Bruce Tuckman, Angel Serrat, Fixed Income Securities: Tools for Today s Markets, 3rd Edition

Transcription

1 P1.T3. Financial Markets & Products Bruce Tuckman, Angel Serrat, Fixed Income Securities: Tools for Today s Markets, 3rd Edition Bionic Turtle FRM Study Notes By David Harper, CFA FRM CIPM and Deepa Raju

2 Tuckman, Chapter 20: Mortgages and Mortgage-Backed Securities DESCRIBE THE VARIOUS TYPES OF RESIDENTIAL MORTGAGE PRODUCTS CALCULATE A FIXED RATE MORTGAGE PAYMENT, AND ITS PRINCIPAL AND INTEREST COMPONENTS

3 Tuckman, Chapter 20: Mortgages and Mortgage-Backed Securities Describe the various types of residential mortgage products. Calculate a fixed rate mortgage payment, and its principal and interest components. Describe the mortgage prepayment option and the factors that influence prepayments. Summarize the securitization process of mortgage backed securities (MBS), particularly formation of mortgage pools including specific pools and TBAs. Calculate weighted average coupon, weighted average maturity, and conditional prepayment rate (CPR) for a mortgage pool. Describe a dollar roll transaction and how to value a dollar roll. Explain prepayment modeling and its four components: refinancing, turnover, defaults, and curtailments. Describe the steps in valuing an MBS using Monte Carlo Simulation. Define Option Adjust Spread (OAS), and explain its challenges and its uses. Describe the various types of residential mortgage products. There are many types of mortgage loans offered by the lenders. These mortgage loans may charge fixed or floating rates of interest from the borrower and can be disbursed against residential or commercial property as shown below: Mortgage Product Interest Rate Mortgage Type Fixed Floating Residential Commercial Agency; aka, conforming Nonconforming (private label) Jumbo Alt-A Subprime 3

4 Types of Residential Mortgages Residential mortgages typically mature in 15 to 30 years and they are primarily classified on the basis of their securitization mechanism. Agency or conforming loans are eligible to be securitized by government entities such as Federal National Mortgage Association (FNMA), Federal Home Loan Mortgage Corporation (FHLMC), or Government National Mortgage Association (GNMA). The loans securitized by aforementioned agencies are assessed as relatively more creditworthy. The guidelines for conforming loans comprise of conditions such as maximum size of loans should not exceed a certain amount, the loan-to-value ratio should not fall below 80 per cent and so on. Non-agency or Non-Conforming Loans As the name suggests, these mortgage loans do not conform to the established guidelines by Fannie Mae and Freddie Mac and therefore, are not eligible for purchase by the same agencies. They are part of private-label securitizations. The non-conforming loans are usually offered to those borrowers which do not qualify for conforming loans and the loan type thus carries higher interest charge. The relevant loan types include: 1. Jumbos These loans are larger in size than the prescribed limit for conforming loans but otherwise similar. 2. Alt-A These types of loans deviate from conforming loans in one requirement. The Alt-A loans are positioned between prime & subprime loans. The interest charged on these loans is lesser than subprime lending rate but higher than prime lending rate. 3. Subprime These types of loans largely deviate from the conforming loan guidelines and are offered to borrowers with poor creditworthiness at very high interest rates. Most of the subprime loans are adjustable-rate mortgages (ARMs). Calculate a fixed rate mortgage payment, and its principal and interest components. As the name suggests, fixed rate mortgage carries constant interest rate throughout its lifetime with level payments. The monthly repayment amount for a fixed rate mortgage is computed such that its present value when discounted at the monthly compounded mortgage (fixed) rate equals the original amount of the loan borrowed by the obligor. The formula can be depicted mathematically as: h ( ) = (0) where, (0) is the original loan amount, is the annual rate of interest and denotes the tenure of the loan in years. For example: Calculate fixed rate mortgage payment with following parameters: Principal Amount: (0) = $100,000 Rate of Interest: = 4% per annum Loan Tenure: = 30 Years 4

5 Applying this long-hand version of the formula (which is tedious), the monthly payment ( ) is computed to be $477.42: $ = $100,000 The fixed monthly payment comprises of two components, interest and principal. The monthly interest payment over a particular period equals the mortgage rate times the outstanding principal amount at the beginning of that period. If ( ) is the outstanding principal amount (total principal amount less principal amount repaid) after the mortgage payment is due on date n, the interest component of the payment on date + 1 would be ( ) 12. The principal component of the monthly payment is the remainder of the monthly payment after deducting the interest component and derived as ( ) 12 Considering our example of fixed mortgage payment, the original balance is $100,000. At the end of the first month, interest of 4.0% is due on this balance, which amounts to $100, /12 or $ The remainder of the monthly payment, $ $ or $144.08, is (scheduled) re-payment of principal. This principal payment reduces the outstanding balance from the original $100,000 to $100,000 $ or $99, at the end of the first month. Then, the interest payment due at the end of the second month is based on the principal amount outstanding at the end of the first month; i.e., $99, Continuing in this way produces an amortization table, the first few rows of which are given below: Original balance: $100,000 Term (years): months Rate: 4.0% 0.33% per month Payment factor: = 0.33%*(1+0.33%)^360/[(1+0.33%)^360-1] Payment Ending Month Interest Principal Total Balance 0 $100, $ $ $ $99, $ $ $ $99, $ $ $ $99, $ $ $ $99, $ $ $ $99, $ $ $ $99, $ $ $ $98, $ $ $ $98, $ $ $ $98, $ $ $ $98,

6 Mortgage payment factor Please note we can retrieve the monthly payment by calculating the mortgage payment factor which is given by: = interest_rate(1+interest_rate)loan_term (1 + interest_rate) loan_term 1 = ( ) ( ) 1 = The monthly payment is simply given by the mortgage payment factor multiplied by the original balance. In this case, the monthly payment is given by $100,000 original balance = $ The graph in below figure depicts the interest and principal components from the full amortization table of this mortgage. The total height is the full monthly payment of $477.42, the blue shaded height is the interest component, and the green shaded height is the principal component. As can be seen from the graph, the early payments during the tenure of the loan are composed mostly of interest while later payments are composed mostly of principal. This is explained by the phrase interest lives off principal. Note that the interest at any time is due only on the then outstanding principal amount and hence as principal is paid off, the amount of interest necessarily declines. 6