Anyone who follows Warren Buffett knows that Apple (AAPL 0.62%) is the largest position in his Berkshire Hathaway (BRK.A -0.28%) (BRK.B -0.24%) portfolio. The technology giant currently makes up a whopping 41.2% of Berkshire's total equity investments.

Which stock ranks second? For now, it's Bank of America (BAC 0.73%). However, the big bank might not hold onto its spot for too much longer. I predict another stock will be Buffett's second biggest holding after Apple by 2027.

The current top contenders

First, I fully expect Apple will remain at the top of the list for Berkshire for years to come. Although the conglomerate trimmed its position in Apple a little in the fourth quarter of 2023, Buffett still thinks highly of the company and its management.

I don't anticipate Apple's shares dropping so much that it falls out of the No. 1 position, either. Sure, the stock is arguably overvalued considering its meager growth. However, artificial intelligence (AI) could provide a much-needed catalyst for Apple over the next few years.

Which stock could knock Bank of America out of its second-place perch? Only three other stocks currently make up more than 5% of Berkshire's portfolio.

It wouldn't be too much of a stretch for American Express to move past Bank of America. Berkshire's stake in AmEx is worth nearly $36 billion compared to $39.1 billion for BofA. I don't think Buffett will pour a lot more money into American Express. However, AmEx stock could grow faster than Bank of America over the next three years -- perhaps enough to slide into the No. 2 spot in Berkshire's portfolio.

The Coca-Cola Company and Chevron have steeper hills to climb. Berkshire owns $24.7 billion of Coca-Cola shares and $20.8 billion of Chevron. I doubt Buffett will buy more Coke stock, but he could increase his stake in Chevron (as he did in Q4). Still, it's unlikely that either stock will replace Bank of America behind Apple, in my view.

Why another stock could leapfrog into No. 2

However, another stock could vault past Bank of America, American Express, Coca-Cola, and Chevron to become Buffett's second biggest position. I think the ingredients are in place for Occidental Petroleum (OXY 0.24%) to leapfrog these stocks.

Buffett loves Oxy. He wrote to Berkshire shareholders earlier this year that he expects to own shares of the oil and gas producer "indefinitely." He also praised Occidental CEO Vicki Hollub, saying she knows "how to separate oil from rock, and that's an uncommon talent, valuable to her shareholders and to her country."

More importantly, Buffett continues to show his affection for Occidental by aggressively buying shares. He initiated a position in the stock in the first quarter of 2022. Berkshire now owns 28% of the company. The conglomerate won regulatory approval in August 2022 to acquire up to 50% of Oxy.

At the rate it's going, Berkshire could easily own half of Occidental by the end of 2027. Based on the company's current market cap, its stake would be worth roughly $30 billion. That's still well below the level needed to replace Bank of America as Berkshire's second largest holding, but I don't expect Oxy's market cap to stay at the current level.

Hollub predicts an oil supply shortage by late 2025. If she's right, Occidental and other oil stocks should move significantly higher. I wouldn't rule out the possibility of a boost from advances in the company's direct air capture technology either.

Should you buy Oxy hand over fist?

Investors shouldn't buy Occidental stock only because I've predicted it could be Buffett's second largest holding by 2027. I've been wrong before; I could be wrong in this case.

However, I like the prospects for oil stocks, in general, over the next few years. Occidental could be one of the industry's top performers, especially if Buffett continues to scoop up shares (which I suspect is likely).