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FRM Part I · FRM Exam Part I

Mortgages and Mortgage-Backed Securities for FRM Part 1

A mortgage is a loan secured by property, repaid in level instalments of interest and principal. A mortgage-backed security (MBS) pools mortgages and passes the cash flows to investors. To solve questions, compute the payment, track the balance, adjust for prepayment, then price using duration, convexity or OAS.

What this chapter covers

This chapter covers how home loans are built, how they are pooled into securities, and how those securities are priced and risked. You start with the level-payment mortgage, then add the feature that makes MBS different from ordinary bonds: the borrower can repay early. That prepayment option drives almost every later topic.

From there you move to agency pass-throughs, where investors receive scheduled principal, interest and prepayments, net of servicing and guarantee fees. Then you see how collateralized mortgage obligations (CMOs) redistribute prepayment risk across tranches. Valuation closes the technical part: negative convexity, effective duration and option-adjusted spread (OAS). The last topic covers non-agency securitization and the subprime crisis, where credit risk, not prepayment, was the main issue.

The chapter connects to several other parts of the paper. Payment calculations use time value of money and the financial calculator. Duration and convexity link to fixed income and bond pricing. The prepayment option links to options and interest rate models. The crisis topic links to Foundations of Risk Management, including credit risk, model risk, incentives and governance.

Mortgages and MBS sit where several FRM themes meet: quantitative calculation, option-like behaviour, interest rate risk and real-world risk failure. Questions are often a mix of short calculations and conceptual judgement, so the chapter rewards both. Learning it well also strengthens your answers on duration, convexity, credit risk and securitization elsewhere in the exam. GARP revises the curriculum every year, so check the current Study Guide and Learning Objectives for the exact scope. Do not skip this chapter because it looks niche. The ideas transfer widely.

Mortgages and Mortgage-Backed Securities: topics in the order to study them

  1. 1Mortgage Basics and Types of MortgagesEverything else builds on the level-payment mortgage, amortization and the differences between fixed-rate, adjustable-rate and other mortgage structures.
  2. 2Prepayment Risk and Prepayment ModelsPrepayment is what separates MBS from regular bonds, so you need it before any security is analysed. Learn CPR, SMM and the PSA benchmark here.
  3. 3Agency Mortgage Pass-Through SecuritiesThis applies mortgage cash flows and prepayment to the simplest MBS, where investors receive a pro rata share of pooled payments.
  4. 4Collateralized Mortgage Obligations and TranchingCMOs reallocate pass-through cash flows, so you must understand the pass-through first. Focus on sequential tranches and who bears extension and contraction risk.
  5. 5Valuation and Risk of MBS: Duration, Convexity and OASWith cash flows and prepayment behaviour clear, you can see why MBS show negative convexity and why OAS removes the value of the embedded option from the spread.
  6. 6Non-Agency MBS, Securitization and the Subprime CrisisThis final topic adds credit risk, structuring and incentive problems, and is easier once you know how agency products work.

How to prepare Mortgages and Mortgage-Backed Securities

Treat this chapter as one story: a loan, an option to repay it, a pool, a split of the pool, a price, and a failure. Study in that order and practise each calculation by hand.

  1. Learn the level-payment formula and use your financial calculator to find the payment from the amount, rate and term. Then build a two-period amortization table so you can see interest and principal each month.
  2. Write down the link between CPR and SMM: SMM = 1 − (1 − CPR)^(1/12). Practise converting both ways, and learn what a PSA speed means as a multiple of the benchmark.
  3. For pass-throughs, list the cash flow components: interest, scheduled principal and prepayment. Note that the pass-through rate is lower than the mortgage rate because of fees.
  4. Draw a simple sequential CMO with three tranches and trace how principal flows when prepayments speed up or slow down. State which tranche gains or loses.
  5. Explain in your own words why falling rates shorten MBS life and cap price gains, and why rising rates extend it. Tie this to negative convexity and to OAS as the spread after removing option cost.
  6. Finish with the crisis. Make a one-page list of causes: weak underwriting, rating reliance, incentive misalignment, complex structures and correlated defaults. Then do timed practice questions mixing calculation and concept.

