The rate after the introductory period is the index plus the margin, and the two halves behave completely differently. CFPB states the mechanics directly. The index is an interest rate that fluctuates with general market conditions; the lender decides which index the loan will use when you apply, and that choice generally will not change after closing. The margin is the number of percentage points the lender adds to the index, it is set in the loan agreement, and it will not change after closing. Their sum is the fully indexed rate.
The margin is where the negotiation is, and virtually no consumer coverage says so. CFPB does: you should pay attention to the margin when shopping because it can vary a lot between lenders, and you can negotiate it just as you would negotiate the rate on a fixed-rate loan. Regulation Z reinforces the point from the disclosure side. 1026.19(b)(2)(iii) requires the loan program disclosure to explain how the rate and payment will be determined, including how the index is adjusted, such as by the addition of a margin, and (b)(2)(iv) requires a statement that the consumer should ask about the current margin value and current interest rate. Two borrowers on the same index with margins a full point apart will pay different rates for the next twenty-five years, and only one of them was ever told to ask.
On which index a loan uses, the honest answer is that it varies and the document says. CFPB's own handbook notes that different lenders use different indexes and gives the U.S. prime rate and the Constant Maturity Treasury rate as common examples, and points the borrower at page 2 of the Loan Estimate, where the index is shown. Anything keyed to LIBOR is stale, since U.S. dollar LIBOR has been discontinued, but the index on any particular loan is a fact about that loan rather than an industry constant.
The caps are not one number, and the Loan Estimate presents them better than the industry shorthand does. CFPB's handbook reproduces the Adjustable Interest Rate table that appears on page 2 of the Loan Estimate, and its rows are the ones to read: index plus margin, the initial interest rate, a minimum and maximum interest rate for the life of the loan, the change frequency for the first change and for subsequent changes, and limits on interest rate changes stated separately for the first change and for subsequent changes. The trade shorthand compresses those into three figures, an initial cap, a periodic cap and a lifetime cap, but the table is what the borrower actually receives. One further point from the handbook is easy to miss: generally, an ARM's interest rate is never lower than the margin, so the margin sets the floor as well as contributing to every rate above it.
Federal law fixes how much warning a borrower gets, and it is more than most people assume. For the first adjustment, 12 CFR 1026.20(d) requires the disclosure to be provided at least 210 but no more than 240 days before the first payment at the adjusted level is due, as a separate document. That is roughly seven to eight months. For subsequent adjustments that change the payment, 1026.20(c)(2) requires disclosure at least 60 but no more than 120 days ahead, shortened to at least 25 but no more than 120 days for ARMs with uniformly scheduled adjustments occurring every 60 days or more frequently. Where the first payment at the adjusted level falls within 210 days of closing, the initial disclosure is given at closing instead. So a borrower has most of a year to prepare for the first reset, and can use it to budget, to sell, or to shop for a refinance.
A note on negative amortization, because both common statements about it are wrong. It is not banned in general. Regulation Z at 1026.19(b)(2)(vii) still requires any negative amortization feature to be disclosed in the loan program disclosure, and the statutory prohibition at 15 USC 1639(f) reaches high-cost mortgages rather than all loans. What is true is that a borrower will not meet it in a mainstream conforming loan today. Read the disclosure rather than assuming either way.
The decision itself is a matter of matching the loan to the holding period and to what happens if the rate reaches its maximum. CFPB's own caution is the right one to repeat: do not assume you will be able to sell the home or refinance before the rate changes, because property values and personal circumstances both move, and if the payment at the maximum rate is not affordable on today's income, that is information about the loan rather than about the future.