5. Using the estimated regression equation for estimation and prediction Aa Aa M

Question

5. Using the estimated regression equation for estimation and prediction Aa Aa Market model is a term used in finance to describe a linear regression model in which the dependent variable is the return on a stock and the independent variable is the return on the overall market. The market model is sometimes extended to include other independent variables-for example, the return on a specific industry sector. Company A is one of the leading software companies in the world. Suppose an analyst in an investment bank is creating a market model to predict returns on Company A stock from both market and industry returns. The multiple regression model is where y daily returns for Company A stock = X1daily returns for the Dow Jones Industrial Average daily returns for the NASDAQ Computer Index Returns for the Dow Jones Industrial Average (DJIA) will indicate market returns, while those for the NASDAQ Computer Index (NCI) will indicate industry returns. The analyst estimates the parameters 0, 1, and 2 using daily returns for the period January 3, 2005, through December 30, 2005. The estimated multiple regression equation is: y = 0.0008 + 0.6404x1 + 0.6869x2 The coefficient 0.6404 in the estimated multiple regression equation is: O The estimated change in average Company A stock return for a one-unit change in NCI return, keeping the DJIA return constant O The estimated average Company A stock return when the DJIA and NCI returns are zero O The estimated change in average Company A stock return for a one-unit change in DJIA return, keeping the NCI return constant O The estimated increase in average Company A stock return when the DJIA and NCI returns change by one unit

Explanation / Answer

The coefficient 0.6404 in the multiple regression model is

The estimated change in average company A stock return for one unit change in DJIA return keeping the NCI return constant.

When DJIA return is -2% and NCI return is -2%, the average company A stock return for all trading days is estimated to be -0.025746 and the predicted company A stock return for any particular day is -0.025746.

When DJIA return is -2% and NCI return is -2%, the 95% confidence interval for company A stock return is -4.94% and -0.21%. and the prediction interval is -14.37% and 9.22%.

An investor has a portfolio consisting of 1000 shares of company A which is priced $40 per share.The DJIA return is -2% and NCI return is -2%. Therefore, the stock return of company A is -2.5746%. The predicted value of stock share is 38.5. The 95% prediction interval for the stock is -14.37% and 9.22%.

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