By David Benoit and Rob Copeland

Aug. 10, 2016 6:13 p.m. ET

Activist investor Marcato Capital Management LP is pushing Goodyear Tire & Rubber Co. to return $4.5 billion to investors over the next three years in a bid to boost the tire giant’s flagging stock price.

In a letter to the Goodyear’s board Tuesday, the activist hedge fund says it is “impressed” by Goodyear’s management and recent performance, but lamented its languishing stock. The company’s shares are down 15% this year, even as rising truck and SUV sales and falling gas prices lifts demand for its tires.

“We believe if the company targets this magnitude of capital return, it would create significant shareholder value, and we would not be surprised to see the share price increase by as much as 50%-100% as a result,” Marcato’s Richard “Mick” McGuire wrote in the letter, which was reviewed by The Wall Street Journal.

A spokesman for Goodyear said the company wouldn’t comment on its plans before its Sept. 15 investor day in Boston.

Mr. McGuire, a protégé of well-known activist investor William Ackman, founded Marcato in 2010. The San Francisco firm first invested in Goodyear in early 2014 and held a 1.9% stake in the company as of June 30, down from 3.8% in September. The fund is down 2.7% this year after rising more than 10% in July, according to a person familiar with the matter.

Tuesday’s letter isn’t a threatening missive and doesn’t push for performance improvements or board changes, like typical activist letters. Rather, it includes a long list of topics Marcato wants the company to address at its investor day next month.

Among other things, the firm calls for Goodyear to implement specific margin targets and provide investors with more data on how the company has handled raw material costs. Marcato said it believes both measures will boost investor confidence.

“A series of fundamental misunderstandings about the company pervade the investor and analyst community,” Mr. McGuire wrote.

The most specific request points to an analyst’s report speculating the company could return about $3 billion to shareholders by 2019. In the letter, Mr. McGuire said he believes that underestimates Goodyear’s profitability and cash flow and suggested it could return as much as $4.5 billion.

Goodyear’s market value currently stands at around $7.3 billion.

Through June, Goodyear had repurchased $563 million of the $1.1 billion it said it would buy back by the end of this year.

The Akron, Ohio-based company has been working to paying down debt, and Chief Financial Officer Laura Thompson last month said the company is evaluating what to do with its cash in the coming years.

The company has pledged to release new long-term plans and address stock buybacks at the September investor day.

Marcato has pushed for stock buybacks and other capital-allocation changes at companies including famed auction house Sotheby’s and Bank of New York Mellon Corp., its two largest investments. The firm recently disclosed new stakes in restaurant chain Buffalo Wild Wings Inc. and crane maker Terex Corp.

Write to David Benoit at and Rob Copeland at