In 2013, 36 million people, or 29.4 percent of U.S. households, owned traditional IRAs. Nearly half of those with traditional IRAs said their accounts included rollover assets.

Roth IRAs are the second most frequently owned IRA, with 19.1 million people, or 15.6 percent of U.S. households, owning them. In May 2013, 7.5 percent of U.S. households owned employer-sponsored IRAs, which include SEP IRAs, SAR-SEP IRAs and SIMPLE IRAs.

The ICI study also found that all age groups own IRAs, but they are most prevalent among the older groups of working-age adults. In 2013, 42 percent of households headed by someone aged 45 to 54 owned IRAs, and 45 percent of individuals 55 to 64 owned IRAs.

IRA ownership tends to increase based on household income. Fifty-four percent of households with incomes of $50,000 or more owned IRAs, compared with just 21 percent of households who earned less than that. Sixty-four percent of households with incomes of $100,000 or more owned IRAs in 2013. It also found that 47 percent of households with IRAs had incomes between $35,000 and $99,999, compared with 42 percent of all U.S. households.

IRA owners tend to be savers. They also are more likely to be married, employed and have college or postgraduate degrees. The ICI found that the median financial assets of IRA-owning households were eight times greater than the median financial assets of households that did not own IRAs.

In 2013, while 28 percent of IRA owners were willing to take substantial or above-average risk, the largest percentage of households owning IRAs, 46 percent, were willing to take average risk for average gain, the study found. Twenty-six percent were willing to take below-average risk for below-average gain or unwilling to take any investment risk.