The past year set a record for sales of cars, but investors are signaling doubts about the companies that make them, reports The Wall Street Journal.

Shares of auto makers such as General Motors Co. and Ford Motor Co. began sliding late last year. This year, they have fallen even faster than the battered broader market.

Analysts and investors attribute the declines to worries that rising U.S. interest rates could crimp auto finance and to fears that auto sales may have peaked. They are also concerned that the slowdown in China, the world’s largest car market, may be worse than expected. The result has been a setback for an industry that in the U.S. just enjoyed its best year ever.

Shares in GM, the No. 1 U.S. auto maker by sales, have dropped 11% this year through Monday’s close. Ford’s stock has fallen 9.4%, and shares in AutoNation Inc., the nation’s largest dealership operator, have slumped 19%.

The drops stand out against the 5.9% decline for the Dow Jones Industrial Average, which posted its worst ever start to a year. They come even after a combination of low gas prices, a strengthening labor market and low interest rates propelled U.S. car sales to 17.5 million in 2015, surpassing a peak last hit 15 years ago.

“How much higher than 18 million units can we go?” said Brian Hennessey, a portfolio manager at Alpine Funds, which manages $4 billion. “It’s pretty much a peak number.”

AutoNation Chief Executive Mike Jackson said he believes the fourth quarter of 2015 will mark the start of a plateauing of sales.

“Everybody was talking about how great the month of December was,” Mr. Jackson said on the sidelines of the North American International Auto Show in Detroit on Monday. “But if you take away the extra selling days and the incentives, sales were flat in what is a bellwether month.”

The auto industry’s seasonally adjusted annual selling pace fell to 17.3 million in December from 18.2 million in November.

Sentiment in the options market has turned sour in recent days, suggesting that traders don’t see the auto makers’ stocks rebounding any time soon. Trading in options to sell Ford or GM stock on Thursday and Friday sharply outpaced trading in options to buy the shares, according to data provider Trade Alert.

A Ford spokeswoman said the company remains focused on delivering profitable growth for its stakeholders. “We do not run our business based on day-to-day stock changes,” she said. GM didn’t immediately respond to a request for comment.

Mr. Jackson is warning auto makers, especially those producing luxury cars, to reduce output or face a pricing war that will hurt the industry overall. He said AutoNation has cut its car orders and is instead bulking up on pickup trucks and sport-utility vehicles.

“Some auto makers have moved to a push rather than a pull mentality,” he said. “Rather than waiting for dealers to order they are sending more inventory. It’s a recipe for disaster.”

Mr. Jackson’s comments echo his warning last Wednesday that a bulging inventory of unsold cars is beginning to erode profit margins.

The comments fueled investors’ concerns that manufacturers will have to turn to deals or discounts to get customers to buy more cars.

“Manufacturers could lose pricing power,” said Peter Stournaras, portfolio manager of the BlackRock Large Cap Series Funds.

Mr. Stournaras said he prefers shares of auto-parts makers to auto makers. He figures that low gasoline prices could encourage consumers to drive more, in turn prompting a greater need for replacement parts.

Shares of Delphi Automotive PLC, a U.S. auto-parts supplier, have dropped 12% so far this year through Monday.

Some investors say the selloff in car makers’ shares has been overdone. Ford recently traded at 9.0 times the last 12 months of earnings, according to FactSet. Its five-year average is 9.5. GM’s price-to-earnings ratio was recently 6.2, less than its five-year average of 9.1. AutoNation recently traded at 12.3 times the past year of earnings versus its five-year average of 18.0.

These investors argue that a monthslong slump in oil prices has fattened consumers’ wallets, and the continued recovery in the labor market has begun to result in slightly higher wages. That, they say, bodes well for continued strength in auto sales.

“All the key metrics that we use to gauge the health of the auto industry are as healthy as they have ever been,” said Amit Kapoor, senior equity analyst at Loomis, Sayles & Co. Mr. Kapoor owns GM shares.

Another reason for optimism, these investors say: Cheap gasoline prices remain a powerful driver for sales of the big cars that are most profitable for car companies.

“The auto makers generally make more money selling big cars, like pickup trucks and SUVs, than they do making sedans,” said Annie Rosen, portfolio manager for Fidelity Select Automotive Portfolio. “When you have low gas prices, like we do today, the average consumer willingness to buy a car that uses more fuel goes up.”

Sales of trucks and sport-utility vehicles helped Ford and GM post record operating profits in North America in the third quarter. Ford is set to report fourth-quarter earnings Jan. 28 and GM is scheduled to post results Feb. 3.