David Lebovitz: Here's what to do amid this volatility

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As one of the most volatile months for equities in recent memory comes to a close, investors need to understand that the days of double-digit returns on low volatility are over, strategist David Lebovitz said Monday.

"The first thing clients need to do is recognize that the environment we've been in over the past five years has not been normal," JPMorgan Asset Management's global market strategist said in a CNBC "Squawk on the Street" interview.

"Double-digit returns and single-digit volatility are not normal. So what we're doing is encouraging clients to look for single-digit returns on double-digit volatility ad a backdrop of diversification they can use to protect themselves against these wild swings," Lebovitz added.

The CBOE Volatility index (VIX), also known as the fear gauge for markets, has risen more than 120 percent in August amid growing global growth concerns.

VIX in August

Lebovitz also said, however, that investors should remain invested in the equities space.

"We're now trading at the long-term valuation for the ; stocks still look cheap relative to bonds, and we do think the returns coming from equity markets will be better than the majority of returns coming from debt markets," he said.

The recent rise in volatility has brought up another round of speculation about whether or not the Federal Reserve will raise rates.

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"I think they should raise rates and get it out of the way," Jeffrey Solomon, CEO of Cowen, said Monday in another "Squawk on the Street" interview, adding that he doesn't think the central bank will move in September.

"The market is totally [scared] by this initial rise in interest rates, which is a measly 25 basis points," Mike Holland, Holland & Co. chairman told "Squawk on the Street" on Monday.

"[Fed Vice Chairman Stanley] Fischer, of the few grownups left in Washington, he's one of the ones who I listen to, and for him to say he thinks [he's] beginning to see the whites of inflation's eyes, for him to say that the underlying economy is OK, I'm listening to him more than any of the talking heads."