Karen N. Horn, president of the Federal Reserve Bank of Cleveland, summed up the larger lesson in the crisis that forced the governor of Ohio on Friday to declare a three-day bank holiday for 71 state-chartered savings and loan associations.

"Financial institutions really don't run on cash as much as they run on confidence," said Horn. "There is no amount of cash delivery in the end that will do the trick" if that confidence is stripped away.

Depositors had been willing to put their $4 billion in the state-chartered savings and loans, in part, because of the oval signs prominently displayed in their windows. "Ohio Deposit Guarantee Fund," the signs read. "All Savings Guaranteed in Full."

But guarantees that a depositor's money is safe, or of anything else, are valuable only to the extent that the guarantor can make good a loss if called upon to do so.

Earlier this year, the nation's second-largest commercial bank, the Bank of America, lost nearly $100 million in a complicated transaction because some insurance companies that had guaranteed mortgages on property were unable to pay off when it turned out that the property values were greatly inflated. The insurance company assets weren't large enough to stand the loss.

In Ohio, the $130 million worth of assets in the private Ohio Deposit Guarantee Fund apparently will be wiped out by the failure of a single institution -- Home State Savings Bank. Details on Page A21.

The Ohio crisis underscores the fragile, interlocking nature of the nation's financial system, and how a problem in one part of it can quickly spread elsewhere. It also is another example of how, with deregulation of that system -- and the desire of both investors and managers of financial institutions to seek out the highest possible yields within that deregulated structure -- risks can be assumed that no one even knew were there.

As more and more types of investments are created by ever more creative wizards in financial markets, officials at the Federal Reserve are becoming increasingly concerned. They are worried both about the actual increase in risks and about the fact that they are sure they haven't been able even to identify all of them. For instance, a new, very broadly based study of the entire problem has been launched at the Federal Reserve Bank of New York.

Before Home State failed, probably few if any of the depositors that were locked out of their savings and loans on Friday had ever heard of a company called ESM Government Securities Inc. of Fort Lauderdale, Fla. Certainly they didn't know that it posed any financial risk to them.

ESM bought and sold for its customers securities such as those issued by the U.S. Treasury. It also executed repurchase agreements, or "repos," under which it would "sell" government securities to an investor in return for cash and simultaneously agree to buy back the securities at a price giving the investor a profit. And then there were "reverse repos," through which ESM paid out cash in exchange for securities while agreeing to sell the securities back later.

When ESM went bankrupt on March 1, it had provided Home State with between $640 million and $670 million using reverse repos, while the savings and loan apparently had provided ESM with government securities worth significantly more than that.

Another key piece of information that many Home State customers may not have known was the dual role of Marvin L. Warner, a politically prominent Ohio Democrat who controlled Home State and also had a large personal account with ESM. As chairman of a Florida thrift institution, American Savings and Loan, Warner also helped channel government securities to ESM.

These securities and those from Home State had helped keep ESM afloat. But American Savings' board had a falling out with Warner and moved to recover its securities from ESM last fall, one of the events that precipitated ESM's collapse and Home State's failure.

Warner, 65, owner of the Birmingham Stallions professional football team, reportedly sold his interest in American Savings in January for $26 million, yielding a substantial profit. Even though his stake in Home State probably has been lost, it amounted to far less -- about $3 million.

Apparently at least $300 million worth of government securities is missing as a result of losses and fraudulent actions at ESM, according to its bankruptcy trustee. What Home State's share of that loss will be is not known.

At the end of 1984, Home State had assets supposedly worth $1.4 billion and deposits of $668 million. Thus, the savings and loan's transactions with ESM involved an amount of money almost equal to the institution's entire deposit base. The difference between Home State's assets and deposits was represented by its capital and funds obtained from other sources, such as the borrowing from ESM.

Firms such as ESM are not regulated as are banks and savings and loans, although regulated institutions have also failed as a result of bad management and the sort of massive fraud authorities say was responsible for the bankruptcy of ESM. A sizeable number of other institutions, as well as cities such as Beaumont, Tex., and Toledo, Ohio, also suffered losses in ESM's failure, though much smaller than those of Home State, the exact amount of which is still unknown.

When news of the Home State involvement with ESM became known, depositors began an old fashioned run on the savings and loan. About $20 million was withdrawn before it closed its doors. The depositors who did not move as fast now have their money tied up and may face a loss.

