The Nasdaq Composite index is up 29.5% year to date, which has some analysts saying the index has entered a new bull market (others contend it still needs to reach a new all-time high to qualify). The S&P 500 has also flirted with bull market territory this year and is currently up 14.5% year to date.

When the new bull market will actually begin is anyone's guess. The more important question for investors is, how will an investment do in the long run beyond any single bull market that is about to begin?

These indexes are up because a lot of growth stocks are seeing their valuations soar in 2023. But two growth stocks are still considered pretty cheap at the moment despite having great long-term potential -- Nasdaq (NDAQ 0.14%) and American Express (AXP 1.15%).

Here's why they are both good stocks to own for the long run, regardless of what kind of market were are in at the moment.

1. Nasdaq

Nasdaq is a publicly traded multinational financial services company that owns and operates three U.S. stock exchanges and seven European stock exchanges. Its stock is a relative bargain right now, with a forward price-to-earnings (P/E) ratio of 18.9, which is below its historical range in recent years. The valuation has dropped because the share price is down nearly 15% year to date, which may seem surprising when Nasdaq's namesake exchange is up nearly 30% this year.

The stock price drop likely comes, in part, from investor reaction to net revenue rising just 4% year over year to $925 million in the second quarter and net income dropping 13% year over year to $267 million. This was related to higher expenses resulting from the recent acquisition of Adenza, a company that specializes in risk management, regulatory reporting, and compliance software. The $10.5 billion price tag for Adenza was seen as a bit too much by the market. But strategically, the acquisition makes a lot of sense because it helps Nasdaq continue to diversify its revenue stream beyond its indexes, exchange, and trading operations.

Adenza's add-ons further bolster Nasdaq's solutions business, including risk management and regulatory compliance software and services. This opens up a new addressable market for Nasdaq. The recurring subscription and fee-based income from Adenza is expected to add approximately $300 million of annual cash flow to Nasdaq.

Nasdaq has been a stellar performer over the years, posting an annualized return of 17.9% over the past 10 years as of Aug. 23. This acquisition should help it become a better, more stable long-term performer, especially during periods when the bulls aren't running.

2. American Express

American Express, the third-largest credit and payment processor in the world, is even cheaper than Nasdaq right now, with a P/E ratio of 16, a forward P/E of 14.3, and a five-year P/E-to-growth (PEG) ratio of just 1.1. That is well below the current P/E ratio of the S&P 500, which is about 25.

American Express has had a good year, with its stock price up about 8% year to date. The most recent quarter was particularly strong; the company posted record revenue of $15.1 billion in the quarter, a 12% year-over-year increase. It was the company's fifth straight quarter of record year-over-year revenue. Net income was up 11% year over year to $2.2 billion. The increased numbers came courtesy of a record level of card member spending, up 8% over the same quarter the previous year.

There are two key trends that bode well for American Express and its ability to continue to have long-term success. The first is travel and entertainment spending. This has always been the company's bread and butter, and it took a big hit after the pandemic. But it has come surging back to surpass pre-pandemic levels, with spending by card members up 14% year over year.

The second major trend is the growth American Express has consistently seen from younger populations, specifically Millennials and Gen Z. These groups are the fastest-growing segment of American Express' clientele. In the second quarter, 70% of new fee-based accounts and 60% of new accounts overall were from these two cohorts. The younger generations are drawn to the perks that come with being an American Express cardholder. In the most recent quarter, spending by these demographics increased 21% year over year. 

Locking in these young consumers now certainly bodes well for the company's continued long-term growth. And it is protected by a competitive moat as one of just a handful of major credit providers.

Like Nasdaq, American Express has an excellent brand, and it is trading at a reasonably low valuation. Investors may find that this is a good time to consider these two solid stocks -- for the bull market and beyond.