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MARKETFI: Market Facilitation Index

Price moves in an empty room; volume tells you how many people showed up.

Property Value
Category Oscillator
Inputs OHLCV bar (TBar)
Parameters None
Outputs Single series (MARKETFI)
Output range Varies (see docs)
Warmup > 1 bars
PineScript marketfi.pine
  • The Market Facilitation Index answers a single question with arithmetic directness: how much price moved per unit of volume traded?
  • No configurable parameters; computation is stateless per bar.
  • Validated against TA-Lib, Skender, and Tulip reference implementations where available.

The Market Facilitation Index answers a single question with arithmetic directness: how much price moved per unit of volume traded? One division. No lookback period. No smoothing. No parameter to debate. What you get is raw market efficiency — the price range a market delivers for each unit of liquidity consumed.

Bill Williams introduced BW MFI in Trading Chaos (1995) as part of his Profitunity trading system, alongside the Awesome Oscillator and Accelerator Oscillator. His central insight was that price and volume carry independent signals, and only their combination reveals whether a trend has genuine participation. A wide range bar on thin volume suggests ease of movement but not conviction. A narrow range bar on heavy volume suggests absorption — large players defending a level.

Historical Context

Williams drew on the earlier work of Mark Chakin, Jesse Livermore's tape-reading intuitions, and his own experience in commodities markets to argue that most technical indicators analyze price alone — a single dimension of a fundamentally two-dimensional market. Volume, he argued, is the missing dimension. The MFI is his most direct formulation of that intuition: strip everything away until you have a pure ratio.

The index predates modern market microstructure theory but anticipated it. Economists later formalized the Kyle lambda (price impact per unit of order flow) and Amihud's illiquidity ratio, both of which are statistical close relatives of MFI's per-bar instantiation. Williams was doing microstructure analysis with a pocket calculator thirty years before the term was fashionable.

Two objections are legitimate. First, raw volume is not normalized across instruments or time — a bitcoin MFI reading is incommensurable with a T-bill MFI reading. Second, the formula is sensitive to bar granularity: the same market on 1-minute bars versus daily bars produces categorically different MFI values on the same trade. Williams intended daily bars. Users who apply MFI to intraday data are extrapolating beyond its design envelope.

Architecture & Physics

1. Formula

$$\text{MARKETFI} = \frac{\text{High} - \text{Low}}{\text{Volume}}$$

Zero-volume guard: When Volume = 0, the result is 0.0. Dividing by zero is undefined; returning 0.0 is the correct semantic choice — if no trades occurred, the market delivered zero facilitation per trade unit.

2. State

Unlike period-based indicators, MARKETFI carries essentially no state. The computation is stateless per bar. The implementation stores only LastValid (for NaN substitution) and Count (for IsHot). No ring buffers, no warmup counters beyond the first bar.

State = { LastValid: double, Count: int }

IsHot fires on bar 1. WarmupPeriod = 1.

3. NaN / Infinity Handling

Input Behavior
NaN High or Low Substituted with LastValid; result uses substituted values
NaN or Infinity Volume Treated as 0 → result = 0.0
Result NaN or Infinity Substituted with LastValid

4. Bar Correction (isNew = false)

The isNew parameter follows the standard QuanTAlib rollback contract. On isNew = true, _ps = _s is saved. On isNew = false, _s = _ps is restored before recomputing. Since MARKETFI state is entirely scalar (no buffers), rollback is a single struct copy — the cheapest possible correction.

Mathematical Foundation

$$\text{MARKETFI}_t = \frac{H_t - L_t}{V_t}, \quad V_t > 0$$

This is equivalent to the per-share price impact in a simplified zero-latency model. In Kyle's framework, the price impact $\lambda$ satisfies:

$$\Delta P = \lambda \cdot Q$$

where $Q$ is order flow. MARKETFI inverts this: given $\Delta P = H - L$ (range as proxy for price impact), and $V$ as volume, $\text{MARKETFI} = \Delta P / V \approx \lambda$ at bar granularity.

