If you invest $100 now in fi rm A, in one year you will get back $(30 + T) where T is the average temperature during the next summer. If you invest $100 now in fi rm B; in one year you will get back $(180 -T). The expected value of T is 70 and the standard deviation of T is 10.
a) Draw a graph showing the combinations of expected return and standard deviation that you can have by dividing $100 between stock in A and stock in B. (Hint: Expected value has the property that E(ax + b) = aE(x) + b and standard deviation has the property that SD(ax + b) = [(absolute value of a) times SD(x)] + b.)
b) What is the expected value and standard deviation of the safest investment strategy you can make by this means?
(c) What is the highest expected value you can achieve?