American Express (AXP -1.44%) is a business icon known the world over. It is also performing well right now as a business. How you view the stock and, more broadly, investing will have a big impact on whether you want to buy, sell, or hold this huge payments processor.

Let's look at these different perspectives and see which one perhaps makes most sense.

Buy American Express

From a big-picture perspective, American Express has a very attractive business. At its core it is a payments processor, allowing customers to pay for products and services with cards that have the American Express logo on them.

American Express charges fees to cardholders and a small fee for facilitating card transactions, which adds up to big numbers across all of its customers. In 2024, the company says it "saw record levels of annual Card Member spending, record net card fee revenues, and a record 13 million new card acquisitions." American Express also expanded the size of the network of retailers that accept its cards.

Image source: Getty Images.

All in, American Express' revenue jumped 6% in 2024 with earnings per share rising 25%. This is a good business that is executing very well today. Part of that has to do with its focus on wealthier customers, which usually spend more. But that focus is also a benefit during economic downturns, as wealthy customers are able to weather recessions better, too.

From a top-level perspective, there's a very good reason to buy American Express stock. However, the success here hasn't gone unnoticed on Wall Street -- which leads to the hold and sell (or avoid) calls.

Hold American Express

If you have owned American Express for a long time, you probably have some paper gains. That's a statement that can easily be made because the stock is currently trading near its all-time highs. This might have some investors considering taking profits. That's not unreasonable, but is it worth selling a good company with the hope of trying to find a better place for the cash? If you have another investment lined up, that's different. Maybe it makes sense to switch.

AXP data by YCharts

However, if you are just worried about the price rise in American Express' shares, well, maybe you should stick it out. As the chart below shows, the stock has experienced many large sell-offs only to rise again to new all-time highs.

You might think selling it and then buying back again after a sell-off makes sense, but would you be able to buy the stock while it is falling? That's a very difficult emotional decision to make. And you'd also have to try to figure out the best point at which to buy back in. Trying to time investments like that is almost impossible.

AXP data by YCharts

For long-term investors, it probably makes sense to stick it out with American Express. If there's a sell-off, which there almost certainly will be, eventually, look at it as an opportunity to buy more of something you already own, know, and like.

Sell (or avoid) American Express

That said, there's a valuation issue to consider here. American Express is trading near all-time highs, its price-to-sales and price-to-earnings ratios are well above their five-year averages, and the 0.8% dividend yield is historically low. This is, without a doubt, an expensive stock.

If you care deeply about valuation, you probably won't want to buy American Express. And if you own it, you might want to move on to a stock that isn't priced so dearly. As noted with the hold thesis, that means selling a well-run company. However, if your investment approach is focused on buying cheap stocks and selling them when they become expensive stocks, you should probably stick with that approach even if it means selling good companies.

American Express is expensive

The buy story here is probably the hardest one to back because paying too much for a good company can turn it into a bad investment. You'll likely need to think in decades if you buy American Express today because there is so much good news priced into the stock price.

Holding is a bit easier to justify. Sticking with a great company for the long term is exactly what some of the best investors do, including American Express shareholder Warren Buffett. The sell or avoid thesis is the easiest, given the lofty valuation. If valuations matter to you, American Express isn't likely to be your cup of tea today.