By Saqib Iqbal Ahmed

NEW YORK (Reuters) - Certain volatility-linked investment strategies could ramp up selling of equities if turbulence in the stock market, which has been stoked by the U.S. Federal Reserve's hawkish stance on interest rate rises, gets much worse.

"Volatility control funds," systematic investment strategies that take their trading cues from market volatility levels, had been steady buyers of equities since mid-June, when U.S. stocks entered a bear market rally, rebounding 17.4% up until Aug. 16.

But the S&P 500's sharp retreat of 8% over the last two weeks, driven by worries the Fed will continue to hike interest rates in a bid to tame inflation, is pushing these funds closer to the levels of market turbulence at which they start to shed stocks at an accelerated pace.

That's a worry for investors since there is evidence volatility-control funds can be a strong pro-cyclical force in bear markets, helping to further exacerbate sell-offs. And September has historically been the toughest month for the U.S. stock market.

"As volatility has trended lower over the last month to month and a half, these strategies had started to innately dip their toes into the market again, buying around $3 billion a day per our model," said Max Grinacoff, equity derivative strategist at BNP Paribas.

"To the extent that realized volatility starts to pick up again, that buying could cease."

One-month realized volatility for S&P 500, a measure of actual stock swings over the past month, dipped to a four-month low of around 16 in mid-August, but has rebounded to 20, as of Thursday.

The exact level of turbulence at which volatility-control funds turn sellers in a big way is hard to estimate, since it depends on various factors, including the funds' current equity exposure and the amount of risk individual funds target.

But Grinacoff estimates that a pickup in S&P 500 one-month realized volatility to between 35 and 40 could cause these funds to sell around $10 billion over the course of a week.

Barclays estimates that volatility-control funds currently have around $200 billion in assets under management (AUM), while Deutsche Bank pegs it at about $250 billion.

Although that is modest relative to the roughly $35 trillion value of the S&P 500 alone, such funds bear watching. As buyers in rising markets and sellers when stocks tumble, they can often accelerate price swings in either direction, said analysts.

"That makes them punch well above their AUM weight," said Parag Thatte, a strategist at Deutsche Bank.