CNBC reports that major U.S. stock indexes may have recovered from their recent lows, but Citi Private Bank warned that the worst may not be over.

"In the event that we have a very significant second wave of disease in the United States that cause a further shutdown of the economy ... that clearly is not priced into the market," David Bailin, the bank's chief investment officer, told CNBC.

"The other thing that may not be priced into the market is the fact that this virus may take another 18 to 24 months to really cycle through the globe, and ultimately have a vaccine," he added.

With the pandemic potentially dragging out a lot longer, Bailin said he has "significantly" lower expectations for company earnings compared to most analysts. He explained that the degree to which the coronavirus pandemic hit businesses in March would "hint" at what will happen in the coming quarters.

"In the second quarter we expect earnings to literally fall by 40% or more across the board, and we don't expect earnings in the United States to get back to their first quarter levels for nine quarters from now," he said.

That doesn't mean that investors should stay out of U.S. financial markets. Instead, Bailin said there are some good opportunities in the markets stateside.