Alpha (α) and Beta (β) Coefficients, Determination Coefficient (R2)
Coefficient Descriptions
Alpha (α) and beta (β) coefficients are quantitative characteristics of the dependence of an individual security price’s change on the change of the index value. In general, this dependence may be represented as follows:
The beta coefficient (β) shows an individual security price’s sensitivity towards the index value. For example, a beta parameter value equal to 2 means that if the index grows by 1 percent, the security price will grow by 2 percent. A negative value of the beta coefficient shows a reverse dependency between the security price change and the index value. A beta coefficient of zero indicates the absence of a connection between the change in the security price and the index.
The alpha coefficient (α) shows the growth (decrease) level of the security price, independent of the index changes.
Coefficients are calculated for one-day price increments.
When calculating the coefficients, the day values of the security price and index are used. The security prices and index values at the close of trading are used as day values. Calculations on one-day price increments are carried out for the previous 50-day time period.
After the alpha and beta coefficients have been calculated, the question arises as to what extent they describe the dependence of the security price on changes in the index values. In order answer this question, the determination coefficient (R2) is calculated. The determination coefficient has values ranging from 0 (explanatory capacity is equal to zero) to 1 (explanatory capacity is maximal).
Coefficients are calculated daily at the close of trading in the MICEX SE CJSC.
Calculation Methodology
1) The alpha (α) and beta (β) parameters are calculated using the following formulae:
Where:
Designations:
αˆ i is the estimation of the alpha coefficient of the i-th security;
βˆ i is the estimation of the beta coefficient of the i-th security;
I k is the index value at the end of the k-th trading day;
ΔP ki is the relative change of the price of the i-th security on the k-th trading day;
ΔI k is the relative change of the index value for the k-th trading day;
ΔP i is the average value of the relative changes in the prices of the i-th security for the calculation period;
ΔI is the average value of the relative changes of index values for the calculation period;
N is the number of days in the period under calculation (N = 50).
2) Formula for calculating the determination coefficient:
Where:
Designations:
R 2i is the determination coefficient;
αˆ i is the estimation of the alpha coefficient of the i-th security;
βˆ i is the estimation of the beta coefficient of the i-th security;
ΔP ki is the relative change of the price of the i-th security on the k-th trading day;
ΔI k is the relative change of the index value for the k-th trading day;
ΔP i is the average value of relative changes in prices of the i-th security for the calculation period;
ΔI is the average value of the relative changes of index values for the calculation period;
ΔP’ ki is the calculation value of the relative change in security price for the k-th trading day.
Calculation Methodology for Analytical Parameters (In Russian)