It's a not so happy anniversary for the bull market.

The Dow and S&P 500 have not hit new all-time highs since this time a year ago -- 18,351,36 for the Dow on May 19, 2015 and 2,134.72 for the S&P 500 one day later.

Both indexes are only about 5% below these peaks. So it's not as if we are in a nasty bear market.

But many experts think that there are no compelling reasons for stocks to hit new records anytime soon. Investors may have to brace themselves for more big swings.

"Investors had gotten used to a low volatility environment but they have been rudely awakened. This could be the beginning of a multi-year period of volatility," said David Jilek, chief investment strategist at Gateway Investment Advisers.

Jilek said that investors have many reasons to be worried.

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There's Great Britain's looming decision about whether or not to stay in the European Union -- the so-called Brexit vote -- next month.

The Federal Reserve may also decide to raise interest rates in a few weeks -- even while many other central banks are doing their best to keep rates low. Concerns about Greece's debt are back in the spotlight too.

China may not necessarily be out of the woods either. There are worries about the sluggishness in its economy. So the U.S. stock market won't be able to keep chugging along to new highs without help from the rest of the world.

"The global economy can't just have one piston firing. You have to have them all firing," said Matt Kaufler, manager of the Federated Clover Value fund.

Results from Corporate America haven't been great either.

"The markets are just treading water here. Normally markets rally on strong earnings and we've seen lackluster corporate earnings," said Stephen Kalayjian, chief market strategist of KnowVera.

"A lot of companies are also talking about cost cutting and that usually means layoffs," he added.

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Then there's the uncertainty surrounding the U.S. presidential election, with Donald Trump being the wildest of wild cards.

It's no wonder then that investors are so unsettled.

CNNMoney's Fear & Greed Index, which measures seven indicators of market sentiment, is currently in Neutral territory. But it began the year showing Extreme Fear and surged all the way to Extreme Greed levels just last month.

Strategists said there are some opportunities though.

Kaufler thinks the U.S. housing market should remain robust. So he owns luxury home builder Toll Brothers (TOL). He also believes QVC (QVCA), the company most famous for its TV shopping network, is positioned to benefit from the rapid shift to mobile commerce.

Arian Vojdani, investment strategist at MV Financial, added that investors should be looking at solid blue chips that pay dividends -- companies like Procter & Gamble (PG), Johnson & Johnson (JNJ), Disney (DIS) and even Apple (AAPL).

These stocks are cheaper than high flying momentum stocks and should be able to hold up better than other more economically sensitive companies if the market remains this volatile.

"It's time to be cautious. Valuations are high and investors are asking if growth is really there," Vojdani said. "There are still a lot of questions about global growth."

Vojdani said he's shunning emerging markets right now, including China, and remains mostly focused on the U.S.

So when you add this all up, it looks like a lot more of the same for the market for the next few months.

Stephen Wood, chief market strategist for North America at Russell Investments, said that he does not expect stocks to plunge anytime soon, but that there's no compelling reason for the market to surge and hit new highs either.

Wood compared stocks to F. Murray Abraham's character in the movie "Amadeus" -- the jealous rival to Mozart.

"This is a Salieri market. It's the patron saint of mediocrity," he said.