Common mistakes in Mortgages and Mortgage-Backed Securities

  • Using the annual rate and years directly in the payment formula.

    Fix: Divide the annual rate by 12 and multiply years by 12 before using the formula or the calculator.

  • Treating CPR and SMM as interchangeable.

    Fix: Remember CPR is annual and SMM is monthly. Convert with SMM = 1 − (1 − CPR)^(1/12), not by simple division by 12.

  • Assuming faster prepayment is always bad for the investor.

    Fix: Ask what the investor paid and which tranche they own. A discount security can benefit from faster prepayment, while a premium security usually loses.

  • Thinking CMOs create or destroy total risk.

    Fix: Say that CMOs reallocate cash flows among tranches. The total pool cash flow is the same, so some tranches take more prepayment uncertainty and others take less.

  • Using plain duration for MBS and ignoring option behaviour.

    Fix: Use effective duration and convexity, which reprice cash flows under shifted rates with prepayments that respond to rates.

  • Describing the subprime crisis only as a housing price fall.

    Fix: Give a layered answer: underwriting standards, originate-to-distribute incentives, rating dependence, complexity and correlated defaults, then house prices as the trigger.

Last-day revision: Mortgages and Mortgage-Backed Securities

  • A level-payment mortgage has a fixed payment; early payments are mostly interest and later ones mostly principal.
  • Payment is found from the loan amount, periodic rate and number of payments, using a financial calculator or the annuity formula.
  • Monthly interest = outstanding balance × annual rate ÷ 12; principal = payment − interest.
  • CPR is an annualized prepayment rate; SMM is the monthly rate. SMM = 1 − (1 − CPR)^(1/12).
  • PSA 100% is a benchmark prepayment ramp; 200% PSA means twice the benchmark speed.
  • Pass-through investors receive interest, scheduled principal and prepayments, net of servicing and guarantee fees.
  • Lower rates usually raise prepayments, shortening life (contraction risk); higher rates slow prepayments, lengthening life (extension risk).
  • CMO tranching redistributes prepayment risk; it does not remove it from the pool.
  • MBS typically show negative convexity because of the borrower's prepayment option.
  • OAS is the spread over the benchmark curve after removing the value of the embedded prepayment option.
  • Effective duration is estimated by shifting rates and repricing with prepayment assumptions that change with rates.
  • The subprime crisis involved weak underwriting, rating reliance, misaligned incentives and correlated defaults.

Mortgages and Mortgage-Backed Securities practice questions

Mortgages and Mortgage-Backed Securities in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Mortgages and Mortgage-Backed Securities: frequently asked questions

How should I use a financial calculator for mortgage questions?

Enter the number of monthly periods as N, the monthly rate as I/Y, the loan amount as PV and zero as FV, then compute PMT. Check the sign convention and that you are in end-of-period mode. Practise until this takes under a minute.

Do I need to memorize the PSA ramp?

Yes, you should know the idea and be able to apply it. The PSA benchmark increases the prepayment rate gradually for the early months of a loan and then holds it constant. A higher PSA percentage scales the benchmark up. Check the current learning objectives for the exact details tested.

Why do mortgage-backed securities have negative convexity?

Borrowers can repay early, and they are more likely to when rates fall. This caps the price rise of the security as rates drop. When rates rise, prepayments slow and the security's life extends, so price falls more. The combination produces negative convexity.

What does OAS tell me that a simple yield spread does not?

OAS removes the cost of the embedded prepayment option from the spread over the benchmark curve. It is estimated using a model of rates and prepayments. That makes it a better measure for comparing MBS with option-free bonds, though it depends on the model used.