Just in time for Halloween, a research institute has published some downright scary data about how some people are investing in their individual retirement accounts.

Fifty-six percent of IRA owners had either all of their IRA money in stocks or absolutely none of that money in stocks in both 2010 and 2012, according to a study by the Employee Benefit Research Institute. (It was 33.2% at the no-equity end of the spectrum and 22.5% at the all-equity end.) EBRI gets its data from financial firms that administer IRAs; for 2012, it has information on 25.3 million accounts with total assets over $2 trillion.

The individuals covered by the EBRI research may own offsetting or more diversified holdings in other accounts, such as workplace 401(k) plans. Still, “it seems likely at least some people, a significant number of people, are investing in a way that probably doesn’t make sense for their situation,” says Craig Copeland, a senior research associate at Washington-based EBRI and the author of the study on IRA asset allocation.

Despite a lot of activity in financial markets, he notes, “there is a lot of inertia at these extreme positions.”

The picture is frightening in very different ways for IRA investors of different ages. Among people ages 25 to 44, who are saving for a distant retirement, 40.5% had no stock exposure in both 2010 and 2012. Meanwhile, among those 85 and older, 18% had all of their IRA money in stocks. Still, Mr. Copeland takes heart from the fact that individuals with larger IRA holdings are generally better diversified. For instance, only a third of those with IRA assets between $100,000 and $150,000 consistently held either 0% or 100% of those dollars in stocks. Extreme positions were even less common among investors with larger IRA balances, suggesting that people become better investors over time as their assets grow.

“There is still time for many of the people who invest [in an unbalanced way] to gain knowledge” and become more diversified, he says.