To see why, let's consider the real $/£ exchange rate. This is the ordinary nominal rate multiplied by the ratio of UK to US prices. The real exchange rate can fall either if the nominal rate falls or if UK prices fall relative to US ones: both imply an improvement in the competitiveness of UK-based companies.
Right now, this real rate is at its lowest level since 1988, when current data on the UK consumer prices index begins.
My chart shows why this matters. Since 1988, there has been a strong correlation between this real rate and changes in the nominal rate in the following three years. You can see from the chart that this relationship isn't driven by outliers. Nor is it just a historical quirk. The same relationship holds whether we look at data since 1988 or just at data since May 1997 when the Bank of England was given operational independence.
For example, low real exchange rates in 2001-02 and in 2008-09 led to the pound rising, And high real rates in 1991-92 and in 2007 led to it falling.
This isn't an oddity of the pound. In a recent paper Martin Eichenbaum and Sergio Rebelo at Northwestern University and Benjamin Johannsen at the Federal Reserve point out that the same relationship holds for many other currencies.
Nor is it a new finding. One of the classic theories of exchange rates, taught to generations of students, is the 'overshooting' model devised by the late Rudiger Dornbusch. This says that exchange rates move a lot in response to shocks and gradually re-adjust later.
Why? One simple possibility is that FX markets overreact to good and bad news just like stock markets do, and so a cheap pound leads to a rising one.
$/£ rate 1988-2017
But there's another possibility, discussed by Messrs Eichenbaum, Rebelo and Johanssen. Imagine something happens which would tend to raise domestic prices, such as a rise in government spending. This should raise the real exchange rate. But if central banks are targeting inflation, relative prices in two countries shouldn't change. The real exchange rate will then have to adjust by the nominal rate rising. And it will gradually fall back as the shock dissipates. This will be consistent with everyone behaving rationally because our central bank will hold inflation down by raising interest rates. But if one country has higher interest rates than another, it should see its exchange rate fall so that profits on the interest rate pick-up are offset by losses on the currency.
In this sense, we don't need to believe investors are irrational to believe that currencies overshoot.
If all this is right, sterling should rise. It's therefore dangerous for UK investors to hold foreign currency assets or stocks with big overseas earnings. And it might be that some companies that have seen their shares fall because of fears of rising import costs are over-sold. It would also mean that fears of a protracted rise in inflation are overstated, because sterling's rise would help cut import prices.
But is it right? There are two big caveats here.
One is that it's dangerous to apply historic patterns to what has been an unprecedented event - the UK's vote to leave the EU. We might regard this not as the temporary shock considered by Dornbusch or Eichenbaum, Rebelo and Johanssen, but rather as a permanent one that will eventually reduce future UK GDP. If this is the case, then we should have a permanently lower real exchange rate. However, even if this is true it won't become clear for some time, during which sterling might rise.
Secondly, the case for holding foreign currency is not that it will deliver good returns but rather that it is a form of insurance. In many types of crisis, sterling falls because investors dump it in favour of currencies they perceive to be safer such as US dollars or Swiss francs.
Even if your central case scenario is for the pound to rise, therefore, there might still be a case for holding some foreign currency as a hedge against the low-probability but high-cost possibility of an unexpected crisis.
