Williams' Percent Range (%R)

1. Summary (Introduction)

Williams' Percent Range, or %R, is a momentum oscillator developed by Larry Williams. It is very similar to the Stochastic Oscillator, but it is plotted on an inverted scale from 0 to -100. Its primary purpose is to identify overbought and oversold conditions in the market.

The indicator measures the current closing price in relation to the highest high and lowest low over a specified lookback period. It shows where the current price is relative to the recent trading range, helping traders to spot potential exhaustion points in a trend.

2. Mathematical Foundations and Calculation Logic

The %R formula is straightforward and compares the current close to the recent high-low range.

Required Components

Period (N): The lookback period for the calculation (e.g., 14).
Price Data: The High, Low, and Close of each bar.

Calculation Steps (Algorithm)

Find the Highest High and Lowest Low: For each bar, determine the highest high and lowest low over the last N periods. \text{Highest High}_N = \text{Max}(\text{High}, N)_i \text{Lowest Low}_N = \text{Min}(\text{Low}, N)_i
Calculate the Williams %R: Apply the main formula. \text{\%R}_i = -100 \times \frac{\text{Highest High}_N - \text{Close}_i}{\text{Highest High}_N - \text{Lowest Low}_N}

The result is a value between 0 and -100. A reading close to 0 means the price is closing near the top of its recent range (overbought), while a reading close to -100 means the price is closing near the bottom of its range (oversold).

3. MQL5 Implementation Details

Our MQL5 implementation is a self-contained, robust, and clear representation of the Williams %R indicator.

Stability via Full Recalculation: We employ a "brute-force" full recalculation within the OnCalculate function. As a non-recursive indicator, this is a simple and highly stable approach.
Self-Contained Logic: The indicator is completely self-contained. It does not use any external indicator handles (like iWPR). All calculations are performed manually within the OnCalculate function using the price data provided.
Reusable Helper Functions: The calculation of the highest high and lowest low is performed by our standard, reusable Highest() and Lowest() helper functions, ensuring consistency across our entire indicator toolkit.
Clear, Staged Calculation: The OnCalculate function uses a single, efficient for loop to calculate the %R for each bar. The logic is clear and directly follows the mathematical definition of the indicator.
Heikin Ashi Variants:
- WPR_HeikinAshi.mq5: Our toolkit includes a Heikin Ashi version of this indicator. The calculation logic is identical, but it uses the smoothed Heikin Ashi ha_high, ha_low, and ha_close values as its input. This results in a smoother oscillator that reflects the momentum of the underlying Heikin Ashi trend.
- WPRMA_HeikinAshi.mq5: We also have a version that adds a moving average signal line to the Heikin Ashi WPR, providing an additional layer of smoothing and potential crossover signals.

4. Parameters

WPR Period (InpWPRPeriod): The lookback period for the indicator. Larry Williams' original recommendation and the most common value is 14.

5. Usage and Interpretation

Overbought/Oversold Levels: The primary use of %R is to identify overbought and oversold conditions.
- Overbought: Readings between 0 and -20 are considered overbought. This suggests that the price is near the top of its recent range and may be due for a pullback.
- Oversold: Readings between -80 and -100 are considered oversold. This suggests that the price is near the bottom of its recent range and may be due for a bounce.
Divergence: Look for divergences between the %R and the price action. A bearish divergence (higher price highs, lower %R highs) can signal weakening bullish momentum. A bullish divergence (lower price lows, higher %R lows) can signal weakening bearish momentum.
Momentum Failure: A common signal is when the %R enters the overbought zone, pulls back, and then fails to re-enter the overbought zone on a subsequent price rally. This "momentum failure" can be an early sign of a trend reversal.
Caution: Like all oscillators, %R can remain in overbought or oversold territory for extended periods during a strong trend. It is not a standalone signal for buying or selling but a tool to gauge momentum within a broader market context.

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