Z-Score Mean Reversion

Z-Score measures how many standard deviations price is from its mean (statistical measure). RSI measures momentum using gains vs losses (bounded 0-100). Z-Score is unbounded and purely statistical; RSI is momentum-based.

Standard threshold is ±2 (2 standard deviations). This represents ~95% confidence level. For fewer, higher-probability signals, use ±2.5 or ±3. For more signals, use ±1.5.

Standard is 20 periods (about a month of trading days). Shorter (10) is more responsive but noisier. Longer (50) is smoother but slower. Start with 20 and adjust based on results.

In strong trends, price consistently stays above or below the mean. The mean slowly catches up, but Z-Score remains elevated. This is why trend filters are important - avoid Z-Score mean reversion in strong trends.

Primary target is Z-Score = 0 (mean). This means price has reverted to its average. Some traders target Z = +1 or even +2 (opposite extreme) for larger profits, but 0 is more reliable.

Calculate the spread between two correlated assets using a hedge ratio. Then calculate Z-Score of the spread. When spread Z < -2, go long the spread (long A, short B). When > +2, short the spread (short A, long B).

Rolling Z-Score recalculates mean and standard deviation each period using a rolling window. This allows Z-Score to adapt to changing conditions rather than using fixed historical statistics.

Use ADX: ADX < 25 = ranging (Z-Score works well). Use MA: Only take Z < -2 buys when price above 50 MA (uptrend). Avoid counter-trend Z-Score signals in strong trends (ADX > 40).

The hedge ratio determines how much of each asset to trade in pairs trading. It's typically the slope from regressing Asset A on Asset B. If hedge ratio = 2.5, for every 1 share of A, trade 2.5 shares of B.

For mean reversion: Exit at Z = 0 (mean reached). Hybrid approach: Exit 1/3 at Z = -1, 1/3 at Z = 0, trail 1/3. This balances taking profits and capturing potential extended moves.

Residual Z-Score applies Z-Score to regression residuals (actual price - predicted from benchmark). This isolates stock-specific deviation from market movement, providing cleaner signals for stock-specific mean reversion.

Cointegration is when two non-stationary series combine to form a stationary (mean-reverting) spread. It's stronger than correlation and provides rigorous statistical basis for pairs trading. Test using Engle-Granger or Johansen tests.

Half-life is the expected time for a deviation to reduce by 50%. Calculate from mean reversion speed (Ornstein-Uhlenbeck parameter). Short half-life (< 10 days) = fast reversion. Long half-life (> 30 days) = slow reversion.

Z = (Today's Return - Mean Return) / Std Dev of Returns. This is more stationary than price Z-Score since returns are typically closer to stationary. Better for short-term mean reversion strategies.

Rank all stocks by Z-Score. Go long bottom decile (most oversold), short top decile (most overbought). This creates market-neutral mean reversion portfolio. Rebalance periodically based on Z-Score changes.