(Reuters) - Activist investor Elliott Investment Management on Monday urged NRG Energy to make leadership and capital allocation changes, and called the U.S. utility's recent acquisition of Vivint Smart Home a "strategic misstep".

The company's shares rose 4.5% to $34.21 in early trading after Elliott's letter.

Elliott called for a review of the company's home services strategy, appointment of new independent directors, cost reductions, and a new capital allocation framework to return to shareholders at least 80% of free cash flow.

Successful execution of the plan could create over $5 billion of shareholder value, driving NRG's stock price to reach or exceed $55, the letter said.

NRG Energy did not immediately respond to a request for comment.

The company said in December it would buy Vivint Smart Home Inc for $2.8 billion in cash, adding security and other automation products to its home service offerings.

The activist investor called the deal "the single worst deal in the power and utilities sector in the past decade".

Elliott said funds it manage have an investment of about $1 billion in NRG Energy, representing a more than 13% interest.

(Reporting by Mrinalika Roy in Bengaluru; Editing by Arun Koyyur and Sriraj Kalluvila)