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Mass Index (MASSI)

Summary

Mass Index: Donald Dorsey's non-directional measure of how the trading range itself is expanding or contracting. The high-low range is smoothed by an exponential moving average, that average is smoothed again by a second one of the same length, and the ratio of the first to the second is summed over a trailing window.

Read it as a bulge detector, not a direction. A ratio above one means the range is widening faster than its own smoothing can absorb, so the sum rises; a narrowing range pulls it back down. Dorsey's own rule is the "reversal bulge": the index rising above 27, then falling back under 26.5, warns that the prevailing trend is about to reverse. Which way it reverses has to come from a trend indicator, because the Mass Index has no sign of its own.

Formula

HL = high - low

single = EMA( HL, optInFastPeriod )

double = EMA( single, optInFastPeriod )

MASSI = SUM( single / double, optInSlowPeriod )

Both averages are the standard TA-Lib EMA: smoothing factor 2 / (optInFastPeriod + 1), seeded with the simple average of the first optInFastPeriod inputs of that stage.

Notes

  • The two periods are not interchangeable and are never swapped: optInFastPeriod is the length of both exponential averages, optInSlowPeriod the length of the summation window. Some implementations reorder them when the summation window is the shorter of the two; this one does not.
  • A window in which every bar is exactly flat, high equal to low, leaves both averages at zero. The ratio is reported as 1 there, its continuous limit, so a flat market yields exactly optInSlowPeriod rather than a spurious zero.
  • Implementations disagree on how the exponential averages are seeded. TA-Lib uses its own EMA convention, the simple average of the first optInFastPeriod inputs, where Tulip Indicators, ta4j and trading-signals seed from a single raw value and converge to these values only after many bars. Published sample vectors, including the one in Achelis, are seeded that way and match only in the tail.
  • MASSI inherits EMA's unstable period rather than owning one, and inherits it twice: TA_SetUnstablePeriod(TA_FUNC_UNST_EMA, u) moves the first output by 2u.

Inputs

  • inHigh — High price
  • inLow — Low price

Outputs

  • outReal — Summed ratio of the two smoothed high-low ranges

Parameters

ParameterTypeDefaultAccepted valuesDescription
optInFastPeriodinteger92–100000Number of bars in each of the two exponential averages of the high-low range
optInSlowPeriodinteger252–100000Number of bars the ratio is summed over

Properties

Numerical Stability: Initial Unstable Period — Inherited from EMA, which MASSI computes internally; tunable via EMA's unstable period.

☐ Overlap Input
✅ Independent Y-Axis i
☐ Candlestick
☐ Can Output NaN or ±Inf
☐ Identity at Period 1

Implementation

TA-Lib Definition: massi.c · massi.yaml

NativeFile
Cta_MASSI.c
Rustmassi.rs
JavaCore_MASSI.java

TA-Lib is also available for Python, R and more using a wrapper.

Aliases

Mass Index, Dorsey Mass Index, Reversal Bulge

See Also

CVI · ATR · NATR · TRANGE · EMA · SUM

References

  • Donald Dorsey, "The Mass Index", Technical Analysis of Stocks & Commodities, 1992 — the original description
  • Steven B. Achelis, Technical Analysis from A to Z, McGraw-Hill, 2nd ed. (p. 182)
  • StockCharts ChartSchool: Mass Index
  • Tulip Indicators, mass — an independent implementation, differing in its seeding
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