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’ve 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 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 buy the home.
  • 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 the same for the entire life of the loan. Your monthly payment stays predictable!

2. Adjustable-Rate Mortgage (ARM): The interest rate "floats" or changes periodically based on a market index. If market rates go up, your payments go up too.

Did you know? Most residential mortgages in the U.S. are fully amortized. This means that by the time you make your very last payment, the loan balance is exactly zero. No "balloon" payment at the end!

Key Takeaway: Mortgages are the "raw materials" for MBS. The cash flows from homeowners making their monthly payments are what investors eventually receive.

2. The Mechanics of Amortization

In a standard fixed-rate mortgage, the monthly payment is constant. However, the composition of that payment changes every month.

Early in the loan, most of your payment goes toward Interest. As the years go by, more and more of your payment goes toward Principal.

The Monthly Payment Formula:

To calculate the monthly payment \( (PMT) \), we use: \( PMT = \frac{L \times [c(1+c)^n]}{(1+c)^n - 1} \)
Where:
\( L = \) Loan amount
\( c = \) Monthly interest rate (Annual rate / 12)
\( n = \) Total number of months

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

3. Prepayment Risk: The "Wild Card"

This is the most important concept in this chapter! Unlike a regular corporate bond, a homeowner has the right to pay back their loan early. This is called Prepayment Risk.

Why do people prepay?

  • Refinancing: If interest rates drop, homeowners take out a new loan at a lower rate to pay off the old one.
  • Housing Turnover: People sell their homes when they move for a new job or a bigger house.
  • Curtailed Payments: Paying a little extra each month to get out of debt faster.

Analogy: Imagine you lent \$100 to a friend at 10% interest. Suddenly, the bank starts offering loans at 2%. Your friend pays you back the \$100 immediately to go borrow from the bank instead. You got your money back, but now you can only reinvest it at 2%. You just experienced Reinvestment Risk due to prepayment!

Key Rule: When interest rates fall, prepayments increase. This shortens the life of the investment just when the investor wants to keep that high yield.

4. Measuring Prepayments: CPR and PSA

We need a way to estimate how fast people will pay off their loans. We use two main benchmarks:

Conditional Prepayment Rate (CPR)

The CPR is an annual rate. If a pool has a 6% CPR, it means 6% of the remaining principal is expected to be prepaid over the next year.

To find the monthly version, we use the Single Monthly Mortality (SMM): \( SMM = 1 - (1 - CPR)^{1/12} \)

The PSA Prepayment Model

The Public Securities Association (PSA) created a standard benchmark. It assumes prepayments start slow (as people are unlikely to move immediately after buying) and then speed up.

  • 100% PSA (The Benchmark): Starts at 0.2% CPR in Month 1, increases by 0.2% each month until Month 30, then stays level at 6% CPR.
  • 150% PSA: Simply multiply the 100% PSA rates by 1.5.
  • 50% PSA: Half the speed of the benchmark.

Quick Review:
PSA = 100: Standard assumption.
PSA > 100: Fast prepayments (usually because rates are falling).
PSA < 100: Slow prepayments (usually because rates are rising).

5. Mortgage-Backed Securities (MBS) Structures

Investment banks take thousands of mortgages and "pool" them together. They then sell pieces of this pool to investors.

Pass-Through Securities

The simplest form. Investors receive a "pro-rata" share of all cash flows (interest and principal) from the pool. If 1% of homeowners prepay, you get 1% of your principal back.

Collateralized Mortgage Obligations (CMOs)

Don't worry if this seems tricky at first! CMOs just take the pool and carve it into Tranches (slices) to redistribute risk.

  • Sequential Pay: Tranche A gets all principal payments first. Once A is paid off, Tranche B starts receiving principal. This creates "short-term" and "long-term" investments from the same pool.
  • Planned Amortization Class (PAC): These are the "safe" tranches. They have a stable payment schedule as long as prepayments stay within a certain range.
  • Support/Companion Tranches: These are the "bodyguards." They soak up the prepayment volatility to keep the PAC tranches stable. They are much riskier!

6. Stripped MBS: IOs and POs

Sometimes, we strip the interest and principal into two separate securities. They behave very differently when interest rates change.

Principal-Only (PO) Strips

You only get the principal. You buy these at a discount.
If rates fall: Prepayments speed up. You get your money back sooner. PO value goes UP significantly.

Interest-Only (IO) Strips

You only get interest on the remaining balance.
If rates fall: Prepayments speed up and the principal balance disappears quickly. There is less balance to charge interest on! IO value goes DOWN.

Memory Trick: IO is the "weird" one. Usually, when rates fall, bond prices go up. But for an IO strip, when rates fall, the price actually drops because the underlying loans are being paid off too fast.

Summary and Key Takeaways

1. Amortization: Monthly payments are fixed, but the mix of interest and principal changes over time.
2. Prepayment Risk: The biggest risk in MBS. It increases when interest rates fall (refinancing incentive).
3. PSA Model: The standard way to describe prepayment speeds. 100 PSA is the baseline.
4. Tranching: CMOs allow investors to choose their level of prepayment risk (PAC vs. Support).
5. IO/PO Strips: POs love fast prepayments; IOs hate them.

Keep practicing the calculations for SMM and CPR, and always ask yourself: "If interest rates move, what happens to the homeowner's behavior?" That is the key to mastering Mortgages and MBS!