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 x2daily 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 βο, β1, and β2 using daily returns for the period January 3, 2005, through December 30, 2005. The estimated multiple regression equation is: 0.00080.6404x1 0.6869x2 The coefficient 0.6869 in the estimated multiple regression equation is: 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 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 NCI return, keeping the DJIA return constant Based on his study, the analyst expects an upturn for the overall market and the computer industry. He expects a 296-0.02 return for the DJIA and a 2%-0.02 return for the NCI when the DJIA return is 2% and the NCI return is 296, the average Company A stock return for all trading days is estimated to be , and the predicted Company A stock return for one specific trading day is . This predicted return has the average returr Using computer software, the analyst generates 95% confidence intervals and 95% prediction intervals for different return values of the DJIA and the NCI. The intervals are shown in the following table: Table of 95% Confidence Intervals and Prediction Intervals Confidence Interval Prediction Interval Lower Limit -4.94% -4.69% -5.35% -5.88% -3.80% -2.59% -2.96% -3.54% -5.04% -3.09% 0.06% 0.26% -6.11% -4.20% Upper Limit Lower Limit Upper Limit -14.37% -13.78% -13.04% -12.88% -13.64% -12.88% -11.84% -11.53% -13.02% -11.94% -10.23% -9.61% -13.08% -11.87% -9.85% -9.06% -0.21% 0.91% 4.32% 6.23% -0.07% 0.09% 3.21% 5.1 6% 3.73% 3.15% 2.75% 3.93% 6.08% 5.54% 4.87% 5.11% 9.22% 10.00% 12.01% 13.22% -2% 1% 2% 10.39% 12.09% 13.16% 11.71% 12.00% 13.04% 13.80% 13.05% 13.22% 13.94% 14.53% 1% 2% 1% 1% 1% 1% 2% 2% 2% 2% 1% 2% 1% 2% 0.36% when the DJIA return is 296 and the NCI return is 296, the 95% confidence interval for the average Company A stock return is " The 95% prediction interval for the predicted Company A stock return is to The interval for the average Company A stock return is return, because you can estimate the average return for all trading days with predict the return for one specific trading day. than that for the predicted Company A stock precision than you can An investor has a portfolio consisting of 1,000 shares of Company A stock, which is priced at $40 per share. Assuming that the D]IA return is 2% and the NCI return is 2%, the 95% prediction interval for the predicted value of the investor's portfolio is of one share will change from $40 to $40(105%) = $42. If the Company A stock return is-596, the value of one share will change from $40 to $40(95%)-$38.) . (Hint: If the Company A stock return is 5%, the value to

Answer 1

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