If you invest $100 now in firm 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 firm 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. You can divide your investment money between firm A and firm B in any way.

a. Draw a graph showing the combinations of expected return and standard deviation by dividing $100 between stock A and stock B. Put the expected return on the vertical axis and the standard deviation on the horizontal axis. [Hints: if the expected value of x is written E(x), then E(ax+b) = aE(x) + b; if the standard deviation of x is written SD(x), then SD(ax+b) = aSD(x) + b whereais the absolute value of a. ]

b. What is the expected value and standard deviation of the safest investment strategy you can make by this means? What is that investment strategy?

c. What is the highest expected value you can achieve? What is the standard deviation associated with that expected value? What is that investment strategy?