Thus, ESM, and the risks taken by Home State's management, brought down Home State. That could have been the end of the ripple if the Ohio Deposit Guarantee Fund had had enough assets to have paid off all of the savings and loan's depositors. The private fund's $136 billion was not enough, and depositors in other institutions who had thought their money was guaranteed perceived a new risk. The ripple continued to spread.

The risk actually had been there all along, but events had never called it to anybody's attention.

First, the fund was not large enough to survive the failure of the largest institution covered by its guarantees. Second, the process of trying to find a buyer for what is left of Home State highlighted the fact that, like the majority of thrift institutions across the country, it had many mortgages on its books with interest rates well below those on mortgages issued today.

If those mortgages, which are part of Home State's assets, have to be sold, their current value may be as much as $100 million less than their face amount. As long as payments are being made on such loans, banks and savings and loans do not have to recognize such paper losses in calculating their income and net worth. However, if an institution goes under and its assets are sold, the losses do have to be acknowledged.

So, for perfectly understandable reasons, depositors have lost confidence in most of the 71 non-federally-insured savings and loans and want to get their money out. And the very act of their taking their money out -- if they can -- will force the institutions to close.

If every one of the beleaguered savings and loans were to disappear, and depositors were to suffer even a substantial loss, the amount of money involved is not large enough to undermine directly the nation's financial system. Far from it. Nevertheless, officials at the Federal Reserve, the Federal Home Loan Bank Board, which oversees federally-chartered savings and loans, and other regulatory agencies are concerned that the crisis in confidence not spill over into other parts of the financial system.

Nearly a year ago, the regulators faced a far more serious situation when the same sort of loss of confidence threatened Continental Illinois National Bank and Trust Co. When news of large loan losses shook depositor confidence in that $41 billion institution, the federal government was forced to bail it out.

In Continental's case, it was simply too big to be allowed to fail. Its collapse would have shaken the entire world. Therefore, the federal government stepped in to guarantee all of Continental's liabilities, from the largest deposit to the smallest bill. Continental has survived, as a much smaller bank, after massive infusions of federal credit and a transfer of billions of dollars worth of problem loans from its books to those of the Federal Deposit Insurance Corp.

In Ohio last week, there was no one immediately ready to say, "We will guarantee that all depositors will be paid. We will absorb whatever loss there may be."

As the word spread about Home State and the danger that the guarantee fund could not make good on losses, depositors began withdrawing their money from the other privately insured savings and loans. None of the federally-insured institutions, including those with state charters, were affected.

Creation of a new $90 million insurance fund, with $50 million from the state and $40 million from the affected institutions, did little to restore depositors' confidence. Nor did a statement from the Cleveland Federal Reserve Bank that the institutions could borrow from it at a low 8 percent interest rates to cover any shortage of liquidity -- cash, in other words.

However, the Federal Reserve banks can loan money only if the loan is fully collateralized. That is what the loans to ESM were supposed to be, with the loan secured by government securities earmarked for the lender or, in some cases, held by third parties. It is not clear that the institutions had enough collateral to get the cash needed to withstand a run.

By Thursday night, anxious depositor's were setting up camp outside the savings and loans, to be first in line the next morning.

Faced with a classic run on a number of institutions -- something unheard of since deposit insurance became widespread in the 1930s -- Ohio Gov. Richard F. Celeste ordered the institutions closed until tomorrow. The order may have to be extended because as of last night, no solution was in sight.

Any plan, Celeste said, must help restore user confidence in the institutions. If it's possible at all, what that will require is reestablishment of a credible guarantee of the safety of the depositors' money.

The remaining savings and loans in Ohio, whether federally- or state-chartered, have their deposits insured by the Federal Savings and Loan Insurance Corp., which ultimately can call on the U.S. Treasury for money to make good on any losses in accounts up to $100,000. Moreover, in instances of failed institutions that have not simply been merged into another stronger savings and loan or bought by a bank with deep pockets, the FSLIC has made depositors' money immediately available.

In Ohio, Home State Savings Bank is shut, and depositors have not been paid anything by the Ohio Deposit Guarantee Fund. Their funds are frozen, and in many cases merchants will not honor their checks. Depositors of the other closed institutions at the very least have been inconvenienced.

After this experience, some were vowing that they would take out their money whatever happens.

The more thoughtful among them probably are wondering how in the future to go about assessing the financial risks they may be assuming. Unfortunately, not even the most knowledgeable of experts can tell them for sure.