Understanding Mean Absolute Deviation (MAD)
Mean Absolute Deviation (MAD) measures the average distance between each data point and the mean. It quantifies typical variation in a dataset. Traders use MAD to assess asset price volatility. They identify potential mean reversion opportunities. A higher MAD indicates greater dispersion from the average price. A lower MAD suggests prices cluster closer to the mean.
Calculate MAD in three steps. First, find the mean of the dataset. Second, subtract the mean from each data point. Take the absolute value of each difference. Third, average these absolute differences.
Consider a stock, XYZ, with daily closing prices over five days: $10.00, $10.50, $9.80, $10.20, $9.90.
-
Calculate the Mean: (10.00 + 10.50 + 9.80 + 10.20 + 9.90) / 5 = 10.08 The mean closing price is $10.08.
-
Calculate Absolute Deviations from the Mean: |10.00 - 10.08| = 0.08 |10.50 - 10.08| = 0.42 |9.80 - 10.08| = 0.28 |10.20 - 10.08| = 0.12 |9.90 - 10.08| = 0.18
-
Calculate the Mean Absolute Deviation (MAD): (0.08 + 0.42 + 0.28 + 0.12 + 0.18) / 5 = 0.216 The MAD for XYZ stock is $0.216. XYZ's daily closing price deviates $0.216 from its mean of $10.08, on average.
Advantages of MAD in Mean Reversion Strategies
MAD offers distinct benefits over standard deviation for mean reversion strategies. MAD is less sensitive to outliers. Standard deviation squares deviations. This amplifies the impact of extreme price movements. MAD uses absolute differences. It provides a more robust measure of typical deviation. This makes MAD useful in financial markets where large, infrequent price shocks occur.
Consider two hypothetical stocks, Stock A and Stock B, with five days of price data.
Stock A Prices: $10.00, $10.10, $9.90, $10.05, $9.95 Mean for Stock A = $10.00
-
MAD for Stock A: |10.00 - 10.00| = 0.00 |10.10 - 10.00| = 0.10 |9.90 - 10.00| = 0.10 |10.05 - 10.00| = 0.05 |9.95 - 10.00| = 0.05 MAD = (0.00 + 0.10 + 0.10 + 0.05 + 0.05) / 5 = 0.06
-
Standard Deviation for Stock A: (0.00^2 + 0.10^2 + 0.10^2 + 0.05^2 + 0.05^2) / 5 = (0.00 + 0.01 + 0.01 + 0.0025 + 0.0025) / 5 = 0.005 Standard Deviation = sqrt(0.005) = 0.0707
Stock B Prices: $10.00, $10.10, $9.90, $10.05, $15.00 (an outlier) Mean for Stock B = (10.00 + 10.10 + 9.90 + 10.05 + 15.00) / 5 = 11.01
-
MAD for Stock B: |10.00 - 11.01| = 1.01 |10.10 - 11.01| = 0.91 |9.90 - 11.01| = 1.11 |10.05 - 11.01| = 0.96 |15.00 - 11.01| = 3.99 MAD = (1.01 + 0.91 + 1.11 + 0.96 + 3.99) / 5 = 1.596
-
Standard Deviation for Stock B: (1.01^2 + 0.91^2 + 1.11^2 + 0.96^2 + 3.99^2) / 5 = (1.0201 + 0.8281 + 1.2321 + 0.9216 + 15.9201) / 5 = 3.9844 Standard Deviation = sqrt(3.9844) = 1.996
The single outlier in Stock B inflates the standard deviation (from 0.0707 to 1.996). MAD also increases (from 0.06 to 1.596). Its increase is less pronounced relative to the standard deviation. This shows MAD's resilience to extreme price spikes. For mean reversion, this resilience prevents outlier-driven false signals. A strategy using standard deviation might interpret the single $15.00 price as sustained high volatility. This leads to incorrect position sizing or entry/exit triggers. MAD provides a more stable baseline for assessing normal price fluctuations.
Implementing MAD in Mean Reversion Strategies
Traders integrate MAD into mean reversion strategies to define bands around a moving average. These bands indicate overbought or oversold conditions. When prices breach these bands, a mean reversion signal triggers.
Consider a 20-day simple moving average (SMA) for SPY. Calculate the 20-day MAD of SPY's closing prices. For example, on January 26, 2024, SPY closed at $488.75. Assume a 20-day SMA of $480.00. Assume a 20-day MAD of $2.50.
Define trading bands using multiples of MAD: Upper Band = SMA + (MAD * Multiplier) Lower Band = SMA - (MAD * Multiplier)
A common multiplier for mean reversion is 2. Upper Band = $480.00 + (2.50 * 2) = $485.00 Lower Band = $480.00 - (2.50 * 2) = $475.00
If SPY's price rises above $485.00, it signals an overbought condition. This potentially triggers a short entry. If SPY's price falls below $475.00, it signals an oversold condition. This potentially triggers a long entry. The MAD-based bands adapt to changing market conditions. A period of higher volatility results in a larger MAD. This widens the bands. It requires a larger price deviation to trigger a signal. This dynamic adjustment supports robust mean reversion systems.
For instance, if SPY's MAD increases to $4.00 during a volatile period, the bands would become: Upper Band = $480.00 + (4.00 * 2) = $488.00 Lower Band = $480.00 - (4.00 * 2) = $472.00
This wider band requires a more significant price move to generate a signal. It prevents premature trades during increased market noise. Conversely, during low volatility, a smaller MAD tightens the bands. This allows for more sensitive signal generation.
Traders can apply MAD to various assets. These include equities, commodities, and foreign exchange. For EUR/USD, a 50-period SMA on a 1-hour chart might have a 50-period MAD of 0.00050. Using a multiplier of 3, the bands would be: Upper Band = SMA + (0.00050 * 3) Lower Band = SMA - (0.00050 * 3)
These bands define the expected range of price fluctuation. Price excursions beyond these bands indicate a potential mean reversion opportunity. Backtest different lookback periods for the SMA and MAD. Vary multipliers. This optimizes performance for specific assets and timeframes. A 20-period MAD on a 15-minute chart for high-frequency equity trading will differ from a 200-period MAD on a daily chart for long-term commodity strategies.