Daily Report: Mr. Dorsey’s Companies Go on a Wild Stock Market Ride

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It isn’t easy being a paper billionaire.

The new year hasn’t been an easy one for the stocks of most companies, even tech giants like Amazon that by most accounts are doing extraordinarily well. For companies like Square and Twitter, which no one would accuse of doing extraordinarily well, 2016 has been even tougher. And for Jack Dorsey, the chief executive of both companies, recent stock drops have resulted in paper losses that have pushed him out of the billionaire’s club.

Twitter dropped dramatically Wednesday morning, only to spike dramatically around midday — thanks to what some reports said was a single, large transaction — and to close up 4.1 percent for the day. The company’s share price is still down 25 percent this year.

Square had an equally odd day on Wall Street. It fell below its $9-a-share I.P.O. before recovering. For the year, Square’s stock price is down 28 percent.

In fairness to Mr. Dorsey, despite outsize expectations from some on Wall Street, few have been as blunt regarding Twitter’s challenges since he returned to the San Francisco company’s chief executive office over the summer. In fact, his first few months on the job looked more like a resetting of expectations than a dramatic turnaround. His efforts so far have appeared focused on the long term — figuring out how to turn a company that seems to have found its natural audience limit into a mainstream fixture.

As for Square, it’s a company with a recent public offering and interesting technology that few seem to know has staying power.

For Mr. Dorsey, it would have been a good thing if he were too busy running both companies on Wednesday to notice their whipsawing share prices.