WHERE in the world should investors buy property? Even if there is an improvement this year on the past 12 months, the search for new opportunities is strictly for the brave. There is no guarantee that the first into the property recession will be the first out. The severity of the property downturns in the United States and Britain - which entered the downturn well before Japan and continental Europe - is so bad that recovery is likely to be slow and halting. Less mature markets also promise a rocky ride. The emerging markets of central and eastern Europe are driven by political and legislative difficulties and even the fast-growing markets of Southeast Asia are suffering from over-supply. The increasingly global flow of funds in the 1980s allowed banks and investors to export property booms from one market to another. At the same time, the rapid expansion of the financial services industry set off periods of heady construction in New York, Tokyo and London. The result is that the world's biggest cities are full of empty offices. More than a fifth of all office blocks in the City of London, Sydney, Melbourne and Perth and the US are empty. Paris is heading towards a vacancy rate of 10 per cent. In Germany, and even Japan, which have had the lowest vacancy rates in the world, rates are creeping up significantly. Rising interest rates towards the end of 1989 dried up liquidity and burst the bubble, leaving an oversupply of buildings, rapidly falling prices, a shortage of capital and credit and a near-crisis in the banking industry, which had lent heavily to the sector. The severity of these problems defies an easy solution. Falling interest rates in Japan and the US have not stopped the rot. Much of Europe does not even have the panacea of cheap money; a tight monetary policy in Germany, the result of the huge cost of reconstructing East Germany, has kept interest rates high across most of the European Community. Between 1985 and 1990, rents in good quality property in leading European cities rose by an average of 14.4 per cent annually and capital values by 17.8 per cent a year, according to Jones Lang Wootton, chartered surveyors. Average capital values across continental Europe have already fallen by 23 per cent from their peak in 1991, says Jones Lang Wootton, and there is every sign that the decline will continue. Only Hamburg posted any rise in rents in 1992. Spain is enduring the steepest fall in values in the EC, apart from Britain. Capital values of prime offices have fallen by about 30 per cent in the past year in Barcelona, and by 28 per cent in Madrid, over the same period. France probably provides the greatest cause for concern. Banks and insurance companies are closing ranks in an attempt to reduce the damage from doubtful debts in their property loan portfolios. The French Government has proposed measures such as granting tax advantages and deferment of stamp duty, to help the industry. However, the government is reluctant to be seen to be bailing out speculators. Recession and high interest rates have sent much of the German market into reverse. The reconstruction of eastern Germany, like other markets in central and eastern Europe, is being held back by problems of land restitution. Economic hardship and the difficulties in imposing a market structure after decades of communist rule are additional difficulties in Hungary, Poland, the Czech Republic and Slovakia. Opinions differ about Britain, the worst-hit market in Europe. In spite of severe structural problems of over-supply and weak demand, a small but growing number of investors believe the decline of the past three years has run its course. Similar arguments are promoted by optimists in Australia and the US. The bull case for US property is that new construction has ground to a halt and recovery is gathering pace. An aspiring investor would do well to examine the property markets of Asia, which in spite of over-supply problems are generally supported by robust economic growth, with the notable exception of Japan. ''Asia still continues to be one of the brightest areas in the world,'' said Mr Alan Hill of Jones Lang Wootton. Malaysia has attracted much attention from investors. Factors such as political stability, a shortage of office space, and its bid to hold the 1988 Commonwealth Games have led to rising values, and the launch of big developments. But there are also many risks in Asia. Thailand and Hongkong are dogged by political uncertainty; Singapore has a large over-supply of office space, which has resulted in a fall in excess of 20 per cent in rents since the end of 1991. Another concern is that Japanese banks and investors, which have supplied much of the capital for investments in the region, have withdrawn.