Stock splits don't do anything to change the fundamentals of a stock, but investors still like them nonetheless.

Some believe they make the stock cheaper, which is not really true. Though stock splits do lower the individual share price, they don't affect the valuation of the stock, which is what actually matters. Additionally, there's some evidence that stocks tend to outperform the S&P 500 after their split. That could be because management chooses the timing of the split, and they're likely to do it when they're confident that the stock can keep rising.

Additionally, if investors see the stock split as a bullish signal, that could become a self-fulfilling prophecy, driving the stock up because people expect growth after the split.

While there are a number of attractive stock-split stocks on the market, not all of them are buys. Let's take a look at one stock-split stock worth buying and another one to avoid.

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One stock-split stock to buy

O'Reilly Automotive (ORLY 1.96%) has quietly been one of the best-performing stocks of the 21st century. The auto parts retailer has delivered a steady stream of growing profits and established a competitive advantage in serving the commercial channel, meaning repair shops. In that business, having the needed part in stock and being able to deliver quickly is essential. O'Reilly has also blanketed the U.S. with stores to drive its growth. Since 2000, the stock is up more than 12,000%, making it a 100-bagger.

Given those gains, it shouldn't be a surprise to see the company finally issuing a stock split. It announced a 15-for-1 split on June 2, which went into effect on June 9.

O'Reilly trades at a premium, but it's well-deserved. In the first quarter, comparable sales rose 3.6%, and the company continues to open new stores, with 38 new locations in Q1. For the full year, it sees comparable sales of 2% to 4%, and earnings per share of $42.90 to $43.40 (before the split was announced). That's about $2.90 in earnings per share.

O'Reilly's distribution network is a key source of competitive advantage for the company. Having the right inventory in stock has helped it serve both the commercial and DIY channels. The company has also benefited as the average age of a car on the road has increased. This means that Americans are spending more money on repairs, instead of buying new cars.

One stock-split stock to avoid

The stock-split stock to avoid is Interactive Brokers (IBKR -3.19%), a leading discount brokerage, which issued a 4-for-1 stock split in June.

It's true that Interactive Brokers' recent performance has been impressive. In Q1, commission revenue rose 27% to $516 million, buoyed by higher trading volume. As with other brokerages, the bull market has been good to Interactive Brokers, as investors tend to be more active when they believe stocks will go up.

Customer accounts in the quarter were up 32% to 3.87 million, and equity rose 34% to $664.5 billion.

Those numbers are all positive and show the business delivering solid growth. However, the reason to avoid the stock is that most of its revenue currently comes from interest income, and that may not be sustainable. While interest rates have remained elevated due to fears about inflation coming back, the Federal Reserve still aims to bring down interest rates, which will cool off Interactive Brokers' most valuable profit stream. The company collects interest on both the cash it holds and margin loans, and says that yields are generally a reflection of benchmark interest rates, which are greatly influenced by the Fed. Cash and margin loans contribute a similar amount of its income.

Additionally, the stock is trading at a price-to-earnings ratio of 35, though interest rate cuts or a sell-off in stocks could wipe out profits. While the company deserves credit for its execution and the growth of the business, the valuation and reliance on interest income set the stock up for a potential pullback.