There can be little doubt that global equity investors are witnessing a bear market. Not everyone agrees on what constitutes a bear phase but most agree it involves a fall of at least 20 per cent, which persists for at least a year.

Most leading indices peaked in early 2000 and at one stage or another during 2001 had fallen by much more than 30 per cent.

In mid-September, just after the terrorist attacks in the US, the Dow Jones Industrial Average had fallen 31 per cent from its peak, the FTSE 100 had fallen 36 per cent while the DAX in Frankfurt had more than halved.

There was heavy selling in mid-September, which some saw as a sign of investor capitulation - the classic signal of the end of a bear market. Sure enough, many markets then rallied rapidly back to their pre-September 11 levels.

But the markets face a lot of hurdles to overcome before it can be said that the bear market is truly over.

The first difficulty is the war in Afghanistan and the possibility of further terrorist attacks. As they showed during the Gulf War, the markets can cope with wars that are confined to one country, far from the US or Europe. But should the war spread to the Middle East, and should terrorists show they can mount repeated attacks in western countries, then confidence would inevitably be undermined.

Second, it remains unclear what the depth and length of the global economic slowdown will be. The first estimate of US third quarter gross domestic product (GDP) showed an annualised decline of just 0.4 per cent, rather milder than expected.

However, with companies announcing big layoffs on an almost daily basis, and the terrorist action weighing on consumer confidence, the fourth quarter is expected to show a greater decline.

Central banks, particularly the US Federal Reserve, have acted aggressively to try to bolster economic activity, cutting interest rates in some cases to the lowest level for a generation.

But there is some doubt whether the interest-rate medicine will be as effective as it was in the past. Their theory is that the global economy is now suffering because of over-investment during the boom years of the late 1990s, particularly in telecoms and technology. This has created over-capacity, squeezing profit margins. Now companies will cut back on investment and borrowing, regardless of interest rates. The slowdown will not be over, if this theory is correct, until the overcapacity is eliminated.

A related problem concerns the levels of debt taken on by consumers and companies during the boom period. Low interest rates make servicing that debt relatively easy in the short term but low nominal income growth means repaying that debt will be tougher in the long term. That debt burden could weigh on corporate and consumer spending for the next few years.

Investors hope economies and corporate profits can rebound fast in 2002. Signs of prolonged sluggishness will weigh on sentiment.

The third issue which dogs equity markets is valuation. Share prices rose to unprecedented levels at the end of the 1990s. Even the sharp falls since the peak have only taken historic price-earnings ratios back to around 20 times, levels that before have only been seen at the end of bull markets.

Many analysts argue that such ratios are justified by lower levels of inflation and equities look cheap compared with alternative assets such as bonds. Others believe it makes no sense to compare a real asset (equities) with a nominal one (bonds). Whether the historic or the relative school of valuation is proved right is vital for the future direction of equity markets.

It is hard to believe, however, that there will be a return to the heady days of the 1980s and 1990s when double digit percentage annual returns on equities were the norm. Equity returns were boosted during the period of disinflation as nominal yields on financial assets fell. But now we have reached a period of low inflation, returns are likely to fall to single digits.

Over the long run, returns are expected to be linked to corporate profits growth, which in turn is linked to the rise in nominal GDP. If the latter is 5 to 6 per cent a year, then investors should expect 5 to 6 per cent plus the dividend yield. In most markets that adds up to between 6 and 8 per cent.

In combination with the poor performance of equity markets over the 2000-01 period, this presents some governments with a problem. Many want to see their citizens save for their retirement through the stock market, in order to ease the burden of ageing populations on the tax system.

But small investors must be rather sick of equities at the moment. Dresdner Kleinwort Wasserstein estimated in October that European investors had lost E75bn in the stock market - having been late into the bull run. Having lost 90 per cent or so in areas such as technology, it is far from clear that annual returns of 6 per cent to 8 per cent will be enough to make equities attractive.

The evidence of the late 1990s is that retail investors only get excited about equities when they are in their most speculative phase - when they offer the chance of getting rich quick. While small investors have not indulged in mass selling during 2000-01, they have not been buying either - inflows into mutual funds have slumped. And the lack of selling may simply reflect the well-known psychological difficulty investors have in taking a loss.