Millionaire investors usually have a large number of items on their metaphorical plate, and it turns out retirement concerns are among those items.

Spectrem researched investors with a net worth between $1 million and $5 million for its 2015 study Financial Behaviors and the Investor's Mindset and determined that more than one-third are concerned about when they are going to be able to retire.

Thirty-seven percent of millionaires expressed the concern about being able to retire when they want to, including 70% of millionaires between the ages of 36-44. The youngest millionaires, aged under 36, are not yet thinking about retirement, as only 28% expressed that particular worry.

Asked about a more specific concern, millionaire investors were asked whether they were worried about depleting their retirement funds too early, placing that worry on a 100-point scale, with "0" being no concern and "100" being very worried. millionaires on average placed their concern at 33, but that worrisome age group of between 36-44 had the concern at 47.

The top concern of the 36-44 age group was the cost of health care, as 80% indicated that was what was bothering them.

Interestingly, approximately one-quarter of all millionaires are concerned either they or their souse will be forced into retirement before they are prepared for that stage of life. That includes 35% of the 36-44 age group and 31% of the 45-54 age group.

The study respondents were segmented by occupation, and the greatest concern was registered among professionals such as doctors, dentists and lawyers. Forty-three percent were concerned about being able to retire when they want to (over the 37% average), and 29% were worried about being forced into retirement prematurely.

Apparently, millionaires are relatively satisfied with their advisor assistance in regards to retirement. Only 26% said they were concerned about getting adequate help and advice leading up to retirement.