Validating intra-day risk premium in cross-sectional return curves

•Time-varying factor exposures and risk premiums are derived at an intra-day level.•Functional Fama-MacBeth approach used to validate the intra-day risk premiums.•Fama-French Carhart risk factors cannot account for systemic comovement over the entire intra-day interval.•Valid risk premiums found over specific intra-day trading hours in Bullish sentiment.