Gross volume is a poor denominator for long-horizon price impact: it runs about six times above net flow even where 13F filers hold 99.7% of a stock.
The price moves; the holdings barely do
Van der Beck, Bretscher and Fu begin with quarterly holdings. Their 13F sample covers 1990 to 2024 and US common stocks with at least 10 institutional holders and 30% institutional ownership. The average stock has return volatility of 22% over a quarter and portfolio turnover of 25%. To calculate that turnover, they sum the absolute quarterly change in every holder's position, divide by shares outstanding and scale by sqrt(π/2). A constructed residual sector accounts for holdings outside the 13F filings. Both moments use five-year backward windows. Stock by stock, the p/q volatility ratio averages 1.16; its median is 0.81, with 0.36 at the 5th percentile and 3.05 at the 95th.
Their mechanism turns on who agrees with whom. Each investor has log-linear demand, Δq = −ζΔp + u, where u shifts demand at a fixed price. Market clearing moves the price by the size-weighted average shift times M, the inverse of aggregate elasticity. Under a common elasticity, an investor trades the gap between its own shift and that average. The average moves prices; disagreement generates flows. Agreement ρ measures the share of demand-shift variance explained by the size-weighted average. Dividing the price and flow variances yields M = (σp/σq) × sqrt(1/ρ − 1). If elasticities vary independently of demand shifts, they generate extra trading without extra price movement. The identity then becomes a lower bound.
The observed ratio is near 1, which makes a low-impact reading demanding. Price impact below 0.1 requires ρ above 0.99. The paper's textbook CRRA calibration, using a gross expected return of 1.08 and a risk-free return of 1.02, gives an elasticity around 18 and requires much the same near-unanimity.
Agreement itself is unobservable. For S&P 500 constituents, the authors use the adjusted R² from regressing analyst forecast updates on time fixed effects. One-quarter EPS updates put ρ at 0.57 in the text; the Table 2 mean is 0.53 across 754 firms. The implied value-weighted average price impact is 0.75. Long-term growth updates give 0.32, against 0.29 for 366 firms in Table 2, and imply an impact of 1.25. Analysts are a homogeneous professional group, the authors concede, and capture only one part of investor disagreement. Their proxy may therefore overstate agreement. Since a higher ρ reduces the bound, that error would make the estimate conservative. Their defence is that sqrt(1/ρ − 1) changes slowly through the middle range. The plain ratio M̃ = σp/σq assumes ρ = 0.5 throughout and correlates 0.84 with the adjusted bound. Event-study impacts imply ρ of roughly 0.1 to 0.75; a Koijen-Yogo demand system gives 0.217 or 0.360.
The contribution relative to demand-system work is a stock-level statistic requiring two unconditional moments and no instrument. The paper cites Gabaix, Koijen and coauthors on a close cousin: household risk transfer of 0.65% a quarter, beside roughly 6% institutional turnover at the market level. Here, net flow is about one sixth of gross.
What gross volume misses
Quite a lot at a quarterly horizon. Gross turnover averages nearly 120%; the paper reports roughly 20% net portfolio turnover in the text. Even in the top institutional-ownership decile, where 13F filers hold 99.7%, gross turnover remains about six times net. Missing holders cannot account for that gap. Gross and net still sort stocks similarly, though: their rank correlation is near 80% in recent years.
The authors also propose a daily shortcut. With fewer round trips in one session, gross volume should approximate net flow from above. Daily return volatility of about 2% divided by gross turnover of about 1% produces a ratio near 2. Gross exceeding net would put the true daily ratio higher. Horizon matters as well. Average daily impact in 2000 exceeded quarterly impact by more than twice, while quarterly stood 50% above annual. Daily impact subsequently fell through the sample; quarterly and annual impact stayed roughly flat.
Do the flow tests favor net turnover?
Flow-induced mutual fund trades supply 152,862 observations. Across bound quintiles, from lowest to highest, their price-impact coefficients are 2.755, 3.175, 4.029, 4.152 and 5.485. The continuous interaction is 1.256, with a standard error of 0.565. S&P 500 reconstitutions have an average abnormal return of 8% and a 12% cross-sectional spread. In those regressions, the bound loads at 0.058 (s.e. 0.025) across 686 events and 0.110 (s.e. 0.046) across 239 pre-2000 events. The authors focus on pre-2000 because front-running later spread out the index effect. They say the full-sample finding is quantitatively and qualitatively unchanged, though statistically weaker. Its coefficient does halve, from 0.110 pre-2000 to 0.058 in the full sample. Full-sample Q1 is 0.046 versus Q5 at 0.140; pre-2000 Q1 is −0.015 versus 0.174.
The paper says gross-volume measures fail to explain these price effects. The coefficients support a narrower reading. The ratios have different scales, making their point estimates unsuitable for direct comparison. For flow trades, the interaction with σp over gross turnover is 2.352 (s.e. 1.277), a t of about 1.8, without a significance star. The bound's interaction is 1.256 (s.e. 0.565), a t of about 2.2. In the index regressions, the gross ratio loads at 0.062 (s.e. 0.046), t about 1.3; the bound loads at 0.058 (s.e. 0.025), t about 2.3. Gross points in the same direction with larger standard errors. The strongest index result belongs to the plain ratio M̃: 0.114 (s.e. 0.027), t about 4.2. Amihud supplies the clear null on flow trades, at 0.014 (s.e. 0.050).
Net turnover gives the more precise sort. These tests concern quarterly fund flows and announcement-window index trades, rather than fills.
A separate weekly trade
We tested the daily version as a trading rule, outside the paper's evidence. Each week we select up to 20 names from the top 100 non-ADR stocks by capitalization, provided they have positive six-month momentum, and assign 5% to each. We hold a name only when its proxy, 63-session return volatility divided by sqrt(π/2) × 2 × mean dollar-volume turnover, is below both the cross-section's 75th percentile and 1.5 times its own trailing median. Failed slots remain in cash. These are our figures for January 2020 to July 2024. The paper reports no trading performance against which to compare them.
Our run returned 94.85% in total, with a Sharpe of 0.92 after $0.004-a-share commissions. It excludes market impact, a consequential omission for an impact-based test. The 29.71% maximum drawdown comes from a long-only large-cap momentum book with periodic cash, beta to SPY of 0.78 and annualized volatility of 22.97%. We cannot isolate the filter's contribution because we did not report a matched unfiltered arm as a separate series. Two implementation weaknesses also remain: recorded fills use the close although the design called for the next open, and annual universe membership has not been verified as point-in-time. This is one automated pass on a daily gross-volume ratio, related to the gross-turnover ratio whose flow-trade interaction had a 1.277 standard error in the paper. It says little about the 13F-based bound or the authors' work.
The remaining trading question
A lagged daily ratio would earn gross volume a larger role if it predicted realized implementation shortfall after controlling for Amihud. Its 0.014 flow-trade coefficient sets a low bar.
The paper's cross-section already has use. A one-standard-deviation increase in size lowers price impact by 0.13 (t of 12), against earlier findings that large stocks are less elastic. M̃ also rises with aggregation: 0.9 for single stocks, 1.05 for industries and 1.3 for the market. Netting reduces turnover faster than diversification reduces volatility. On this measure, a demand shift across a basket moves the basket's price more per unit than a single-stock shift moves that stock, unless agreement increases with aggregation.
Our backtest stops at 2024-07-01, and everything after that date is deliberately left untouched so the same strategy can be checked out of sample later.