At first glance the dollar appears to be defying the dire predictions made by many economists at the start of the week.

Since last Tuesday's terrorist attack the US currency's response has seemed relatively stoic. Against the currencies of its main trading partners, it has fallen just 1.6 per cent.

But sighs of relief would be premature, in part because foreign exchange trading has not yet fully returned to normal.

In the immediate aftermath of last week's attacks, the foreign exchange industry association and central banks put pressure on banks to eschew large bets - fearing violent gyrations in the market and problems in processing trades. Although banks now feel more able to take positions, the central banks are still using moral suasion to stave off speculation, says Avinash Persaud, head of research at State Street, the US investment bank.

"We are still operating in a slightly artificial market," he says. "Banks still feel they may need the central banks if their systems fail and do not want to antagonise them by taking big speculative bets."

After this week's display of co-ordination by central banks in cutting rates, traders are also more convinced that policymakers would step in to prevent a sharp fall in the dollar. This also looks to have damped any desire to move against the dollar.

Even so, the modest trade weighted fall of the dollar already conceals a worrying trend for the US currency. The bloated US current account - running at around $30bn (£20bn) a month - has long been seen as the currency's Achilles' heel. A league table of the best and worst performers over the past week suggests that currencies are increasingly being judged according to their current account and foreign asset positions - a country's net ownership of overseas investments.

Once seen as the main determinant of currency movements, current accounts have recently seemed less relevant. A surge in cross-border investment flows has made it easier for countries to run large deficits without seeing their currencies fall.

The slowdown of the global economy had already started to weaken these flows. Last week's attacks threaten to undermine cross-border flows still further by undermining confidence among investors and discouraging them from increasing their exposure to foreign markets.

If risk aversion mounts there is a threat that investors will go further and bring overseas assets back to the safety of their home market. "In times of risk aversion, home is generally seen as the safest place," said Paul Meggyesi, a senior economist at Deutsche Bank.

This is certainly bad for the dollar. But it is even worse for those with even worse national balance sheets - hence the relatively modest fall in the trade-weighted dollar.

Since Tuesday's attack the dollar has fallen most against the Swiss franc, around 5.5 per cent. This is no coincidence since Switzerland is running a current account surplus equivalent to more than 12 per cent of gross domestic product and has net foreign assets worth 97 per cent of GDP. The dollar has also fallen 3 per cent against the yen, which still runs a respectable current account surplus and has net foreign assets worth 13 per cent of GDP.

Against the euro - which has a current account position close to balance - the dollar has slid 3.1 per cent.

But these falls have partly been offset by the dollar rising against countries with even worse net foreign asset positions than the US, such as Australia, New Zealand and Canada.

The emerging message is that although the dollar would not be the worst hit by a period of risk aversion in the market, it would be the most important casualty.