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Deep inside the Federal Reserve Bank of New York, the $600 billion man is fast at work.

In a spare, government-issue office in Lower Manhattan, Josh Frost and a band of market specialists are making the Fed’s ultimate Wall Street trade. They are buying hundreds of billions of dollars of U.S. Treasury securities on the open market in a controversial attempt to keep interest rates low and, in the process, revive the economy.

To critics, it is a Hail Mary play — an admission that the economy’s persistent weakness has all but exhausted the central bank’s powers and tested the limits of its policymaking. Around the world, some warn the unusual strategy will weaken the dollar and lead to crippling inflation.

But inside the Operations Room, on the ninth floor of the New York Fed’s fortresslike headquarters, there is no time for second-guessing. Here the second round of what is known as quantitative easing — QE2, as it is called on Wall Street — is being put into practice almost daily by the central bank’s powerful New York arm.

Each morning Frost and his team face a formidable task: They must try to buy Treasuries at the best possible price from the savviest bond traders in the business.

The smallest miscalculation, a few one-hundredths of a percentage point here or there, could unsettle the markets and cost taxpayers dearly. It could also embolden critics at home and abroad who say QE2 represents a dangerous expansion of the Fed’s role in the markets.

“We are looking to get the best price we can for the taxpayer,” said Frost.

Whether Frost will reach that goal is uncertain. What is sure is that market interest rates have risen, rather than fallen, since the Fed embarked on the program in November. That is the opposite of what was supposed to happen, although rates might have been even higher without the Fed program.

Frost’s task is to avoid paying top dollar for bonds that could be worth less when the Fed tries to sell them one day.

Frost and his team drew up the daily schedule for what the Fed calls its Large-Scale Asset Purchase program. And that program is, by any measure, large scale: Through next June, these traders will buy roughly $75 billion of Treasuries a month — on top of another $30 billion it is reinvesting in Treasuries from its mortgage-related holdings.

But depending on daily market conditions, Frost can decide not to buy certain bonds if they are already in short supply.

As offers to sell Treasuries flash on a bank of trading screens, a computer algorithm works out which ones to accept. The computer compares the offers from Wall Street against market prices and the Fed’s own calculation of what constitutes a “fair value” price.

When devising the program, Frost and his team decided to focus most on buying Treasury notes with an average maturity of five to six years. That is because the yields on these notes have the biggest impact on interest rates for mortgage holders, consumers and companies issuing debt, and on banks’ decisions to lend to businesses. Over the weeks and months of the program, his purchases should drive up the prices of these securities — because they will be in greater demand — and consequently push down their yields.

The trouble is, though yields fell sharply between August and November as the markets anticipated the new program, they have risen since it was formally announced in November, leaving many in the markets puzzled about the value of the Fed’s bond-buying program.

Frost, and his boss, Brian P. Sack PhD ’97, insist the program has succeeded. Sack, 40, joined the Fed 18 months ago to run the entire markets group. He has a Ph.D. from MIT and worked most recently for a Washington consulting firm. In 2004, he wrote a paper with Ben S. Bernanke PhD ’79, the future chairman of the Federal Reserve, and another economist about unconventional measures for stimulating the economy in extraordinary times — just like large-scale purchases of Treasuries.

“We didn’t know then that the Fed would be putting it to the test,” he said. He said the Obama administration’s $858 billion tax compromise with congressional Republicans in December complicated the macroeconomic picture.

But the biggest reason for the rise in interest rates was probably that the economy was, at last, growing faster. And that’s good news.

“Rates have risen for the reasons we were hoping for: Investors are more optimistic about the recovery,” said Sack. “It is a good sign.”