The present study examines the effect of moments of crude oil prices including the variance, skewness and kurtosis, on the returns of the Dow Jones Sustainability Index (DJSI) of the Eurozone. The GARCH model is employed to examine the relationship of these moments with the DJSI of the Eurozone, for the time period from November 2001 until March 2015. According to our findings, an increase in the oil returns, as well as in the oil price volatility, leads to a decrease in the value of the Index employed. It was also found that asymmetry affects positively the stock price of the Eurozone social responsibility companies, because the more the asymmetry increases, the less the concentration of the prices to the right side of the distribution, consequently the more the investors feel that the related risk is reduced, as the frequency of oil prices is below the average oil price. On the contrary, it was found that the interaction of asymmetry and kurtosis of oil prices affect negatively the DJSI of the Eurozone, a fact that is attributed to the kind of the oil price distribution for the above mentioned time period