Homework 6

Homework 6 - Finance Homework 6 ARE 171A Winter 2011 A...

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ARE 171A Finance Homework 6 Winter 2011 A. Havenner The first four questions use the Merrill Lynch "beta book" table at the end of this assignment. The data are up to 60 monthly observations on changes in the logarithms of prices of various stocks and the S&P 500. For each stock, a straight line was fitted by a least squares regression of the monthly stock price changes on the S&P 500 price changes, resulting in an intercept alpha and a slope beta. Beta you should already know. The intercept alpha can be interpreted as the percent change per period (here per month) that would be expected for the stock if the market didn't change at all (if the S&P 500 remained constant that month). For example, MMM stock appreciated by +.22 percent per month (about 12 x .22 = 2.6 percent per year, or more precisely, 1.002zt 2 -1 = 2.67 percent per year) after correcting for the market movements. The column R-SQR gives the proportion of the total variance of the MMM price changes than can be explained by market movements, i.e., 37% of the MMM risk is market (undiversifiable) risk, and 63% is idiosyncratic (unique, diversifiable) risk. The next column measures the unique risk as a standard deviation, the standard deviation of the estimated regression error term (the residual). The next two columns give the standard errors (standard deviations) of the estimates of beta and alpha. These can be used to set up confidence intervals for the estimates of beta and alpha. For example, assuming normality and rounding the statistical table value (from your stat book) of 1.96 to 2, the MMM standard error of beta (0.12) implies that the 95% confidence interval for the true beta is bounded by .71- 2 x .12 and .71 +2 x .12, i.e., the true beta is expected to lie between.47 and .95 with a 95% probability. A similar confidence interval can be calculated for alpha. Ignore the adjusted beta 1 column, and use "raw" betas for all calculations.

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Homework 6 - Finance Homework 6 ARE 171A Winter 2011 A...

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