COP21 implementation should lead to a decline in the future demand for fossil fuels. One key implication for investors is how to manage this risk. We construct a monthly stock and oil market integration index and demonstrate that oil investors can offset adverse oil price risk by holding diversified global stock portfolios. The portfolios are formed from eight different combinations of developed and emerging stock markets. We show that measuring the degree of stock-oil market integration is critical to managing the time-varying degrees of integration. Under normal market conditions markets are segmented and this yields the opportunity for oil investors to diversify energy price risk through the purchase of stocks. The optimal oil-stock diversified portfolio provides risk-adjusted positive benefits to investors, with portfolio weights changing over time as COP21 implementation proceeds.