Stochastic optimal hedge ratio: Theory and evidence

The minimum variance hedge ratio is widely used by investors to immunize against the price risk. This hedge ratio is usually assumed to be constant across time by practitioners, which might be a too restrictive assumption because the Optimal Hedge Ratio (OHR) might vary across time. In this article we put forward a proposition that a stochastic OHR performs differently than an OHR with constant structure even in the situations in which the mean value of the stochastic OHR is equal to the constant OHR. A mathematical proof is provided for this proposition combined with some simulation results and an application to the US stock market during 1999-2009 using weekly data.