The Stochastic Properties of Systematic Risk for U.S. Mutual Funds

Abstract

This paper investigates three possible processes by which mutual fund betas may develop over time. The paper proposes the idea that the underlying structure of fund returns can be interpreted as an indicator of management style. Due to the pressures placed on fund managers to remain within certain risk guidelines, laid out in the funds prospectus, over time the beta of an actively managed fund should exhibit mean reversion. We impose three different time-varying models on mutual fund betas using the Kalman filter algorithm. The three processes are: Firstly a random coefficient with constant mean model where any disturbance or shock to the funds systematic risk in one period has no effect on future beta values, possibly indicating an immediate re-alignment of the funds risk profile by the manager. Secondly an AR(1) model where shocks would have some persistence, and finally a random walk process where shocks will persist indefinitely. Our findings, over all funds in the sample, show an equal split between the random coefficient model and the random walk model. Furthermore, when we split the sample into fund classifications we find that the random walk model dominates the small company funds, suggesting these funds have adopted a more passive management style, possibly due to the reduced liquidity of the underlying stocks. The random coefficient model on the other hand dominates growth funds and speciality funds, indicating a more active management style is being used to counteract any shocks to the underlying systematic risk of the fund.