What is Forecast calibration, alpha scaling rule?

Forecast calibration is the mapping of a score into an expected return such that, among the names given any forecast, the average realised return equals the forecast. The alpha scaling rule sets the expected residual return of a name to $\alpha_i = \mathrm{IC}\cdot\omega_i\cdot z_i$, with $z_i$ the standardised score and $\omega_i$ the name’s residual volatility over the horizon.