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Tesla shares rose almost 20% Monday, hitting an all-time high, only to spike another 14% Tuesday. The question is why? The move, frankly, baffled investment pros.

Few dispute things are looking up for the electric vehicle pioneer, but few understand the magnitude and persistence of the rally. The pros, however, offered a few ideas when asked. And some even guessed what could be next for shares.

But first a rundown of recent numbers. They are incredible. Monday was the largest percentage increase in Tesla (ticker: TSLA) stock since May 9, 2013, when shares rose 24.4%. The shares are up more than 120% year to date and up almost 195% over the past 12 months, crushing comparable gains for the S&P 500 and Dow Jones Industrial Average.

Cathie Wood, founder, CEO and CIO of Ark Invest, updated her bullish base case for Tesla to reflect a price target of $7,000 by 2024. With that, Wood discusses the key factors that will continue to drive the market for electric vehicles in quarters to come.

Tesla shares are up about 400% from their $178 52-week low. The rally off the June 3, 2019 low has created almost $130 billion in shareholder value. That is more than the market capitalization of General Electric (GE). Just incredible.

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(Oh, by the way, Tesla stock hit $968.99 a share at one point on Tuesday, before closing with about $80 lost. Shares were up almost $12 in after-hours trading.)

Now for the 20% move. On Monday, one analyst at a smaller brokerage firm suggested Tesla shares could hit $7,000 by 2024 Monday. It is a bold call, but it isn’t the reason shares rocketed higher. Wall Street has influence, but not that much influence.

Analysts, for the most part, have been chasing Tesla’s rally, just like investors. Wall Street’s consensus price target for Tesla stock has gone from about $300 a share to $500 a share over the past three months. It is a large move, but it lags far behind even the year-to-date gain in Tesla stock.

The biggest fundamental news anyone could point to Monday was an earnings report from Tesla battery partner Panasonic (6752.Japan). Management talked about profits from a North American battery facility and improving utilization. Profits on batteries for Panasonic is a sign battery costs are falling. It is good news because it means that everyone in the electric-vehicle value chain can make money, including Tesla.

But whether it’s 20% worth of good news is still debatable. After all, that works out to about $25 billion in Tesla market value.

That leads to the inevitable short-squeeze explanation for the violent stock rally. Tesla shares are more heavily shorted than average, meaning lots of bearish investors have borrowed stock and sold it, betting on price declines. If the price falls, they can buy shares back at a lower price, replace the borrowed stock, and pocket the price difference.

The shorts, in the case of Tesla, are getting slaughtered. Short interest data provider S3 Analytics notes bears have been covering short bets lately, but Tesla remains one of the most heavily shorted stocks in the market. The shorts lost more $2.5 billion on Monday alone. Year-to-date losses exceed $8 billion.

The biggest risk traders see is the parabolic move in Tesla’s share price. Traders prefer stable, consistent gains. And when stocks get far away from their moving averages, traders start to worry. Stocks, of course, go up and down. And moving averages are levels where stocks often pause when rallying off lows, or dropping from highs. Tesla’s 50-day moving average is about $450 a share. It is unusual when a stock is about 100% higher than its 50-day moving average. That makes traders nervous.

On Tuesday morning, New Street Research analyst Pierre Ferragu lowered his rating for Tesla to the equivalent of Hold from Buy. His target price for shares, the highest on the Street, is $800. He’s a longtime bull and believes in Tesla’s technological lead in electric-vehicle production. Still, his new found conservatism couldn’t derail the stock rally.

Tesla bull Gary Black—former Wall Street analyst and former chief executive of Aegon Asset Management—weighed back into the Tesla debate Tuesday via Twitter.

He sees sales volumes tripling by 2024. That, Black says, justifies a $360 billion market value, or about $2,000 a share.

There is a saying in the stock market that the market will cause the most pain for the most investors most of the time. It is a useful rule of thumb. It means you never can tell what the stock market will do over a short period.

In the case of Tesla, investors were sure the rally couldn’t continue. So, of course, that’s just what happened.

The effect of the surge is that Tesla becomes more heavily weighted in benchmarks used to track funds’ performance, forcing asset managers to buy to keep up, Baird analyst Ben Kallo told Barron’s. Like Ferragu, he has long been a bull on the stock, but recently changed his rating from the equivalent of Buy to Hold.

Corrections & Amplifications:

Monday’s gain in Tesla’s stock price was the biggest percentage move since May 9, 2013. An earlier version of this article said it was the largest leap since May 9, 2019.

Write to Al Root at allen.root@dowjones.com