Subprime Mortgage-Backed Securities An investment bank designs CDOs backed by a
ID: 2753333 • Letter: S
Question
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?
Explanation / Answer
Subprime borrowers are charged higher rate of interests because they generally have a below-average credit history and are thus penalized for their poor credit with higher interest rates. The term subprime refers to the credit quality of particular borrowers. Subprime borrowers may qualify only for higher-interest mortgages. Subprime borrowers may have an extensive history of late or missed payments, default debt, excessive debt or no property assets that could be used as security
Ans b) Over collaterization is the collateral amount in excess of loan amount.
Principal $100,000,000
CDO
AAA
81,000,000
AA
7,000,000
A
5,000,000
BBB
5,000,000
Total
98,000,000
Over Collaterization
2,000,000
Ans c)
Interest rate
Interest Amount
AAA
81,000,000
2.1
1701000
AA
7,000,000
2.2
154000
A
5,000,000
2.3
115000
BBB
5,000,000
3.3
165000
98,000,000
2,135,000
Total interest received from subprime borrowers = LIBOR +6% =8% * 100,000,000 = 8,000,000
Total residual interest = 8,000,000 – 2,135,000 = $5,865,000
Hedge fund paid 5,000,000, so interest of 865,000 on $5,000,000
= 865,000/5,000,000 = 17.3 %
They get such high rate of interest because they are bearing very high risk of default.
Ans d) Investment bank income
Outflow = $2,135,000 + $865,000 + 2,000,000 (originator fee) = $5,000,000
Inflow = $8,000,000, thus investment banker’s income = 3,000,000
And d)
After default
AAA
81,000,000
40,500,000
3,240,000
AA
7,000,000
3,500,000
280,000
A
5,000,000
2,500,000
200,000
BBB
5,000,000
2,500,000
200,000
Total
12,550,000
3,920,000
Total interest received = 8% of 50,000,000 = 4,000,000
f) Hedge fund receives $865,000
=$80,000 (in scenario d)
AAA
81,000,000
AA
7,000,000
A
5,000,000
BBB
5,000,000
Total
98,000,000
Over Collaterization
2,000,000