Finance & Markets — Conceptual Series
Vol. I · Defining Flow · 2026
Essay · Part 1 of 3
What Exactly
Is Flow?
The word "flow" appears constantly in finance research, but its precise meaning varies across papers. This essay defines it, reconciles six influential definitions, and shows why it matters.
§ 01 — The Core Definition
Flow Is What You Do, Not What You Have
In finance, a flow measures the active reallocation of capital over a period of time. It captures the part of a change in holdings that is not explained by returns on existing positions. If a fund's stock portfolio grew by $12 million last quarter, and $10 million of that came from the stocks going up in value, then the flow is $2 million — the new money the fund actively moved into stocks.
Every paper in the recent demand-system asset pricing literature defines flow the same way at its core:
The Universal Flow Formula
Flow = ΔHoldings − Return Effect
ΔHoldings
Total Change
The raw change in the dollar value of a position from one period to the next. This includes both active trades and passive price appreciation.
Return Effect
Passive Component
What the position would be worth if no trades had occurred — just the prior holdings multiplied by the asset's return over the period.
Flow
Active Component
The residual. This is the new money that was actively moved in or out — the part that shifts the demand curve rather than moving along it.
This is a simple but powerful idea. A stock portfolio can change in value for two reasons: the stocks you already own go up or down (the return effect), or you buy and sell stocks (the flow). Separating the two tells you how much of the change was a deliberate act by the investor.
Why this matters: When a fund's holdings increase, we need to know: did the fund actively put new money into stocks (a potential cause of price change), or did the stocks it already owned simply rise in value (a consequence of price change)? Without stripping out the return effect, you can't tell whether the fund is driving prices or being carried by them. Flow isolates the cause.
§ 02 — How Flow Is Measured
Six Papers, One Concept, Different Levels
The same core definition — change in holdings minus return effect — is applied at different levels of aggregation across the literature. Understanding how each paper implements it reveals that these are not competing definitions but the same concept measured at different scales.
Level 1: Individual fund flows
Frazzini & Lamont (2008) and Coval & Stafford (2007) both compute flow at the individual mutual fund level. The formula, standard in the literature, is:
Ft = TNAt − TNAt−1 · (1 + Rt)
where TNAt is total net assets at the end of the period, Rt is the fund's return over the period, and TNAt−1 · (1 + Rt) is what assets would have been if no money came in or went out — just passive growth. The difference is the net new money from investors: subscriptions minus redemptions.
This is the "tap" — the raw inflow or outflow that forces a fund manager to trade. Coval & Stafford (2007) show that when outflows force mutual funds to sell their holdings, the stocks they sell drop in price and later rebound — evidence of price pressure from flow. Frazzini & Lamont (2008) use fund flows to construct a measure of which stocks are being pushed by "dumb money" — retail investors chasing returns — and show that these stocks subsequently underperform.
Level 2: Investor × asset flows
Koijen & Yogo (2019) move up one level. Using quarterly SEC 13F filings — which report the holdings of every U.S. institution managing over $100 million — they estimate how each institution's demand for each stock depends on observable characteristics (market equity, book-to-market, profitability, investment, and beta). The changes in demand that are not explained by these characteristics show up as "latent demand" — the flow-like component in their demand system.
Van der Beck (2025) applies the same logic to ESG investing specifically. He estimates each institution's "ESG tilt" — the fraction of their portfolio allocated toward ESG stocks versus the market portfolio — and then computes the flow as the return-adjusted change in that tilt:
Fi,ESGt+1 = Ai,ESGt+1 − Ai,ESGt · RESGt+1
Same formula as Level 1, but applied per investor per portfolio dimension. Van der Beck finds that total institutional ESG flows cumulated to $3 trillion by 2023 — far exceeding the $350 billion in branded ESG mutual funds. The visible "tap" dramatically understated the true flow.
Level 3: Aggregate market flow
Gabaix & Koijen (2022) operate at the highest level: the entire stock market. They define the aggregate flow into equities as:
fS = Σ Si · (ΔFi / Wi)
where ΔFi is the dollars flowing into fund i, Wi is that fund's total wealth, and Si is its share of total equity holdings. This weights each investor's flow by their importance to the equity market.
This is where the "for every buyer there is a seller" paradox gets resolved. At the individual stock level, net shares traded is always zero. But at the asset-class level, dollars can flow from bonds into equities — and this reallocation is what moves the aggregate market. Gabaix & Koijen show the net total dollar flow across all investors is zero (Σ ΔFi = 0), yet the equity-share-weighted flow fS is not zero. It captures how the composition of the economy's wealth shifts toward or away from stocks.
