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Suppose you are going to invest $ 1 0 0 0 in some stocks and hold them for one year. Suppose Safe Corp. stock currently

Suppose you are going to invest $1000 in some stocks and hold
them for one year. Suppose Safe Corp. stock currently costs $100.
Its price a year from now is a random variable X with mean $105
and standard deviation of 10.Risky Business stock also currently
costs $100. But its price a year from now is a random variable Y
with mean $110 and standard deviation of 20. Suppose the correla-
tion coefficient of X and Y is 0.2.
(a) How much should you invest in each stock if you want to max-
imize the expected value of what your stocks are worth one year
from now?
(b) How much should you invest in each stock if you want to mini-
mize the variance of what your stocks are worth one year from now?
NOTE: You are allowed to buy part of a stock. So for example,
you could invest $333.33 in Safe Corp. and $666.67 in Risky
Business.(It may be useful to use the formula:
var(X+Y)= var(X)+ var(Y)+2cov(X,Y)

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