portfolio (top minus bottom equally weighted deciles) over a two-year period following the most crowded periods or the least crowded periods. Crowdedness was measured on a weekly basis. The figure contains 95% confidence interval bands estimated using Newey–West (1987) standard errors. The sample period for determining the most and least crowded periods is October 2005–May 2018.

Table 2. Performance of Divergence Premia Conditional on the Level of Asset Excess Comovement

Asset Class		Obs.	Month 1	Months 1–6	Year 1	Year 2
Equity momentum	High	173	0.64%	–2.25%	–5.91%**	1.42%*
	Low	173	1.21%**	4.58%**	6.86%**	–0.52%
	H – L		–0.57%	–6.83%**	–12.78%**	1.63%
Equity low beta	High	173	–2.25%	–13.75%**	–20.11%**	–6.97%
	Low	173	0.40%	3.61%**	8.74%**	9.26%**
	H – L		–2.66%	–17.36%**	–28.85%**	–16.25%*
Equity quality	High	173	–0.11%	–3.64%**	–4.74%**	–0.60%
	Low	173	0.61%	4.16%**	8.72%**	0.53%
	H – L		–0.72%	–7.80%**	–13.47%**	–0.76%
FX momentum	High	248	0.17%	–0.21%	–1.05%	–0.04%
	Low	248	0.20%	1.04%**	1.38%**	1.46%**
	H – L		–0.04%	–1.26%**	–2.44%**	–1.43%*
Commodity momentum	High	260	0.33%	1.28%	–3.21%*	5.59%**
	Low	260	0.64%*	0.77%	2.32%	5.43%**
	H – L		–0.31%	0.51%	–5.53%**	–0.18%

Notes: This table shows average returns of buy-and-hold long–short divergence strategies in equity, currency, and commodity markets following periods of high and low levels of asset excess comovement. Newey–West (1987) robust standard errors were used to account for heteroskedasticity and serial correlation.

*Statistically significant at the 5% level in a two-tailed test.

**Statistically significant at the 1% level in a two-tailed test.

Figure 7. Divergence Event Study

Notes: This figure shows average buy-and-hold performance of various long–short divergence portfolios (see Table 1 for specification details) over a two-year period following the most crowded periods or the least crowded periods. Crowdedness was measured on a weekly basis.

Figure 8. Equity Value Event Study

Notes: This figure shows average buy-and-hold performance of a long–short equity value portfolio (top minus bottom equally weighted deciles) over a two-year period following the most crowded periods or the least crowded periods. Crowdedness was measured on a weekly basis. The figure contains 95% confidence interval bands estimated using Newey–West (1987) standard errors. The sample period for determining the most and least crowded periods is October 2009–May 2018.

Table 3. Performance of Convergence Premia Conditional on the Level of Asset Excess Comovement

Asset Class		Obs.	Month 1	Months 1–6	Year 1	Year 2
Equity value	High	111	0.69%*	5.85%**	5.45%**	–4.64%**
	Low	111	–0.85%*	–5.71%**	–11.61%**	–6.91%*
	H – L		1.54%**	11.56%**	17.05%**	0.54%
Equity size	High	173	0.86%**	2.19%**	3.55%**	–4.63%**
	Low	173	0.87%	4.76%**	7.67%**	2.19%
	H – L		–0.00%	–2.58%	–4.12%*	–7.41%**
FX value	High	186	0.62%**	2.72%**	5.04%**	2.26%*
	Low	186	0.29%**	0.94%**	1.32%**	0.97%**
	H – L		0.33%	1.78%**	3.72%**	1.29%

Notes: This table shows average returns of buy-and-hold long–short convergence strategies in equity and currency markets following periods of high and low levels of asset excess comovement. Newey–West (1987) robust standard errors were used to account for heteroskedasticity and serial correlation.

*Statistically significant at the 5% level in a two-tailed test.

**Statistically significant at the 1% level in a two-tailed test.

Figure 9. Convergence Event Study

Notes: This figure shows the average buy-and-hold performance of various long–short convergence portfolios (see Table 1 for specification details) over a two-year period following the most crowded periods or the least crowded periods. Crowdedness was measured on a weekly basis.