Question: there are 5 companies each sells a bond that will...
There are 5 companies, each sells a bond that will pay $20 in one month. For each company the bond costs $10. All of these companies have probability .01 of default, and whether one defaults is independent from whether any of the others default.
a) Let X be the number of companies that default. What is the distribution of X? What is the expected value of X? What is the variance of X?
b) Consider two portfolios. In portfolio I, we buy one bond from each of these companies. In portfolio II, we buy 5 bonds from one of these companies. How much does portfolio I cost? How much does portfolio II cost?
c) Let Y be the amount of money that we get in one month if we have portfolio I, and let Z be the amount of money that we get in one month if we have portfolio II. Find the mean and variance of Y and Z. Which has a higher mean and which has a higher variance?
d) What is the probability that I get at least my money back from portfolio I.
e) What is the probability that I get at least my money back from portfolio II.
f) Which portfolio would you choose to buy? Why?