William Ackman's $12 billion hedge fund, Pershing Square Capital Management, lost 2.2 percent in July, according to an investor familiar with the numbers.

The fund remains up 3.8 percent year to date, according to the investor.

The firm's short position in nutritional supplements company Herbalife Ltd performed poorly in July, with the stock rising, as did a long position in retailer J.C. Penney Co Inc., with the stock falling.