Momentum

Trend-following strategies

Momentum strategies profit from the tendency of assets that have performed well to continue performing well in the near term.

1 Abstract

Momentum is one of the most robust and persistent anomalies in financial markets. Assets that have outperformed over the past 3-12 months tend to continue outperforming, while underperformers continue to lag. This note explores both cross-sectional momentum (ranking assets) and time-series momentum (trend following).

2 The Momentum Effect

Jegadeesh and Titman (1993) documented that stocks with high returns over the past 3-12 months (“winners”) outperform stocks with low returns (“losers”) over the subsequent months.

Key characteristics:

• Works across asset classes (stocks, bonds, commodities, currencies)
• Formation period: typically 3-12 months
• Holding period: typically 1-12 months
• Strongest at 12-1 (skip recent month to avoid reversal)

3 Cross-Sectional Momentum

Rank assets by past returns and go long winners, short losers.

\[ r_{i,t} = \text{Return of asset } i \text{ over lookback period} \]

\[ \text{Signal}_i = \text{Rank}(r_{i,t}) \]

4 Time-Series Momentum

Each asset’s signal depends only on its own past return:

\[ \text{Signal}_i = \begin{cases} +1 & \text{if } r_{i,t} > 0 \\ -1 & \text{if } r_{i,t} < 0 \end{cases} \]

Or continuously: position size proportional to past return.

5 Compute (Python)

Universe: 10 sector ETFs
Period: 2016-01-13 to 2026-01-13

6 Cross-Sectional Momentum Strategy

7 Strategy Performance

8 Performance Statistics

	Strategy	Ann. Return (%)	Ann. Volatility (%)	Sharpe Ratio	Max Drawdown (%)
0	Long/Short	3.09	15.41	0.20	-28.90
1	Long-Only	12.06	18.00	0.67	-34.87
2	Equal Weight	11.74	17.12	0.69	-39.54

9 Time-Series Momentum

Each asset’s position based on its own past return.

10 Momentum by Lookback Period

Different lookback periods capture different momentum effects.

	Strategy	Ann. Return (%)	Ann. Volatility (%)	Sharpe Ratio	Max Drawdown (%)
0	1mo	-0.55	15.26	-0.04	-31.05
1	3mo	-7.20	15.69	-0.46	-60.24
2	6mo	0.65	15.25	0.04	-34.57
3	12mo	2.48	15.48	0.16	-30.59

11 Current Momentum Rankings

12 Momentum Crashes

Momentum strategies can experience severe drawdowns, especially after market recoveries.

13 Risk Management

Momentum strategies benefit from:

• Volatility scaling: Reduce position size when volatility is high
• Drawdown control: Cut exposure after large losses
• Diversification: Combine with value or other factors

	Strategy	Ann. Return (%)	Ann. Volatility (%)	Sharpe Ratio	Max Drawdown (%)
0	Unscaled	3.09	15.41	0.20	-28.9
1	Vol-Scaled	3.32	10.77	0.31	-18.2

14 Conclusion

Momentum is a robust anomaly that works across asset classes and time periods. Key implementation considerations include:

• Lookback period: 6-12 months works best historically
• Skip period: Exclude recent month to avoid short-term reversal
• Risk management: Volatility scaling and diversification reduce crash risk
• Transaction costs: Monthly rebalancing balances signal decay vs. costs

The persistence of momentum is attributed to behavioral factors (underreaction, herding) and institutional frictions (slow information diffusion). While momentum can experience severe crashes, proper risk management makes it a valuable component of systematic strategies.