Average Deviation: Volatility Measure | AlfaTactix

Average Deviation Indicator Explanation

The Average Deviation (also known as Mean Absolute Deviation or MAD) is a statistical volatility indicator that measures the average absolute difference between each price value and the mean price over a specified period. Unlike Standard Deviation, which squares the differences, Average Deviation uses absolute values, making it less sensitive to outliers and providing a simpler, more intuitive measure of price dispersion. Higher Average Deviation values indicate greater price volatility (prices deviate more from the mean), while lower values indicate lower volatility (prices are closer to the mean).

How Average Deviation Works: Average Deviation is calculated by first computing the mean (average) of closing prices over a specified period (typically 20 periods), then calculating the absolute difference between each price and the mean, and finally averaging these absolute differences. The formula is: Mean = Σ(Close) / n, and Average Deviation = Σ|Close - Mean| / n, where n is the period. This statistical measure provides a straightforward representation of price volatility: values near zero indicate low volatility (prices are close to the mean), while higher values indicate high volatility (prices are spread out from the mean). Average Deviation is less influenced by extreme price movements than Standard Deviation, making it more stable in volatile markets.

When to Use Average Deviation:

• Volatility Assessment: Average Deviation is highly effective at identifying periods of high and low volatility with less sensitivity to outliers than Standard Deviation. Rising Average Deviation indicates increasing volatility, while falling Average Deviation indicates decreasing volatility and potential market consolidation.
• Risk Management: Average Deviation can be used to adjust position sizes and stop-loss levels based on current volatility, similar to Standard Deviation but with greater stability. Higher volatility requires wider stops and smaller position sizes.
• Breakout and Reversal Identification: Low Average Deviation periods (volatility contraction) often precede significant breakouts or reversals, as periods of low volatility are typically followed by periods of high volatility. Rising Average Deviation during a breakout confirms strong price movement.

Advantages:

• Provides a clear, objective measure of price volatility through simple statistical analysis, making it easier to interpret than Standard Deviation. The absolute value calculation ensures stability.
• Less sensitive to outliers than Standard Deviation, making it more stable in volatile markets with extreme price movements. The absolute difference approach provides more intuitive volatility measurement.
• Works effectively across multiple timeframes and asset classes, including stocks, forex, commodities, and cryptocurrencies. The mathematical simplicity ensures reliability.

Limitations:

• Average Deviation does not indicate price direction or trend strength, only the magnitude of price dispersion around the mean. Traders must combine it with directional indicators for entry and exit signals.
• The indicator may lag behind rapid volatility changes, as it relies on historical price data. The calculation uses a moving average of absolute differences, which can delay response to sudden volatility spikes.
• Average Deviation alone does not provide specific entry or exit signals, only volatility measurement. Traders should use it in combination with other indicators for comprehensive analysis.

In summary, Average Deviation is a valuable volatility indicator that provides a stable, intuitive measurement of price dispersion, making it ideal for risk management and volatility assessment with less sensitivity to outliers than Standard Deviation. For comprehensive understanding, refer to statistical analysis literature on mean absolute deviation, Investopedia's Average Deviation guide, and academic research on volatility measurement in financial markets published in journals such as the Journal of Financial Markets and Quantitative Finance journals.

import backtrader as bt
import numpy as np

class AverageDeviationPositionSizingStrategy(bt.Strategy):
    params = dict(
        ad_period=20,
        volatility_threshold=1.5,
        stop_multiplier=2.0
    )
    
    def __init__(self):
        # Calculate Average Deviation: mean absolute deviation
        self.sma = bt.ind.SMA(self.data.close, period=self.p.ad_period)
        # Simplified: calculate absolute differences and average
        self.price_diff = bt.ind.AbsDifference(self.data.close, self.sma)
        self.avg_dev = bt.ind.SMA(self.price_diff, period=self.p.ad_period)
        self.avg_ad = bt.ind.SMA(self.avg_dev, period=20)  # Average of AD
        
    def next(self):
        if not self.position:
            # Calculate position size based on volatility
            if self.avg_dev[0] > self.avg_ad[0] * self.p.volatility_threshold:
                # High volatility: smaller position
                size = self.broker.getcash() * 0.01  # 1% of cash
            else:
                # Low volatility: normal position
                size = self.broker.getcash() * 0.02  # 2% of cash
            
            if self._entry_signal():
                self.buy(size=size)
        else:
            # Dynamic stop-loss based on Average Deviation
            stop_distance = self.avg_dev[0] * self.p.stop_multiplier
            if self.position.size > 0:  # Long position
                stop_price = self.data.close[0] - stop_distance
            else:  # Short position
                stop_price = self.data.close[0] + stop_distance
            
            if self._stop_triggered(stop_price):
                self.close()
    
    def _entry_signal(self):
        # Add entry logic
        return False
    
    def _stop_triggered(self, stop_price):
        # Add stop logic
        return False

# Usage
cerebro = bt.Cerebro()
cerebro.addstrategy(AverageDeviationPositionSizingStrategy)