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Unformatted text preview: University of California, Los Angeles Department of Statistics Statistics C183/C283 Instructor: Nicolas Christou Accuracy of historical betas Forecasting betas with accuracy is important because they affect the inputs for the portfolio analysis problem. The variance covariance matrix is based on the value of beta for each stock. Different techniques have been proposed for better estimation of betas. a. Unadjusted betas: These are the betas obtained by the regression of the returns of the stock on the returns of the market. R it = + R Mt + it . b. Blumes technique (1975): The betas are adjusted as follows. Let us assume that we want to forecast betas for the period is 2007-11. Then we will need two five-year periods, 2002-06 and 1997-01. First, we calculate the betas for all stocks of interest for the period 1997-01. We then calculate the betas for the same stocks for the period 2002-06. And then we run the regression of the betas in 2002-06 on the betas in 1997-01 to get the equation i 2 = + i 1 . Assume now that we want to forecast the beta of a stock in 2007-11. Then we find its beta in the period 2002-06 and substitute it in the equation above. For example, if the equation that connects the betas in the two historical periods is i 2 = 0...
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