Transaction Costs of Factor-Investing Strategies

Figures & data

Exhibit 1. Literature in Capacities of Factor Investing

Study	Factor Definition	Maximum Capacities Reported	Key Assumptions
Chen, Stanzl, and Watanabe (2002)	Long–short arbitrage strategies formed in the larger half of the US market	US$0.4, US$5, and US$2 billion for, respectively, size, value, and momentum factors	(1) Trade size cannot exceed 1% of market cap.(2) Expected market impact erodes historical excess returns entirely.
Frazzini, Israel, and Moskowitz (2012)	Long–short arbitrage strategies across developed markets	US$2,735, US$1,755, and US$159 billion for, respectively, size, value, and momentum factors in the United States; US$0, US$753, and US$50 billion for, respectively, size, value, and momentum factors in the international markets	(1) Restrict trading to no more than 5% of daily volume; allow up to 2% of tracking error against intended strategies.(2) Expected market impact erodes historical excess returns entirely.
Novy-Marx and Velikov (2016)	Long–short arbitrage strategies in the United States	US$0.7 to US$131 billion for low-turnover factors, which included size and value at, respectively, US$20 and US$21 billion;US$1 to US$12 billion for mid-turnover factors, which included momentum at US$5 billion	(1) Apply trade restriction based on factor signal ranking to lower turnover.(2) Effective bid–ask spread and expected market impact erode historical excess returns entirely.
Ratcliffe, Miranda, and Ang (2017)	Six MSCI factor strategies in the United States	US$25,435, US$1,765, US$324, US$6,765, US$1,437, and US$1,579 billion for, respectively, size, value, momentum, low-volatility, quality, and multifactor strategies	(1) Trading takes place over five days.(2) Explicit cost and market impact erode historical excess returns entirely.
Our study	Popular factor-investing strategies in US, developed, and emerging markets	US$291, US$2, US$108, US$45, US$8, and US$41 billion for, respectively, value, momentum, low-volatility, quality, income, and multifactor strategies in the United States; US$357, US$4, US$104, US$54, US$7, and US$36 billion for, respectively, value, momentum, low-volatility, quality, income, and multifactor strategies in developed markets	(1) Trading takes place near the close of rebalancing dates.(2) Expected market impact reaches 50 bps.

Table 1. Distribution of Asset Levels on Rebalancing Dates of the Underlying Indexes, 1968–2016

Underlying Indexes	No. of Rebalancings	5th	25th	50th	75th	95th
By region
United States only	35	92.9	647.6	1,123.2	4,504.2	9,698.7
Other single country	62	5.8	114.4	149.6	1,603.8	9,563.7
Developed markets, multicountry	78	59.5	248.9	727.1	1,727.4	9,180.1
Emerging markets, multicountry	19	65.9	583.4	1,289.2	1,685.8	3,709.7
By size group
Benchmarked to large cap or all cap	178	22.3	156.1	540.1	1,745.9	9,571.6
Benchmarked to small cap	16	na	112.6	202.4	1,032.1	na
By subsample
2009–2012	75	5.3	153.7	464.2	524.2	5,184.7
2013–2016	119	29.5	167.4	751.4	1,801.6	10,241.0
All	194	24.6	153.7	520.3	1,643.2	9,563.6

Note: Asset levels in US$ millions as of rebalancing dates. na = not applicable.

Source: Research Affiliates, based on data from Bloomberg.

Table 2. Distribution of Relative Trade Size

Region	No. of Obs.	Avg. Market Cap (US$ millions)	1st	5th	10th	25th	50th	75th	90th	95th	99th
United States	20,462	6,900	0.007%	0.056%	0.140%	0.503%	1.62%	4.63%	12.4%	21.0%	42.5%
Developed markets ex. United States	20,405	7,895	0.008	0.050	0.108	0.411	1.57	4.99	12.8	21.4	43.4
Emerging markets	8,788	5,524	0.002	0.021	0.084	0.471	2.14	7.30	17.6	27.9	51.4
All	49,655	7,066	0.005%	0.046%	0.116%	0.458%	1.67%	5.16%	13.6%	22.6%	44.9%

Note: Relative trade size is defined as the trade size in dollars divided by the dollar volume on the trade day.

