The sensitivity of beta to the time horizon when log prices follow an Ornstein-Uhlenbeck process

This paper provides a new theoretical approach to investigate the sensitivity of the familiar beta of the capital asset pricing model to the length of the return measurement interval; a phenomenon known as the intervalling effect. By setting the problem in a continuous time setting, and using exact results, we are able to generalize existing results in the literature. We derive an expression for beta as a function of the time horizon <italic>h</italic>, conditional on current time <italic>t</italic>. We show that beta is monotonic in <italic>h</italic> and derive conditions for it to be increasing or decreasing.