We introduce the realized co-range, utilizing intraday high-low price ranges to estimate asset return covariances. Using simulations we find that for plausible levels of bid-ask bounce and infrequent and non-synchronous trading the realized co-range improves upon the realized covariance, which uses cross-products of intraday returns. One advantage of the co-range is that in an ideal world it is five times more efficient than the realized covariance when sampling at the same frequency. The second advantage is that the upward bias due to bid-ask bounce and the downward bias due to infrequent and non-synchronous trading partially offset each other. In a volatility timing strategy for S&P500, bond and gold futures we find that the co-range estimates are less noisy as exemplified by lower transaction costs and also higher Sharpe ratios when using more weight on recent data for predicting covariances.

a r t i c l e i n f o JEL classification: C58 C53 G17 Keywords: Realized variance Realized range Two time scales High frequency data Market microstructure noise Forecasting a b s t r a c tWe introduce a heuristic bias-adjustment for the transaction pricebased realized range estimator of daily volatility in the presence of bid-ask bounce and non-trading. The adjustment is an extension of the estimator proposed in Christensen et al. (2009). We relax the assumption that all intraday high (low) transaction prices are at the ask (bid) quote. Using data-based simulations we obtain estimates of the probability that a given intraday range is (upward or downward) biased or not, which we use for a more refined bias-adjustment of the realized range estimator. Both Monte Carlo simulations and an empirical application involving a liquid and a relatively illiquid S&P500 constituent demonstrate that ex post measures and ex ante forecasts based on the heuristically adjusted realized range compare favorably to existing bias-adjusted (two time scales) realized range and (two time scales) realized variance estimators.

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