Stiller, who was Krispy Kreme's second largest shareholder, sold about 8.1 million shares in the doughnut chain on Monday, according to a regulatory filing.
At an average price of $6.15 a share, the stake sale was valued at about $49.6 million. Krispy Kreme's stock closed up 5 percent at $6.67 on the New York Stock Exchange Wednesday.
"Clearly with Green Mountain's stock sell-off last week, Stiller had margin calls against his position," B Riley & Co analyst Conrad Lyon said.
"And to satisfy those calls he has been selling his holdings in not only Green Mountain, but in Krispy Kreme (as well)."
The margin calls stemmed from a near 50 percent drop in Green Mountain's stock price since it reported disastrous quarterly results last week.
Investors can borrow money from banks or brokerages using their stock holdings as collateral. A margin call occurs when the value of those holdings falls below a threshold that forces the investor to put up more cash or sell shares to repay the loan.
Stiller was removed as Green Mountain chairman for selling at a time when trading by insiders was prohibited.
Following his most recent sale, Stiller controls about 7 percent of Green Mountain's stock.
(Reporting by Arpita Mukherjee in Bangalore; Editing by Viraj Nair, Saumyadeb Chakrabarty)