Fixed Income Homework3 Hariharan Alavandan

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Apr 3, 2024

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Submitted by Hariharan Alavandan alavanhn@mail.uc.edu Class Number: 11660 Section 001 HOMEWORK 3: FIN7037 FIXED INCOME
FIN7037: Fixed Income Security Analysis Homework 2 1. a. Amortization schedule for the first 10 months Amount $100,000 Periods 360 Rate 0.8333% Payment $877.57 Months Beginning Payment Interest Principal Ending Balance 1 $100,000.00 $877.57 $833.33 $44.24 $99,955.76 2 $99,955.76 $877.57 $832.96 $44.61 $99,911.15 3 $99,911.15 $877.57 $832.59 $44.98 $99,866.18 4 $99,866.18 $877.57 $832.22 $45.35 $99,820.82 5 $99,820.82 $877.57 $831.84 $45.73 $99,775.09 6 $99,775.09 $877.57 $831.46 $46.11 $99,728.98 7 $99,728.98 $877.57 $831.07 $46.50 $99,682.48 8 $99,682.48 $877.57 $830.69 $46.88 $99,635.60 9 $99,635.60 $877.57 $830.30 $47.27 $99,588.32 10 $99,588.32 $877.57 $829.90 $47.67 $99,540.65 b . As you can see from the amortization table for the last 3 months, mortgage balance at the end of 360 th month assuming no prepayment is 0 c. Mortgage balance at the end of month 270 assuming no prepayment The remaining principle at the end of the month 270 is simply the present value of the remaining 90 months of payment of Coupon = PMT= 877.57 in 360-month payment period. So, PMT = -877.57, N = 90, I/Y = 0.8333%, FV = 0, We use financial calculator to compute PV = 55409.40. Mortgage balance at the end of month 270 assuming no prepayment = 55409.40 Month s Beginning Payment Interest Principa l Ending Balance 358 $2,589.44 $877.57 $21.58 $855.99 $1,733.45 359 $1,733.45 $877.57 $14.45 $863.13 $870.32 360 $870.32 $877.57 $7.25 $870.32 $0.00
(Note: - As explained in the partial answers, this can also be calculated by computing beginning balance for N = (90+ 1) and then subtracting respective interest from Principle payment and calculating the ending balance) 2. 1) 2-Bedroom condo in Boston. The price is $300,000. You have a 30-year 3% APR mortgage with 20% down payment N=360, I/Y= 3/12= 0.25, PV = 240,000, FV = 0, Calculating Monthly mortgage payment using financial calculator PMT = 1011.849 Monthly mortgage payment = PMT = 1011.85 2) Annual investment return on rental Using financial calculator, N = 60 (semiannual 30 years), PV = - 60,000, FV = 300,000, PMT = 0, we compute semi-annual yield = 2.718% Annual yield = Bond- equivalent yield = 2.718*2 = 5.437 3) Using financial calculator, N = 360, PV = - 60,000, PMT = 2000- 200- 1011.85= 788.15, FV = 390,000 Monthly yield = 1.3702% Semi-annual yield = (1.013702) ^ 6 = 8.51% Bond – equivalent yield = 8.51%*2 = 17.02% 3. ( Calculated from excel) a) CPR = 6%*(t/30) t < 30 months CPR = 6% t > 30 months Mont h 100% PSA 70% PSA 320% PSA     (0.7*100% PSA) (3.2*100% PSA) 1 0.002 0.0014 0.0064 4 0.008 0.0056 0.0256 9 0.018 0.0126 0.0576 27 0.054 0.0378 0.1728 40 0.06 0.042 0.192 b) (From excel) SMM = (1- ((1-CPR) ^ (1/12)) Month 100% PSA 70% PSA 320% PSA CPR SMM CPR SMM CPR SMM 1 0.002 0.01668% 0.001 4 0.01167% 0.006 4 0.05349% 4 0.008 0.06691% 0.005 6 0.04679% 0.025 6 0.21588% 9 0.018 0.15125% 0.012 6 0.10561% 0.057 6 0.49316% 27 0.054 0.46154% 0.037 8 0.32059% 0.172 8 1.56848% 40 0.060 0.51430% 0.042 0 0.35692% 0.192 0 1.76092%
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4. Original balance: $100,000,000 Pass-through rate: 9.0% WAM: 360 months WAC: 9.65% A WAM of 360 months means that the mortgages were newly originated. CPR = 6% *(1/30) = 0.2% at 100% PSA For month 1, at 165% PSA 1) To compute SMM, we start with CPR = 0.0033 (=1.65*0.2%) SMM = (1- (1 - CPR) ^ (1/12) = 0.00027542 2) N = 360; I/Y = 9.65/12; PV = -100,000,000; FV=0 Mortgage payment = PMT = 851,820 3) Interest payment of the MBS = (Beg. Balance * Pass through/12) 100,000,000* 9% /12 = 750,000 4) Interest payment of the mortgage = (WAC*outstanding mortgage balance/12) 9.65%*100,000,000/12 = 804,167 Scheduled Principal payment = 851820 – 804167 = 47,653 5) Prepayment = SMM*(100,000,000 – scheduled payment) = 27,528 6) Total Principal