Estimating realized covariance using high frequency data

Assessing the economic value of increasingly precise covariance estimates is of great interest in finance. We present a realized tick-time covariance estimator that incorporates cross-market tick-matching and intelligent sub-sampling. These features of the estimator offer the potential for improved performance in the presence of asynchroneity and market microstructure noise. Specifically, tick-matching preserves information when arrival structures are asynchronous, and intelligent sampling and averaging across sub-samples reduces microstructure-induced noise and estimation error. We compare the performance of this estimator with prevailing methodologies in a simulation study and by assessing out-of-sample volatility-timing portfolio optimization strategies. We demonstrate the benefits of tick time over calendar time, optimal sampling over ad-hoc sampling, and sub-sampling over sampling. Results show that our estimator has smaller mean squared error, smaller bias, and greater economic utility than prevailing methodologies. Our proposed optimized tick-time estimator improves upon both prevailing calendar-time methods and ad-hoc sampling schemes in tick time. Empirical results indicate substantial gains; approximately 70 basis points improvement against the 5 minute calendar time sampling scheme; approximately 80 basis points against optimally sampled calendar time; and 30 basis points against tick time sampled every 5th tick. Both simulation and empirical results indicate that tick time is the better sampling scheme for portfolios with illiquid securities.Asset allocation is inherently a high dimensional problem and estimated realized covariance matrices fail to be well-conditioned in high dimensions. As a result, the portfolios constructed are far-from optimal. Factor modeling offers a solution to both the growing computational complexity and conditioning of the covariance matrices. We find that risk averse investors would be willing to pay up to 30 basis points annually to switch from the best performing exponentially smoothed portfolio to the best performing single-index portfolio. As the number of assets increases, portfolio allocation using the single-index model is better able to replicate the benchmark index. For high-dimensional allocation problems, factor models are a more natural setting for employing realized covariance estimators.