•The market will continue to plow higher. Stocks might not be as cheap as they were a few years ago, but there's plenty of room to make new highs, says Dan Chung, chief investment officer at Alger Funds, who called this "one of the most hated bull markets in equities of all time." Investors will just have to be more selective in picking spots in the market that still have plenty of upside left, says Rupal Bhansali, chief investment officer of international equities at Ariel Investments.
•Higher rates aren't a bull killer. It's likely the Federal Reserve will raise short-term rates, currently pegged between 0% and 0.25%, to 1% next year, says Rick Rieder, chief investment officer of fundamental fixed income at BlackRock. But that's still "incredibly accommodating," he says. The key to the market's reaction will be the pace at which the Fed hikes rates. But Rieder expects the Fed's moves to be measured and says there are other forces in play that should keep long-term interest rates from spiking sharply. Short-term rates will continue to trade south of 2% for at least a couple of years, he adds.
More from USA Today:
Data on police killings 'hit or miss'
As economy slides, Japan waits for good times
Poll: This year bad. Next year? Maybe worse
•Nasdaq is going to see more action. If there's been one blemish on this bull market it's that the Nasdaq remains the last major stock index to be unable to notch a new record high. But that will change next year, says Chung, who predicts the tech-focused stock index will finally take out its March 10, 2000, record close of 5048.62. Stocks in the Nasdaq are in much better health now than they were in 2000. Much lower valuations and improved profitability — not to mention companies such as Google that weren't even publicly traded companies 15 years ago — will finally put the Nasdaq on new high ground, Chung says.
•Rise of volatility. The panelists agreed that while market gains might be modestly upward, they won't be easy. Chung says he wouldn't be surprised to see periods of intense volatility next year, not unlike the biotech-stock drubbing in early 2014 and the nearly 10% broad market decline in the fall. But that's why these stock pickers think that stock picking will be more important in 2015. "Volatility is an opportunity," says Bhansali. For instance, she thinks that many health care companies will find demand for their services to be so great that earnings will benefit.
Read MoreOil has become the new housing bubble: Trader
•It's not a risk-free market. Stocks have room to run, but there are still concerns. Many equity and fixed-income investors, for example, have been piling into the same trades, which increases the risks of losses if those trades reverse. Many investors, for example, are shorting short-term interest rates, going long the U.S. dollar and building long positions in shorter maturity European bonds, according to Rieder. "You have to diversify like crazy," he says. Similarly, some panelists worry that investors that have rushed into bond-like stocks — such as high-dividend-paying stocks and utilities -- might be paying too much.
One big worry for foreign-stock focused Bhansali is China. She fears the real estate bubble there led to an overload of debt — one that the government might find itself on the hook for, she says. Big debt binges tend to end badly, and that's a concern for China. Growth in China and India is especially important, since that could be the needed antidote to sluggish growth in Europe, Chung says.
Read MoreIs there risk in rebalancing?
But despite these risks, stocks are the place to be, Bhansali says. "There is a scarcity of growth and yield in the world," she says. "Get the best of both worlds from the equity market," where many stocks yield more than 10-year U.S. government bonds.