Many sovereign wealth funds have expansive portfolios that give them the chance to influence markets through their investment choices. In this study, we analyze how oil extraction as a source of wealth influences portfolio allocation. We find that revenues from oil extraction affect the speculative motive and the hedging motives in opposite ways and create a portfolio allocation bias for oil-based funds. A numerical application of the model disentangles the motives and quantifies the bias. We find a positive bias in the portfolio allocation of an oil-based fund, which is increasing in the correlation of assets. Sensitivity analyzes show which parameters reduce the portfolio bias, turning the bias from "dirty" to "green" for large deviations from the default calibration. When a price on carbon is introduced, the intended reallocation of assets away from the oil-intensive sector is dampened by an amplification of the portfolio bias.