payment = Scheduled Principal payment + Prepayment = 75,181 7) Cash flow to MBS investor = Interest Payment of the MBS + Total Principal payment = 825,181 For month 2, at 165% PSA CPR = 6% *(2/30) = 0.4% at 100% PSA At 165 PSA, CPR = 1.65*0.4% = 0.0066 1) To compute SMM, SMM = (1- (1 - CPR) ^ (1/12) = 0.055167% = 0.00055167 2) N = 359; I/Y = 9.65/12; PV = -999,248,19; FV=0 3) Mortgage payment = PMT = 851,585 4) Interest payment of the MBS = 999,248,19* 9% /12 = 749,436 5) Interest payment of the mortgage = 9.65%*99,924,819/12=803,562 Scheduled Principal payment = 851,585 – 803,562 = 48,023 6) Prepayment = SMM*(99,924,819 – scheduled payment) = 55,099 7) Total Principal payment = Scheduled Principal payment + Prepayment = 103,122 8) Cash flow to MBS investor = Interest Payment of the MBS + Total Principal payment= 749,436 + 103122 = 852,558 Tabulating in excel, Mont h Balance SMM Mortgag e Payment Interes t Schedule d Principal Prepaymen t Total Principa l Cash Flow 1 $100,000,00 0 0.0002754 2 851,820 750,00 0 47,653 27,528 75181 825,18 1 2 $ 0.0005516 851,585 749,43 48,023 55099 103122 852,55
99,924,819 7 6 8 5. “Nobel Economics Prize Is Awarded to U.S.-Based Trio” The Nobel Prize in Economic Sciences was awarded to David Card, Joshua D. Angrist and Guido W. Imbens for their work on natural experiments, in particular their contributions to better understanding how the job market works . Their research has substantially improved the ability to answer key causal questions, which has been of great benefit to society. In one paper, Mr. Card and his co-author, Alan Krueger, looked at an increase in New Jersey’s minimum wage to $5.05 an hour from $4.25 . The two economists compared restaurants in the state and in neighboring eastern Pennsylvania and found that there was no fall in employment in the New Jersey restaurants subject to the higher minimum wage. In another experiment, Mr. Angrist compared the employment history of people who had been drafted to serve in the Vietnam War with those who had not and found that those who had been randomly selected to serve earned less in the years after their service than those who hadn’t. Mr. Imbens has studied whether people who win the lottery are more likely to stop working than those who don’t . Natural experiments differ from the laboratory experiments that physical scientist use to test their theories in that economists can’t choose the subjects that take part . The Royal Swedish Academy of Sciences said Messrs. Angrist and Imbens had advanced the understanding of the conditions under which natural experiments can help to establish causal links . They showed it is possible to estimate a well-defined causal effect of an intervention, even when the researcher cannot control who takes part in the intervention. Ratings Last Sale Issuer Name Symbol Callable Sub-Product Type Coupon Maturity Moody' s S&P Price Yield TESL A INC TSLA4474416   Corporate Bond 2.38 3/15/2022   BB 1150 -206.495 TESL A INC TSLA4530906 Yes Corporate Bond 5.30 8/15/2025 B3 NR 102.66 3.885 TESL A INC TSLA4830349   Corporate Bond 2.00 5/15/2024   BB 1430 -80.623 TESL A INC TSLA4103350   Corporate Bond 0.25 3/1/2019   NR 99.13 105.438 TESL A INC TSLA4103351   Corporate Bond 1.25 3/1/2021   NR 1039.24 -3612.92 TESL A INC TSLA4530907   Corporate Bond 5.30 8/15/2025     102.68   6. Ratings for bonds issued by Tesla from Finra Market Data Yield of the first bond Issuer Name Symbol Yield
TESLA INC TSLA4474416 -206.5 Price chart Yield chart Price of the bond increases from 100 in 2017 to 1150 in 2021 as on 04/10/2021 Yield of the bond decreases from 2.38% to -206.495% in 2021 as on 04/10/2021 As yield decreased, price of the bond increased . Negative yields happened after 2019-20 due to low interest rates , many large institutional investors were willing to pay a little over face value for high-quality bonds.
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They accepted a negative return on their investment for the safety and liquidity that high-quality government and corporate bonds offer.