Accounting for the Accuracy of Beta Estimates in CAPM Tests on Assets with Time‐varying Risks

Abstract

This paper advocates two ways to make more efficient use of available information in reducing the bias of the risk premium estimate in two-pass tests of the CAPM. First, explicit modelling of the time-variability of betas can improve the accuracy of the beta forecasts. Second, the cross-sectional information available can be exploited more efficiently using individual stocks instead of portfolios provided that noisy beta predictions are given a smaller weight than more accurate ones. This paper proposes an adjustment of the cross-sectional regressions of excess returns against betas to give larger weights to more reliable beta forecasts. A significant positive relationship between returns and the beta forecast is obtained when the proposed approach is applied to data from the Helsinki Stock Exchange, while the traditional Fama-MacBeth approach as such finds no relationship at all.

Conditional Asset Pricing and Stock Market Anomalies in Europe

“…The null hypothesis that expected returns on portfolio i only depend on its sensitivity to the risk factors in the model, measured by , implies that all loadings c m on the non‐risk factors must be zero. As noted by Berglund and Knif (1999), the Fama‐MacBeth (1973) two‐step procedure commonly used to test this hypothesis suffers from an errors‐in‐variables problem, since the betas included as regressors in the second stage cross‐sectional regressions are estimated with error in the time‐series regressions.…”

Cross‐sectional Tests of Conditional Asset Pricing Models: Evidence from the German Stock Market

“…6 6 For an empirical investigation of the impact of errors‐in‐variables problem associated with traditional two‐pass cross‐sectional tests, see e.g. Berglund and Knif (1999). …”

Are Calculated Betas Worth for Anything?

“…They also show that adding systematic co-moments (not standard) of order 3 through 10 reduces the explanatory power of the Fama-French factors to insignificance in almost every case. Berglund and Knif (1999) propose an adjustment of the cross-sectional regressions of excess returns against betas to give larger weights to more reliable beta forecasts. They find a significant positive relationship between returns and the beta forecast when the proposed approach is applied to data from the Helsinki Stock Exchange, while the traditional Fama-MacBeth (1973) approach as such finds no relationship at all.…”