On the Assessment of Risk: Some Further Considerations

Abstract

STATISTICALLY, a beta coefficient is the slope coefficient of a linear function relating the return on a security or portfolio to the return on a market index. Substantial interest has focused on beta coefficients because of hypothesis suggesting them as indices of asset risk. This concept arises from two sources: the market model developed in Sharpe [4] as a technique for portfolio analysis; and, the full equilibrium Capital Asset Pricing Model developed in Sharpe [5], Lintner [2], and Mossin [3]. Recently in this Journal, Marshall Blume [1] reported results of an empirical investigation of the stationarity of beta coefficients over time. In investigating this question, Blume estimated portfolio betas using monthly data over several successive seven year periods, and comparing the betas on successive intervals. His results indicated that beta coefficients were highly stable for portfolios containing large numbers of securities but unstable for individual securities.' The present paper presents results of research which investigated the impact of the length of the estimation interval on stability of the beta estimated. Using monthly data, betas were estimated using estimation intervals of one year, two years, four years, six years and nine years. The results indicate that the stability of the beta increases substantially as the length of the estimation interval increases.

The dynamic and stochastic instability of betas: Implications for forecasting stock returns

“…The conclusion that beta is nonstationary is in complete agreement with the assertion of existing work, though our concept of nonstationarity defined and methodologies and data used differ from those used in previous research. We also have found evidence that departs from the assertion (Altman et al, 1974; Baesel, 1974) that nonstationarity is inversely related to the interval of the time period. We have cited three signals that emerged from the empirical results as evidence of the departure.…”

“…100 during the 1974-83 subperiod. The empirical VMR function obtained by FGLS was As a comment, we note that our empirical evidence tends to contradict the conclusion that stationarity of individual stock betas increases with the increase in the length of the estimation period (Altman et al, 1974;Baesel, 1974). One obvious signal which has been stated before is that the number of the stocks with significant estimates of LY(D), q p ) , and y ( p ) rises as the length of the time period increases.…”

An Analysis of the Market Model and Beta Factors Using U.K. Equity Share Data

“…The correlations were all significant, but somewhat lower than those found by Blume (1971) for U.S. stocks and Cunningham, for U.K. stocks. However, Blume's results relate to betas estimated over seven-year sample periods, and Baesel (1974) has shown empirically for U.S. stocks that beta stationarity is an increasing function of the period over which beta is estimated. This phenomenon was found to be exhibited by the present sample, since the correlations uniformly decreased when the beta stationarity was investigated for betas estimated over thirty-month sample periods.I6 Cunningham made no adjustments for non-trading effects, which will mean that his degree of stationarity, as measured by correlation coefficients, w i l l be biased upwards.…”

Stability of Alphas and Betas over Bull and Bear Markets: An Empirical Examination

“…Both methods give almost consistent results that betas are unstable over time. The results of the studies conducted by Altman, Jacquillat and Levasseur (1974) and Baesel (1971) show that the stability of individual betas increases with increase in the length of estimation period. The work of Baesel's (ibid) was criticized by Alexander, Sharpe and Chervany (1980) who showed that the optimal estimation time interval to get stable betas is generally four to six years.…”