HW4
FOR ANY SPREADSHEET, YOU MUST HIDE REPETITIVE ROWS THAT DO NOT ILLUSTRATE ANYTHING SUBSTANTIALLY NEW. Do not make any one spreadsheet printout more than 2 pages max (you will generally need only one). Do not continue table columns across several pages (best to print in landscape mode). FAILURE TO DO ALL THIS WILL RESULT IN A LOSS OF FIVE (5) POINTS. 41 points total.
ANNOTATE any formulae that involve more than addition and subtraction (e.g., using a pen or Office’s comment feature – just one period will suffice, of course)
- [22pts]
- [20pts] Consider a 100,000,000 CMBS pass-through (PT) security consisting of fresh 15 year fixed rate loans that 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 (assume for the entire term), but default occurs according to the standard 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. To simplify, assume that there is no recovery (unrealistic, of course). 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. Use par pricing. See notes below for further assumptions and hints.
- [2pts] Why is there generally a large fraction of outstanding principal that defaults at maturity?
- [8pts] Consider the following par yield curve for semiannual bonds, all quoted as BEY:
- [6pts] What are the corresponding zero rates?
- [2pts] What is today’s lockable rate for a 6 month loan 1 year from now?
- [10pts] Stratify the following Agency mortgages at a deal coupon of 4%. What are the initial pool and PO principals, and what are the initial notional principal and coupon of the IO?
Maturity [yr] |
Par Yield |
0.5 |
1% |
1 |
2% |
1.5 |
3% |
Gross |
Net |
Balance (mln $) |
4.10% |
3.852% |
50.343 |
4.20% |
3.934% |
101.435 |
4.30% |
4.071% |
123.777 |
4.40% |
4.153% |
40.123 |
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Notes for question 1:
- Note that there is no messy tranching going on here.
- Allow for a general SDA; see the graph and spreadsheet in your lecture notes.
- 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),0.006-(0.006-0.0003)/(120-60)*(A13-60),0)+IF(A13>120,0.0003,0))*SDA/100
- Assume that loss recovery is zero – any loan that defaults is a completely written down.
- 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 apply the appropriate pool survival factor to get the realized “mortgage payment.”
- Make sure you create a column of the PT cash flows, including the initial investment at par, so that you can calculate the CF yield.
- Balloon losses are quoted as a fraction of the final outstanding principal.
- 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.
- Display all cash flows to the nearest dollar (use format → cell).