Investors might be able to time the market—or they might not.

That sums up the positions taken during a debate at the 2015 Schwab IMPACT conference between Yale professor Roger Ibbotson and Research Affiliates founder Rob Arnott. In the end, they didn’t settle the age-old argument over whether the markets can be timed, but these two icons of investment did offer insight on where they agree and disagree.

Ibbotson argued that popularity is the best determinant of an investment’s future performance in the standing-room only event moderated by Omar Aguilar, CIO of Charles Schwab Investment Management.

“The stocks that are the most popular will do the worst,” Ibbotson said. “Go after the unpopular ones, tremendous amounts of money can be generated by taking some risk. I’m not suggesting you go in and out of the market, I’m suggesting you stay there.”

Arnott chose not to engage Ibbotson directly, but said that there was some truth to his contrarian argument. “There’s more that I agree on than I disagree on,” Arnott says. “Market timing, loosely defined, is not difficult. You just have to find the flows and do the opposite.”

Ibbotson said that investors should not only go against the herd, but against their own instincts. “We’re wired to avoid small-cap stocks. We don’t like them for some reason,” Ibbotson says. “When it comes to value stocks, we often feel like something must be wrong with those companies. We forget that it’s easier to improve a bad company than it is to improve a great company.”

Arnott largely agreed, but said that by averaging out of equities with high valuation and into equities with lower valuation, investors were in a sense timing their way in and out of the market. “You have to remember that getting investors to sell what’s doing well and buy whatever is savage to them doesn’t come easily,” Arnott says. “Picking tops and bottoms through averaging is not hard. Averaging out of an expensive market is easy.”

Arnott noted that an investment made 220 years ago would have increased by 10 billion times if dividends were reinvested — with dividends, not valuation, responsible for most of the growth.

“We should look for incremental returns within markets. We don’t want to popularity weight,” Arnott says. “We should weigh companies based on their macroeconomic footprint. These are objective measures. Use the size of a business to contratrade against the markets’ bets.”

But Ibbotson said that for most investors, averaging based on valuation doesn’t come easy. “If you go against what everybody else is doing, you can do well,” Ibbotson says. “If we’re telling people to put themselves back in after we’ve been through a crisis, or to sell at a peak, people can’t really follow that kind of advice.”