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W5_PracSolution - Week 5 Risk and Return CHAPTER 10 SOME...

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Week 5 - Risk and Return CHAPTER 10 SOME LESSONS FROM CAPITAL MARKET HISTORY Answers to Concepts Review and Critical Thinking Questions 4. On average, the only return that is earned is the required return—investors buy assets with returns in excess of the required return (positive NPV), bidding up the price and thus causing the return to fall to the required return (zero NPV); investors sell assets with returns less than the required return (negative NPV), driving the price lower and thus the causing the return to rise to the required return (zero NPV). Solutions to Questions and Problems 7. The average return is the sum of the returns, divided by the number of returns. The average return for each stock was: [ ] % 7.20 or .0720 5 04 . 18 . 09 . 16 . 21 . 1 = + + + - = = = N x X N i i [ ] % 80 . 12 or .1280 5 30 . 13 . 26 . 03 . 24 . 1 = + - + - = = = N y Y N i i Remembering back to “sadistics,” we calculate the variance of each stock as: ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 { } ( 29 ( 29 ( 29 ( 29 ( 29 { } 037770 . 128 . 30 . 128 . 13 . 128 . 26 . 128 . 03 . 128 . 24 . 1 5 1 021470 . 072 . 04 . 072 . 18 . 072 . 09 . 072 . 16 . 072 . 21 . 1 5 1 1 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 = - + - - + - + - - + - - = = - + - + - + - - + - - = - - = = Y X N i i X N x x σ σ σ The standard deviation is the square root of the variance, so the standard deviation of each stock is: σ X = (.021470) 1/2 σ s X = .1465 or 14.65% σ Y = (.037770) 1/2 σ Y = .1943 or 19.43% 25 . The mean return for small company stocks was 16.4 percent, with a standard deviation of 33.0 percent. Doubling your money is a 100% return, so if the return distribution is normal, we can use
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the z-statistic. So: z = (X – μ)/ σ z = (100% – 16.4)/33.0% = 2.533 standard deviations above the mean This corresponds to a probability of 0.565%, or less than once every 100 years. Tripling your money would be: z = (200% – 16.4)/33.0% = 5.564 standard deviations above the mean.
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