1. Two independent loan prospects exist, call them A and B. Both will pay the agreed-upon $12 return (on $100) with probability 3/4. With probability 1/4, on the other hand, they default and pay only $4.00.
a. For an individual saver investing in one or the other, what is the average return (expected return)? What is the variance?
b. Suppose that an intermediary forms by merging the funds of the 2 savers and investing in both projects, splitting the total return equally between the 2 savers. What is the average return to the individual saver? What is the variance?
c. Compare a. and b. Does your result confirm the Law of Large Numbers? Explain.