Covariance estimation using random permutations

This paper explores a novel technique to compute the level of covariance between any two genuinely correlated assets by adopting the idea of random permutations by proposing an unbiased covariance estimator "RPAvg" based on daily high-low prices. The main goal is to boost the relative efficiency of the estimator by increasing the number of random permutations. We validate this claim with the help of simulations later. Further, we prove theoretically and through simulations that the proposed estimator is unbiased for a pair of random walks. Upon empirically implementing the estimator in a dataset of three sets of stock indices: Nifty, FTSE100 and S&P500 after accounting for exchange effects (USDINR and GBPINR) over a sample period of 252 months (Jan 1996-Dec 2016), we do not find evidence of any bias in the estimator. Also, there is a visible asymmetry in the correlation between US-Indian markets from the two investor's point of view.