When it comes to bank stocks, there is a lot riding on deposits.

The KBW Nasdaq Bank index (.BKX) is up 11% over the past month, nearly three times the gain of the S&P 500 (.SPX). Behind that rally isn’t so much confidence that rates or the economy will suddenly zoom higher, but a belief that banks can manage through the Federal Reserve’s easing, thanks to some help on funding costs. Analyst estimates for 2020 net interest margins at Bank of America (BAC) and Wells Fargo (WFC), for example, have ticked higher since the end of October.

Banks now get a historic proportion of their funding from deposits, the cheapest form of liability, versus bonds or short-term borrowing. Overall year-over-year deposit growth was 5.8% across the largest U.S. banks in the third quarter—the fastest pace since the start of 2017, according to Federal Reserve figures. The upshot is that some 89% of large U.S. banks’ total liabilities are now deposits, the highest proportion since 1979, according to Federal Reserve figures.

Importantly, banks’ so-called golden deposits, the noninterest-bearing ones, ticked higher. These are typically day-to-day checking accounts for people and corporations on which they expect no interest—making them nearly free funding for banks. Depositors had been shifting this money into more productive places for a while, drawn by higher rates on offer elsewhere. But these deposits actually grew by a median 0.1% from the second quarter to the third across the biggest banks, the first sequential jump in at least five quarters, according to JPMorgan Chase analysts.

Another reason for optimism is that deposit costs didn’t fall as much as they could have in the third quarter, suggesting there could be pent-up declines to come.

Interest-bearing deposit costs at the biggest banks ticked down only 0.01 percentage point sequentially in the third quarter, according to Autonomous Research figures. That is despite a drop of half a percentage point in the effective fed-funds rate. There is usually a lag after Fed actions, as banks take some time to push through pricing changes. So the pace of decline has plenty of room to accelerate, if historical patterns hold.

Autonomous’s Brian Foran says big banks seem to be pointing to a roughly 0.15-percentage-point decline in deposit costs from the third quarter to the fourth.

There are still some good reasons to be cautious going into next year. For one, banks are competing as intensely as ever for customers, and the biggest banks are thinking longer-term than just 2020 net interest margin. JPMorgan Chase (JPM) Chief Financial Officer Jennifer Piepszak, for example, said the bank wouldn’t risk a relationship with a corporate customer over “a few ticks” of interest by demanding they accept a lower or zero rate. Banks might also give corporate clients breaks on fees to retain deposits, sacrificing noninterest revenue.

“Clients are…going to continue to be disciplined” about seeking the best deals from their banks, State Street (STT) CFO Eric Aboaf said in October when asked by analysts if he expected noninterest-bearing deposit growth to rebound.

Plus, if customers were to start keeping money in checking accounts at no interest, that might not be a great sign. Mr. Aboaf also warned that clients are more likely to leave cash in noninterest accounts “in a quick recessionary environment.”

Finally, the usefulness of cheap deposits is lessened if banks have nothing to do with the money. Sequential loan growth dropped from 1.1% in the second quarter to 0.7% in the third quarter for the biggest U.S. banks, Fed figures show.

Bank investors have seemed happy with “not as bad as feared” lately. But they would be smart not to get too giddy here, either.