The four-quadrant interpretation Williams used:

MFI vs Previous Volume vs Previous Quadrant Interpretation
↑ ↑ Green Trend acceleration — price and volume agree
↑ ↓ Fade Price moves easily; volume not confirming
↓ ↑ Squat Volume absorbed; breakout pending (brown)
↓ ↓ Fake No trend, no volume — false move likely

QuanTAlib computes the raw scalar index. The four-quadrant coloring requires comparing current bar against prior bar — implementable in the Quantower adapter or downstream.

Performance Profile

Aspect Detail
Time complexity O(1) per bar
Space complexity O(1) — 2 scalar fields
Allocations (hot path) 0
SIMD applicable No — single division, no vectorizable loop
FMA applicable No — no a*b + c pattern
Warmup bars 1
Buffer None

Operation Count (Streaming Mode)

MarketFi is pure O(1): a single division of range by volume, no lookback or state.

Operation Count Cost (cycles) Subtotal
Range = High - Low 1 1 cy ~1 cy
MFI = Range / Volume 1 5 cy ~5 cy
Zero-volume guard 1 1 cy ~1 cy
Total O(1) — ~7 cycles

Absolute minimum complexity — one subtraction and one division per bar. No circular buffers, no warmup, no state.

Batch Mode (SIMD Analysis)

Operation Vectorizable? Notes
Range = High - Low Yes Vector<double> subtract
MFI = Range / Volume Yes Vector divide with zero-guard mask

Fully vectorizable — both operations are elementwise with no data dependencies across bars.

Operation count per bar: 1 subtraction + 1 division + 1 comparison (zero guard) = 3 FP ops. This is the minimum possible for any meaningful price indicator.

Quality metrics (1–10):

Dimension Score Note
Mathematical precision 9 Exact division — no approximation
Interpretability 7 Simple ratio; requires context to act on
Lag 10 Zero lag — pure current-bar measure
Noise sensitivity 4 Sensitive to outlier bars; no smoothing
Volume dependency — Requires real volume data; meaningless on synthetic feeds

Validation

No external library (TA-Lib, Skender.Stock.Indicators, Tulip, OoplesFinance) implements the Market Facilitation Index. Validation is via:

Test Method
Identity (H - L) / V matches direct computation for known inputs
Scaling Doubling volume halves MFI; doubling range doubles MFI
Batch == Streaming All bars agree to 1e-10
Determinism Two instances with same seed produce identical output
Non-negativity H >= L always → MFI >= 0 always
Zero-volume guard Volume=0 → MFI=0 for all range values

Common Pitfalls

  1. Zero volume on data gaps. Many data providers fill weekend or holiday bars with Volume = 0. These produce MFI = 0, which is correct but may be misread as a "squat" signal. Guard your data feed or filter these bars upstream.

  2. Tick data vs bar data. MFI on tick bars is nonsensical — range is nearly always nonzero, volume is always 1. Use OHLCV bars with meaningful aggregation periods.

  3. Cross-instrument comparison. A crude oil MFI of 0.0001 and a gold MFI of 0.00003 say nothing relative to each other. Normalize by ATR or recent MFI average before comparing instruments.

  4. Intraday granularity. Williams calibrated BW MFI on daily commodity bars. Applying it to 1-minute equity bars produces different distributional properties. Signals may not transfer.

  5. Treating MFI alone as a signal. Williams explicitly used MFI in conjunction with AO and AC. Raw MFI without the quadrant comparison (prior bar) loses most of its analytical content.

  6. Volume data quality. Crypto exchanges report volume in base currency; futures report contracts; equities report shares. Ensure units are consistent within a single instrument's time series before trusting MFI readings.

References

  • Williams, Bill (1995). Trading Chaos: Applying Expert Techniques to Maximize Your Profits. Wiley.
  • Williams, Bill and Justine Gregory-Williams (2004). Trading Chaos: Maximize Profits with Proven Technical Techniques (2nd ed.). Wiley.
  • Kyle, Albert S. (1985). "Continuous Auctions and Insider Trading." Econometrica, 53(6), 1315–1335.
  • Amihud, Yakov (2002). "Illiquidity and stock returns: cross-section and time-series effects." Journal of Financial Markets, 5(1), 31–56.