BOSTON, Oct 4 (Reuters) - Hedge fund Marcato Capital Management, which owns nearly 6 percent of Deckers Outdoor Corp , said shares in the maker of UGG boots could more than double by 2020 if it sells off pieces of its footwear business, buys back shares and overhauls executive compensation.

The shares could trade somewhere between $135 and $158 per share by 2020, according to a presentation by Marcato's founder Mick McGuire for the Sohn San Francisco Conference which was seen by Reuters.

The stock price closed at $69.22 on Wednesday.

Marcato, which unveiled its investment in Deckers in February has been stepping up pressure on management and plans to replace all 10 directors at the company's Dec. 14 annual meeting, arguing that management has moved too slowly and secretively for its taste in exploring options to sell itself.

Marking the first time McGuire has laid out his hopes for Deckers' future in public, he also said the company should focus on the UGG brand, including its popular sheepskin boots, and sell off non-core brands like its Sanuk sandals and Hoka One One running shoes among others.

If the company follows Marcato's suggestions, the hedge fund manager said that return on invested capital could rise 82 percent by fiscal year 2021 and that earnings per share could climb from $3.82 in fiscal year 2017 to $12.68 in fiscal year 2021.

Marcato is also proposing that the company's outstanding shares should be cut by more than half. (Reporting by Svea Herbst-Bayliss; Editing by Edwina Gibbs)