Picking a Forecast Horizon

"This signal predicts returns" is an incomplete sentence. Predicts returns over the next hour? The next day? The next month? A momentum signal and a value signal can both be real and both be useless if you plug them into the wrong horizon — the momentum signal decays within weeks, the value signal barely moves week to week but plays out over years. Picking a forecast horizon is not a formality before the real research starts; it is one of the first and most consequential choices a researcher makes.

The decay curve

Most signals have an information half-life: a burst of predictive power shortly after the signal is observed, decaying as the information gets priced in or goes stale. Plotting a signal's correlation with forward returns against the length of the forward window traces out this decay.

Adjust the decay rate above and picture it as a signal's edge over time: fast decay means a signal that is powerful today and worthless in a week, useful only for strategies that can trade quickly and cheaply; slow decay supports a longer holding period but usually with a smaller peak edge.

Horizon interacts with cost, not just decay

A signal that decays fast but is expensive to trade can still be a bad strategy at its "best" horizon, because trading fast to capture a fast-decaying signal means trading often, and trading often means paying costs often. The right horizon balances the strength of the forecast at that horizon against the cost of turning the portfolio over fast enough to capture it — a slower, weaker signal traded patiently can beat a faster, stronger one that gets eaten alive by transaction costs.

Worked example

A signal shows the following correlation with forward returns at different horizons, estimated from five years of history: 1-day, $\rho = 0.06$; 5-day, $\rho = 0.09$; 20-day, $\rho = 0.05$; 60-day, $\rho = 0.02$. The 5-day horizon has the highest raw correlation. But trading a 5-day-horizon signal means rebalancing roughly every 5 trading days, and the desk's cost model (from its own fill history) prices a round trip at 12 basis points on this name. At a 20-day horizon, correlation drops to 0.05, but round-trip frequency falls by a factor of four, so total annual cost paid drops proportionally too. Running both through the desk's expected-net-return calculation (correlation scaled to expected return, minus annualized cost) shows the 20-day horizon nets out ahead — the "worse" forecast is the better trade.

What this means in practice

Researchers typically compute the decay curve first, on paper, before committing to a target holding period, because picking the horizon after seeing a single backtest's Sharpe ratio invites overfitting — there is always some horizon in a finite sample that looks best by chance. The decay curve, estimated across many horizons at once, is far harder to fool.