Question: How would you do question d) and e)?

1) In an economy, there are many identically distributed and independent projects, that is, each project requires $10m of investment and pays back in a year of either $15m with probability 90% or $0m (fails) with probability 10%, while the payout of each project does not depend on the payout of other projects.

1. (Diversification of Risk through Financial Intermediation) In an economy, there are many identically distributed and independent projects, that is, each project requires $10m of investment and pays back in a year of either $15m with probability 90% or $0m (fails) with probability 10%, while the payout of each project does not depend on the payout of other projects.

a) What is the expected rate of return on each project, what is the standard deviation of rate of return? Note: The rate of return refers to net rate of return.

Answer ROR = 35%

Std deviation = sqrt (0.9 (0.5-0.35)^2 + 0.1(-1-0.35)^2)

b) Suppose a bank is to invest in two such projects, what is the payout structure of the investment? That is, lay out the possible outcomes and the probability of each outcome. What is the mean rate of return on this investment?

Answer: 30m with p=0.81 15m with p=0.18 0m with p=0.01

Net ROR = 35%

c) What is the mean and standard deviation of the rate of return if a bank is to investment in N projects? What happens if N goes to infinity (N)?

Answer: When N goes to infinity, risk goes down, std = 0

d) Suppose the asset of a bank is many such projects (N), and the secondary security this bank offers to its customers is a one-year CD with fixed return 1 + r, what is the maximum rate of return r a competitive bank can offer? Ignore the operational cost and other costs

e) If an investor has $10m and he can either invest in one project or buy the one-year CD with the maximum rate of return offered by the bank. He is risk averse, with expected utility function as: Eu(c ) = E(20c - 0.5c^2 ) , where c is his consumption at the end of year 1, uncertain at the beginning of the year. Suppose he will only consume at the end of year one and will consume whatever he has at that time. At the beginning of the year, will he invest in CD or the project to maximize his expected utility?