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gateway/knowledge/trading/strategies/stocks/price-momentum.md

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+---
+description: "Ranks stocks by past cumulative or risk-adjusted returns and buys winners while selling losers, exploiting the empirical momentum effect in cross-sectional equity returns."
+tags: [stocks, momentum]
+---
+
+# Price-Momentum
+
+**Section**: 3.1 | **Asset Class**: Stocks | **Type**: Momentum
+
+## Overview
+The momentum effect describes the empirical tendency for future stock returns to be positively correlated with past returns. Stocks are ranked by a performance criterion computed over a formation period and a portfolio is constructed by buying the top-ranked stocks (winners) and shorting the bottom-ranked stocks (losers). The portfolio is then held for a predefined holding period before being reconstituted.
+
+## Construction / Signal
+Let `P_i(t)` be the fully split- and dividend-adjusted price for stock `i`, with `t` measured in months and `t=0` the most recent time. The monthly return is:
+
+```
+R_i(t) = P_i(t) / P_i(t+1) - 1                          (266)
+```
+
+Cumulative return over the T-month formation period starting S months ago:
+
+```
+R_i^cum = P_i(S) / P_i(S+T) - 1                          (267)
+```
+
+Mean monthly return over the formation period:
+
+```
+R_i^mean = (1/T) * sum_{t=S}^{S+T-1} R_i(t)              (268)
+```
+
+Risk-adjusted mean return (Sharpe-like):
+
+```
+R_i^risk.adj = R_i^mean / sigma_i                         (269)
+
+sigma_i^2 = 1/(T-1) * sum_{t=S}^{S+T-1} (R_i(t) - R_i^mean)^2   (270)
+```
+
+Stocks are sorted by `R_i^cum`, `R_i^mean`, or `R_i^risk.adj` (descending). The trader buys stocks in the top decile (winners) and shorts stocks in the bottom decile (losers).
+
+## Entry / Exit Rules
+- **Entry**: At rebalance, buy top-decile stocks and short bottom-decile stocks according to the chosen ranking criterion.
+- **Exit**: Hold for the predefined holding period (typically 1 month, but can be longer). Liquidate before end of holding period if unforeseen events occur (e.g., market crash).
+- **Skip period**: Typically skip the most recent S=1 month to avoid short-term mean-reversion / microstructure effects.
+
+## Key Parameters
+- **Formation period T**: Typically 12 months
+- **Skip period S**: Typically 1 month
+- **Holding period**: 1 month (longer periods show diminishing returns as momentum fades)
+- **Ranking criterion**: `R_i^cum`, `R_i^mean`, or `R_i^risk.adj`
+- **Portfolio construction**: Long-only (sum w_i = 1) or dollar-neutral (sum |w_i| = 1, sum w_i = 0)
+- **Weights**: Uniform (1/N), or volatility-suppressed (w_i ∝ 1/sigma_i or 1/sigma_i^2)
+
+## Variations
+- **Long-only**: Buy top-decile only; weights w_i ≥ 0, sum w_i = 1.
+- **Dollar-neutral (long/short)**: Buy winners, short losers; sum |w_i| = 1, sum w_i = 0. Modulus-uniform weights: w_i = 1/(2*N_L) for longs, w_i = -1/(2*N_S) for shorts.
+- **Overlapping portfolios**: Multi-month holding via overlapping 1-month-holding portfolios (Jegadeesh and Titman, 1993).
+- **Nonuniform weights**: w_i ∝ 1/sigma_i or w_i ∝ 1/sigma_i^2 to suppress volatile stocks.
+
+## Notes
+- The momentum effect is well-documented but fades over longer horizons; holding periods beyond 12 months tend to reverse (value effect).
+- Transaction costs can be significant, especially for high-turnover monthly rebalancing.
+- The 1-month skip period is empirically motivated by microstructure/liquidity mean-reversion observed at the 1-month horizon.
+- Dollar-neutral construction removes broad market beta exposure.
+- Typical holding period: 1 month; diminishing returns for longer holds before trading costs.