# Question: there are 5 companies each sells a bond that will...

###### Question details

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?