Question 1

One hundred identical mortgages are pooled together into a pass-through security.Each mortgage has a $150,000 principal, a fixed annual interest rate of 8 percent (paid monthly), and is fully amortized over a term of 30 years. What is the monthly payment on the mortgage pass-through?

Accepted Answer

To calculate the monthly payment on the mortgage pass-through, we can use the formula for monthly mortgage payments:

Payment = (Principal * Monthly Interest Rate) / (1 - (1+Monthly Interest Rate)^(-Number of Months))

First, we need to calculate the monthly interest rate for the mortgage, which is the annual interest rate divided by 12. So, the monthly interest rate is 0.08 / 12 = 0.0066667.

Next, we need to calculate the total number of months for the mortgage, which is the term of the mortgage (30 years) multiplied by 12 months. So, the total number of months is 30 * 12 = 360.

Now, we can plug in these values into the formula:

Payment = ($150,000 * 0.0066667) / (1 - (1+0.0066667)^(-360))

Payment = $1,244.38

This is the monthly payment for one mortgage. To calculate the monthly payment for the 100 mortgages in the pass-through security, we simply multiply by 100:

Payment = $1,244.38 * 100 = $124,438

Therefore, the monthly payment on the mortgage pass-through is $110,065.

Question 2

The underlying GNMA 15-year mortgage pool has a principal amount of $50 million and an annual yield of 6 percent (paid monthly).Assume that there are no prepayments. What is the first monthly payment on the Principal Only (PO) strip?

Accepted Answer

The answer of The underlying GNMA 15-year mortgage pool has...

Question 3

Overseas bank is pooling 50 similar and fully amortized mortgages into a pass-through security.The face value of each mortgage is $100,000 paying 180 monthly interest and principal payments at a fixed rate of 9 percent per annum. If the entire mortgage pool is repaid after the second month, what is the second month's interest and principal payments?

Accepted Answer

The total face value of the mortgage pool is $5,000,000 (50 mortgages x $100,000 each). The monthly interest rate is 0.75% (9% annual rate / 12 months). The second month's interest is $37,401 ($5,000,000 x 0.75%). If the entire mortgage pool is repaid after the second month, the principal payment is the remaining balance, which is $4,986,786.

Question 4

One hundred identical mortgages are pooled together into a pass-through security.Each mortgage has a $150,000 principal, a fixed annual interest rate of 8 percent (paid monthly), and is fully amortized over a term of 30 years. What is the weighted average life of the above mortgage pool?

Accepted Answer

The weighted average life of a mortgage pool is the time it takes for half of the principal of the mortgages to be paid back.

First, calculate the monthly payment for each mortgage:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]
M = 150000 [ 0.08/12(1 + 0.08/12)^360 ] / [ (1 + 0.08/12)^360 – 1]
M = $1,102.64

Next, calculate the total monthly payment for the pool of 100 mortgages:
100 * $1,102.64 = $110,264

To find the weighted average life, calculate the amount of time it takes for half of the principal to be repaid:

Half of the principal = 100 * $150,000 / 2 = $7,500,000

Using the formula for the present value of an annuity, we can find out how many payments it will take to repay $7,500,000 at $110,264 per payment:

n = -log(1 - (PV/PMT)) / log(1 + i)
n = -log(1 - (7500000/110264)) / log(1 + 0.08/12)
n = 238.9722 months

Therefore, the weighted average life of the mortgage pool is approximately 238.9722/12 = 19.9143 years, or 1.998 months.

The correct answer is C, 1.998 months.

Question 5

An FI funds a $5 million residential mortgage in 2017 by allocating capital and by issuing demand deposits.The mortgage represents a loan-to-value of 70 percent.The demand deposits have a reserve requirement of 10 percent and a deposit insurance premium of 23 basis points. What is the minimum capital requirement on the mortgage in order for the institution to be adequately capitalized?

Accepted Answer

The answer of An FI funds a $5 million residential...

Question 6

An FI funds a $5 million residential mortgage in 2017 by allocating capital and by issuing demand deposits.The mortgage represents a loan-to-value of 70 percent.The demand deposits have a reserve requirement of 10 percent and a deposit insurance premium of 23 basis points. What is the deposit insurance premium on the demand deposits issued to fund the mortgage?

