Suppose $10 million mortgages of 5 years, 11% fixed interest rate have been pooled as security for an issue of 50 pass-through securities. The mortgages require annual mortgage payments. The mortgage bank that issues the pass-through will charge 1% servicing fee.

According to the past experience of the mortgage bank, if the market interest rate falls within 2 percent, the mortgage borrowers will prepay at the rate of 100% PSA. However, if market interest rate falls by more than 2 percent up to 6 percent, the prepayment rate will double to 200% PSA. If interest rate falls by more than 6%, prepayment will increase to 500% PSA. (100% PSA: 2%, 4%, 6%, 6%, 6%)

(a) Determine the pricing function of the mortgage pass-through securities for market interest rate ranging from 0% to 20%. (Hint: You have to solve the net pass-through rate yourself before considering prepayment level among different ranges of interest rates; you may use equations or words to describe the pricing function, depending on your own decision.)

(b) Plot a graph of value of mortgage pass-through securities against market interest rate.

(c) Compare the price of the pass-through with the price of a special 5-year mortgage-backed bond that guarantees 5 annual bond payments and that the annual bond payments are set equal to the mortgage payments without prepayment. (Hint: You may describe the differences between the two verbally or graphically using the range of interest rate from 0%-20%, whichever way you prefer. But you are NOT required to calculate an exact price of the 5-year MBB, given that the market interest rate/discount rate is not provided in the question.)

2588 2596 2605 2615 2 Value of Mortgage-Pass Throughs Value of,MPT (0%) + 08000 2861 2778 2447 Value Of MPT (100%) = 2788 258,000 Mort Pocl 10,000,000.00 208,000 Morgage Hate me to Maturity Years Sarvicina For 47851 4339 134a 50 51454 47629 23987 108,000 Value 0%PSA 58000 391733 VALUE 0% 5% 19% Market Interest Rate No Pr ment 0%PSA Year Pool BalancelP Total PMTs Sevice Fees PMTs 10 Inwestors PMT per Share Market Interst Rane Value 0% PSA Value with Prop yment $8,394,296.90 $8,811,968.47 50.00 $2,705,703.10 32,705,703.10 50,000.00 S0.CO $2,705,703.10 $2,705,703.10 $41,97148 50.00 $2,705,703.10 52,705,703.10 $33,059.83 S0.00 $2,706,703.10 32,706,703.10$23,167.90 S0.CO $2,705,703.10 $2,705,703.10$12,187 85 52,655,703.10 $2,883,731.61 52,672,643.26 $2,682,535.20 52.693.515.24 553,114.06 $53.274.83 553,452.87 63,860.70 29,B07 248,854 242 15 235747 222,60 $4,633,579.69 231,430 nt Rate(1% PS Poal BalanceP Total PMTs Service Fees PMTs to Ivestars PMT 213,388 510,000,000.00 207,432 202 422 S8,194,298.90 $200.000.00 2,705,703.10 $2,905,703.10$50,00000 $2,855,703.10 52,328,038.22 52,844,075.58 367.114.06 $58,560.76 556,881.51 202,SET 6,00% $1,429,722.23 $235,553.01 $2,292,455.52 $2,528,008.83$19,829.42 59,148.61 188543 $0.00 50.00 $2,030,991.67 $2,030,991.67 52,021,843.06 540,436.86 Upper Limit of Prepayment Rate Year Pool Balance Prepayment Mortgage PM Total PM Service Fe8s PMTs to Investors PMT 188,630 $10,000,000.00 $6,611,966.47 $4,833.579.89 $2,437,570.36 $0.00 $0.00 $2,TOS,TO3.10 $2,705,703.10$50,o0.a0 50.00 $2,705,703.10 $2,705,703.10 41,971.48 S0.CO $2,705,703.10 $2,705,703.10$33,069.43 50.00 $2,705,703.10 $2,05,703.10 $23,167.90 S0.00 $2,705,703.10 $2,706,703.10 $12,18786 52,663,731.61 $2,672,843.28 52,682,535.20 S2,693,516.24363,870.30 553,274.63 63,452.4T 553,550.70 2588 2596 2605 2615 2 Value of Mortgage-Pass Throughs Value of,MPT (0%) + 08000 2861 2778 2447 Value Of MPT (100%) = 2788 258,000 Mort Pocl 10,000,000.00 208,000 Morgage Hate me to Maturity Years Sarvicina For 47851 4339 134a 50 51454 47629 23987 108,000 Value 0%PSA 58000 391733 VALUE 0% 5% 19% Market Interest Rate No Pr ment 0%PSA Year Pool BalancelP Total PMTs Sevice Fees PMTs 10 Inwestors PMT per Share Market Interst Rane Value 0% PSA Value with Prop yment $8,394,296.90 $8,811,968.47 50.00 $2,705,703.10 32,705,703.10 50,000.00 S0.CO $2,705,703.10 $2,705,703.10 $41,97148 50.00 $2,705,703.10 52,705,703.10 $33,059.83 S0.00 $2,706,703.10 32,706,703.10$23,167.90 S0.CO $2,705,703.10 $2,705,703.10$12,187 85 52,655,703.10 $2,883,731.61 52,672,643.26 $2,682,535.20 52.693.515.24 553,114.06 $53.274.83 553,452.87 63,860.70 29,B07 248,854 242 15 235747 222,60 $4,633,579.69 231,430 nt Rate(1% PS Poal BalanceP Total PMTs Service Fees PMTs to Ivestars PMT 213,388 510,000,000.00 207,432 202 422 S8,194,298.90 $200.000.00 2,705,703.10 $2,905,703.10$50,00000 $2,855,703.10 52,328,038.22 52,844,075.58 367.114.06 $58,560.76 556,881.51 202,SET 6,00% $1,429,722.23 $235,553.01 $2,292,455.52 $2,528,008.83$19,829.42 59,148.61 188543 $0.00 50.00 $2,030,991.67 $2,030,991.67 52,021,843.06 540,436.86 Upper Limit of Prepayment Rate Year Pool Balance Prepayment Mortgage PM Total PM Service Fe8s PMTs to Investors PMT 188,630 $10,000,000.00 $6,611,966.47 $4,833.579.89 $2,437,570.36 $0.00 $0.00 $2,TOS,TO3.10 $2,705,703.10$50,o0.a0 50.00 $2,705,703.10 $2,705,703.10 41,971.48 S0.CO $2,705,703.10 $2,705,703.10$33,069.43 50.00 $2,705,703.10 $2,05,703.10 $23,167.90 S0.00 $2,705,703.10 $2,706,703.10 $12,18786 52,663,731.61 $2,672,843.28 52,682,535.20 S2,693,516.24363,870.30 553,274.63 63,452.4T 553,550.70