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# Suppose all the stocks in bobs portfolio double in

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18. Suppose all the stocks in Bob’s portfolio double in price. a. What happens to the mean of Bob’s stocks? Want E(2X) = 2x20 = \$40 b. What happens to the variance? Want V(2X) = 4x25 = 100 19. Suppose all of Sue’s stocks each increase \$10.00 in price. a-b. What happens to the mean and variance of her stock prices? E(Y+10)=30+10=\$40; V(Y+10)=36 20. Assume Bob and Sue’s stocks are independent. a. What is the mean and standard deviation of their combined stock prices? E(X+Y)=20+30=\$50 V(X+Y) = 26+36=61 by independence; SD(X+Y)=square root of 61=\$7.8 b. What is the mean and standard deviation of the difference in their stock prices? E(X-Y)=20-30=\$-10 V(X-Y)=26+36=61 by independence; SD(X-Y)=\$7.8 21. Assume Bob and Sue’s stocks have correlation 0.4. a. What is the mean and standard deviation of their combined stock prices? E(X+Y)=\$50 as before V(X+Y)=25 + 36 + 2(.4)(5)(6)=85; SD(X+Y)=square root of 85 = 9.22 b. What is the mean and standard deviation of the difference in their stock prices? E(X-Y)=\$-10 as before V(X-Y)=25 + 36 - 2(.4)(5)(6)=37; SD(X-Y)=square root of 37=6.08 3
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