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THESE have not been good times for those highly paid folk who forecast currency movements. At the start of last year, almost all of them predicted that the euro would climb against the dollar, and that the yen and the pound would slide. And what happened? The opposite: the euro fell sharply against the dollar, and the yen and the pound have risen. Traditional models used to forecast currencies seem to have developed a serious fault. Having seen their old bangers break down, some forecasters are turning to newer models. Fancier they may be, but will they prove any more reliable?

Behind most exchange-rate forecasting models is the idea that currencies have an equilibrium level to which they will eventually return. Awkwardly, however, economists find it difficult to pin down the factors that determine that equilibrium level; indeed those factors have probably changed. Trade in goods and services was once the linchpin. Then bond markets became more important. Now, some say, equity markets are increasingly the main force steering exchange rates.

The oldest theory of foreign-exchange equilibrium is purchasing-power parity (PPP). This is based on the notion that, in the long run, exchange rates should move to a level that makes a basket of tradable goods and services cost the same in any two countries. The Economist’s Big Mac index, which compares the price of a Big Mac in different countries, is a crude version of PPP. But in the short and even medium term PPP might as well stand for “pretty poor predictor”. Sterling, for example, has been overvalued on this measure for several years—ie, consumer goods, from clothes to CDs to hamburgers, have consistently cost far more in London than in Manhattan or Munich, say.

A second, related concept of equilibrium is the exchange rate that is required to achieve current-account balance. If an overvalued currency falls towards its PPP, this should help to reduce a trade deficit by making exports cheaper and imports more expensive. However, if an economy has large debt-service payments as a result of years of current-account deficits—as in America—it will need to run a trade surplus to balance its overall current account. So its equilibrium exchange rate may, for some time, be below the PPP level.

The Fundamental Equilibrium Exchange Rate (FEER) is based on this approach. The FEER is the exchange rate that produces a “sustainable” current-account balance. Most estimates suggest that, for the dollar, it is around ¥90 and euro0.75. On this basis, therefore, the dollar is overvalued at its current rates of ¥105 and euro1.03.

Both PPP and the FEER focus mainly on the prices of traded goods and services. That was fine when tight controls restricted the movement of capital around the world. But now that those controls have been largely scrapped, capital flows have become more important than trade in determining exchange rates. Only 1% of all foreign-exchange transactions are trade-related. Despite America’s huge and growing current-account deficit in recent years, the dollar has been strong because foreign investors have been happy to finance that deficit.

On this view, the relative prices of financial assets in different countries matter more than the prices of goods. Investors will shift funds until expected returns are equal. Things that change expectations about interest rates and bond yields—such as growth rates or inflation—will move exchange rates.

Until recently, the financial assets involved were largely government bonds. International money tended to move in response to differences in bond yields. Now, however, some economists reckon that equity markets are increasingly in the driving seat. In the past year or so, there has been a strong correlation between the dollar and the American stockmarket, and between the yen and the Japanese stockmarket. A net inflow of equity capital into both countries has supported their currencies. In contrast, the net outflow from the euro zone has more than offset its current-account surplus, depressing the euro.

Equity markets have become more important for two reasons. The first is that they have grown rapidly compared with government-bond markets. In 1990 America’s stockmarket capitalisation was only 50% bigger than the stock of Treasury bonds. Today the value of equities is four times as large (see chart). This is partly due to higher share valuations, but it is also because the government, now in surplus, is issuing fewer bonds.

The second reason is that cross-border equity investment has increased even more dramatically. When they ventured abroad, investors used to buy government bonds almost exclusively. Now they are increasingly buying equities. In 1990 foreigners’ dealings in American Treasury bonds were ten times bigger than their equity transactions. By the end of last year they were less than twice as large—and these figures do not include mergers or direct investment.

There have also been good economic reasons for the dollar to move in step with American shares. The spurt in productivity growth in America has pushed up share prices in anticipation of future productivity gains, and also improved the competitiveness of American goods, thus increasing the dollar’s long-term equilibrium level.

Can the increased influence of stockmarkets on currency movements be incorporated into a forecasting model? Cameron Crise, an analyst at Warburg Dillon Read, has tried to do this by making use of equity risk premiums. The equity risk premium is usually viewed as the extra return that investors demand for holding equities rather than risk-free bonds. However, Mr Crise suggests that it could be viewed in the same way as varying risk premiums on different countries’ government bonds, meaning that it reflects uncertainty about the relative attractiveness of a country’s equity markets.

The risk premium is thus, he suggests, also the market’s best guess of the risk and opportunities attached to consensus profit forecasts. A country such as America, with a low equity risk premium, implying that the market expects less risk or greater opportunity for future profits, will attract foreign money—and its exchange rate will rise.

So long as foreign investors favour American equities, then, its large current-account deficit will not drag down the dollar. Likewise, the yen is unlikely to weaken unless and until foreign buying of Japanese equities declines. And the euro will recover against the dollar, argues Mr Crise, only if the gap between equity risk premiums in America and Europe is closed. That might happen either because belief in America’s new economy fades or because Europe also enjoys a productivity spurt, thanks to technology and deregulation, which boosts shares.

Are equity flows any better as a predictor than trade or bonds? The key to the dollar’s future almost certainly lies in Wall Street; a bursting of stockmarket euphoria would drive the dollar down sharply. But forecasting when a stockmarket will correct is even harder than predicting movements in interest rates and bond yields.

Moreover, the new correlation between stockmarkets and exchange rates may be fickle. A sudden increase in inflation, or a global financial crash, could well send investors scurrying back to safer bond markets, thereby breaking the link between currencies and shares.

If (when) America’s stockmarket falls sharply, the dollar will surely tumble. However, the last thing the fragile Japanese economy needs is a stronger yen, which would squeeze exports and exacerbate deflationary pressures. That is why the Bank of Japan has (unsuccessfully) intervened to sell yen several times in recent weeks. The yen probably needs to fall. But the only way that both the dollar and the yen can weaken is if both currencies fall against the euro. A good punt for the next year or so: buy euros, whatever the models tell you.