Welcome to the World of Mortgages and MBS!

Hello future FRM holders! Today, we are diving into one of the most significant sectors of the fixed-income market: Mortgages and Mortgage-Backed Securities (MBS). If you followed the news during the 2008 financial crisis, you have heard these terms before. But beyond the headlines, understanding how these instruments work is crucial for any risk manager. We will break down how a simple home loan gets transformed into a complex tradable security, and how to evaluate and manage the unique risks involved.

1. The Basics: What is a Mortgage?

At its simplest level, a mortgage is a loan secured by the collateral of a specified real estate property. The borrower (homeowner) is obligated to pay back the loan with interest over a set period.

Key Components of a Mortgage:

  • Principal: The actual amount borrowed to purchase the property.
  • Interest Rate: The cost of borrowing (can be fixed or variable).
  • Maturity: The length of the loan (commonly 15 or 30 years).

Types of Mortgages:

1. Fixed-Rate Mortgage: The interest rate remains identical for the entire life of the loan, ensuring level and predictable monthly payments.

2. Adjustable-Rate Mortgage (ARM): The interest rate floats or resets periodically based on a reference benchmark. If benchmark rates rise, borrower payments adjust upward.

Did you know? Most residential mortgages in the U.S. are fully amortized. This means that with every scheduled payment made, the loan balance reaches exactly zero at final maturity without any balloon payment.

2. The Mechanics of Amortization

In a standard fixed-rate mortgage, the periodic payment is constant. However, the internal composition of that payment shifts over time. Early on, the vast majority of each payment covers accrued Interest. As the loan matures and principal is paid down, a progressively larger portion is applied to Principal.

The Monthly Payment Formula:

To calculate the fixed monthly payment \( (PMT) \), we apply: \( PMT = \frac{L \times [c(1+c)^n]}{(1+c)^n - 1} \)
Where:
\( L = \) Initial mortgage loan balance
\( c = \) Monthly interest rate (Annual mortgage coupon rate / 12)
\( n = \) Total number of monthly payments (e.g., 360 for a 30-year loan)

Common Mistake to Avoid: When using this formula, remember to convert the annual rate to a monthly decimal (e.g., 6% becomes 0.005) and loan tenure into months (e.g., 30 years becomes 360 months).

3. The Prepayment Option and Its Four Drivers

Unlike standard corporate bonds, residential mortgages grant the borrower an embedded call option: the right to repay the loan balance ahead of schedule without punitive penalties. This introduces Prepayment Risk.

The Four Drivers of Prepayment:

  • Refinancing: When prevailing mortgage rates drop significantly below the borrower's coupon rate, the borrower can refinance into a cheaper loan, prepaying the original balance in full.
  • Housing Turnover: Homeowners sell their residences when relocating for employment, family changes, or lifestyle upgrades, repaying their mortgage with sale proceeds.
  • Curtailments: Homeowners make supplemental principal payments above their mandatory monthly amortization schedule to retire debt early.
  • Defaults: When a borrower defaults on an agency-guaranteed mortgage, the guaranteeing agency (e.g., Fannie Mae, Freddie Mac, or Ginnie Mae) pays off the remaining principal balance to investors, terminating the loan as an effective full prepayment.

Analogy: Imagine you lent \$100 to a friend at 10% interest. Soon after, market rates plunge to 2%. Your friend pays back the \$100 early and borrows at 2%. You receive your principal back early, but you can only reinvest it at 2%. This is the essence of Contraction Risk and Reinvestment Risk.

Negative Convexity: Because homeowners prepay when rates fall, an MBS cannot appreciate in price beyond a certain ceiling (price compression). Conversely, when interest rates rise, homeowners stop prepaying, locking investors into low yields for longer (extension risk). This asymmetric dynamic causes agency MBS to exhibit negative convexity.

4. Measuring Prepayment Speeds: SMM, CPR, and PSA

To analyze MBS cash flows, market participants quantify prepayment velocity using standardized metrics:

Single Monthly Mortality (SMM) and CPR

The Single Monthly Mortality (SMM) is the percentage of the remaining pool principal balance that is prepaid in a given month beyond scheduled amortization:

\( SMM = \frac{\text{Prepayments during month}}{\text{Beginning balance} - \text{Scheduled principal payment}} \)

The Conditional Prepayment Rate (CPR) is the annualized equivalent of \( SMM \):
\( SMM = 1 - (1 - CPR)^{1/12} \)
\( CPR = 1 - (1 - SMM)^{12} \)

The PSA Prepayment Benchmark

The Public Securities Association (PSA) benchmark models mortgage seasoning over time for a 30-year fixed-rate pool:

  • 100% PSA: Assumes \( CPR \) begins at 0.2% in month 1, increases by 0.2% each month until reaching 6.0% in month 30, and remains constant at 6.0% \( CPR \) for the remaining life of the mortgage pool.
  • \( CPR = 6\% \times \frac{t}{30} \) for \( t \le 30 \), and \( CPR = 6\% \) for \( t > 30 \).
  • Multiplier Speeds: \( 150\% \text{ PSA} = 1.5 \times 100\% \text{ PSA} \); \( 50\% \text{ PSA} = 0.5 \times 100\% \text{ PSA} \).

Quick Review:
\( PSA = 100 \): Standard baseline assumption.
\( PSA > 100 \): Accelerated prepayment environment (typically declining interest rates).
\( PSA < 100 \): Sluggish prepayment environment (typically rising interest rates).

5. Mortgage Pool Descriptors, Agency Trading, and Dollar Rolls

Individual mortgages are securitized by pooling hundreds or thousands of homogeneous loans into tradable MBS pools.

