Measuring difference of optimal hedge ratios between long position and short position using lower partial moments

Asymmetry and fat-tail are both stylized facts of financial return data. The correlation between futures contracts and spot assets in bull market is asymmetric to that in bear market. So for the same quantity spot assets the optimal hedge ratio(OHR) of long position should be different to that of short position. This paper advocates the superiority of the method of Lower Partial Moments by incorporating the negative deviation from a reference point, rather than deviations around the mean, and estimates OHR using the data on the Chinese copper futures contracts. Results indicate that for the same quantity spot assets the OHR of long futures is higher than that of short futures. Using Sharp Ratio to compare the effectiveness, results show the superior performance of this hedge ratio compared to the naive method and the equivalent performance compared to the OLS method.