Firm A sells lemonade and firm B sells hot chocolate.If you invest $100 if firm A, in one year you will get back $(30 + T)where T is the average temperature (Fahrenheit)during the summer.If you invest $100 in firm B, in one year you will get back $(150 - T), where T is the average temperature during the summer.The expected value of T is 70 and the standard deviation of T is 10.If you invest $50 in firm A and $50 in firm B, what is the standard deviation of your return on your investment?
A)10
B)20
C)5
D)0
E)None of the above.

Question

Quizplus · Accepted Answer

The standard deviation of the return on investment when investing in both firms is 0 because the returns from Firm A and Firm B are perfectly negatively correlated with respect to temperature. Any variation in temperature that increases the return from one firm decreases the return from the other by the same amount, resulting in no variability in the total return.

Firm a Sells Lemonade and Firm B Sells Hot Chocolate