Pool Aggregation Metrics:

  • Weighted Average Coupon (WAC): The average gross mortgage interest rate of all underlying loans in the pool, weighted by the outstanding principal balance of each mortgage.
  • Weighted Average Maturity (WAM): The average remaining time to maturity (in months) of the underlying loans, weighted by each loan's outstanding principal balance.

Trading Agency MBS: Specified Pools vs. TBAs

  • To-Be-Announced (TBA) Market: The forward market for agency pass-through securities. TBAs are forward contracts where buyers and sellers agree on key parameters (agency issuer, coupon rate, settlement month, par amount, and price), but the specific mortgage pools delivered are announced 48 hours prior to trade settlement. This high degree of fungibility creates immense liquidity.
  • Specified Pools: Non-TBA pools traded directly based on specific prepayment and borrower characteristics (e.g., low loan balances, specific geographic concentrations, or high loan-to-value ratios) that trade at a premium or discount relative to TBA pricing.

Dollar Roll Transactions:

A dollar roll is an agency MBS financing strategy structured as two simultaneous TBA trades: an investor sells a TBA contract for settlement in the front month and buys back a substantially identical TBA contract for settlement in a forward month at a lower price (the drop). The investor relinquishes the right to receive principal and interest cash flows during the roll period in exchange for investing the sale proceeds in short-term money markets. A dollar roll is economically advantageous when the forward drop is wide enough that the implied financing rate trades below alternative repo borrowing rates (referred to as trading 'on special').

6. MBS Tranching: Pass-Throughs and CMOs

Pass-Through Securities

In a simple mortgage pass-through, investors receive a pro-rata share of all cash flows (interest, scheduled principal, and prepayments) generated by the underlying pool, minus servicing and guarantee fees.

Collateralized Mortgage Obligations (CMOs)

CMOs redistribute prepayment risk across distinct investor classes by restructuring pool cash flows into targeted Tranches:

  • Sequential-Pay Tranches: Cash flows are structured chronologically. Tranche A receives all principal payments (scheduled plus prepayments) until fully retired, while subsequent tranches (B, C, etc.) receive interest only. Once Tranche A is retired, principal flows to Tranche B. This segments the collateral into distinct short-, intermediate-, and long-duration assets.
  • Planned Amortization Class (PAC) Tranches: PAC tranches offer strict cash flow protection by adhering to a predefined principal repayment schedule, provided the actual prepayment speed stays within an established upper and lower PSA boundary (the PAC collar).
  • Support (Companion) Tranches: Support tranches absorb the excess prepayments or shortfalls relative to the PAC schedule. They experience severe extension risk when prepayments slow and severe contraction risk when prepayments accelerate, thereby insulating the PAC bonds.

7. Stripped MBS: IOs and POs

Securitizers can split mortgage cash flows into separate interest-only and principal-only components:

Principal-Only (PO) Strips

Purchased at a deep discount to par value, the PO holder receives only principal distributions.
When interest rates fall: Prepayments surge. Principal is returned to the PO investor much earlier than expected, dramatically accelerating the realization of par value. PO prices rise substantially. POs have a very large positive duration.

Interest-Only (IO) Strips

IO holders receive no principal; they receive interest payments calculated on the declining outstanding principal balance (notional balance).
When interest rates fall: Prepayments surge and deplete the underlying principal balance rapidly. The future stream of interest payments vanishes, destroying the cash flow value of the security. IO prices fall when interest rates fall, demonstrating a negative effective duration in declining rate environments.

8. MBS Valuation: Monte Carlo Simulation and Option-Adjusted Spread (OAS)

Because mortgage prepayments depend on the path interest rates take (path dependency), standard backward-induction binomial lattices cannot accurately value MBS. An interest rate drop in year 2 induces heavy refinancings that permanently reduce the pool balance for year 3.

Monte Carlo Valuation

MBS valuation requires generating thousands of simulated interest rate paths via Monte Carlo simulation. On each path, an econometric prepayment model forecasts monthly cash flows based on rate paths, mortgage age, seasonality, and burnout. The cash flows are discounted along that specific interest rate path back to the present, and the average across all paths yields the theoretical MBS price.

Option-Adjusted Spread (OAS)

The Option-Adjusted Spread (OAS) is the constant spread that, when added to the short-term forward interest rates on all simulated paths, equates the model-derived present value of the MBS cash flows to its observed market price.

  • OAS vs. Zero-Volatility Spread (Z-Spread): The Z-spread measures the static spread over the Treasury spot curve assuming zero future prepayment volatility. The difference reflects the Option Cost: \( \text{Option Cost} = \text{Z-Spread} - \text{OAS} \).
  • For securities with embedded short prepayment options (like agency MBS pass-throughs), the Option Cost is positive, meaning \( \text{OAS} < \text{Z-Spread} \).

Summary and Key Takeaways

1. Embedded Prepayment Option: Driven by refinancing, housing turnover, curtailments, and defaults; creates negative convexity for fixed-rate MBS.
2. Prepayment Benchmarks: CPR is the annualized form of SMM; the 100% PSA benchmark increases linearly to 6% CPR by month 30 and remains flat.
3. Trading Mechanics: Fungible pools trade in the forward TBA market, while distinctive pools trade as Specified Pools. The dollar roll finances TBA positions via calendar rolls.
4. Tranching and Strips: CMOs redistribute prepayment risk into sequential and PAC/support structures. POs thrive on fast prepayments (positive duration), whereas IOs suffer from accelerated principal runoff (exhibiting negative effective duration over low-rate regimes).
5. Valuation: Due to path dependency, MBS require Monte Carlo simulation. The Option-Adjusted Spread (OAS) separates pure credit/liquidity compensation from the cost of the borrower's embedded prepayment option.