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account_balance_wallet $15 Question description 1. [10pts] Consider the following bond (assume: credit risk free, no embedded options, pays interest semiannually):  Coupon 9% YTM 8% Term (yrs) 5 Par 100.00 Compute the following • [1pt] The price value of a basis point; • [4pts] The modified duration and convexity; • [1pt] Calculate the exact price change for a 100bp increase in the bond yield; • [1pts] Using duration only, estimate the price of the bond for a 100bp increase in yields; [1pts] Using duration and convexity, estimate the price change of the bond for a 100bp increase in Due: May 31 (a) (b) (c) (d) (e) (f) 1. [10pts] Consider the following bond (assume: credit risk free, no embedded options, pays interest semiannually): Coupon 9% YTM 8% Term (yrs) 5 Par 100.00 Compute the following [1pt] The price value of a basis point; [4pts] The modified duration and convexity; [1pt] Calculate the exact price change for a 100bp increase in the bond yield; [1pts] Using duration only, estimate the price of the bond for a 100bp increase in yields; [1pts] Using duration and convexity, estimate the price change of the bond for a 100bp increase in yields; [2pts] Without an actual calculation, indicate (“explain”) whether the duration of the bond would be higher or lower if the YTM were 10%, rather than 8%. Hint: recall that the price-yield curve is convex for risk- and option-free bonds Also, think in terms of Macauley duration as a weighted time average. 2. [10pts] Stratify the following Agency mortgages at a deal coupon of 4%. What are the initial pool, passthrough, and PO principal amounts, and what are the initial notional principal and coupon of the IO? Gross 4.10% 4.20% 4.30% 4.40% Net 3.852% 3.934% 4.071% 4.153% Balance (mln$) 50.343 101.435 123.777 40.123 3. [20pts] a. [18pts] Consider a 100,000,000 CMBS pass-through (PT) security consisting of fresh 15-year fixed rate loans that would fully amortize over a period of 30 years, and have a WAC of 7%, with fees amounting to 0.5%. For purposes of this HW, a CMBS is like a RMBS, except that all loans have a prepayment lock-out (e.g., defeasance, assume for the entire term), but default occurs according to the standard residential SDA function. Additionally, since the loans do not fully amortize, there is generally a balloon loss - quoted as a fraction of the outstanding balance at mortgage maturity. Assume that the PT is sold at 94.345. Allow for loans to default at the PSA’s SDA CDR, and allow for balloon risk. The current (corresponding maturity) Treasury yield is 5%. Create a table and graph of the spread (in bps) of cash flow yield to Treasury versus SDA, for 0% and 10% balloon loss. In the spreadsheet that you hand-in, show the situation for 100 SDA and 10% balloon loss. See notes below for further assumptions and hints. b. [2pts] Why is there generally a large fraction of outstanding principal that defaults at maturity? Notes for question 3: 1. Note that there is no messy tranching going on here; it is pass-through. 2. Allow for a general SDA; see the graph and spreadsheet in your lecture notes. 3. Here is one way to get the CDR (as there are better versions, feel free to use your own, extra points if you can show me that the formula below is wrong); “A13” refers to the month and “SDA” to the SDA factor: =(IF(A13<=30,A13*0.006/30,0)+IF(AND(A13>30,A13<=60),0.006,0)+IF(AND(A13>60,A13<=120),0.0 06-(0.006-0.0003)/(120-60)*(A13-60),0)+IF(A13>120,0.0003,0))*SDA/100 4. Assume that loss recovery is zero – any loan that defaults is a completely written down. 5. Defaults work much like prepayment, with one exception: the monthly default happens just before the payment (why pay interest and principal if you are defaulting anyway). So, take default = beginning balance × MDR and then amortize the “non-defaulted” balance over the remaining number of payments to get the realized “mortgage payment.” 6. Make sure you create a column of the PT cash flows, including the initial investment, so that you can calculate the CF yield. 7. Balloon losses are quoted as a fraction of the final outstanding principal. 8. In your graph, show a range of SDA’s of 0 to 1,000. You will find that you do not have to compute very many values in that range. 9. Display all cash flows to the nearest dollar (use format → cell). 4. [30pts] Consider a 1,000,000 (for convenience) GNMA pass-through security consisting of fresh 30-year fixed rate, fully amortizing mortgages, with a WAC of 7%, and servicing/guarantee fees totaling 0.5%. Allow for a general PSA prepayment rate. a. [10 pts] Construct an IO/PO stripped MBS from this MPT above, showing the total cash flows to investors of each piece. For simplicity, price each piece so that the IRR at PSA 165 equals the MPT coupon. You must show your amortization table at a 165 PSA. b. [15 pts] Suppose you bought the tranches at the rice obtained in part a., but that mortgage rates (MR) suddenly change just after the purchase (just after t=0). Make a graph of the market value of the MPT and each piece as the MR varies from 2% to 12% in steps of 1%. To simplify, use MR less fees as the discount rate (DR) in your calculation. Also, to make things a little more realistic, assume that prepayment PSA changes with MR as PSA = 165*max(1,WAC/MR). Hand in your amortization table for the case when MR=7%. c. [5pts] Explain the shape of each of the three curves you obtain in part b.

TutorJustene
School: Carnegie Mellon University

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Environmental Science
SOLUTION 1.

Environmental Science

F,
YTM is the return that investor can realize if the bond is held till maturity. If a person sells
the bond before maturity, he generally ensures that YTM is realized. Thus he will observe
whether price in the market is at least equal to the total present value of cash flow from
bond. Use YTM in calculating this total present value. Thus price should be the sum of the
present value of coupon receivable in remaining period of bond plus amount receivable
on maturity.
Here Coupon is 9%, YTM=8% Par value =100. So price is expectedP=\frac{9}{1.08}+\frac{9}{1.08^2}+..............+\frac{9}{1.08^5}+\frac{100}{1.08^5}

Environmental Science
As the YTM is lower than coupon rate, bond is more attractive own. It should be sold at a
price higher than face value. Note that 9% is appearing in emulator and 8% is appearing in
denominator. So P must be high. As stated in the p...

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Anonymous
Top quality work from this guy! I'll be back!

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