Bill Ackman's Pershing Square Capital Management hedge fund has cut its holdings in Target Corp.

According to an amended Schedule 13D filing with the Securities and Exchange Commission this week, the fund now owns 4.4% of Target's outstanding shares, down from 7.8% in May. The lower exposure is a result of the expiration of some options.

Ackman lost a bitter proxy battle for Target board seats earlier this year.

Filers of 13Ds, which typically own more than 5% of a company's shares and intend on communicating with management or forcing changes at companies, must file within a few days after every transaction in a company's stock. Once the threshold is under 5%, such filings are not necessary.

During the battle for board seats, critics had asked Ackman if he was just a short-term investor who would sell part or all of his Target stake if he lost — or even won — the proxy fight. Ackman responded that he would convert options to stock at some point and that some options would expire, but that he would not quickly liquidate his stake. But some of those options were out of the money, and have now expired. That means Pershing Square now has a lower economic interest in Target's 752.3 million outstanding shares.

According to filings, Pershing Square's May 26 Target stake consisted of 3.3% in common shares and 4.5% in stock-settled call options. Between then and last week, Pershing Square sold options and bought common stock, reducing its beneficial ownership to 4.4% — 3.5% in stock and 0.9% in options.

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