Borrow short and lend long. What once was a simple formula for easy profits now is a common; problem for most of the nation's financial institutions.

Savings and loan associations have been hit hardest, largely because they borrowed the shortest and lent the longest. It used to be normal practice for a savings and loan to pay 5 percent to short-term depositors and then lend the funds at 8 pecent to mortgage borrowers.

That normal practice generated comfortable profit margins in the bygone era of low inflation and stable interest rates. Those comfortable proft margins crumbled as inflation drove up both the level and volatility of interest rates.

Rising interest rates drove up savings and loans' cost of deposits faster than the returns earned on mortgages. Their short-term deposits quickly rolled over into high yielding certificates or simply departed for the higher returns of money market mutual funds. Their mortgage loans rose far more slowly in yield and even today more than half of savings and loan mortgages carry an interest rate of under 10 percent. A 10 percent mortgage is a distinctly unprofitable investment to a savings and loan, which must pay up to 15 percent for short-term funds in today's high interest economy.

Interest rates rose in volatility as well as in yield, putting savings and loans in a double bind. High interest rates make their present operations unprofitable, while volatile interest rates make savings and loans future profits uncertain. An unprofitable present plus an uncertain future equals an uncomfortable situation for most savings and loan executives.

Many bankers share the same discomfort arising from borrowing short and lending long. Bankers make fixed rate loans when they expect interest rates to fall, a practice which leaves them exposed if interest rates rise instead. Citibank reported sharply lower profits last fall when the rising cost of deposits eroded profit margins on its fixed rate loans.

Foreign bankers have the same problem, often to a greater degree. West Germany's giant Commerzbank recently took the unprecedented step of cutting its dividend, due partially to losses from borrowing short and lending long.

Insurance companies also borrow short and lend long, a fact that even some of their own managements did not recognize until recently. When a policyholder buys a whole life policy, the issuing insurance company assumes it will have the use of the funds for a long period except in the case of a predictable number of deaths and policy lapses. The insurance company then uses the funds to make long-term investments in mortgages and bonds.

Recently insurance companies have made the unpleasant discovery that many policyholders view their policies as short-term investments, not long-term ones. To capitalize on today's double-digit interest rates, many policyholders are borrowing on their policies at single-digit interest rates guaranteed in their policies. In many cases, they simply allow the policies to lapse because higher investment returns are available elsewhere. Both policy loans and policy lapses are methods of converting formerly long-term life insurance policies into short-term investments for the policyholder.

Life insurance companies have a similar problem with pension funds. A few years ago they offered long-term contracts to pension funds at guaranteed rates of 8 percent to 10 percent and then invested the funds in long-term bonds and mortgages. Now pension funds are breaking those contracts to secure much higher current interest rates, leaving the life insurance companies stuck with low-interest bonds and mortgages whose current market values are far below the original prices paid for them.

Casualty insurance companies also are discovering the perils of borrowing short and lending long. The typical casualty insurer makes no underwriting profit on auto, fire and similar insurance. Every dollar it takes in goes to pay claims and expenses. Casualty insurers make their profits by investing the cash they hold between the time it comes in as premiums and the time it goes out as policyholder claims. In effect, casualty insurers make their money by borrowing short-term funds from their policyholders and then investing them.

They generally invest in long-term bonds, which is the problem. The typical casualty insurer has a 21-year average maturity in its bond portfolio, which implies large losses in today's market of high interest rates. If casualty insurers revalued their bond portfolios at current prices, they would suffer dramatic declines in their net worths.

Fortunately for both life and casualty insurers, they do not have to value their long-term bonds and mortgages at current market prices. Accounting principles force insurers to value stocks at current market prices, but permit them to carry bonds at amortized cost. If an investor buys a bond whose value drops by 30 percent, then he knows he is stuck with a large loss. If an insurance company does the same thing, it can maintain the fiction that no loss has taken place until the bond is sold, which it seldom is.

Virtually all the nation's financial institutions have suffered from borrowing short and lending long. Some have found ways to cope with the situation better than others.

Banks have fared best. Most of their loans are tied to the prime rate or the London InterBank Offered Rate, both of which generally fluctuate with their cost of funds. This enables banks to pass the risk of high and volatile interest rates along to their customers.

Savings and loans are still groping for a way to pass that risk along to their customers. Variable rate mortgages and mortgages subject to renegotiation are currently popular ideas. Some savings and loans favor shared appreciation mortgages, where the savings and loan profits from any gain in the price of the home. Home Savings & Loan, the nation's largest savings and loan, recently stopped making new first mortgage loans until some new financing vehicle is devised to neutralize the risk of borrowing short and lending long.

Insurance companies are using a similar approach to cope with borrowing short and lending long. They are beginning to avoid the long-term bonds and mortgages they once bought automatically in favor of intermediate-term bonds or short-term money market instruments. Insurance company managements are coming to realize that, since they are borrowing short-term funds from policyholders, they should invest those funds short term as well.

Mismatching maturities was no problem when interest rates were low and stable, but those halcyon days are a thing of the past. Viewing the chaos caused by high and volatile interest rates, a contemporary Shakespeare might amend his classic dictum to read: neither a short-term borrower nor a long-term lender be.