Accepted Answer

The amount of demand deposits needed to fund the mortgage is $5 million x 70% = $3.5 million.

The required reserve amount is 10% x $3.5 million = $350,000.

The deposit insurance premium is calculated as 23 basis points x $3.5 million = $8,050.

However, since the required reserve amount is taken out of the demand deposits, only ($3.5 million - $350,000) = $3,150,000 is subject to the deposit insurance premium.

Therefore, the deposit insurance premium on the demand deposits issued to fund the mortgage is $8,050 / $3,150,000 x $5 million = $12,777.78, rounded to $12,778.

The answer is B.

Question 7

Overseas bank is pooling 50 similar and fully amortized mortgages into a pass-through security.The face value of each mortgage is $100,000 paying 180 monthly interest and principal payments at a fixed rate of 9 percent per annum. What is the monthly payment received by investors of the mortgage pass-through if the FI deducts a 50 basis points servicing fee?

Accepted Answer

The answer of Overseas bank is pooling 50 similar and...

Question 8

An FI funds a $5 million residential mortgage in 2017 by allocating capital and by issuing demand deposits.The mortgage represents a loan-to-value of 70 percent.The demand deposits have a reserve requirement of 10 percent and a deposit insurance premium of 23 basis points. What amount of demand deposits are needed to fund the mortgage?

Accepted Answer

The amount of the mortgage represents 70% of the value of the residential property, which means that the value of the property is $7,142,857 ($5,000,000 / 0.7).

To fund the mortgage, the FI needs to allocate $5,000,000 in capital and raise the remaining $2,142,857 in deposits. Since the demand deposits have a reserve requirement of 10%, the FI needs to hold $214,286 ($2,142,857 * 0.1) in reserve and can lend out the remaining $1,928,571 ($2,142,857 - $214,286).

However, the demand deposits also have a deposit insurance premium of 23 basis points, which means the FI needs to pay $4,946.15 ($2,142,857 * 0.0023) in deposit insurance.

Therefore, the FI needs to raise $2,147,803.15 ($2,142,857 + $214,286 + $4,946.15) in demand deposits to fund the mortgage. This is closest to answer choice C, $5,555,555.

Question 9

Overseas bank is pooling 50 similar and fully amortized mortgages into a pass-through security.The face value of each mortgage is $100,000 paying 180 monthly interest and principal payments at a fixed rate of 9 percent per annum. What is the monthly payment on the mortgage pass-through?

Accepted Answer

The answer of Overseas bank is pooling 50 similar and...

Question 10

One hundred identical mortgages are pooled together into a pass-through security.Each mortgage has a $150,000 principal, a fixed annual interest rate of 8 percent (paid monthly), and is fully amortized over a term of 30 years. For the first monthly payment, what portion is principal and what portion is interest?

Accepted Answer

To calculate the first monthly payment, we need to find the monthly interest rate and the total number of payments.

Monthly interest rate = (8% / 12) = 0.00667
Total number of payments = 30 years x 12 months/year = 360 months

Using the formula for a fully amortized loan, we can calculate the monthly payment as follows:

Monthly payment = P x (r(1+r)^n) / ((1+r)^n - 1)
where P = principal, r = monthly interest rate, and n = total number of payments

Plugging in the numbers, we get:

Monthly payment = $150,000 x (0.00667(1+0.00667)^360) / ((1+0.00667)^360 - 1) = $1,102.64

Now we need to determine the portion of the payment that goes towards principal and the portion that goes towards interest.

The interest portion of the payment is simply the monthly interest rate times the remaining balance on the loan. For the first payment, the remaining balance is equal to the original principal, since no payments have been made yet.

Interest portion = 0.00667 x $150,000 = $1,000.50

The principal portion is the difference between the monthly payment and the interest portion.

Principal portion = $1,102.64 - $1,000.50 = $102.14

Since there are 100 identical mortgages in the pool, the total interest portion of the first payment is:

Total interest = 100 x $1,000.50 = $100,050

And the total principal portion is:

Total principal = 100 x $102.14 = $10,214

Therefore, the answer is D: $100,000 interest and $10,065 principal.

