Here's something to ponder while we await Tesla's (NASDAQ:TSLA) first-quarter earnings report after the bell on Wednesday: One of the company's biggest shareholders has been selling steadily for a while now.

No, CEO Elon Musk isn't preparing to slip out the back door -- at least, not as far as we know. And I'm not talking about insiders selling pursuant to a "Rule 10b-5" plan.

A prominent portfolio manager at Tesla's largest institutional shareholder seems to be in the process of gradually cashing out. If others follow, that could quickly become a problem for other Tesla shareholders.

A dark blue Tesla Model 3, a sleek compact luxury sports sedan, on a beach road at sunset.

Tesla's burn rate, and its ongoing struggles to get the Model 3 sedan into full production, have called key parts of the investment case for Tesla's stock into question. Image source: Tesla, Inc.

Is Fidelity losing faith in Tesla?

The first name on the list of Tesla's top institutional shareholders might seem a bit cryptic: "FMR, LLC." I'll decode it for you: That's Fidelity Investments, or properly, "Fidelity Management & Research," the old name for Fidelity's mutual-fund management arm.

As of the end of 2017, FMR owned 16,698,292 shares of Tesla, a 9.89% stake in the company. Nearly a quarter of those shares were held by one of Fidelity's biggest and most prominent funds: Fidelity Contrafund (NASDAQMUTFUND:FCNTX), managed since 1990 by ace stock-picker Will Danoff.

With $124.1 billion in assets, Contrafund is a giant. But Danoff has managed to outperform the S&P 500 for years with a simple strategy: Buy well-managed, "best-of-breed companies" with growing earnings at good prices, and hold them for a while.

Tesla doesn't necessarily fit that description. But Danoff isn't averse to the occasional momentum play, and he clearly saw something he liked: As of June 30, 2017, Contrafund held 5,678,382 shares of Tesla, a roughly 3.4% stake.

That was a good moment to be holding a whole lot of Tesla shares. The stock had just hit an all-time high on June 19.

TSLA Chart

TSLA data by YChartsChart shows Tesla's share price history from March 1, 2017 through May 1, 2018. 

At the end of June, it looked to some like Tesla's share price was headed for the moon. But at some point in the next few months, Danoff started selling. Look at how Contrafund's Tesla holdings have fallen over the last nine months.

Date Tesla Shares Held Source
June 30, 2017 5,678,382 Semi-annual report
Dec. 31, 2017 3,936,442 Annual report
March 31, 2018 2,326,168 Most recent monthly holdings report 

Data source: Fidelity Investments. 

It looks like Danoff is quietly selling down his stake. There's no way to tell whether he plans to sell all of the fund's Tesla shares or not, of course. But he has cut Contrafund's stake in Tesla by more than half since the end of June. Will other fund managers follow his lead? 

Are other Fidelity fund managers selling?

There are three other actively managed Fidelity funds with big Tesla holdings. None are selling at the rate Contrafund has been selling. 

Fund Date Tesla shares held Source
Fidelity Blue Chip Growth Fund (NASDAQMUTFUND:FBGRX) July 31, 2017 1,837,333 Annual report
  Jan. 31, 2018 1,613,430 Semi-annual report
  March 31, 2018 1,712,253 Monthly holdings report
Fidelity Growth Company Fund (NASDAQMUTFUND:FDGRX) May 31, 2017 2,042,700 Semi-annual report
  Nov. 30, 2017 1,749,000 Annual report
  March 31, 2018 1,697,813 Monthly holdings report
Fidelity OTC Portfolio (NASDAQMUTFUND:FOCPX) July 31, 2017 2,095,101 Annual report
  Jan. 31, 2018 2,038,321 Semi-annual report
  March 31, 2018 1,917,121 Monthly holdings report

Data source: Fidelity Investments.

A fund's holdings will fluctuate a bit as the manager makes trades to meet redemptions or invest new money; the shifts we see in Tesla holdings at Fidelity OTC Portfolio and Fidelity Blue Chip Growth Fund are probably normal.

Fidelity Growth Company Fund's holdings of Tesla are down 17% from May 31, 2017, but that's probably not the beginning of a sell-off. It looks like Steven Wymer, who has managed Fidelity Growth Company Fund since 1997, might have taken some profits as Tesla's share price peaked last year. 

So what does this mean for Tesla's stock?

Here's the thing about Tesla stock: Between Elon Musk, other Tesla insiders with significant stakes, and institutional holdings, about 87% of Tesla's shares outstanding are sitting still. The stock that's traded every day represents just 13%, roughly, of Tesla's shares outstanding.

That's one reason why Tesla's stock is so volatile. It may also be a reason why Tesla's share price has been sky-high relative to fundamentals: Demand for shares has exceeded supply.

But the flip side of that is this: If the institutions start selling off Tesla's stock in a serious way, without other institutional buyers stepping in to buy at high prices, the supply of Tesla shares in the market might very quickly grow to exceed demand. And that could happen: If there are signs that a few other fund managers (at Fidelity or elsewhere) are joining Danoff, we might see a rush for the exits.

Or put another way, if institutional fund managers start to lose faith in Tesla, Tesla's stock price is likely to head south in a hurry -- no matter what tonight's earnings report looks like.

John Rosevear has no position in any of the stocks mentioned. The Motley Fool owns shares of and recommends Tesla. The Motley Fool has a disclosure policy.