The goal of this paper is to examine whether the volatility of the growth in the US oil stocks has changed overtime, and if it has then whether or not this change is real. We find that the growth in volatility of oil stocks has declined overtime. We conduct a Monte Carlo simulation exercise to investigate whether this decline is real or an artefact of the growth definition. Our findings support the fact that the decline in growth volatility of oil stocks is an artefact of the growth definition. This is because a data generating process having a unit root with drift has a tendency to grow and thereby pulls the variance of growth down with time.