Erasmus university rotterdam

Beta estimation

Following the methodology used by Fama & Macbeth (1973), historical returns of the individual stocks are calculated following equation [2] and beta is estimated following equation [3] using the Ordinary Least Squares (OLS) regression method. For each company in the sample the returns are regressed on the stock index to estimate beta. A similar methodology will be used to estimate the different versions of the CAPM.

The first stage is the time series regression of individual stock returns on the proxy for the market index. The second stage is a cross section regression of average returns for each security on each security’s beta, skewness, and kurtosis. The regression residuals are checked for heteroscedasticity and normality (Omran 2007).

In the first stage regression, time series data is used to estimate market risk. The second stage regression is a cross sectional regression. Afterwards two diagnostics test are applied to the residuals from the regression; the White Heteroscedasticity test, since cross sectional data could suffer from the variance of the error term being large for large beta stocks and small for small beta stocks. The second diagnostics test is testing for normality of the residuals using Jarque-Bera test for normality, skewness and excess kurtosis. is the ratio of market risk to the total variance of the returns on a particular stock. The percentage of variation not explained by the market is .

Beta estimation has some problematic issues. The value of beta depends on the length of the time series taken, taking a 2 year or a 5 year time interval will result in different measures of beta. As a result there exists more than one beta for the same company (Pereiro, 2001). In addition beta changes over time. The beta of a company tends to shrink as the company matures. It is difficult to account for these changes.