Previous studies indicate an asymmetry in the amplitude and persistence of El Niño (EN) and La Niña (LN) events. We show that this observed EN-LN asymmetry can be captured with a linear model driven by correlated additive and multiplicative (CAM) noise, without resorting to a deterministic nonlinear model. The model is derived from 1-month lag statistics taken from monthly sea surface temperature (SST) data sets spanning the twentieth century, in an extension of an empirical-dynamical technique called Linear Inverse Modeling. Our results suggest that noise amplitudes tend to be stronger for EN compared to LN events, which is sufficient to generate asymmetry in amplitude and also produces more persistent LN events on average. These results establish a null hypothesis for EN-LN asymmetry and suggest that strong EN events may not be more predictable that what can be accounted for by a multivariate linear system driven by CAM noise.