Spot beta estimation with asynchronous noisy prices

We introduce a consistent estimator of the spot asset beta based on the Fourier estimator of the multivariate spot volatility. Firstly, we prove the rate-efficient pointwise asymptotic normality for theFourier spot covariance estimator in the presence of asynchronous observations and microstructure noise. Using this result, we obtain a consistent estimator of the spot beta. Then, we investigate the performance of this estimator when employed to reconstruct the sample path of the spot asset beta. In this regard, we provide simulation results that suggest that our spot beta estimator has a robustfinite-sample performance in the presence of realistic market features such as rough volatility, inhomogeneous asynchronous sampling, autocorrelated and price-dependent noise and price rounding. Additionally, we conduct an empirical study with tick-by-tick prices of 100 US stocks, sampled overthe period January 1, 2023–December 31, 2023, in which we reconstruct intraday spot beta pathsand obtain evidence of the existence of a statistically significant link between the intraday cross-sectional dispersion of spot betas and the intraday cross-sectional average and standard deviation of the microstructure noise variance, used as an inverse proxy of liquidity and informational efficiency. This empirical evidence suggests that intraday changes in microstructural features of the market might contribute to explaining high-frequency beta dynamics.