Subprime Mortgage-Backed Securities

An investment bank designs CDOs backed by a pool of 1000 interest-only subprime mortgages. The principal value of each mortgage in the pool is $100,000. Suppose that the LIBOR (interest rate at which banks charge each other) is 2% and the annual interest rate at which the subprime borrowers from the pool have to pay is LIBOR + 6%. The pool is then sliced into tranches. The AAA tranche corresponds to the first $81M worth of principal of the pool and receives an interest rate of LIBOR + 10 basis points. The AAA tranche is sold at $81M. The AA tranche corresponds to the next $7M worth of principal from the pool and receives an interest rate of LIBOR + 20 basis points. The AA tranche is sold at $7M. The A tranche corresponds to the next $5M worth of principal from the pool and receives an interest rate of LIBOR + 30 basis points. The A tranche is sold at $5M. The BBB tranche corresponds to the next $5M worth of principal and receives an interest rate of LIBOR + 130 basis points. The BBB tranche is sold at $5M. The claim to the residual interest payments from the pool, after the interest paid to all the tranches, is sold to hedge funds at $5M.

a) Explain why the subprime borrowers have to pay such a high interest rate.

b) What is the amount of over-collateralization of this pool?

c) How much interest payment do the hedge funds, who buy the residual claims, get each year? What is the interest rate these hedge funds get from their investment? Why do they get such a high interest rate?

d) The investment bank has to pay the mortgage originators $2M for originating these 1000 mortgages. How much does the investment bank make for pooling and tranching these mortgages?

Now, suppose that a large financial crisis hits the economy that leads to 40% default rate. From each defaulted mortgage the banks recover 50% of the initial principal value, after all transaction costs. For simplicity suppose that the bank lends again all the recovery proceeds at the same interest rate of LIBOR + 6% and put the new lending into the pool.

e) What are the tranches remaining and the principal amounts corresponding to each remaining tranche?

f) What is the total interest the hedge funds get each year?