When it comes to owning strong, well-run companies, Warren Buffett's preferred holding time is "forever," but the man known as the Oracle of Omaha will sell a stock when he thinks that the money would be better utilized elsewhere. Read on to learn why our writers thinks Mondelez International (NASDAQ:MDLZ) and Wal-Mart (NYSE:WMT) could be the next stocks to be unloaded by Buffett's  Berkshire Hathaway (NYSE: BRK-A) (NYSE: BRK-B).

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Will Buffett lose his appetite for this stock?

Dan Caplinger (Mondelez International): Among the positions that Warren Buffett has in his portfolio, some clearly carry more conviction than others. Mondelez International is on the low end of Buffett's holdings list, with his company reporting holdings of just 578,000 shares of the food giant, worth only a bit more than $25 million. That might sound like a lot, but when you consider the many positions that Buffett owns that are worth hundreds of millions or even billions of dollars, the small stature that Mondelez enjoys within his pantheon is much clearer.

Rumors had surfaced that more extensive Buffett holding Kraft Heinz (NASDAQ: KHC) might want to merge with Mondelez to take advantage of greater scale in the food industry; that might ordinarily explain a small position in Buffett's portfolio. Yet if any such rumors seemed credible in the past, that credibility largely evaporated when Kraft Heinz instead decided to offer $143 billion to purchase industry rival Unilever (NYSE: UL) (NYSE: UN). Unilever rejected that proposal, and given that Buffett has denied the Kraft Heinz and Mondelez rumors in the past, there's little reason to think the issue will come back up now.

Mondelez has also seen some struggles recently. In its most recent quarterly report, the food giant said revenue fell 7% from year-ago levels, leading the company to perform more poorly on the bottom line than investors had expected. CEO Irene Rosenfeld pointed to "significant economic disruptions, political uncertainties, and slower global category growth" for the poor performance, although she also emphasized that her views on the company's longer-term growth prospects were sound.

In the end, Mondelez is little more than an afterthought in Buffett's portfolio. Buffett might well end up selling the position to help fund a more promising acquisition elsewhere.

Wal-Mart loses its luster

Keith Noonan (Wal-Mart): After reducing its position in Wal-Mart by roughly 90% last quarter, it's not a stretch to imagine that Berkshire Hathaway will liquidate the rest of its stake in the world's largest retailer. Buffett's company has held Wal-Mart shares since 2005, but began rapidly unloading the stock last year -- bringing its holdings in the retail chain down from $3 billion in mid-2016 to roughly $100 million by the end of the year.

Increased competition from online retailers, and Amazon (NASDAQ: AMZN) in particular, was apparently at the heart of Berkshire's decision to shed Wal-Mart shares. Buffett has indicated that the retail sector now looks too challenging. That suggests he will have little reason to hold onto Wal-Mart, and his recent comments back the idea that his company will sell the rest of its position in the big-box retailer -- if it hasn't already.

Check out Buffett's take on Amazon from a recent interview on CNBC's Squawk Box:

It's an entity that's gonna have everybody in their sights. And they have got delighted customers. And it's extraordinary what they've accomplished. And a lot of people like the delivery. That is a tough, tough, tough, competitive force.

He went on to say that, while Wal-Mart has strengths that could aid the company's crucial push into online selling, he also thinks "the online thing is very hard to figure out." So, between the recent divestiture and Buffett's own comments on the tough competitive retail climate, there's a good chance that Berkshire will complete its exit from Wally World in the near future.

Wal-Mart's time may be past for Buffett

Jason Hall (Wal-Mart): I agree with Keith and think Berkshire will soon sell off the last of its Wal-Mart stake. Furthermore, there's a good chance that Buffett has already sold off all of "his" Wal-Mart stock; the small position (less than $100 million in shares) the company still held at last reporting is likely in the portfolio managed by one of Berkshire's other two portfolio managers.

Why has Wal-Mart lost favor at Berkshire Hathaway? In short, Wal-Mart's competitive advantages in scale and distribution may not be as valuable as they once were.

The fact is, fewer people are choosing to go to physical stores, and this trend seems far more likely to accelerate than it is to slow. In the past, Wal-Mart has been able to fuel growth by expanding into new segments, such as groceries, as well as expanding its store base. But at this stage of the game, the dynamic has shifted: Wal-Mart is being forced to play defense simply to maintain current sales, as online competition ramps up, and the power of the company's massive distribution network is watered down by the high fixed expense of its underperforming retail stores.

At the same time, there's an argument to be made that Wal-Mart is actually worth buying; it trades at 16 times last year's earnings, and pays a 2.9% dividend yield. But when it comes to long-term prospects for the retailing behemoth, I think its best days are behind it.

Dan Caplinger owns shares of BRK-B. Jason Hall owns shares of AMZN and BRK-B. Keith Noonan has no position in any stocks mentioned. The Motley Fool owns shares of and recommends AMZN and BRK-B. The Motley Fool recommends UL. The Motley Fool has a disclosure policy.