Greer cited a study that compared two people retiring just two years apart; the first one in a market downtown and the second in an upturn. She said the impact can be "huge."
Fifteen years later, if you look back, "that person who retired and took withdraws during that early period can have two-thirds less" for the rest of their lives, Greer said on "Squawk Box."
Greer also talked about the results of another study, conducted by AIG in January, saying 79 percent of investors are concerned about a stock market decline, with good reason.
The stock market hit records in late January but plunged shortly thereafter. It took until the summer to eclipse those all-time highs. But earlier this month, the market came under severe pressure on fears of rising interest rates. Trading has been highly volatile ever since.
The AIG data also showed 61 percent of those surveyed said their "greatest fear" is outliving retirement savings.
The best way to fight off that anxiety is to develop other sources of protected lifetime income like a pension or an annuity, "things that you can rely on that are stable that are going to give you a monthly check for life," Greer said.
"You can cover your expenses and then you don't have to do the withdraws," she added. "Otherwise, you're going to have to withdraw right at the wrong time."
That's important for the aging U.S. population where 1 in 4 adults will soon be of retiring age, Greer said.