The stock market moved lower on Monday morning, with the Nasdaq Composite (NASDAQINDEX:^IXIC) having been down as much as 230 points at its worst levels. By just before 1 p.m. EST, however, the Nasdaq had rebounded significantly and was down less than half a percent.

Among big-name stocks, Tesla (NASDAQ:TSLA) got a lot of attention, as today marked the first day that the EV manufacturer's stock traded in the S&P 500 Index. Elsewhere in the index world, six new stocks joined the Nasdaq-100 Index, with mixed levels of success.

Tesla hits the brakes

Shares of Tesla were down almost 5% in early afternoon trading on Monday. The stock has been on a huge run higher in anticipation of today's inclusion in the S&P 500, and now that index-fund investors have bought into the automaker's stock, bulls are taking a well-deserved breather.

Blue Tesla Model S pointed away from a sunset on a road, with picturesque landscape nearby.

Image source: Tesla.

Right before S&P Dow Jones Indices announced that it would add Tesla stock to their top index, the shares traded at just over $400. On Friday, they hit a high of $695 per share, for a gain of more than 70%. In the process, the company's market capitalization topped $600 billion.

There's a lot of disagreement about what happens to Tesla from here. Some point to rising competition in the EV industry as a potential headwind to Tesla's success. The company is also facing its usual pressure to get more cars delivered to customers as the end of the quarter approaches, drawing criticism for what seems like a never-ending struggle in managing its distribution chain.

Nevertheless, many have high hopes for Tesla's long-term prospects. Few would have expected the stock to soar eightfold in a single year, but it did. And even if share prices take a break from here, there could still be big things ahead for Tesla.

New stocks for the Nasdaq-100

Meanwhile, the S&P 500 wasn't the only index making changes. The Nasdaq-100 list of top nonfinancial stocks trading on the Nasdaq Stock Market also welcomed new companies.

On the plus side, Peloton Interactive (NASDAQ:PTON) was the biggest gainer, rising nearly 2%. Okta (NASDAQ:OKTA) added more than 1%.

Peloton has had an impressive run higher, and today's news about a new mutation of coronavirus causing problems in Europe helped contribute to its bullish thesis. Peloton's connected home-fitness equipment has been a must-have for exercise fans during the pandemic, and even with vaccines coming soon, traditional gyms and fitness centers might not get up and running as quickly as many hope. Similarly, Okta has capitalized on the need for security verification in a remote-work environment, and that trend looks likely to continue regardless of when the pandemic gets under control.

But the move wasn't positive for all the stocks joining the index. Atlassian, Match Group, and Marvell Technology Group were down as much as 1.5% by early Monday afternoon. American Electric Power, which joined by virtue of switching from the New York Stock Exchange to the Nasdaq, was down almost 2%.

In the end, the moves that indexes make aren't really that important. If the fundamental businesses underlying companies do well, then their stocks are likely to go up. Investors shouldn't panic about Tesla and some of the Nasdaq-100's newest members falling on Monday, because in the long run, it won't make a bit of difference.

This article represents the opinion of the writer, who may disagree with the “official” recommendation position of a Motley Fool premium advisory service. We’re motley! Questioning an investing thesis -- even one of our own -- helps us all think critically about investing and make decisions that help us become smarter, happier, and richer.