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This paper develops a new framework and statistical tools to analyze stock returns using high frequency data. We consider a continuous-time multi-factor model via a continuous-time multivariate regression model incorporating realistic empirical features, such as persistent stochastic volatilities with leverage effects. We find that conventional regression approach often leads to misleading and inconsistent test results. We overcome this by using samples collected at random intervals, which are set by the clock running inversely proportional to the market volatility. We find that the size factor has difficulty in explaining the size-based portfolios, while the book-to-market factor is a valid pricing factor.

Evaluating Factor Pricing Models Using High Frequency Panels