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# Ch8.Answers (1) - Chapter 8 Answers 1 Nominal rate = real...

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Chapter 8 Answers 1. Nominal rate = real rate + inflation 2.25 + 1.75 = 4.00% 2. Real rate = nominal rate – inflation 4.5 – 4.25 = .25 3. Expected return: (.15 x -.02) + (.38 x .03) + (.30 x .04) + (.17 x .05) = 2.89% Standard deviation: (-.02 - .0289) 2 (.15) + (.03 - .0289) 2 (.38) + (.04 - .0289) 2 (.30) + (.05 - .0289 2 )(.17) = .00035868 + .00000046 + .00003696 + .00007569 = .00047179 sq. root (.00047179) = .0217 or 2.17% No, the security has greater risk than the T-bill (which has a standard deviation of 0) and a lower return. 4. Common stock 1 Expected return: (.30 x .10) + (.60 x .13) + (.10 x .16) = 12.4% Standard deviation: (.10 - .124) 2 (.30) + (.13 - .124) 2 (.60) + (.16 - .124) 2 (.10) = .0001728 + .0000216 + .0001296 = .000324 sq. root (.000324) = .018 or 1.8% Common stock 2 Expected return: (.20 x .04) + (.40 x .08) + (.30 x .18) + (.10 x .21) = 11.5% Standard deviation: (.04 - .115) 2 (.20) + (.08 - .115) 2 (.40) + (.18 - .115) 2 (.30) + (.21 - .115) 2 (.10) = .001125 + .00049 + .0012675 + .0009025 = .003785 sq. root (.003785) = .0615 or 6.15% Stock 2 has a lower return and a higher standard deviation. Based solely on this data, stock 1 appears to be the better investment. However, this is based only on total risk. The story is not complete until we’ve analyzed systematic risk. 5. Expected return: (.02 + .03 + .05 + .05 + .08 + .10)/6 = 5.5%

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Standard deviation: Variance =[ (.02 - .055) 2 + (.03 - .055) 2 + (.05 - .055) 2 + (.05 - .055) 2 + (.08 - .055) 2 + (.10 - .055) 2 ]/ (6-1)= [.001225 + .000625 + .000025 + .000025 + . 000625 + .002025] /5 = .00455/5 = .00091 Standard deviation = √variance = √.00091 = .03016 or 3.016% 6. CAPM = Rf + B(Rm – Rf) .05 + 1.4(.12 - .05) = 14.8% 7. CAPM = Rf + B(Rm – Rf) Security 1 .0475 + 1.45(.14 - .0475) = 18.16%
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