An Atlanta-based mutual fund company that bet big on Apple may have seen as much as a $3.6 billion loss, at least on paper, as a result of the tech giant’s recent stock slide.

According to regulatory filings, Invesco Ltd. was the ninth-largest holder of Apple stock, with nearly 14.5 million shares.

While it's unclear if the company still holds the entire stake, it reported Wednesday that it still held nearly 10 million shares in one type of fund called an exchange-traded fund, a basket of stocks tied to a stock index.

Apple’s stock has dropped nearly $250 a share since September, meaning that fund has lost nearly $2.5 billion in market value on its investment. If Invesco still holds the larger stake, the loss is about $3.6 billion.

The Apple holdings were spread among about 20 funds that Invesco markets to investors.

Despite the rocky ride on Apple, Invesco, which also reported its 2012 earnings Thursday, said investors are becoming more tolerant of risk as they position themselves for greater returns.

January has started strong, company executives said in a fourth quarter conference call. The company, which had $687.7 billion under management at the end of the year, did not comment on its large stake in Apple stock.

“It is a very different start to the year than I can tell you that I’ve seen in the last five years,” president and CEO Martin Flanagan said. “We are seeing investment in active equities to a degree that we have not seen in a period of time.”

Invesco’s quarterly profit fell 21.6 percent, to $158.7 million. For all of 2012 profit was down 7.2 percent, to $677.1 million.

But revenue rose 9.6 percent in the fourth quarter and assets under management gained 10 percent for the year.