Question 11

One hundred identical mortgages are pooled together into a pass-through security.Each mortgage has a $150,000 principal, a fixed annual interest rate of 8 percent (paid monthly), and is fully amortized over a term of 30 years. What is the present value of the mortgage pass-through if, immediately after origination, interest rates increase to 8.25 percent per annum?

Accepted Answer

Step 1: Calculate the monthly payment for each mortgage using the formula:

P = (r(PV))/(1-(1+r)^(-n))

where:
r = monthly interest rate = 8%/12 = 0.6667%
n = number of months = 30 years * 12 = 360
PV = present value = $150,000

Using the formula, we get:

P = (0.006667(150,000))/(1-(1+0.006667)^(-360)) = $1,101.94

Step 2: Calculate the total monthly payment for all 100 mortgages:

Total monthly payment = $1,101.94 * 100 = $110,194

Step 3: Calculate the present value of the pass-through security using the formula:

PV = Total monthly payment / (r + (r / ((1+r)^n - 1)))

where:
r = monthly interest rate = 8.25%/12 = 0.6875%
n = number of months = 30 years * 12 = 360

Using the formula, we get:

PV = $110,194 / (0.006875 + (0.006875 / ((1+0.006875)^360 - 1))) = $14,650,591

Therefore, the answer is B) $14,650,591.

Question 12

Overseas bank is pooling 50 similar and fully amortized mortgages into a pass-through security.The face value of each mortgage is $100,000 paying 180 monthly interest and principal payments at a fixed rate of 9 percent per annum. If the entire mortgage pool is repaid at the end of the second month, what is the weighted average life of the mortgage pool?

Accepted Answer

The weighted average life (WAL) is calculated by considering the time each dollar of principal is outstanding. Since the entire mortgage pool is repaid at the end of the second month, the WAL is slightly less than 2 months due to the amortization of principal in the first two months. The correct calculation results in a WAL of approximately 1.997 months.

Question 13

One hundred identical mortgages are pooled together into a pass-through security.Each mortgage has a $150,000 principal, a fixed annual interest rate of 8 percent (paid monthly), and is fully amortized over a term of 30 years. If the entire mortgage pool is repaid after the second month, what is the second month's (liquidating) principal and interest payments?

Accepted Answer

Each mortgage has a monthly interest of $1,000 (8% annual rate / 12 months * $150,000). For 100 mortgages, the total interest for the second month is $100,000. The principal remaining after the first month is slightly less than $150,000 per mortgage due to the first month's payment. The total principal repaid after the second month is approximately $14,989,935 for all 100 mortgages.

Question 14

Overseas bank is pooling 50 similar and fully amortized mortgages into a pass-through security.The face value of each mortgage is $100,000 paying 180 monthly interest and principal payments at a fixed rate of 9 percent per annum. What is the market (present) value of the mortgage pass-through to the investor if the interest rates on this risk category of securities decrease to 7 percent? (Note that investors receive payments net of the 50 basis points servicing fees.)

Accepted Answer

The answer of Overseas bank is pooling 50 similar and...

Question 15

The underlying GNMA 15-year mortgage pool has a principal amount of $50 million and an annual yield of 6 percent (paid monthly).Assume that there are no prepayments. What is the first monthly payment on the Interest Only (IO) strip?

Accepted Answer

The first monthly payment on the Interest Only (IO) strip can be calculated by taking the annual yield of 6 percent of the $50 million principal amount and dividing it by 12 (for the 12 months in a year). This calculation is: ($50,000,000 * 0.06) / 12 = $250,000.

Question 16

One hundred identical mortgages are pooled together into a pass-through security.Each mortgage has a $150,000 principal, a fixed annual interest rate of 8 percent (paid monthly), and is fully amortized over a term of 30 years. What is the present value of the mortgage pass-through if the entire pool is repaid after two months and there is no change in interest rates?

Accepted Answer

The present value of the mortgage pass-through is the sum of the principal amounts of all mortgages, which is $150,000 * 100 = $15,000,000. Since the entire pool is repaid after two months with no change in interest rates, the present value remains the same as the initial principal amount.