Source: Research Affiliates, based on data from Bloomberg.

Figure 1. Average Market Impact by Trade Size

Source: Research Affiliates, based on data from Bloomberg.

Figure 2. Market Impact and Reversal across Different Regions and Trade Directions

Note: Market impact factors are in percent, estimated by Equation 2.

Source: Research Affiliates, LLC, using data from Bloomberg.

Table 3. Estimates and Significance of Trade-Day and Reversal Impact Factors

	All Trades	United States	Developed Ex. US	Emerging Markets	Purchases Only	Sales Only
Trade day
Impact factor (k0)	4.27%	4.70%	3.83%	4.30%	4.60%	4.16%
t-statistic	8.15	3.38	11.99	18.36	6.37	6.29
Reversal
Impact factor (k+4)	–2.42%	–3.53%	–1.42%	–2.34%	–1.74%	–3.73%
t-statistic	–5.67	–5.53	–1.74	–5.76	–1.25	–4.43

Note: Market impact factors are in percent, estimated by Equation 2.

Source: Research Affiliates, LLC, using data from Bloomberg.

Table 4. Market Impact Costs and Liquidity Characteristics of US Factor-Investing Strategies, 1968–2016

Strategy	Return	Volatility	Market Impact Cost	Capacity (US$ billions)	Portfolio Volume (US$ millions)	Turnover	Turnover Concentration	Tilt
Value strategies
Concentrated value	11.6%	16.1%	0.28%	17.7	39,299	25.1%	77.2%	1.5
Fundamental indexing	11.6	14.8	0.02	290.7	96,651	11.4	21.9	1.6
Income strategies
High dividend	12.1%	14.4%	0.61%	8.2	13,464	20.1%	67.5%	9.3
Dividend growth	12.1	14.1	0.76	6.6	26,016	37.5	49.5	4.5
Low-volatility strategies
Minimum volatility	11.2%	13.3%	0.39%	12.9	34,290	24.8%	73.3%	2.3
Low volatility	11.1	12.0	1.90	2.6	21,382	71.6	84.3	2.1
Defensive	10.6	13.2	0.07	72.7	68,539	14.1	83.6	1.5
Fundamental low volatility	12.5	13.4	0.05	107.8	42,257	23.1	44.9	1.5
Quality strategies
Quality	11.1%	15.7%	0.37%	13.5	35,029	23.8%	71.9%	1.3
Conservative profitable	11.5	14.2	0.11	44.6	35,794	19.1	38.4	1.5
Momentum strategies
Sharpe momentum	11.9%	17.3%	2.05%	2.4	35,797	108.5%	88.4%	1.3
Standard momentum	11.9	17.7	2.72	1.8	37,928	155.8	90.2	1.3
Multifactor strategies
Quality/value/low volatility	11.2%	14.1%	0.22%	22.6	52,410	23.4%	71.2%	1.6
Mathematical beta 6	11.5	14.9	0.12	40.6	99,997	36.8	47.9	2.3
Dynamic multifactor	12.6	14.8	0.23	21.3	96,739	51.6	60.0	1.8
Other
Equal weight	10.8%	17.1%	0.20%	25.0	109,263	29.8%	47.6%	2.0

Notes: Return, volatility, and turnover are averaged over the period. Other characteristics are based on the most recent rebalancing up to the end of 2016. Market impact costs assume US$10 billion in AUM and are averaged over the most recent five years, with the cost of each trade capped at 2%. (Note that this assumption would imply a trade that consumes 66% of daily volume. Many practitioners would be unwilling to trade more than this percentage or would stop trading upon incurring a cost of 2%. This limit also reduced the incidence of volume data outliers.) Capacity is the estimated AUM at which the strategy is expected to have 50 bps of market impact cost. See Appendix A for strategy descriptions.

