Ridge estimators are usually examined through Monte Carlo simulations since their properties are difficult to obtain analytically. In this paper we argue that a simulation design commonly used in the literature will give biased results of Monte Carlo simulations in favour of ridge regression over ordinary least square (OLS) estimators. Specifically, it is argued that the properties of ridge estimators that are functions of pdistinct regressor eigenvalues should not be evaluated through Monte Carlo designs using only two distinct eigenvalues.