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A growing phenomenon among wealthy investors-wrap accounts-has come under increasing scrutiny because of their high annual fees and the fact that investors can’t compare the performances of investment managers.

Nevertheless, these accounts have attracted an estimated $40 billion in investments, most of it since 1987, from individuals with $100,000 or more to invest.

Well-heeled investors have sought out the accounts to command greater personal attention than that offered by mutual fund companies. Others turn to them out of concern that their brokers want to sell them only the latest hot stock or the investment that brings the highest fee.

Here’s how a wrap account works:

If you have $100,000 or more in investments, your broker may offer you the prestige of having them managed by a money manager, or group of money managers, who normally wouldn’t touch a sum below $1 million.

To start, the broker asks you to fill out a questionnaire detailing your risk tolerance, investment time horizon and other questions to determine an appropriate investment mix. Based on those needs, the broker recommends an outside manager (or managers) chosen from a group with whom the firm has developed a relationship.

The money manager invests your funds, paying attention to certain wishes-such as a ban on tobacco or defense stocks-and can tailor the portfolio to comply with tax or other considerations.

The brokerage firm sends you quarterly reports, detailing your portfolio’s performance, usually by comparing it with appropriate market indexes.

For this effort the customer pays a flat, all-inclusive 3 percent annual fee. Customarily, two-thirds of that fee goes to the brokerage firm setting up the account and one-third to the manager.

Brokerage firms find the arrangement lucrative because the continuing 3 percent fee is based on assets under management, so it grows as the account grows even though the broker has no active involvement in investing the portfolio.

Money managers enjoy having additional sums to invest, and can leave burdensome reporting and marketing efforts to the brokerage firm.

Theoretically, investors enjoy the prestige of having their investments handled individually by a proven money manager, based on a carefully drafted personal plan. Regardless of how actively the manager trades the account, the fee remains a flat 3 percent.

But critics say investors may be buying prestige and certainty for too high a price.

“You get the illusion that you are getting something like the Rockefellers,” said Don Phillips, publisher of Chicago-based Morningstar, a mutual fund tracking service.

“The expenses tend to be fairly high,” he said. “It’s an idea that might have worked better in the last decade, when returns were high and you could absorb higher fees.”

Mutual funds that charge a 4 percent load, for instance, charge that only once, then assess continuing fees of about 1 percent in subsequent years.

Other critics note that the financial-planning aspect of wrap accounts is most useful in the beginning of the process, but is paid for every year.

To cover a 3 percent annual fee, the money manager must beat the market by 3 percent each year for the customer just to come out even with the market.

Leonard Reinhart, president of Shearson Lehman Brothers’ Consulting Group, has become accustomed to defending wrap account fees as being competitive with what they replace.

A financial planner charges a fee for advice in setting up a financial plan, he said, and trading fees on an actively traded $100,000 account can amount to 1.5 to 3 percent on top of that fee. An investor can buy a group of mutual funds, but unless he pays for good advice on which ones to choose, he may be choosing blindly.

As of the end of the first quarter, Shearson, considered the largest purveyor of wrap accounts, with $19 billion under management, will report its performance results to clients in figures that take into account the wrap fee, he said.

Merrill Lynch, which rivals Shearson in wrap accounts, is moving toward the same goal, said David Ferrier, vice president and manager of Merrill Lynch Consulting Services.

With that move, investors will get a better picture of real returns. But they still won’t be able to compare results with those provided by other money managers-a mainstay of the mutual fund industry.

“To me, the bigger issue is the lack of third-party reporting,” said Morningstar’s Phillips. “They’re not printed in all the newspapers like all the mutual funds. You can’t see how did Dean Witter’s wrap account do compared to Shearson’s; is Shearson’s better than Merrill Lynch?”

Shearson’s Reinhart contends that mutual fund investors may be swamped by too much choice. With more than 4,000 funds from which to choose, many investors end up simply confused.

Shearson selects the managers for its wrap accounts and monitors them closely, he said, and it fits appropriate managers with individual clients.

“If you are a person who knows about mutual funds and does due diligence on them, makes decisions based on that and not just last year’s performance, you don’t need us,” he said.

The growth of wrap accounts in the last three years has prompted the Securities and Exchange Commission to examine how its rules apply to such accounts. Marianne Smythe, director of the division of investment management, said she believes existing laws cover most aspects, but she said the SEC should clarify exactly how they apply.

Some investors have complained, for instance, that the “custom-made” portfolios they pay for are in reality variations of a standard offering by a money manager. Smythe, aware of such complaints, said the SEC should spell out exactly what individual service entails in such accounts.