Source: Research Affiliates, based on data from Worldscope and Datastream.

Table

Strategy	Description
1. Concentrated value	The semiannually rebalanced strategy selected the top 20% from the large-cap and midcap universe on the basis of a value score calculated from the ratios of price to book value, price to earnings, and enterprise value to cash flow from operations. It weighted selections by market cap times the value score.
2. Fundamental indexing	The strategy selected and weighted companies according to four fundamental measures of company size: book value, cash flow, dividends plus buyback, and adjusted sales. It was implemented in four annually rebalanced tranches in such a way that trades were spread over four quarters.
3. High dividend	After screening for dividend growth and dividend coverage, the annually rebalanced strategy selected 100 stocks by dividend yield from the large-, mid-, and small-cap universes and weighted selections by indicated dividend yield.
4. Dividend growth	For US market simulations, the strategy rebalanced quarterly, selecting companies from the top 1,500 by market cap that had stable or increasing dividends in the last 20 years. For developed-market simulations, stocks with stable or increasing dividends in the last 10 years were selected from the large-, mid-, and small-cap universes and weighted by indicated dividend yield. In emerging-market simulations, stock selections were based on growing earnings and high dividend yields and were weighted by annual dividend yield. Portfolios for both developed and emerging markets were rebalanced semiannually.
5. Minimum volatility	The strategy minimized the volatility of a large- and midcap portfolio by means of a constrained optimization. Constraints included maximum single-holding weight, country and sector active weights, and turnover limits. The optimization was recomputed semiannually.
6. Low volatility	The quarterly rebalanced strategy selected the 20% lowest-volatility stocks from the parent universe and weighted them by 1/Volatility.
7. Defensive	The strategy reweighted stocks from the parent universe according to a stability score, which captured low volatility, low earnings variability, low leverage, and high return on assets. The portfolio was rebalanced annually.
8. Fundamental low volatility	The strategy selected companies from each sector and region of the parent universe with low valuations and low systemic risk and weighted selections by their fundamental size. It was implemented in four annual rebalancing tranches in such a way that trades were spread over four quarters.
9. Quality	The semiannually rebalanced strategy selected companies from the large- and midcap parent universe on the basis of a quality score that combined high return on equity, low debt to equity, and low earnings variability. Selections were weighted by market cap times a quality score.
10. Conservative profitable	The strategy selected the top 25% of large companies with high profitability and low investment and weighted selections by fundamental size. It was implemented in four annual rebalancing tranches in such a way that trades were spread over four quarters.
11. Sharpe momentum	The strategy selected companies from the large- and midcap parent universe on the basis of a momentum score reflecting prior 6-month and 12-month Sharpe ratios. Selections were weighted by market cap times a momentum score. The portfolio was rebalanced semiannually, with additional ad hoc rebalances triggered by volatility spikes.
12. Standard momentum	The quarterly rebalanced strategy selected the top third of companies from the large-cap and midcap parent universe by momentum, defined as prior-year return. It skipped the most recent month and weighted selections by market cap.
13. Mathematical beta 6	The quarterly rebalanced strategy equally weighted six factor indexes: value, momentum, midcap, low volatility, profitability, and investment. Each factor was constructed by selecting half the companies from regional large-cap universes by characteristics, and the selections were weighted via five diversification methods.
14. Quality/value/low volatility	The fund equally weighted quality, low-volatility, and value strategies that reweighted the large-cap and midcap parent universe by fundamental size.
15. Dynamic multifactor	At every quarter, the strategy dynamically weighted five factor indexes—value, low volatility, quality, momentum, and size—based on long-term reversal and short-term momentum. The large-cap size factor was constructed by selecting the top 25% of the large-cap and midcap company universes (50% for momentum). Selections were then weighted by fundamental size (market capitalization for momentum). The small-cap size factor was constructed by equally weighting the other four factors constructed within the small-company universe.
16. Equal weight	The quarterly rebalanced strategy equally weighted all stocks in the parent universe.