'83 pickup in overseas stock markets is bouncing into the new year

From Stockholm to Amsterdam to Tokyo, stock market indexes are near or well above their peaks, with only the exchanges in Johannesburg and Hong Kong showing normal or less-spectacular results.

Much of the boom can be traced back to the American economy and to encouraging economic projections in Western Europe and Japan. A major role is also being played by the record highs posted by the American dollar against most other currencies. The dollar reached all-time highs against the British pound, the French franc, the Italian lira, and several other European currencies in the first two weeks of January and scored a 10-year high against the usually robust West German mark. Only the Japanese yen, frequently said to be undervalued, has held its own against the soaring greenback.

European experts report that American investors, especially the wealthy institutional ones, have been taking advantage of the relative cheapness of foreign stocks (resulting from the strength of the dollar) and have been buying heavily on the world's exchanges. Important pension funds such as those of General Motors and American Telephone & Telegraph last week were reported seeking to increase overseas portfolios to capitalize on exchange-rate advantages and better growth prospects in some foreign stocks.

The value of these international shares would rise even more if and when the exchange rate of the dollar faltered, as is ultimately expected.

The run on foreign shares began in 1983, despite the relatively grim economic performance in many countries. The value of shares on the Mexico City exchange, for example, soared about 140 percent last year, followed by increases of about 60 percent in Paris, Stockholm, Sydney, and Oslo. Strong gains were also registered last year in Amsterdam, up 50 percent; Brussels, 36 percent; Frankfurt, West Germany, 35 percent; London, 30 percent; and Zurich, 23 percent. Values in New York also rose 23 percent.

Varous advisory services have been noting that mutual funds concentrating on Japanese and European portfolios in some cases doubled in value, while the best American funds recorded normally healthy 40 percent growth.

Throughout the world, this surge accelerated in the first two trading weeks of this year. Records were posted in many marketplaces. In London, one analyst remarked that ''records fell like ninepins.'' The Financial Times daily spoke of a ''huge equity boom'' in the City. A broker cited in the Paris daily Le Monde exclaimed, ''It's crazy. . . . In two days there's been a rise of 4 percent, and they're still pushing from behind.''

The Amsterdam Stock Exchange broke records for seven consecutive sessions late in 1983 and last week. In fact, it seemed last week as if traders at each exchange or bourse in succession around the world were stimulated by the sparkle of counterparts in preceding time zones, with the New York results fueling Tokyo , and then excitement in Western Europe.

Improving economies and more pro-business attitudes in Western Europe - even in countries with socialist governments - have contributed somewhat to the improvement in the stock markets. Technical factors also sometimes intervene. In France and West Germany, legal and tax reasons stimulated investors to shift massively into corporate shares rather than other forms of investments. This benefited nearby exchanges.

''The Brussels Bourse used to be a graveyard,'' a Belgian source remarked, ''but now it's been discovered by foreign investors who lead the way for Belgians.'' A Zurich broker noted: ''I'm still bullish about Switzerland, because I still see a lot of foreigners buying.''

Nevertheless, the possibility that the bubble could burst remains a constant preoccupation in such fragile circumstances. Some European analysts say this could serve as a brake to the market's climbing to even dizzier heights.