Wilder’s DMI (ADX)

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Wilder’s DMI (ADX): Definition, Calculation, and Trading Use

What it is

Wilder’s Directional Movement Index (DMI) is a set of three lines that measure trend direction and strength:
– +DI (Plus Directional Indicator) — measures upward movement.
– −DI (Minus Directional Indicator) — measures downward movement.
– ADX (Average Directional Index) — measures the strength of the trend (non‑directional).

Typical defaults use a 14‑period lookback. When +DI is above −DI price momentum is upward; when −DI is above +DI momentum is downward. A higher ADX value indicates a stronger trend; readings are usually interpreted relative to thresholds such as 20, 25, or 30.

How to calculate (summary)

  1. Choose a period length (commonly 14).
  2. Calculate directional movement (+DM and −DM) for each period:
  3. upMove = Current High − Previous High
  4. downMove = Previous Low − Current Low
  5. +DM = upMove if upMove > downMove and upMove > 0, otherwise 0
  6. −DM = downMove if downMove > upMove and downMove > 0, otherwise 0
  7. Calculate True Range (TR) for each period:
  8. TR = max(Current High − Current Low, abs(Current High − Previous Close), abs(Current Low − Previous Close))
  9. Smooth the series using Wilder’s smoothing (first value is a simple sum, subsequent values use the recursive formula):
  10. FirstSmoothedTR = sum of first N TR readings
  11. SmoothedTR_next = SmoothedTR_prior − (SmoothedTR_prior / N) + CurrentTR
  12. Apply the same smoothing to +DM and −DM
  13. Equivalent recursive form: Smoothed_next = (Smoothed_prior*(N−1) + Current) / N
  14. Compute directional indicators:
  15. +DI = (Smoothed +DM / Smoothed TR) × 100
  16. −DI = (Smoothed −DM / Smoothed TR) × 100
  17. Compute DX (Directional Index) for each period:
  18. DX = (|+DI − −DI| / (+DI + −DI)) × 100
  19. Smooth DX to obtain ADX:
  20. First ADX = average of first N DX values
  21. ADX_next = ((Prior ADX × (N−1)) + Current DX) / N

Interpretation

  • ADX ranges from 0 to 100 and measures trend strength, not direction.
  • Common threshold: ADX > 25 indicates a strong trend (some traders use 20 for earlier signals or 30 for conservative confirmation).
  • If +DI > −DI and ADX is high → strong uptrend. If −DI > +DI and ADX is high → strong downtrend.
  • ADX can remain high during a strong reversal because it measures strength of movement, not its direction.

Trading applications

  • DI crossovers:
  • Long when +DI crosses above −DI, ideally confirmed by ADX above the chosen threshold.
  • Short when −DI crosses above +DI, again with ADX confirmation.
  • Use stop-losses (e.g., below recent swing low for longs, above recent swing high for shorts) and consider trailing stops to lock in profits.
  • Volatility expansions/contractions:
  • When +DI and −DI converge (“squeeze”), volatility is low and breakouts may follow.
  • When they diverge, volatility is increasing; short‑term traders may look for entries as the lines separate.
  • Use ADX to decide strategy type:
  • ADX below ~20: consider range‑trading or mean‑reversion tactics.
  • ADX above threshold: favor trend‑following strategies.

Example (conceptual)

A stock can show frequent +DI/−DI crossovers. Only take crossover signals when ADX confirms sufficient trend strength (e.g., ADX > 25). Periods where +DI and −DI are “squished” often precede breakouts — monitor for separation with rising ADX for higher‑probability moves. Be aware that crossovers alone generate many false signals; confirmation and filtering are advisable.

Comparison with Aroon

  • DMI measures directional movement and trend strength by smoothing price fluctuations (+DI, −DI, ADX).
  • Aroon measures how recently highs or lows occurred within the lookback period (time‑based), so it captures momentum in a different way. Both produce crossover signals but are calculated differently and reflect different market characteristics.

Limitations and risks

  • DMI/ADX is based on past data and lags; signals can arrive after a move has begun or reversed.
  • Whipsaws: frequent crossovers in choppy markets can generate losing trades.
  • ADX does not indicate direction — a high ADX after a trend reversal still signals strong movement but not its direction.
  • No fixed threshold guarantees future trend persistence; thresholds may need tuning for each market and time frame.
  • Best used in combination with price‑action analysis and other indicators/filters.

Reference

  • J. Welles Wilder, New Concepts in Technical Trading Systems, 1978.