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Unformatted text preview: Chapter 14 Simple Linear Regression Chapter 14 Simple Linear Regression Case Problem 1: Measuring Stock Market Risk a. Selected descriptive statistics follow: Variable N Mean StDev Minimum Median Maximum Microsoft 36 0.00503 0.04537 0.08201 0.00400 0.08883 Exxon Mobil 36 0.01664 0.05534 0.11646 0.01279 0.23217 Caterpillar 36 0.03010 0.06860 0.10060 0.04080 0.21850 Johnson &amp; Johnson 36 0.00530 0.03487 0.05917 0.00148 0.10334 McDonalds 36 0.02450 0.06810 0.11440 0.03700 0.18260 Sandisk 36 0.06930 0.19540 0.28330 0.07410 0.50170 Qualcomm 36 0.02840 0.08620 0.12170 0.03870 0.21060 Procter &amp; Gamble 36 0.01059 0.03707 0.05365 0.01333 0.08783 S&amp;P 500 36 0.01010 0.02633 0.03429 0.01034 0.08104 From the descriptive statistics we see that six of the companies had a higher mean monthly return than the market (as measured by the S&amp;P 500): Exxon Mobil, Caterpillar, McDonalds, Sandisk, Qualcomm, and Procter &amp; Gamble. Microsoft and Johnson &amp; Johnson had lower mean monthly returns. Using the standard deviation as a measure of volatility, Sandisk was the most volatile stock with a standard deviation of .1954. The stocks of Johnson &amp; Johnson and P &amp; G exhibit less volatility than the other individual stocks. But, all of the individual stocks are more volatile than the market as a whole. The diversification embodied in the S&amp;P 500 reduces its volatility. b. The estimated regression equation relating each of the individual stocks to the S&amp;P 500 is shown below. The value of 2 R for each equation is also shown. Microsoft = 0.00040 + 0.458 S&amp;P 500 RSq = 7.1% Exxon Mobil = 0.00926 + 0.731 S&amp;P 500 RSq = 12.1% Caterpillar = 0.015000 + 1.49 S&amp;P 500 RSq = 32.9% Johnson &amp; Johnson = 0.00521 + 0.009 S&amp;P 500 RSq = 0.0% McDonalds = 0.00930 + 1.500 S&amp;P 500 RSq = 33.8% Sandisk = 0.04300 + 2.600 S&amp;P 500 RSq = 12.3% Qualcomm = 0.01410 + 1.410 S&amp;P 500 RSq = 18.7% Procter &amp; Gamble = 0.00548 + 0.507 S&amp;P 500 RSq = 12.9% CP  39 Chapter 14 Simple Linear Regression The betas (slope of estimated regression equation) for the individual stocks can be obtained from the regression output. Company Beta Microsoft .458 Exxon Mobil .731 Caterpillar 1.490 Johnson &amp; Johnson .009 McDonalds 1.500 Sandisk 2.600 Qualcomm 1.410 The beta for the market as a whole is 1. So, any stock with a beta greater than 1 will move up faster than the market when the market goes up. Any stock with a beta less than 1 will not go down as fast as the market in periods where the market declines. We would expect Sandisk, with a beta of 2.6, to benefit most from an up market. Johnson &amp; Johnson, with a beta of .009 is least affected by the market. The effect of the market going down cannot be expected to exert much downward pressure on shares of Johnson &amp; Johnson....
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 Spring '09
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