Question

6.

a) Explain why adjustment to beta such as Blume’s and Vasicek’s are necessary.

b) Assume betas for two stocks A and B are estimated to be 1.6 and 0.7 respectively. Calculate adjusted betas by using Blume’s method.

Answer 1

solution to question a).
Adjusted Beta
To correct the tendency towards one, two main models were suggested in the literature: Blume‟s Model and Vasicek‟s Model.

A research found that well-diversified portfolios of extreme betas are significantly non- stationary. Therefore it is concluded that in order to improve performance on beta forecasts; adjustments should be made not only to take into consideration the regression tendencies but the market trends too.

According to Blume, the systematic risk of stock portfolio tends to show relatively stable characteristics. However, he observed a tendency of betas to converge towards the mean of all betas (1.0). He corrected past betas by directly measuring this adjustment toward one and assuming that the adjustment in one period is a good estimate of the adjustment in the next. It modifies the average level of level of betas for the population of stocks.

Vasicek has suggested the following scheme that incorporates these properties: If we let β1 equal the average beta, across the sample of stocks, in the historical period, then the Vasicek procedure involves
taking a weighted average of β1 and the historic beta for security i. The weighting procedure adjusts
observations with large standard errors further toward the mean than it adjusts observations with small standard errors. As Vasicek has shown, this is a Bayesian estimation technique. The estimate of the average future beta will tend to be lower than the average beta in the sample of stocks over which betas are estimated.

solution to question b). Computation of adjusted beta using Blume model

To calculate the adjusted beta , Blume has proposed formula

= (2/3) Beta + (1/3)

Beta of stock A = 1.6

Beta of stock B= 0.7

Adjusted Beta of stock A= 2/3*1.6+ 1/3= 1.4

Adjusted Beta of stock B= 2/3*0.7+ 1/3= 0.8