New York Financial Services Superintendent Benjamin Lawsky is concerned that some insurance companies may be giving buyers overly optimistic projections of potential gains in the policies, known as indexed universal life, according to the letter and people familiar with the investigation. The policies combine a tax-advantaged savings part with a death benefit.

The twist that makes these policies popular is that the insurers pay interest into the policyholder’s account with formulas tied to the performance of a benchmark stock-market index, often the S&P 500-stock index, up to a specified cap. At the same time, the policies come with protection from market losses.

Amid rallying stock markets, sales of indexed universal life rose 13% last year, by one measure of premiums, and were up 13% in this year’s first half, according to Limra, an industry-funded research firm. Overall, life-insurance sales were flat last year and down 4% through June. Indexed universal life represented 17% of individual life premiums in the second quarter.

The letter from Mr. Lawsky’s office was sent earlier this month to 134 insurers that operate in the state, one of the biggest markets for life insurance in the U.S. The letter seeks responses by Oct. 1 to questions about the insurers’ presentations of potential gains to prospective buyers in so-called illustrations.

Investigators are trying to discern whether the projections in the illustrations are unduly optimistic or misleading, said one person familiar with the matter.

Many insurers show hypothetical interest of 8% a year, according to industry executives and financial advisers, but rates can go higher because there aren’t regulations in place directly pertaining to the projections. Many insurers cap the interest they will pay annually–in recent months at about 12%–in return for the downside protection.

John Bruins, a vice president with the trade group American Council of Life Insurers, said many insurance companies agree that “tighter rules are needed” for the policies to help clarify for consumers that any presentation of robust index-based returns isn’t guaranteed. The council earlier this year presented proposed guidelines to the National Association of Insurance Commissioners, a standards-setting organization for state insurance departments.

Pacific Life Insurance Co., a top seller of the product for nearly a decade, said in a Sept. 5 letter to the commissioners’ group that it supports the trade-group proposal because it would “provide the consumer additional important information about the variability of the credited rate and its impact on policy values.” A spokesman said last week that the company “welcomes working with the NAIC to establish uniform IUL illustration standards.”

The industry isn’t united on the subject. Not all insurers sell indexed policies, and some prominent ones that don’t–including New York Life Insurance Co.–maintain that the trade group’s proposal isn’t tough enough, according to comments they have submitted to the NAIC. These insurers earlier this month submitted a competing proposal, and the regulatory organization is studying both approaches, according to materials on the organization’s website and state officials.

Indexed life insurance is a type of “permanent life” insurance, meaning it is intended to be in force until the owner dies, in contrast to basic “term life,” which provides a death benefit if the insured person dies during a specified period. Many well-to-do people buy permanent-life policies because of the tax-deferred savings buildup.

With stock markets rebounding from the financial crisis, many insurance agents, who are paid by commission, have gravitated to indexed policies because more-conventional types of permanent life can be a tough sale in a low-interest-rate environment. That is because insurers peg the interest paid in these conventional policies to their bond-heavy investment portfolios. These older-type policies have long been subject to illustration rules.