Stock return prediction based on a functional capital asset pricing model

The capital asset pricing model (CAPM) is frequently used to capture a linear relationship between the daily returns of an asset and a market index. We extend this model to an intraday high-frequency setting by proposing a functional CAPM. The functional CAPM is a stylized example of a function-on-function linear regression with a bivariate functional regression coefficient. The two dimensional regression coefficient measures the cross-covariance between cumulative intraday asset returns and market returns. We apply it to the Standard and Poor’s 500 index and its constituent stocks to demonstrate its practicality. We investigate the functional CAPM’s in-sample goodness-of-fit and out-of-sample prediction for an asset’s cumulative intraday return. The findings suggest that the proposed functional CAPM methods have both superior model goodness-of-fit and forecast accuracy in comparison to the traditional CAPM. In particular, the functional methods produce better model goodness-of-fit and prediction accuracy for those stocks that are traditionally considered less price-efficient or information-opaque.