An alpha signal forecasts relative return before a trade. Distinguish a ranking score, a model-relative return estimate and realised performance.
Alpha signal
An alpha signal is information used to forecast which assets or trades will earn attractive returns relative to a stated reference. In systematic trading, it may be a ranking score or a forecast expressed in return units. It helps decide where to take exposure; it does not, by itself, specify an order or establish that an edge exists.
The reference matters. A signal might predict performance relative to a market benchmark, a cross-sectional average or a factor model. A forecast of a rising stock price is not automatically evidence of return beyond the risk exposures being taken.
A forecast with a named baseline
Consider a fictional stock and a single future holding period. A researcher forecasts a simple total return of 2.0%. A specified risk model, called Model M in this example, forecasts 1.2% for the same asset and period from its risk exposures. Both forecasts use only information available at the decision time and are before trading costs.
Define the estimated alpha under this convention as
αi,t,h=μi,t,h−μi,t,hM,
where i identifies the asset, t the decision time and h the holding horizon. The two μ terms are the research forecast and Model M's baseline forecast. Here,
This is an estimated prospective residual return. It is 0.8 percentage points, not a percentage change calculated by dividing the two forecasts. Changing the baseline can change what is labelled alpha even if the research forecast stays fixed. A risk model that supplies only covariances does not, on its own, supply an expected-return baseline: Model M explicitly includes that additional assumption here.
Fictional one-period total-return forecast of 2.0% separates into a Model M baseline of 1.2% and estimated alpha of 0.8 percentage points, or 80 basis points. The realised return is unknown.
Original synthetic decomposition, using the same one-period simple total-return basis for both forecasts. The blue segment is estimated alpha before costs; the figure contains no realised return.
Score, forecast and trade are different objects
A raw signal can be a valuation ratio, a recent-return measure or an earnings revision. Transforming it into a rank or standardised score helps compare names, but a score has no automatic interpretation as a percentage return. That requires a separately estimated mapping, with a stated horizon and reference. Narang describes alpha models as forecasting components and notes that practitioners use overlapping names for them; the data contract is more useful than the label alone. Narang, Chapter 3.
Even a calibrated positive forecast need not cause a purchase. Portfolio construction weighs that forecast against current holdings, transaction costs, risk limits and other signals. A concentrated portfolio may already have enough of the exposure; a small forecast change may not justify paying the spread. Ciliberti and Gualdi study precisely this step from predictors to positions, including the effect of costs. Portfolio Construction Matters.
The From Signal to Executed Position Capstone follows a stipulated forecast through limits, orders, partial fills and accounting. A public preview is available; the full lesson requires membership.
What would make the signal credible?
A signal is available before the outcome. A realised regression-based Jensen's alpha summarises historical performance under a specified model. Neither a favourable future outcome nor a favourable fitted historical intercept turns today's forecast into a guaranteed return.
A useful research record fixes the input availability, transformation, forecast horizon and evaluation target before measuring performance. Look-ahead bias can otherwise make a signal appear predictive by letting tomorrow's information enter today's decision. Out-of-sample testing then asks whether the frozen process predicts later outcomes, with appropriate allowance for how many alternatives were tried.
For the fictional forecast, costs and estimation error can consume the entire estimated advantage. The question is whether repeated, implementable forecasts add value after costs under the declared reference—not whether one trade happens to win.
Sources
Rishi K. Narang, Inside the Black Box, second edition, Wiley, 2013, Chapter 3, printed pp.23–24: alpha models as forecasts and the need to survive forecasting errors and costs.
Stefano Ciliberti and Stanislao Gualdi, Portfolio Construction Matters, 2018, Sections I–II and VI: predictors, portfolio construction and transaction costs. The numerical illustration above is original and hypothetical.
