INSTITUTIONS based in major North American, European and Far Eastern cities manage equities worth around US$6 trillion. Tokyo, followed by London, New York, Zurich and Boston are wielding the most power in fund management, according to Technimetrics, a Londonresearch and investor relations firm. They are followed by Geneva, Paris, San Francisco, Los Angeles and Chicago (see table). Fund management in Hong Kong is also growing rapidly and the city is among the leaders. Technimetrics estimated that funds managed worldwide reached a massive $6.4 trillion in 1993. Although share prices, declined this year, the total amount invested was still near this mark. In the Asia-Pacific region, Tokyo leads the way by a huge margin with $1.16 trillion under management, followed by Hong Kong, which has $81 billion of equities controlled by institutions. Sydney is next with $52 billion, followed by Singapore with $28 billion and Melbourne $17 billion. ''No theme has dominated institutional equity investment in the past few years as much as the shift towards global diversification of portfolios,'' said Fred Stone, managing director of Technimetrics. In 25 cities alone, the amount of equities controlled by institutions is as much as $5.24 trillion. This is equivalent to 82 per cent of all equity investments under management in North America, Europe and the Far East. London has overtaken New York and is second after Tokyo in the ranking of world equity centres. ''British pension fund managers rely more heavily on equity investments than foreign colleagues,'' said Mr Stone. The outlook for Hong Kong and other Asian markets is vitally dependent on the relatively new strategy of American funds investing a growing proportion of their portfolio overseas. Last year, US funds bought $67 billion worth of foreign shares. More than eight per cent of equities under management in the US are international equities, compared with five per cent three years ago. Illustrating the new fashion of investing in foreign stock markets, the aggregate value of international equities owned by US investors soared by 88 per cent last year, said Mr Stone. Although Tokyo is still the world leader, equity holdings of Japanese institutions, mainly banks and insurance companies, have declined. In Hong Kong, however, equity funds under management jumped to $81 billion in 1993 from $67 billion in 1992, boosting the city's ranking to 16. ''Typically, Hong Kong institutions allocate between a third and a half of their equity portfolios to domestic issues,'' Mr Stone said. The remainder is placed in other Asian and international markets. In 1993, Hong Kong investors were the sixth largest investors in US stocks, adding $1.1 billion to their existing portfolios. Equities under management in Australia reached almost $70 billion and a quarter of this amount was dedicated to European and US shares. ''Many Australian institutions appoint European and Asian managers to invest in international markets,'' he said. ''Singapore has grown as a regional centre for fund management and several European and US firms have established research and investment operations in the city.'' Last year, Singapore investors were the second largest foreign buyers of US stocks, after Japan. Institutions based in Singapore bought $3.1 billion of American equities in 1993.