Question

An investor is considering the purchase of either an IO or PO strip from a CMO offering. The portion of the mortgage pool backing this tranche consists of $1,000,000 in mortgages with a remaining maturity of 10 years and an 8 percent interest rate.

a. Assuming annual payments and a zero prepayment rate, prepare a schedule showing the IO and PO cash flows that would be payable to investors in this tranche. If the interest rate demanded by investors on this investment is also 8 percent, what would be the prices of the IO and PO strips?

b. If interest rates increased to 10 percent and prepayments remained at a zero rate, how would the price of the IO and PO strips change? Which security, the IO or PO, exhibits the greatest price change from (a)? Why?

c. Investor interest rates now decline to 6 percent. What is the price of the IO? PO? Prepayments now increase to a rate of 20 percent per year because mortgage borrowers in the pool begin to refinance at lower interest rates. What would prices for the IO and PO be now? (Assume that the 20 percent prepayment received at the end of each year is based on the outstanding loan balances at the end of the preceding year.) Which security, the IO or PO, exhibits the greatest change in price when compared to (a) and (b) above? Why? What does this pattern suggest about the relative risk of each security?

Answer 1

(a)

Beginning Balance                            =                           $1,000,000

Prepayment Rate                              =                                        0.00

Interest Rate                                      =                                        0.08

 

	Beginning	Interest	Principal	PO	Ending
Period	Balance	IO/Strip	PO/Strip	Prepayment	Balance
1	$1,000,000	$80,000	$69,029	$0	$930,971
2	930,971	74,478	74,552	0	856,419
3	856,419	68,513	80,516	0	775,903
4	775,903	62,072	86,957	0	688,945
5	688,945	55,116	93,914	0	595,032
6	595,032	47,603	101,427	0	493,605
7	493,605	39,488	109,541	0	384,063
8	384,063	30,725	118,304	0	265,759
9	265,759	21,261	127,769	0	137,990
10	137,990	11,039	137,990	0	0

 

The price of the IO and PO strips is the PV of the cash flows at 8%

 

	IO/Strip	PO/Strip
PV/Price at 8%	$360,838	$639,162

 

(b)

If interest rates increase to 10% then the price of the IO and PO is the PV of the respective cash flows at 10%

 

	IO/Strip	PO/Strip
PV/Price at 10%	$337,113	$578,608

 

The percentage change in the IO and PO price is:

 

	IO/Strip	PO/Strip
% change in price	-6.57%	-9.47%

 

The PO strip has the greatest change in price which demonstrates it has greater amounts of convexity than the IO

 

(c)

Cash flow schedule at 0% prepayment

Beginning Balance                            =                             $1,000,000

Prepayment Rate                              =                                        0.00

Interest Rate                                      =                                        0.08

 

	Beginning	Interest	Principal	PO	Ending
Period	Balance	IO/Strip	PO/Strip	Prepayment	Balance
1	$1,000,000	$80,000	$69,029	$0	$930,971
2	930,971	74,478	74,552	0	856,419
3	856,419	68,513	80,516	0	775,903
4	775,903	62,072	86,957	0	688,945
5	688,945	55,116	93,914	0	595,032
6	595,032	47,603	101,427	0	493,605
7	493,605	39,488	109,541	0	384,063
8	384,063	30,725	118,304	0	265,759
9	265,759	21,261	127,769	0	137,990
10	137,990	11,039	137,990	0	0

 

The price of the 0% prepayment IO and PO strips is the PV of the cash flows at 6%

 

	IO/Strip	PO/Strip
PV/Price at 6%	$387,480	$709,390

 

Cash flow schedule at 20% prepayment

Beginning Balance                            =                             $1,000,000

Prepayment Rate                              =                                        0.20

Interest Rate                                      =                                        0.08

 

 

	Beginning	Interest	Principal	PO	Ending
Period	Balance	IO/Strip	PO/Strip	Prepayment	Balance
1	$1,000,000	$80,000	$69,029	$200,000	$730,971
2	730,971	58,478	58,536	146,194	526,241
3	526,241	42,099	49,474	105,248	371,518
4	371,518	29,721	41,637	74,304	255,578
5	255,578	20,446	34,839	51,116	169,623
6	169,623	13,570	28,913	33,925	106,785
7	106,785	8,543	23,698	21,357	61,730
8	61,730	4,938	19,015	12,346	30,369
9	30,369	2,430	14,601	6,074	9,695
10	9,695	776	9,695	0	0

 

 

The price of the 20% prepayment IO and PO strips is the PV of the cash flows at 6%

 

	IO/Strip	PO/Strip
PV/Price at 6%	$221,902	$833,574