Few announce their divorce on social media. But then, Amazon founder and Chief Executive Officer Jeff Bezos isn't most people.

The world's richest man tweeted Wednesday that after a "long period of loving exploration and trial separation," he and his wife, MacKenzie, would split.

Also, unlike other people, Bezos' divorce may impact one of the world's most valuable publicly traded companies. Bezos's wealth is largely based on his shares of Amazon stock. And since Washington State, where the couple has lived, has community property divorce laws, that could give MacKenzie Bezos a claim on half of Jeff Bezos' fortune, as they married one year before he started the company. That raises questions of what impact the divorce might have on the company and its leadership.

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A 2013 Stanford study, "Separation Anxiety: The Impact of CEO Divorce on Shareholders," noted that there are three different ways in which the end of a chief executive's marriage can have an effect on a company.

One concerns the productivity and concentration of the CEO. The emotional impact and distractions from the practical issues that come up in a divorce proceeding can affect how well a chief executive can manage a company. Although not routinely, CEOs, even at prestigious companies, will resign in under two years.

A second issue is the perception of risk. Companies typically grow by undertaking strategies that come with a degree of inherent risk, like acquiring another business or introducing new product lines. A CEO during and after a divorce will have concerns about personal wealth that can be greatly reduced. The executive might become too risk adverse to protect existing wealth in corporate stock or, on the contrary, chase after too much risk in a hope to "win back" what was lost.

The third issue is control. A CEO with a large ownership stake — and Bezos is Amazon's single-largest shareholder, with 16.3 percent of the stock — might be forced to sell shares to satisfy a divorce settlement. That would reduce the executive's control over the company and possibly cause a drop in share value because of the large amount sold.

Investors don't seem too worried, at least for the moment. Amazon shares were up slightly on Wednesday a few hours after Bezos released the information. That may be due to the way Bezos phrased his message, stressing the continued good relations and sense of partnership between him and his wife.

Knowing what will happen is impossible. West Palm Beach divorce attorney Jeffrey Fisher told CNBC that valuing the stock could be contentious. "There would be an argument by the attorneys that the Amazon stake is not worth as much without Bezos in control, so that would affect any settlement," Fisher said.

On the contrary, MacKenzie Bezos might, instead, opt for a settlement that didn't require a sale of shares and the corresponding dilution of control and value.

But, knowing the future is impossible. Particularly when $137 billion is on the line.