By playing one of the favorite games of international financiers, small investors have found a way to borrow money for 9 to 10 percent, then turn around and invest it at 12 percent, earning an automatic profit with no risk.

The name of the game is "arbitrage" and it usually means borrowing money in one place, where rates are low, and investing the money somewhere else, where rates are higher.

Only in this case, the small-time arbitrageurs are borrowing and investing in the same place -- their local banks and loan associations.

Like a lot of fads, the arbitrage game got its start in California, but executives of Washington financial institutions report it has quickly worked its way across the country.

And it can be a very good deal for those who play, the game results in a costly increase in the interest rates that banks and savings and loans must pay on deposits -- an increase that fuels inflation, pushes up the cost of mortgages and other loans and pinches the profits of financial institutions that are already hard-pressed by high interst rates.

Both the Federal Reserve Board and te Federal Home Loan Bank Board are looking into the problem, but so far neither can tell how wide spread it has become.

As explained, with some reluctance, by financial executives, savings account arbitrage works this way.

The typical player, is someone who, a year or so ago, invested money in a medium-term savings certificate -- say a four-year certificate paying 8 percent interest on a minimum investment of $10,000.

Today similar certificates are paying nearly 12 percent, and an investor with $100,000 cash can get 14 percent on a "jumbo certificate."

Cashing in an old 8 percent certificate and reinvesting the money in a 12 percent one doesn't make sense, because the penalty for early withdrawal would wipe out much of the interest already earned and make the switch unprofitable.

But most banks and savings and loan associations allow savers to borrow against their certificates, at an interest rate pegged to the rate paid on the certificate.

Federal law requires the loan rate to be at least 1 percent more than the interest rate paid on the certificate. Typically lenders charge 1.5 to 2 percent more and will loan up to 90 percent of the amount of the certificate.

Thus someone with $10,000 in an 8 percent certificate can borrow $9,000 and pay 9.5 to 10 percent interest on the loan.

He or she takes the $9,000, adds another $1,000, buys a new $10,000 certificate yielding 12 percent, and gets a profit of 2 or 2.5 percent just for shuffling the money around.

In most cases, the bank and S & L executives acknowledge, the small-time arbitrageur reinvests the money in the same place the original certificate came from.

Sometime, however, the money goes elsewhere, such as into the money market mutual funds that pay a point or two more than the highest-paying savings certificates.

Kenneth Biederman, chief economist for the Federal Home Loan Bank Board, which oversees the savings and loan industry, said a surge of interest in the tactic was reported this week, apparently starting on the West Coast.

Biederman said the new small-time arbitrage game amounts to a do-it-yourself version of the "loophole certificates" that some financial institutions began to offer last summer.

To get around a federal law which restricts the highest-paying forms of savings accounts to persons who invest at least $10,000, some banks began to loan small savers enough money to meet the minimum requirement.

The saver with $5,000 to invest would borrow another $5,000 from the bank to qualify for the higher rates. Even after paying interest on the borrowed $5,000, the saver would be ahead.

The banks that created "loophole certificates" said the tactic allowed them to compete with other investments and to get new deposits.

But most banks refused to offer the certificates, contending they brought in little money. The funds they did generate cost the bank so much it was difficult to lend them at a profit.

For the same reason, financial institutions are not encourgaging their customers to pay the savings arbitrage game.

But financial institutions also are reluctant to try to stop the practice.

"Savings and loans have always made loans against various types of deposits," explained Elwyn Raiden, senior vice president of Home Federal Savings and Loan. "I don't know of anyone in town who doesn't offer to make these loans."

An association that refused to make such a loan would run the risk of alienating the customer and losing the business, he added, and the extra interest the institution has to pay is not enough of a problem to justify that. i

"We've found a few people with four-year, 7.5 percent certificates who want to borrow at 8.5 percent so they can but a 12 percent certificate, but not very many." he said.

Martin Wiegand, president of Metropolis Federal Savings and Loan, said he has "seen a little of it, but fortunately, not too much." The game, he complained, raises the costs of funds for savings institutions which are already having a difficult time making money.

Biederman noted that arbitrage like this works only when interest rates are rising rapidly. "As soon as rates start down, the game is over," he said. a

The bank board's concern, he said, is that the practice may tend to create a misleading impression that new funds are flowing into savings and loan associations because of "double counting." A new savings certificate financed with a loan against an existing certificate, would show up on the books as new money, but it would actually represent no additional funds.