Lecture 9: Amortizing Adjustable-Rate Mortgages

FRM vs ARM

FRM: rate fixed, payment fixed, balance always falls

ARM: rate and payment can jump, and the balance can actually rise even when every payment is made on time

4-Step Procedure for Solving ARM Problems

Step 1: Compute the initial monthly payment from the initial rate over the full n (e.g., $200,000, 0.5% monthly, 360 months → $1,199.10).

Step 2: Compute the remaining principal balance at the reset date using the old payment and old rate with the remaining months (348 months → $197,543.99).

Step 3: Find the new effective rate: fully indexed rate = index + margin, then apply the periodic and lifetime caps.

Step 4: Solve for the new payment that fully amortizes that same remaining balance over the remaining months at the new rate, so the lender loses nothing.

Why do Lenders Issue ARMs

ARMs push future interest-rate risk onto the homeowner instead of the bank They are the direct lesson banks learned from the S&L crisis

Why Borrowers Take Out ARMs

Low initial rate and payment during the lockup period (discount or teaser-rate ARMs) appeal to borrowers who (

1) need time to build income and accept rate risk

(2) expect to move soon and have a prepayment option

(3) speculate on rising home prices and falling rates so they can refinance and pull equity out

How ARMs Can Hurt the Economy

From June 2004 to June 2006 the Fed raised rates 17 times in a row

Home prices then fell while rates rose, triggering defaults on teaser-rate subprime ARMs and starting the crisis