On a rumored buyout by private equity firm TPG Capital, shares of Avon Products Inc. (NYSE: AVP) popped 15% in late January. When that buyout did not happen, the shares gave almost all that gain back.

Avon’s shares were subjected to a brief trading halt on Tuesday following a report in The Wall Street Journal citing people familiar with the matter who say the company is exploring strategic alternatives, including the possible sale of its North American business. Shares have popped 15% again.

On Monday, Avon postponed its 2015 investor day presentation from mid-May to “Fall 2015,” explaining that the change will give the company’s recently hired chief financial officer (CFO) “adequate time to prepare for a more robust discussion at the meeting.” Unless Avon somehow persuades a buyer to pony up some serious money for some or all of the company, the new CFO could face more than robust discussion.

In early 2012, Avon received an offer of $22.35 per share in cash from Coty Inc. (NYSE: COTY) before Coty became a publicly traded company. Avon’s board, which had recently fired former CEO Andrea Jung, called the offer “opportunistic” and rejected it.

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Coty raised its offer to $24.75 on condition that Avon allow the prospective buyer to conduct due diligence. Avon refused and an offer worth north of $10 billion was taken off the table. Monday’s closing price on Avon’s stock was $8.01 per share. That equates to a market cap of around $3.5 billion.

Avon posted an earnings per share loss of $0.88 in 2014, following a $0.13 per share loss in 2013 and a $0.10 per share loss in 2012. And that is after the board fired former CEO Andrea Jung. Somehow there is nothing here to inspire confidence that Avon will accept an offer, even if someone else is careless enough to make one.

Shares traded up nearly 14% in the mid-afternoon Tuesday, at $9.16 in a 52-week range of $7.10 to $15.46.

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