FIN $6550$

Homework $4$

Consider a $$600,000,000$ mortgage pool consisting of $60$ mortgages of $$10,000,000$ each. Each

mortgage is an interest$-$only loan at a $7\%$ loan interest rate with a balloon payment at the end of $3$

years and a loan to value ratio of $75\%.$ Twenty loans mature in one year, twenty loans mature in

two years, and twenty loans mature in $3$ years. No prepayment is allowed.

The mortgage pool has been securitized into three tranches of Commercial Mortgage Backed

Securities. Tranche $A$ is the senior tranche that is rated as investment grade with par value of

$$450,000,000$ and a $7\mathrm{.}5\%$ coupon rate. Tranche A has $30\%$ credit support. Tranche $B$ is the junior

tranche and is rated as non$-$investment grade; tranche B has $$150,000,000$ par value and a $12\%$

coupon rate. Tranche $x$ is an interest only tranche that is senior for interest only with a notional par

value of $$100,000,000,$ a $2\%$ coupon in Year $1,$ a $1\mathrm{.}5\%$ coupon in Year $2,$ and a $1\%$ coupon in Year $3.$

Currently, the YTM for A is $8\%,$ the YTM for B is $15\%,$ and the YTM for X is $9\%.$

$1.$ Calculate the scheduled $($ex ante$)$ cash flows $($principal$,$ interest, and total$)$ for $A,B,$ and $x$ for

Years $1,2,$ and $3.$

$2.$ Calculate the Weighted Average Maturity $($WAM$)$ for A$,$ B$,$ and X$.$

$3.$ Calculate the price $($value$)$ for A$,$ B$,$ and C$.$ Compare the sum of the values of the tranches to

the value of the mortgage pool. Is there added value? If so$,$ how much added value exists?

$4.$ Suppose that two of the loans that are supposed to mature in Year $3$ default and do not pay

interest or principal in Year $3.$ Otherwise, all loans perform. Calculate the actual $($ex post$)$ cash

flows $($principal$,$ interest, and total$)$ for A$,$ B$,$ and X for Years $1,2,$ and

$5.$ Suppose that investors pay the prices calculated in #$3$ at the start of the investment but actually

receive the cash flows from #$4$ due to the projected credit losses. What rate of return will the

investor earn for A$?$ For B$?$ For X$?$ Compare the actual $($calculated ROR$)$ to the original YTM$.$