We analyse the role of cointegration for hedging an asset using other assets, when the prices are generated by a cointegrated vector autoregressive model allowing for stationary martingale errors. We first note that if the price of the asset is nonstationary, the risk of keeping the asset diverges. We then derive the minimum variance hedging portfolio as a function of the holding period, h, and show that it approaches a cointegrating relation for large h, thereby giving a serious reduction in the risk. We then take into account the expected return and find the portfolio that maximizes the Sharpe ratio. We show that it also approaches a cointegration portfolio, with weights depending on the price of the portfolio. We illustrate the finding with a data set of electricity prices which are hedged by fuel prices. The main conclusion of the paper is that for optimal hedging, one should exploit the cointegrating properties for long horizons, but for short horizons more weight should be put on remaining part of the dynamics.
We then analyse the situation with some heteroscedasticity, and find the same results provided one applies the average conditional variance of the return to measure the risk.