Functional Data Analysis : Estimating Beta in the Capital Asset Pricing Model for High-frequency U.S. Stock Data

This paper proposes estimating β in the capital asset pricing model (CAPM) using a functional data analysis approach. After explicitly deriving parameter estimates and a prediction function for a functional CAPM, this paper compares the predictive power of the functional CAPM against two distinct linear CAPMs. The analysis of the model’s predictive power is based on an application to cumulative intra-day returns of 40 randomly drawn stocks listed on the S&P 500. This paper finds that a functional CAPM has a larger predictive power than a more simple linear CAPM, but is equal in predictive power to a more complex linear CAPM