Caution was the theme of the day, with people "scared" and running into gold, Treasurys and the VIX, Guilfoyle noted.
The U.S. 10-year Treasury yield was down but above lows of the year so far, last trading near 1.64 percent, while the two-year yield was near 0.73 percent.
"It's obviously a risk-off atmosphere and people are going to find cover wherever they can," he said.
Jim Swanson, chief investment strategist at MFS Investment Management, has gone from overweight to neutral in equities and instead now favors credit.
He expects more slow growth for the economy and is concerned that companies have lost pricing power.
"Disinflation, not deflation, [is] robbing these companies of the ability to raise prices and their margins are getting squeezed. That's why I'm concerned about money leaving bonds [and going] into the stock market, which are riskier assets," he told "Closing Bell."
While the U.S. stock market isn't doing fantastic, it is not as bad as other markets, said Sarah Hunt, portfolio manager at Alpine Funds, which oversees $4 billion in assets.
In this atmosphere, investors need to be picking individual stocks, she told "Closing Bell."
She specifically likes BP for its "strong" dividend and Home Depot because people are still spending on their houses.
"You still have a lot of people who have a lot of work to do and DIY is becoming more and more something that they're doing as they are looking to sell houses, as the housing market is picking up," she said.
—CNBC's Evelyn Cheng and Stephen Desaulniers contributed to this report.
Disclosures: Sarah Hunt owns BP and Home Depot through Alpine's funds