Gabaix, Koijen, Mainardi, Oh & Yogo (2023) extend this to household portfolios using security-level data from a wealth management platform covering 439 billionaires. They find household flows are small and largely insensitive to returns — even wealthy households provide little stabilizing force to financial markets.
§ 03 — Flow vs. Inventory
The Bathtub and the Tap
The simplest way to understand the distinction between a holding and a flow is the bathtub analogy.
Inventory (Stock Variable)
The Water Level
How much water is in the tub right now
A snapshot at a point in time. Koijen & Yogo (2019) observe this in the 13F data: each quarter, they see what every institution holds. This is the water level — the inventory — but it tells you nothing about what changed.
Flow (Rate Variable)
The Tap
How fast water is pouring in (or draining out)
A rate over a period. Gabaix & Koijen (2022) isolate this by stripping out the return effect. The tap is what you actively control. A full bathtub can have zero flow. A tiny tap can flood a small tub.
The critical insight from the inelastic markets literature is that the financial market's "tub" is remarkably small relative to the flows that hit it. Not because the stock market is small in dollar terms — it isn't — but because so few market participants are willing to adjust their positions when prices change. Institutional mandates, benchmark constraints, and passive strategies mean that most of the water in the tub is effectively frozen. Only a thin layer sloshes around, and that thin layer is what flows act upon.
This is why every $1 flowing into equities can produce $5 of market value change (Gabaix & Koijen, 2022). The effective tub — the amount of elastic, price-responsive capital — is much smaller than the total tub. Most of the market is held by investors who won't sell regardless of price.
§ 04 — Why Flow Moves Prices
The Multiplier: $0.80 Moves Prices by $4
Gabaix & Koijen (2022, pp. 16–17) walk through a concrete example that makes the multiplier tangible. There are two funds: a pure bond fund and a mixed fund with a mandate to hold θ = 80% of its assets in equities. An outside investor moves money from the bond fund into the mixed fund. Only 80% of that inflow actually reaches the stock market — the rest goes to bonds per the mandate. Yet the market value gain is five times the amount that reaches equities.
Use the sliders below to replicate this example and see how the multiplier changes with different mandates and inflow sizes.
The multiplier M = 1/ζ = 1/(1−θ). When the mandate is 80% equities, ζ = 0.20 and M = 5. This means every dollar that reaches the equity market produces five dollars of market value change. Of the $1.0 total inflow, only $0.80 directly buys stocks (the rest goes to bonds per the mandate). That $0.80 produces a $4.00 gain — a five-fold multiplier, as Gabaix & Koijen (2022, p. 17) show. The extra gain comes from the cascade: higher stock prices raise the fund's wealth, which forces it to buy even more stocks to maintain its mandate, which pushes prices higher still.
The stock market in this simple model is a very reactive economic machine, which turns an additional $1 of investment into an increase of $5 in aggregate market valuations.
Gabaix & Koijen (2022), p. 1§ 05 — Exploring the Equation
Flow vs. Price Impact: p = f / ζ
The equation p = f/ζ says that price impact equals the flow (as a fraction of the market) divided by the elasticity. Adjust the sliders to see how different elasticities amplify or dampen the same flow. At ζ = 0.20, the empirical estimate, a 1% flow produces a 5% price move. At ζ = 2.0, what conventional models assume, the same flow barely registers.
§ 06 — What Comes Next
Flow Is Not Liquidity
This essay has defined flow: the active reallocation of capital, stripped of passive return effects, measured at scales from the individual fund to the aggregate market. Across six papers, the definition is consistent: Flow = ΔHoldings − Return Effect.
But there is a concept that flow is often confused with: liquidity. Liquidity measures how easily you can execute a trade at the current price — the tightness of the bid-ask spread, the depth of the order book, the speed of execution. Flow measures something different: how much the price must change to accommodate the trade in the first place.
An asset can be perfectly liquid and still have enormous flow-driven price impact. Coval & Stafford (2007) document this directly: U.S. equities are among the most liquid assets on Earth — tight spreads, deep markets, fast execution — yet forced selling by distressed mutual funds pushes their prices well below fundamental value. The problem is not that trades are hard to execute. It is that aggregate demand is inelastic, so nobody on the other side absorbs them without a large price concession.
The next essay in this series will develop this distinction in full: what liquidity measures, what flow measures, why they are different, and why confusing them leads to systematic misunderstanding of how financial markets work.
If investors create a flow of 1% as a fraction of the value of equities, the model implies that the value of the equity market goes up by 5%. If the price of the equity market portfolio goes up by 5%, demand falls by only 1%... the price elasticity is 0.2.
Gabaix & Koijen (2022), p. 2