The stock market's performance hasn't been pretty lately, and bank stocks have been hit particularly hard. While nobody enjoys watching their portfolio's value drop, situations like this produce some of the best long-term investment opportunities. With that in mind, here's why three of our contributors think Synchrony Financial (NYSE:SYF), First Hawaiian (NASDAQ:FHB), and American Express (NYSE:AXP) are worth a look right now.

A beaten-down Buffett bank stock that's worth a look

Matt Frankel, CFP (Synchrony Financial): There are many great bargains in the financial sector after the recent stock market plunge, but one that I'm keeping a close eye on right now is Synchrony Financial.

Hand inserting card into an ATM.

Image source: Getty Images.

If you aren't familiar, Synchrony is a bank with two major business activities. The company is a massive issuer of store-branded credit cards, with partners such as Amazon, Lowe's, and dozens more. And Synchrony has a rapidly growing high-yield savings account platform.

Here's why Synchrony is such a great business. Store credit cards tend to have sky-high interest rates when compared with traditional credit cards. They do have slightly higher delinquency rates, but the high interest income more than makes up for it. And even though Synchrony's deposit platform pays significantly higher interest than most bank savings accounts, it is an excellent source of low-cost capital.

Think of it this way. If you can lend money out at APRs of close to 30%, borrow at 2.2% (the current yield of Synchrony's savings accounts), and about 5% of your loans end up defaulting, there's lots of room for profit. This is an oversimplification, of course, but even after accounting for loss reserves and other factors, Synchrony's net interest margin is a staggering 16.4%.

Synchrony has been especially hard hit recently for a few reasons. Obviously, the broader market sell-off didn't help. In addition, Synchrony's business is seen as especially recession-prone (and it is), so recession fears have caused concern. And Synchrony recently lost a major partner (Walmart), and it will take some time to replace the lost revenue.

In a nutshell, this is an excellent business to invest in, especially while it's beaten down due to recession fears and lost revenue that it should ultimately recover.

Check out the latest Synchrony earnings call transcript.

Surf's up for this bank stock

Jordan Wathen (First Hawaiian): The Hawaiian banking market is unlike anything in the lower 48 U.S. states. Just two banks, First Hawaiian and Bank of Hawaii, control 67% of the state's deposits, making them the go-to banks for local consumers and commercial customers alike.

Less competition for loans and deposits means First Hawaiian can earn attractive returns on its loan portfolio while paying a pittance on deposits. Consider that it doesn't pay any interest at all on nearly 35% of its deposits, and on those on which it does pay interest, it pays very little -- just 0.71% annualized in the most recent quarter.

First Hawaiian shares have been battered this year as the market worries that interest rates may not rise as high as once thought, which is fair given the bank's earnings are highly sensitive to interest rate fluctuations. Even still, First Hawaiian earned attractive returns even during the banking doldrums of 2011 to 2015, when near-zero interest rates weighed on bank earnings across the industry. And with little local competition, it's hard to believe that it will be forced to pay higher deposit rates if rates simply level out from here.

At current market prices, Wall Street has effectively priced First Hawaiian as if to remove any expectation of increased earnings from rising rates. Thus, shareholders are paying only for what they get -- a well-run banking institution in an attractive market -- and pay no premium for the potential lift that rising rates give to the bank's margins. That kind of "free" upside makes First Hawaiian a very attractive investment for buy-and-hold investors.

Check out the latest First Hawaiian earnings call transcript.

Don't leave home without this stock

Dan Caplinger (American Express): Most people see American Express solely as the provider of its namesake charge cards, which has been a successful business almost since its inception. Many American Express cardholders are willing to pay pricey membership fees in exchange for the cachet that the company's cards have among luxury merchants, and despite stiff competition from other credit card network providers, Amex has been able to sustain much of its competitive advantage.

Yet what many investors don't realize about American Express is that it's working hard to keep up with the rapid pace of change in the payment processing industry. A recent partnership with PayPal Holdings and Venmo allows users to pay their monthly Amex bills and send payments using the PayPal and Venmo platforms, and that could drive further revenue growth for the banking company.

Amex's consumer banking unit is another potential growth driver. The company offers online savings accounts and certificates of deposit, and that gives it a chance to cross-sell card customers with banking products. Even as the stock has taken a tumble on increased fears of an economic slowdown, Amex's delinquency rates have thus far remained healthy, and that makes the stock look like a relative bargain at these levels.

Check out the latest American Express earnings call transcript.