An Analysis of the Forecast Error Impact of Alternative Beta Adjustment Techniques and Risk Classes

Abstract

THE PURPOSE OF THIS paper is to examine empirically the relationships among the stability of security and portfolio betas and (1) beta adjustment techniques, (2) beta risk classes, and (3) the length of the sample periods used to calculate betas. The beta coefficient of the familiar market model has emerged in recent years as an important tool for assessing the risk associated with individual securities and portfolios. The usefulness of an ex post beta for measuring the ex ante risk of an investment depends, however, upon the temporal stability of the asset's beta coefficient. While there have been numerous studies concerned with an empirical examination of beta stability [1, 2, 3, 6, 7, 8, 10], there has been no examination of forecast error components associated with different beta groups classified according to beta magnitude or with different beta estimation and prediction period lengths.' Typically, studies have used a single length beta estimation and prediction period [2, 3, 5, 6, 7], and if the lengths of the beta estimation and prediction periods were varied, the two period lengths were always equal for each comparison [1, 8]. Alternative estimation and prediction period lengths are used in this study to examine the impact of beta adjustment techniques, risk classes, and portfolio size on the beta forecast error and its components. The results of this study indicate that beta forecast errors may be substantially reduced when (1) beta adjustment procedures are utilized, (2) portfolio size is increased, and (3) the estimation or prediction period is increased. When securities or portfolios are grouped into risk classes, adjustment techniques are very effective in reducing the size of the inefficiency and bias components of the forecast error, but they show little impact on the random error components. Furthermore, for more extreme risk classes, the primary source of error is bias for portfolios when no adjustments are made, while random error is the major source of forecast error for single securities for longer estimation periods.