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 he CMBS is sold at par (again, unrealistic)

a. Assume there are no defaults. Compute the PT cash flows and show that the cash flow yield is 6.5% (MEY), the McCauley duration is 8.8 years, and the average life is 13.4 years (annotate your formulae). Hint: 1. To make sure you get it right, you may want to start out pretending that the loan has a term of 30 years to check that the ending balance is zero. 2. To compute the CF yield, use the function IRR and make sure that you (a) include the t=0 CF and (b) use, say, 0.05/12 as the initial guess and then multiply the answer by 12 to get the MEY.

b. Now introduce credit risk by allowing 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.

c. Why is there generally a large fraction of outstanding principal that defaults at maturity?