The stock has doubled in the past three months, up 101% in a run fueled by optimism about its vehicle deliveries, expanding production and overall profitability.
Baird downgraded Tesla to neutral from outperform on Thursday before the bell, while CFRA downgraded Tesla to sell from hold after the bell Wednesday. Bernstein technology analyst Toni Sacconaghi also said the stock's run-up may have gone too far.
"We have become incrementally cautious on the stock, given its huge recent surge in price," Sacconaghi said in a note to investors Thursday.
Although Bernstein did not change its rating or price target, Sacconaghi warned that Tesla's fourth-quarter results have "the potential for weaker margins" while the first-quarter may see "softness" after the elimination of subsidies in the U.S. and the Netherlands. Bernstein has a market-perform rating on the stock.
Tesla shares closed heavy trading Thursday down 2.2% at $481.34. The stock opened trading up as much as 1%, nearing $500 a share, before later reversing and falling.
Baird recommended that investors take profits after Tesla's recent stock run.
"While we remain constructive on TSLA's long-term prospects, we now believe estimates are properly calibrated (particularly on the buy-side) and valuation appears more balanced. Admittedly battle-worn after a contentious two year period (reach out to hear our best stories) we will wait for further execution to get more positive on the name," Baird analyst Ben Kallo said.