FMP18 - Mortgages and Mortgage-Backed Securities

Question 1

Describe the various types of residential mortgage products

Answer 1

Mortgages can be fixed rate or adjustable rate, adjustable riskier for borrowers

Question 2

Calculate a fixed-rate mortgage payment and its principal and interest components

Answer 2

(X / (R/12)) * (1 - (1 / ((1 + R/12)^(12*T)) = A

X = monthly payment
R = interest rate
A = amount borrowed
T = years (life of the mortgage)

Interest rate payment is R * amount left
Principal payement is X - (R * amount left)

Question 3

Summarise the securitisation process of mortgage-backed securities (MBS), particularly formation of mortgage pools including specific pools and to-be-announceds (TBAs)

Answer 3

Mortgage pools created for investment purposes, mortgages in pool are all similar.

Three agencies buy mortgages from banks and create pools, seen as government backed. Investors buy from these agencies to get a share of cashflows from the mortgages, all investors get same return.

Specific pools is where traders agree to trade specified pool at specified price.

TBAs agree on agency, maturity, coupon etc and then seller acts on a cheapest to deliver basis, depending on which pools can be delivered cheapest.

Question 4

Calculate weighted-average coupon, weighted-average maturity, single monthly mortality rate (SMM), and conditional prepayment rate (CPR) for a mortgage pool

Answer 4

WAC = sum(i=1 to n) w_i * c_i
WAM = sum(i=1 to n) w_i * L_i
w_i = Ai / sum(j = 1 to n) Aj
SMM = % of outstanding principal that was PREPAID in that month
CPR = 1 - (1 - SMM)^12

Ai is outstanding principal on mortgage i
c_i = coupon of i
L_i = time remaining in months of i

Question 5

Explain the mechanics of different types of agency MBS products, including collateralised mortgage obligations (CMOs), interest-only securities (IOs), and principal-only securities (POs)

Answer 5

CMOs created into tranches that bear different levels of prepayment risk, first layers bear the most prepayment risk

IOs receive only the interest payments from mortgage pools, decrease in value with increasing prepayments

POs receive only principal payment component from mortgage pools, increase in value with increasing prepayments

Question 6

Describe a dollar roll transaction and how to value a dollar roll

Answer 6

Dollar roll involves selling a TBA for one month and buying a TBA for another - like a repo but no interest added but prepayment properties may be worse

Value = price pool sold for during first month including accrued interest - price pool is bought for in second month including accrued interest + interest earned on proceeds from sale for first month - coupon of principal payments that would’ve been earned on first month pool

Question 7

Describe mortgage prepayment option and factors that affect it; explain prepayment modelling and its four components: refinancing, turnover, defaults, and curtailments

Answer 7

1. Refinancing mortgage, occurs when interest rates decrease or borrowers credit rating increases
2. Turnover is where borrower sells the house so no prepayment occurs, seasonal and geographical
3. Default occurs and agency will pay outstanding balance of the mortgage, this is a prepayment
4. Curtailments are partial prepayments

All four need to be considered when modelling prepayments

Question 8

Describe the steps in valuing an MBS using Monte-Carlo simulation

Answer 8

1. sample from prob dist to determine hypothetical month by month path for risk free rate and housing prices
2. determine prepayment rate using 1 and a specified prepayment model
3. use prepayment rate for month by month cashflows arising from an MBS
4. discount cashflows using each months interest rates for the MBS
5. repeat and average

Question 9

Define Option Adjusted Spread (OAS) and explain its challenges and its uses

Answer 9

OAS is excess return from a fixed-income security compared to treasury investments

Useful for relative valuation of MBS pools, very dependent on prepayment model