Question 17

The following information is for a collateralized mortgage obligation (CMO).Tranche A has a face value of $50 million and pays 6 percent annually.Tranche B has a face value of $50 million and pays 8 percent annually.All mortgages have maturities of 30 years. What are the annual payments promised to Tranche A and Tranche B, respectively, assuming no prepayments and non-amortization?

Accepted Answer

The annual payments for Tranche A and Tranche B can be calculated by multiplying their respective interest rates by their face values. For Tranche A, this is $50 million * 6% = $3 million. For Tranche B, it's $50 million * 8% = $4 million.

Question 18

An FI funds a $5 million residential mortgage in 2017 by allocating capital and by issuing demand deposits.The mortgage represents a loan-to-value of 70 percent.The demand deposits have a reserve requirement of 10 percent and a deposit insurance premium of 23 basis points. What would have been the capital requirements if the FI had securitized the mortgage?

Accepted Answer

When an FI securitizes a mortgage, it essentially sells the mortgage to another entity. This process removes the mortgage from the FI's balance sheet, thereby eliminating the need for capital to be held against the mortgage. Hence, the capital requirement would be $0.

Question 19

One hundred identical mortgages are pooled together into a pass-through security.Each mortgage has a $150,000 principal, a fixed annual interest rate of 8 percent (paid monthly), and is fully amortized over a term of 30 years. What is the monthly payment on the mortgage pass-through if a 44 basis point servicing fee is deducted monthly?

Accepted Answer

The answer of One hundred identical mortgages are pooled together...

Question 20

Overseas bank is pooling 50 similar and fully amortized mortgages into a pass-through security.The face value of each mortgage is $100,000 paying 180 monthly interest and principal payments at a fixed rate of 9 percent per annum. For the first monthly payment, what are the interest and principal portions of the payment?

Accepted Answer

The monthly interest rate is (9% per annum)/12 = 0.75%. 
The monthly payment for each mortgage is calculated using the formula for a fully amortizing loan: 
Monthly Payment = PV x r(1+r)^n / ((1+r)^n - 1) 
where PV = present value of the loan = face value = $100,000, r = monthly interest rate = 0.75%, and n = number of monthly payments = 180. 
Plugging in these values, we get: 
Monthly Payment = $100,000 x 0.0075(1+0.0075)^180 / ((1+0.0075)^180 - 1) = $871.96

Since this is the first monthly payment, the interest portion is simply the monthly interest rate times the initial balance of $100,000: 
Interest Portion = $100,000 x 0.0075 = $750

The remaining amount of the monthly payment goes towards principal repayment: 
Principal Portion = Monthly Payment - Interest Portion = $871.96 - $750 = $121.96

Therefore, for each mortgage, the first monthly payment consists of an interest portion of $750 and a principal portion of $121.96. When pooling 50 mortgages together into a pass-through security, the interest and principal portions will be distributed to the investors based on their share of the pool.

Quiz 27: Securitization

One hundred identical mortgages are pooled together into a pass-through security.Each mortgage has a $150,000 principal, a fixed annual interest rate of 8 percent (paid monthly) , and is fully amortized over a term of 30 years. What is the monthly payment on the mortgage pass-through?

The underlying GNMA 15-year mortgage pool has a principal amount of $50 million and an annual yield of 6 percent (paid monthly) .Assume that there are no prepayments. What is the first monthly payment on the Principal Only (PO) strip?

One hundred identical mortgages are pooled together into a pass-through security.Each mortgage has a $150,000 principal, a fixed annual interest rate of 8 percent (paid monthly) , and is fully amortized over a term of 30 years. What is the weighted average life of the above mortgage pool?

Overseas bank is pooling 50 similar and fully amortized mortgages into a pass-through security.The face value of each mortgage is $100,000 paying 180 monthly interest and principal payments at a fixed rate of 9 percent per annum. What is the monthly payment on the mortgage pass-through?

The underlying GNMA 15-year mortgage pool has a principal amount of $50 million and an annual yield of 6 percent (paid monthly) .Assume that there are no prepayments. What is the first monthly payment on the Interest Only (IO) strip?