Random Walk Test on Hedge Ratios for Stock and Futures

The long memory properties of the hedge ratio for stock and futures have not been systematically investigated by the extant literature. To investigate hedge ratio' long memory, this paper employs a data set including KOSPI200 and S&P500. Coakley, Dollery, and Kellard(2008) employ a data set including a stock index and commodities foreign exchange, and suggested the S&P500 to be a fractionally integrated process. This paper firstly estimates hedge ratios with two dynamic models, BEKK(Bollerslev, Engle, Kroner, and Kraft) and diagonal-BEKK, and tests the long memory of hedge ratios with Geweke and Porter-Hudak(1983)(henceforth GPH) and Lo's modified rescaled adjusted range test by Lo(1991). In empirical results, two hedge ratios based on KOSPI200 and S&P500 show considerably significant long memory behaviours. Thus, such results show the hedge ratios to be stationary and strongly reject the random walk hypothesis on hedge ratios, which violates the efficient market hypothesis.