（Diversification of Risk through Financial Interme...

(Diversification of Risk through Financial Intermediation) In an economy, there are many independent and identically distributed 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. 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 and standard deviation of the rate of return on this investment？ 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→∞)？ d) Suppose the banks in this economy are competitive, what is maximu rate of return a bank can offer on the one-year fixed time deposit if the bank has sufficient fund to invest, i.e. N→∞ ？ e) If a risk averse investor has $10m and he can either invest in one project or buy the one-year Certificate Deposit (CD, fixed time deposit) with the maximum rate of return offered by the bank. He is risk averse, with expected utility function as , where is his consumption at the end of year 1 (the consumer may not know the value 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？ f) Suppose the project in part a) is the only type of project in this economy, and a fund manager tell you that his fund can offer you an investment opportunity with promised return of 30% in a year and no risk. Would you want to invest？ Why and why not？