This paper develops a new framework and statistical tools to analyze stock returns using high‐frequency data. We consider a continuous‐time multifactor model via a continuous‐time multivariate regression model incorporating realistic empirical features, such as persistent stochastic volatilities with leverage effects. We find that the conventional regression approach often leads to misleading and inconsistent test results when applied to high‐frequency data. We overcome this by using samples collected at random intervals, which are set by the clock running inversely proportional to the market volatility. Our results show that the conventional pricing factors have difficulty in explaining the cross section of stock returns. In particular, we find that the size factor performs poorly in fitting the size‐based portfolios, and the returns on the consumer industry have some explanatory power on the small growth stocks.

Panel high frequency time change realized variance Fama–French regression C12 C13 C33