NEW YORK — Millions of shares of stock change hands every day at Investment Technology Group Inc., but hardly a word is exchanged among the roomful of traders.

ITG’s quiet trading floor on tony Madison Avenue offers a hushed contrast to the yelling frenzy that occurs at the Big Board 70 blocks south on Wall Street.

“Our clients either send their trades to us electronically, and we will get them executed, or we offer them the software and they can trade into the marketplace from their offices,” said Anthony Huck, managing director at ITG. “Our programs will search everywhere to find the best prices.”

ITG sits on the front lines of program trading — the computerized, big-lot transactions for institutional clients that now account for nearly 30 percent of the daily volume on the New York Stock Exchange, about double the level of just two years ago.

The use of computers with programmed instructions to ram through orders has changed the rhythms of Wall Street pros and, in subtle ways, touches Main Street investors, too.

Ever notice how often stocks make their biggest moves in the first and last hour of trading? That’s usually the result of millions of program trades kicking in, rather than millions of small investors trading. Often the trades have little to do with the day’s market news.

And if you consider yourself unaffected by the computerized stock churning just because you’re a cautious, casual dabbler in mutual funds, think again.

Even average mutual fund investors benefit from program trading to the extent that it allows their funds’ managers to execute trades faster and cheaper.

“The more money we are able to save in execution costs, then the more money we are able to put into the pockets of our shareholders,” said Kevin Cronin, director of equity trading at Aim Investments, a Houston mutual fund company.

All this activity occurs well upstream of most American shareholders.

Program trading is loosely defined as an electronic transaction involving 15 or more stocks with a combined value of at least $1 million.

These thousands of daily deals wash in waves across big brokerage firms, investment banks, mutual funds, hedge funds and market regulators, before finally showing up as a mere ripple in a small investor’s portfolio.

“It’s just a fact of life for us,” said John Thain, chief executive of the NYSE. “I just have to make sure we are able to deal with that volume and make sure we are fast enough.”

Three factors help to explain the explosion in program trading. First, technological advances spawned the growth of electronic communication networks, often called ECNs. These electronic exchanges, like Instinet and Archipelago, allow thousands of buy and sell orders to be matched at the speed of light without any human intervention.

“Now you can just put a sell order into a machine, and maybe there isn’t a buyer right now, but it will scan all the major exchanges and the ECNs and find a buyer,” said Gabe Butler, vice president of ITG, which has about 500 or so institutional clients.

Second, the Securities and Exchange Commission mandated in 2001 that the major stock exchanges price stocks in dollars and cents instead of fractions. A stock previously priced at 7 1/8 is now listed at $7.13.

Pricing stocks in penny increments instead of 1/16 increments means 100 price points within a dollar instead of the previous eight price points. That means all the willing buyers and sellers are dispersed over many more prices, making it more difficult for them to meet on price.

“In the past you could execute 5,000 shares at a time, but now you have to execute 100, 200, 300 shares at a time,” Butler said. “It takes many more small orders to add up to a substantive position. It’s physically impossible for a human to make all those trades. It’s too time-consuming.”

Third, and perhaps most significant, the proliferation of hedge funds with all their sophisticated trading strategies are driving program-trading volume.     Hedge funds  are investment companies that use high-risk techniques, such as borrowing money and selling short, in an effort to make extraordinary capital gains.    Selling short is the tactic of selling borrowed stock or other financial assets on the assumption they will become less valuable, so the investor can buy the asset back at a lower price and pay the debt with a profit. 

Hedge fund managers rarely pick up the phone and place orders with brokers, said Steve Summers, chief executive officer and founder of Discovery Management, a Dallas hedge fund.

Typically, they have machines in their offices linked to their brokers’ offices that electronically execute the trades. The Discovery fund typically holds 250 small- to mid-cap stocks, but the managers occasionally change or rebalance the portfolio.

“We might have 50 stocks we want to buy and 50 stocks we want to sell, representing millions of shares,” Summers said. “You don’t want to just call that into a broker and have it slammed through.”

The Discovery fund, like most hedge funds, engages in a newer kind of program trading called algorithmic trading. Algorithms are trading instructions embedded in a computer program that break large orders into smaller pieces.

When the portfolio manager of the Discovery fund wants to buy, say, 100,000 shares of a particular stock, he won’t transmit one buy order for 100,000 shares, because that would push the price dramatically higher, especially in some of the less liquid small-capitalization stocks that it buys.

One of the most basic algorithm programs — called Volume Weighted Average Price — will process the order according to the stock’s historical trading pattern. For example, if over the past three months 10 percent of the stock’s trading volume occurs in the first 30 minutes of trading, then the algorithm will execute 10 percent of Discovery’s buy order in the first 30 minutes.

The idea is to reduce the trade’s impact on the market.

Summers said the first algorithm programs were developed years ago and were very crude. They might break up the trades into seven one-hour blocks during the day. Now the algorithms spit out trades by the second, but typically with most of the volume early and late in the day to mimic the historic pattern.

Hedge fund managers and other large money managers are really playing a giant game of hide-and-seek within the nation’s stock exchanges.

Large buyers and sellers of stock — mutual funds, pension funds and hedge funds — naturally want to hide their orders, while others are trying to sniff them out.

One of the fastest-growing algorithmic trading strategies is “statistical arbitrage.”

A computer program monitors the spread between the current price of, say, the Standard & Poor’s 500 index exchange-traded fund (known as Spiders) and its futures price.

For brief moments during the day, the spread may diverge from the norm, and that’s when computer programs kick in to take advantage of the divergence.

Virtually all large investment management companies use algorithms, according to the Tabb Group LLC, which tracks institutional investing.

“The anonymity of algorithms solves the large firms’ biggest complaint about brokers — information leakage,” according to a Tabb report.

“Not only do algorithms not talk, but they also lower the cost of trading by automating execution, and that frees traders to concentrate on their more difficult orders.”

Algorithms may not talk, but the volume of program trading could help shed some light on a huge, hidden corner of the stock market.

John Coffee, a law professor at Columbia Law School, said the source of all this program trading is a mystery. But he suspects that hedge funds are mostly responsible.

There are thousands of hedge funds, but no one knows exactly how many.

 This year the SEC adopted a rule to begin requiring most of the large hedge funds to register with the agency.

“When you see this kind of program trading volume, it is time for us to recognize the hidden significance of hedge funds,” he said. “We don’t really know how big they are; how much trading they do; even how many there are.”