Estimating and Adjusting for the Intervalling-Effect Bias in Beta

Abstract

The concept of beta as the measure of systematic risk has been widely accepted in the academic and financial community. Increasingly, betas are being used to estimate the cost of capital for corporations. Despite this, however, biases are generally present in ordinary least squares (OLS) estimates of beta. In particular, empirical estimates of beta are affected by friction in the trading process which delays the adjustment of a security's price to informational change and hence leads to an "intervalling-effect" bias. In this paper, we present and empirically test two procedures for correcting this bias. The first is to estimate the asymptotic value that OLS beta approaches as the differencing interval is lengthened without bound. The second procedure is to infer the value of beta by adjusting OLS beta for cross-sectional differences in the intervalling effect as a function of the depth of the market for a security (as measured by its value of shares outstanding). Our results suggest that a substantial correction is needed to get "true" beta estimates from short differencing interval data.beta estimation, intervalling-effect bias, systematic risk

The Behavior of Beta in the 19th Century

“…For example, Hawawini and Michel (1979) found a similar pattern of results on the Belgium stock exchange by using weekly interval returns data between 1963 and 1976. The result also follows Cohen et al (1983) hypothesis that there is a strong relationship between beta estimates and the length of the interval over which returns are measured. They established that beta bias mostly shows up in the short length interval (daily) of returns, and the bias disappears when the difference of the interval is lengthened (monthly).…”

“…They proposed a variant version of Scholes and Williams model which yields betas which are consistent and unbiased. We use only three months lag and lead because beta bias has been documented as not prevalent in monthly returns data (see Cohen, Hawawini, Maier, Schwartz and Whitcomb (1983) …”

“…We use only three months lag and lead because beta bias has been documented as not prevalent in monthly returns data (see Cohen, Hawawini, Maier, Schwartz and Whitcomb (1983) is approximately zero for most of the stocks. Unsurprisingly, there are some stocks with lead and lag coefficients that are statistically significant, but their numbers does not exceed the coefficients corresponding to the match.…”

Systematic risk and time scales: New evidence from an application of wavelet approach to the emerging Gulf stock markets

“…Vasicek (1973) suggests a Bayesian correction for the bias. Cohen, Hawawini, Maier, Schwartz, and Whitcomb (1983) present an analytical model to adjust estimated beta by estimating the cross-sectional intervalthinness relationship. There is no agreement in the literature on which adjustment method is superior over the rest.…”

“…There is no agreement in the literature on which adjustment method is superior over the rest. Diacogiannis and Makri (2008) tested the efficiency of the Scholes and Williams (1977) and Cohen et al (1983) methods using Greek data. They found that neither method provides any incremental benefit over standard OLS estimation.…”