We conjecture for a linear stochastic differential equation that the predictability of threshold exceedances (I) improves with the event magnitude when the noise is a so-called correlated additive-multiplicative noise, no matter the nature of the stochastic innovations, and also improves when (II) the noise is purely additive, obeying a distribution that decays fast, i.e., not by a power law, and (III) deteriorates only when the additive noise distribution follows a power law. The predictability is measured by a summary index of the receiver operating characteristic curve. We provide support to our conjecture-to compliment reports in the existing literature on (II)-by a set of case studies. Calculations for the prediction skill are conducted in some cases by a direct numerical time-series-data-driven approach and in other cases by an analytical or semianalytical approach developed here.