Business F723

Fixed Income Analysis

Week 7

Mortgage Backed Securities

2

Monthly Cash Flows

• Example p. 243, for a 100 PSA with a pass through rate of 7.5% a WAC of 8.125% and WAM of 357 months

• The calculations for this table are a bit involved, because the monthly payments on the mortgage pool decrease as prepayments are made on some of those mortgages

3

Monthly Payments

• Calculating the scheduled monthly payment requires keeping track of the total amount of accumulated prepayments as a fraction of the initial principal

• Exact formula for this calculation is not given in this textbook

4

Principal

• The scheduled principal is the difference between the monthly payment and the interest on the outstanding principal

• Prepayment estimates = SMM multiplied by (the outstanding principal less the scheduled principal payment)

• Outstanding balance = previous balance less scheduled principal and prepayment

5

Actual Cash Flows

• The cash flows forecast in the previous table are just predictions

• If the estimate of 100 PSA is reasonable, the cash flows will still be different from what was predicted

note: most of the PSA benchmark is based on experience, but the linear slope for the first 30 months is just an assumption

6

Prepayment Rate

• The actual rate of prepayments can vary over time for several different reasons– Prevailing mortgage rates; spread, path

(refinancing burnout), and level– Characteristics of the loans– Seasonal factors (low housing turnover in

winter months)– General economic activity

7

Prepayment Models

• To account for the changing factors over the life of MBS, some have built models to predict prepayment behaviour– From Goldman, Sachs: monthly prepayment =

(refinancing incentive)x(seasoning multiplier) x(month multiplier)x(burnout multiplier)

• Typically not publicly reported

8

Non-Agency Pass-throughs

• Since these mortgages are not fully insured, we need to adjust for potential defaults

• Public Securities Association has also defined a benchmark for the default rate

• Standard Default Assumption (SDA)• ## SDA is the relative rate of defaults

expected compared to the average (100 SDA)

9

Standard Default Assumption

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0.60%

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10

Cash Flow Yield

• Similar to IRR, the discount rate that sets the present value of the forecast cash flows equal to the price

• Market convention converts the monthly yield into a bond equivalent basis

112yield equivalent bond 6 my

11

Limitations of Cash Flow Yield

• Can not be used for future value calculation due to reinvestment risk

• Assumes security is held to maturity (price risk)

• Prepayment rates and default/delinquency rates must be equal to what was predicted

12

Yield Spread

• The main difference between treasury bonds and agency (fully modified) MBS is the prepayment risk

• What level of spread would compensate for the added risk?

• Option pricing models have been used to determine the appropriate spread

13

Average Life

• To which maturity treasury bond should we compare the MBS?

• Could use Macaulay duration, but main measure in use is average life

monthsin time

principal total

at time received principal12life average

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14

Average Life vs. PSA

• The average life will be different with different prepayment assumptions

• As prepayments increase, average life will decrease

PSA speed 50 100 165 300 500 700Average Life 15.11 11.66 8.76 5.63 3.68 2.78

Average Life of 357 month example

15

Negative Convexity

• Prepayments are similar to call provisions with no call premium

• Not all mortgages will prepay since there is a cost to the borrower to refinance

• Price increases will be limited due to the increased likelihood of prepayments as the interest rate declines

16

Contraction Risk

• If interest rates decrease, the amount of prepayments will increase

• As prepayments increase, the principal will have to be reinvested at lower rates

• Average life, and Macaulay’s duration will decrease… this is called contraction risk

17

Extension Risk

• If interest rates rise, prepayments will decline

• Expected cash flows will be unavailable for reinvestment at new, higher rates

• Average life, and Macaulay’s duration will increase… this is called extension risk

18

Asset/Liability Management

• Depository institutions are more concerned with extension risk

• Pension funds and others with very long investment horizons are more concerned with contraction risk

• Synthetic securities can be built to transfer some of these risks

19

Prepayments and Return

• Prepayments can enhance the return compared to the cash flow yield, if the MBS trades at a discount

• A prepayment causes the realized capital gain to occur earlier

• If the MBS trades at a discount, its coupon rate is lower than required, so prepayments allow beneficial reinvestment

20

CMOs

• Collateralized Mortgage Obligations are a variant of MBSs

• Called a pay-through structure rather than a pass-through structure because there are different classes of owners receiving different cash flows, but having the same level of seniority

• Different classes are called tranches

21

Sequential Pay Tranches

• Principal payments are directed at each tranche in turn until that tranche is paid off

• principal pay-down window is the time period in which that tranche is receiving payments towards the principal

• Tranche B in example on p. 261 has a principal pay-down window from month 81-100

22

Accrual Bonds

• A class of tranche that receives no interest or principal until the other tranches have been fully paid off

• The interest payments that this tranche would have received are treated as principal prepayments for the other tranches

23

Floating Rate Tranches

• A floating rate tranche can be created by splitting a tranche into a floating rate tranche and an inverse floating rate tranche

• The total interest paid to the two tranches will be the same as the interest paid to the original tranche

• coupon leverage will be created if the two tranches are not of the same size

24

Planned Amortization Class

• A PAC tranche is protected from prepayment risk because it gets principal payments at a fixed rate

• This is accomplished by issuing support bond tranches

• The PAC gets principal payments according to the schedule, anything left over goes to the support bond tranche

25

PAC Collars

• If the support bond tranche is paid off, the PAC tranche will lose its protection

• The range of prepayment speeds that can be handled is called the collar

• The size of the collar can change over time based on the actual speed of prepayments

26

Targeted Amortization Class

• A TAC bond tranche is protected against contraction risk, but not extension risk

• Prepayments in excess of a certain rate are borne by the support bonds, but slower than expected prepayments are shared equally

• A reverse TAC bond protects vs. extension risk, but not contraction risk

27

VADM

• Very Accurately Determined Maturity bonds are created much like PACs except that there is also an accrual bond tranche

• The accrued interest for the accrual bond tranche can be used to satisfy the scheduled principal payments if the prepayment speed is slower than expected

28

Support Bonds

• These bonds are the tranches that take extra prepayment risk to allow the PAC, TAC, or VADM to reduce that risk

• As such these bonds are very risky and investors will demand a higher rate of return to buy these tranches

29

Credit Risk

• A CMO is a business entity

• If issued by an agency or fully modified, there is no credit risk

• If issued by a private conduit, the level of credit risk must be assessed– Private label CMO; assets are agency MBS– Whole loan CMO; assets are mortgages

Structural Credit Enhancement

• Senior/subordinated tranches

• Subordinated tranches absorb the first wave of defaults

• Given the example on p. 302 you can give the different tranches credit ratings from NR to B to AAA depending on how much protection they have

30

31

Stripped MBS

• Interest only or principal only tranches

• All interest collected is paid to one tranche, all principal payments, scheduled or prepayments is paid to the other tranche

• Interest only tranche hurt by prepayments

• Principal only tranche gets money quicker if prepayments increase

32

Notional Interest Only

• A tranche that is created by paying one or more tranches lower coupon payments than the WAC

• The excess interest is paid out to a tranche as a percent of a notional value– e.g. $100 m tranche receives 6%, WAC 7%– 1% of $100 m = 5% of $20 m– so a tranche can be created paying 5% on a

notional value of $20 m