Datastream beta calculations

Methodology

The derivation of Datastream betas is based on the method described in 'Predictability of British Stock Market prices' by S. Cunningham, Journal of Royal Statistical Society Series C, 1973.

Note:

For the purpose of this explanation, observations under exceptional conditions (such as stocks traded for less than 2½, large price changes and so on) are ignored. The sample used is in the normal case 60 months of monthly returns.

The implementation of this method uses logarithmic monthly returns which Cunningham found to fit slightly better than percentage returns. The basic model estimated is for each stock in a market or market list the following standard bivariate regression:

is the market logarithmic return at time t, the logarithmic return for an equity, and the alpha and beta are parameters to be estimated. Cunningham showed that the coefficients are effectively constant across all stocks; they are important to this description only in that they are necessary for the derivation of thefor a stock. The adjustment of the estimated beta coefficients can be broken up into three stages:

Step 1

The following estimates are created for each equity:

Ordinary least squares (OLS) estimate of beta

OLS estimate of alpha

Variance of regression residuals

The variance of the beta estimate is the standard expression

where T is the number of valid observations for the two variables and

Step 2

The average alpha and beta coefficients are calculated over J constituents

Average alpha

Average beta

Estimated variance of the theoretical beta value

Step 3

Finally, the beta estimate and correlation are calculated for each stock. This is the value displayed on equity programs:

The adjusted beta is a weighted average of the ordinary beta and the average beta if the alpha estimate is close to the average alpha coefficient. The weight on average beta is then increasing in the residual variance, decreasing in variance of the theoretical beta value. The weight on the ordinary beta is increasing in market volatility.

The formula used for beta correlation is:

This is equal to the ordinary correlation coefficient, given that the data sample is chosen as for the estimation of the ordinary beta coefficient.

See also

Beta correlation