Time-series momentum and trend following
Use each asset’s own history to set direction; separate it from cross-sectional winner selection.

The idea · in two minutes

Rose asks each market about its own trend, not who won the cross-section

Jack ranks stocks, bonds and commodities by their latest 12-month returns and wants to buy the winner. Rose explains that this is cross-sectional momentum. A time-series rule asks whether each asset’s own return has been positive.

She builds a long-only ETF allocation from positive cumulative returns, scaled by inverse volatility squared; non-positive trends stay in cash. A futures version can trade both signs, but introduces shorting, margin and directional exposure.

Signals lag turning points, whipsaw in ranges and can give back gains in sharp reversals. Same-close execution or reporting only the best of many lookbacks distorts results.

• Positive signalsThis simulator uses a positive-momentum long-only version, not a long/short futures rule.
• Volatility-scaled weightsWeights are proportional to max(cumulative return,0)/volatility², normalised before user-set costs.
• Assumed next-period portfolio after costForward returns are scenario inputs, not model forecasts.

Illustrative research examples only. They are not live signals or a recommendation.

The mechanics · payoff and exposure

m_{i,t}=\operatorname{sign}(R_{i,t-k:t-1}),\quad \tilde w_{i,t}=\frac{\max(R_{i,t-k:t-1},0)}{\sigma_{i,t}^2},\quad w_{i,t}=\frac{\tilde w_{i,t}}{\sum_j\tilde w_{j,t}}

R_{i,t-k:t-1} is asset i’s cumulative return through t−1 and σ_i its volatility estimated at the signal time. The example holds positive signals only and scales by 1/σ²; if all signals are non-positive, the portfolio stays in cash.

Greeks: the directional intuition

Lookback window

Measures sensitivity to implied volatility.

Volatility scaling

Measures sensitivity to implied volatility.

Long-only vs long/short

Measures sensitivity to implied volatility.

Crash/reversal

Measures sensitivity to implied volatility.

m_{i,t}=\operatorname{sign}(R_{i,t-k:t-1}),\quad \tilde w_{i,t}=\frac{\max(R_{i,t-k:t-1},0)}{\sigma_{i,t}^2},\quad w_{i,t}=\frac{\tilde w_{i,t}}{\sum_j\tilde w_{j,t}}

Practical context · published observations

Time-series momentum and trend following: read the record with its caveats.

The chart uses the published figures or explicitly labelled study inputs below. A historical index or model replay is not the same as an investor’s realised account return.

這不是歷史行情回測，也不包含資產總報酬、期貨展期、融資、保證金或真實成交。正式驗證需按時間順序走動式估計，在下一可交易價格執行，並分開報告 ETF long-only 與期貨 long/short。 Source ↗ · Methodology ↗