American Express (AXP -0.62%) has been quite the express to wealth in recent times. Over the past three years alone, the stock's price has risen by 76%, a rate that tops the S&P 500 index's 45% gain. It also handily beats the increases of payment card rivals Mastercard (MA 0.07%), at 28%, and Visa (V -0.23%) at 20%.

What's the secret sauce that makes AmEx such an attractive investment? Let's pick that apart and, while we're at it, determine whether the stock is a buy at its current price.

Credit where credit is due

To put a dollar figure on AmEx's performance across that stretch of time, had you plonked down $10,000 on the stock in June 2020, that stake would be worth $17,077 today. That's not bad at all for a three-year span, huh?

As a famous payment card giant with a long history, AmEx probably doesn't need much of an introduction. However, it's important to understand how the company differs from Visa and Mastercard, and how it goes about making its money.

It's a closed-loop operator, which means that it acts as both the issuer of the credit on its credit cards and the processor of the purchases made on them.

This sets it apart from both of its rivals, as Visa and Mastercard are open-loop companies. They are processors, but not issuers. This is why your bank or other financial institution is the entity issuing your Visa credit card and sending you reminders if you don't pay your bills on time.

So the game is different for AmEx. Its goal is to win over the more credit-worthy card holders who don't mind paying a standard annual fee for their plastic (e.g., a hefty $695 for the Platinum Card). In return, those cardholders (or "members" in AmEx's elevated way of referring to them) gain access to the company's sprawling, perk-filled Rewards program.

By contrast, Visa and Mastercard aim for volume; as processors only, they take only a tiny cut of each transaction. The trick here, then, is to have a vast number of cards in circulation, which all things being equal translates to a higher volume of purchasing.

As a result, AmEx has far higher revenue -- after all, it's collecting interest and late fees on unpaid credit -- than its pair of peers. In fact, its 2022 top line exceeded $55 billion, which topped the $51 billion-and-change revenue of Visa and Mastercard combined for that year.

Swipe and win

As the company behind the more exclusive credit cards on the scene, AmEx undeniably benefits from snob appeal. It's the card brand for those with disposable income who want an instrument that can substantially leverage their buying power. 

As such, a long-tail rise in the economy nicely supports its business. Since the dark days of the coronavirus pandemic, AmEx has really been on the rise. Its annual revenue leaped from just over $38 billion in 2020 to nearly $44 billion the following year, then jumped again to a cool $55.6 billion in 2022. The public loves their AmEx cards, and they're not shy to buy plenty of stuff with them.

Of course, this doesn't necessarily mean the stock is a good investment. Let's take a gander at its valuations. Its forward P/E currently stands at under 16, which is cheap compared to both Visa (at 23) and Mastercard (31). AmEx also has the edge over its rivals with its dividend; it currently yields 1.4%. That's hardly the most generous payout on the market, but it handily beats Visa's 0.8% and Mastercard's 0.6%.

Meanwhile, analysts are (reasonably) expecting continued growth for this always-effective payment card operator. They're modeling hefty 17% growth in annual income this year over 2022, accompanied by a 13% improvement in per-share profitability.

And that's for 2023 alone. We're still in the midst of the war on cash, and as more consumers -- particularly the more affluent ones -- gravitate to plastic and digital means of payment, AmEx will gain more "members." And the company will surely continue to be an effective marketer of those ever-attractive cards. So, in my estimation at least, its stock continues to look like a buy.