District savings and loan associations posted unprecedented operating losses of $42 million -- their worst record in history -- in the first half of 1982, according to the Federal Home Loan Bank Board semiannual report issued yesterday.

The losses represent primarily the difference between the yields the institutions make on their older loans and the higher interest rates they must pay on savings accounts.

This compares with losses of $39 million during the second half of 1981 and $14.8 million in the first two quarters of that year. Reserves, or net worth, shrank by as much as 50 percent at several associations. Only one out of 10 S&Ls, tiny OBA Federal, eked out a modest $44,241 profit.

But since the end of June, which was the cutoff date for this report, the outlook has brightened. Falling interest rates, coupled with general capital assistance and new asset powers recently passed by Congress, suggest less bleak results in the latter half of this year and a brighter picture in early 1983.

S&Ls will soon be able to prop up their sagging balance sheets until the returns on their loan portfolios catch up with the amount of interest they pay on deposits. Meanwhile, industry officials hope the new money market fund equivalent account, due around the end of the year, will stop the drain on deposits and give S&Ls enough cash to become active mortgage lenders, now that rates have fallen.

The loss of more than $81 million over the past 12 months has taken its toll on District associations. Their total net worth has been cut about one-third to $238 million. (Net worth is the excess of assets over liabilities and is often used as the equivalent of corporate profits for mutual S&Ls.) This figure will be reduced by more than half at the end of the year as the result of Perpetual American moving its headquarters to Virginia and the merger of Jefferson Federal into Washington Federal. National Permanent Federal Savings and Loan also has applied to leave the District.

The largest losses in percentage terms were suffered by Capital City Federal Savings and Loan. Its net worth dropped by almost $5 million, or 52.7 percent. Independence Federal Savings and Loan lost half of its reserves due to an operating loss of $706,320. Perpetual American, the largest and strongest in terms of reserves, had a loss of $8 million, or a 7 percent drop in net worth. Jefferson lost 39 percent. Washington Federal experienced a drop of just 3.7 percent.

National Permanent lost the largest dollar amount, $10.6 million, which is a drop of 32 percent. The size of the loss was increased by the use of purchase accounting principles applied to its merger last year with troubled Eastern Liberty Federal Savings and Loan. This causes an immediate drop in the value of an association's reserves, a loss that is recovered over a period of years.

The ratio of reserves to insured deposits for the 10 District S&Ls dropped from an average of 7.9 percent at the end of last year to 6.6 percent. Without OBA -- which has the enviable ratio of 23.3 percent -- the average for the District's S&Ls was 4.7 percent in June. Perpetual American again had the second highest ratio, 10.17 percent.

The smallest reserve ratio, 1.2 percent, belonged to Independence. Capital City Federal Savings and Loan Association had a 2.16 ratio. These two S&Ls will become eligible for up to 50 percent of the operating losses they suffered under the capital assistance provisions of the Depository Institutions Act passed this fall. This law is designed to slow the tide of federally arranged mergers by adding to the net worth of S&Ls through paper transactions. This involves the exchange of income capital certificates by the S&Ls for promissory notes from the Federal Savings and Loan Insurance Corp. The notes can be redeemed for cash only if an S&L fails.

Complete results for savings and loan associations in the District and nearby Maryland and Virginia will be printed in Monday's Washington Business.