Goldman Sachs is to inject $2 billion (€1.47 billion) to bail out its Global Equity Opportunities hedge fund after the investment bank's computer models failed to predict last week's market turbulence - leading to losses of about $1.5 billion, or more than 30 per cent of its value.

Goldman has also raised $1 billion for the $3.6 billion Global Equity Opportunities fund from a group of other investors, including Hank Greenberg, former chairman of American International Group, hedge fund Perry Capital and Eli Broad, the US billionaire.

Goldman, the second-largest hedge fund manager, said its computer-driven, or quantitative, funds had been hit as rivals with similar strategies dumped shares in order to cut their borrowing, causing unpredictable price movements.

But it said it saw opportunities in markets and believed most of the reduction in leverage by quantitative hedge funds was complete, helping reassure equity investors.

David Viniar, chief financial officer at Goldman, said valuations had got "way out of whack", and denied the bank was rescuing the fund.

"Given the dislocation in the markets we believe this is a good investment opportunity for us and the other investors we have brought in," he said.

The problems at Goldman's fund reflect wider difficulties for computer-driven quantitative hedge funds, known as equity market neutral or statistical arbitrage funds, as stock markets oscillated wildly in the past two weeks.

"It has been a great time to use your mind rather than a machine," said a senior executive at one large fund of hedge funds.

Many of the big names in hedge funds have suffered as their computer models failed to respond correctly to the swinging markets. Renaissance Technologies, one of the most respected managers, lost 8.7 per cent in August up to Thursday - before bouncing on Friday to start this week down just 4.9 per cent.

Other big-name funds hit included one from Highbridge Capital Management, controlled by JPMorgan, DE Shaw, AQR Capital and Barclays Global Investors, investors said.

But another fund of hedge funds manager said the entire sector had recovered in the past two days, making back a large chunk of their losses.

Goldman's two other large quantitative hedge funds - its flagship Global Alpha and the smaller North American Opportunities fund - have also been hard-hit by the failure of their models. Global Alpha dropped 27 per cent so far this year, with Mr Viniar saying more than half of the loss was last week.

The scale of the losses at Goldman's funds reflect the high level of borrowing at the funds, with one investor putting gearing at eight to 10 times before it began to cut back last week.