When do 1.5 and 16 add up to 72?

That’s the riddle confronting investors in Pershing Square Holdings Ltd, the closed-end fund run by the prominent activist investor Bill Ackman.

In a letter to investors this month, Ackman disclosed that through the end of November, the fund had declined 13.5 per cent this year after accounting for fees. (Pershing Square Holdings shouldn’t be confused with Pershing Square LP, Ackman’s hedge fund, although the two vehicles have the same investment strategy.)

That’s obviously a big disappointment, considering the Standard & Poor’s 500-stock index was up 7.6 per cent over the same period. But that’s not what some big investors were complaining about to me this week.

In the same letter, Ackman reported that during the nearly four years since it began, Pershing Square Holdings had gained a total of 20.5 per cent. That would be considered mediocre at best, considering the S&P 500 gained over 67 per cent during the same period.

And that’s a 20.5 per cent gain before deducting fees. Pershing Square Holdings charges investors a 1.5 per cent management fee and takes 16 per cent of any gains. After those fees were deducted, investors gained just 5.7 per cent.

That means Pershing Square kept approximately 72 per cent of the fund’s gains for itself, leaving investors with the measly remains.

The reality is that many hedge funds, not just Ackman’s, reap far higher percentages of their gains than that stated in their fee structure. That’s because when they experience substantial losses — as Pershing Square did last year and is on track to do this year (its year-to-date loss through Tuesday was 12.4 per cent) — they don’t have to give anything back.

And for many hedge funds the results are even worse. Most hedge funds charge the proverbial 2-and-20 — 2 per cent of assets under management and 20 per cent of any gains above a certain threshold. By these measures, Pershing Square Holdings’ lower fee structure is a relative bargain.

How could Pershing Square have kept 72 per cent of the gains, given that its fee structure calls for a performance fee of just 16 per cent?

The answer can be found in relatively simple math. As a simple example, consider an investment of $1 million in a fund that generates a 10 per cent return in years 1 and 2 and then loses 5 per cent in years 3 and 4. The investor would end up with about $1.09 million, a total gain of $90,000, or 9 per cent, over the 4 years before fees.

But now consider the return after deducting a 20 per cent performance fee. In years 1 and 2, the fund manager earns $20,000 and $20,400 for a total of $40,400. The fund’s manager earns nothing in years 3 and 4. After deducting the fees, the investor would end up after the four years with just $1.05 million, a total return of 5 per cent. But the $40,400 earned by the fund is nearly 45 per cent of the investor’s total gains before fees — not 20 per cent. (And that’s not even figuring in a 1.5 or 2 per cent management fee.)

If the losses are big enough, the hedge fund manager can capture 100 per cent of the gross return, or investors can lose money even as fund managers line their pockets.

Investors seem to be finally catching on to the fact that most hedge fund managers share generously in the good times, but are exposed to none of the losses in bad.

Because of concerns over high fees and disappointing results, some endowments and pension funds — including those in Illinois, New Jersey and Rhode Island — have cut back substantially on their hedge fund allocations this year, following the lead of CalPERS, the largest pension fund in the United States, which said in 2014 that it would exit hedge funds entirely.

Through the third quarter of this year, investors had withdrawn about $51.5 billion from hedge funds, according to Hedge Fund Research.

“I’ve been saying for some time that the 2-and-20 model is dead,” said Christopher J. Ailman, chief investment officer for the California State Teachers Retirement System, which manages assets of close to $200 billion.

“Take the Pershing Square example,” he said. “Investors are only capturing 28 per cent of the gains, which is totally out of whack. If it were my money, I’d say it should be the other way around — the investors should be keeping 70 per cent, or even more, like 75 to 80 per cent. That’s what I’d consider fair.”

Ailman said that he and the chief investment officers for several large pension funds were seeking an alternative fee structure that would preserve a performance incentive for managers but more equitably share the risk.

“A few very big states are really thinking through this,” he said.

One approach under consideration, he said, is to use a rolling multi-year period for measuring performance fees. In year one, for example, an investor would pay only a portion of the performance fee if there was a gain. If there were losses in subsequent years, the investor would claw back the withheld compensation. That would solve the Pershing Square Holdings problem.

“Quite a few large investors are thinking along these lines,” Ailman told me. “Of course the devil is in the details.”

Such an approach is anathema to most hedge funds, which rely on annual performance fees to compensate their highly paid — some would say overpaid — staffs.

Even so, hedge funds are competing more fiercely over fees. In a nod to investor concerns, earlier this year Ackman offered investors an option to pay no performance fees on gains of less than 5 per cent, but a steeper 30 per cent on gains above that level.

“Management fees pretty much used to be 2 per cent,” Ailman said. “Now we’re seeing them as low as 70 basis points.” And performance fees, known as carried interest, have dropped in some cases from 20 per cent “to the low teens and even as low as 10 per cent. And these are large, well-known funds.”

Hedge fund defenders have said it isn’t fair to pick just four years of performance, like the Pershing Square Holdings example, saying it is too short a track record. Thanks to Ackman’s early successes, his longtime investors have fared much better than the more recent ones, and cumulative fees are closer to the percentages in the stated fee structures.

In his letter to investors, Ackman pointed to much better results for his older hedge fund, Pershing Square LP. Since it started in 2004, it has produced annualised compounded returns after fees of 14.9 per cent, more than double the S&P 500’s 7.6 per cent.

Still, he acknowledged, “while this is a good result, it is below our long-term goals and not much solace” for “investors who joined us in recent years.”