Variance minimizing strategies for stochastic processes with applications to tracking stock indices

Abstract

This paper extends the notion of variance optimal hedging of contingent claims under the incomplete market setting to the hedging of entire processes and applies the results to the problem of tracking stock indices. Sufficient conditions under which this is possible are given, along with the corresponding variance minimizing strategy. The performances of tracking error variance (TEV) minimizing, locally risk minimizing, and variance minimizing strategies in tracking stock indices are investigated using both simulated and historical market data. In particular, it is shown using S&P500 data over the period 2000 and 2015 that the TEV of the variance minimizing strategy is statistically lower than other strategies at the 95% confidence level for 6-month holding periods.