American Express (AXP 0.14%) stock has been a rocket. During the past 90 days, the shares have risen by more than 30%.

With the stock trading at all-time highs, it's reasonable to question whether the valuation has gotten out of hand. The stock is no longer the bargain it was a couple of months ago, but there are many reasons American Express remains a wonderful buy-and-hold investment.

These numbers tell a promising story

If a certain investment rises considerably in value, that doesn't always mean it's become overpriced. It's important to dig into the numbers to understand what's driving the performance. Many times, a stock can skyrocket in price and still be a relative bargain. That appears to be the case for American Express.

Before the stock went on its latest run, the shares traded at a free cash flow yield of nearly 18%, notable for a brand that's globally renowned and has repeatedly earned the praise of investing greats like Warren Buffett. In retrospect, this was a mistake by the market. The shares have traded at such levels only briefly over the past decade. Add in a rapid decline in debt levels right as interest rates started to rise, and American Express was in a terrific position to succeed.

AXP Financial Debt to Equity (Quarterly) Chart

AXP Financial Debt to Equity (Quarterly) data by YCharts

On paper, American Express stock was a steal back in November. In many ways, the stock remains a bargain today. Investors still secure a nearly 11% free cash flow yield, and debt levels remain well below historical norms, giving American Express operational flexibility while interest rates remain elevated.

Equally impressive, American Express continues to generate high returns on equity despite falling debt levels. Often, return on equity, a rough measurement of how efficient a company is at converting earnings into shareholder wealth, can be boosted by increasing debt levels.

The fact that American Express has been able to maintain a high return on equity even with relatively lower debt levels is a sign of its efficient business model and competitive advantages. At its foundation, American Express is an asset-light business. That means it can generate profit without needing to invest heavily in physical assets like property and equipment. Moreover, the company's brand alone is likely worth tens of billions of dollars. It would take a competitor decades to replicate its business model and brand recognition.

AXP Return on Equity Chart

AXP Return on Equity data by YCharts

Is this a forever stock?

What is a forever stock? As the name implies, it's a stock you can buy and hold forever. American Express is such a stock.

There are several things to look for when identifying forever stocks. The most important, however, is finding a company that creates a positive feedback loop. That is, whenever the business grows, that past growth creates future growth.

Consider a company like Amazon, arguably another forever stock. The more that buyers flock to its platform, the more sellers are encouraged to follow suit. That attracts even more buyers, attracting yet more sellers. It's a positive feedback loop that propelled Amazon to a trillion-dollar valuation.

American Express benefits from its own feedback loops. The company has roots going back to 1850 . Closing in on two centuries of operation, American Express has built an enviable brand, earning eighth place on Fortune's 2024 list of the most admirable brands.

American Express has a trusted name, which attracts a constant influx of new customers. Having more customers use its products only accrues more brand value, attracting even more customers.

American Express also benefits from powerful network effects, similar to both Visa and Mastercard. When using a credit card, for example, you have a finite list of accepted networks. Visa, Mastercard, and American Express are almost always on that list. So many people use these card networks that merchants are in many ways forced to accept them. Having more merchants accept American Express means more people will use American Express products, thus forcing more merchants to follow suit -- yet another positive feedback loop.

From a financial standpoint, American Express shares are hardly overpriced, even following the latest spike. The most attractive aspect of this stock, however, isn't short-term performance. American Express has built a business that will continue to benefit from positive feedback loops for decades. Getting a bargain valuation is nice, but the best strategy for stocks like American Express is simply to buy and hold them forever.