The answer here is surprisingly clear. Falls in sterling have traditionally been more good than bad for equities. Since 1990 there has been a negative correlation (minus 0.17) between monthly changes in sterling's trade-weighted index and monthly changes in the All-Share index. What's more, except for a brief period in 2008 when a rush for liquidity caused traders to close off carry trades and thus dump sterling, the correlation between sterling and equities has been pretty consistently negative.
To put this another way, since 1990 there have been 64 months in which sterling fell more than 1 per cent and the FTSE All-Share rose by an average of 1.1 per cent across those 64 months. There have been 79 months in which sterling rose more than 1 per cent. On average, the All-Share fell by 0.6 per cent in these months.
The fact that shares have risen recently as sterling has fallen therefore conforms to the usual pattern.
But in theory there's no necessary reason for a lower pound to boost shares. Quite the opposite. If sterling falls because investors anticipate lower growth, or because they dump UK assets generally, shares should fall as sterling falls. Or if investors regard exchange rate moves as mere noise, they would have no implication for equities and so we'd expect a zero correlation.
So, why don't these mechanisms usually operate? One reason - highlighted by Bank of England governor-elect Mark Carney's comments on the need to achieve "escape velocity" - is that sterling often falls because of, or in anticipation of, weaker monetary policy, which tends to support share prices.
Also, a falling pound for any reason should raise the sterling value of overseas earnings and exporters' competitiveness, which benefits shares; the fact that the negative correlation between sterling and shares is stronger for the FTSE 100 than it is for small caps suggests that markets are putting more weight upon the former than the latter.
Whatever the reason, history is reasonably clear. Falls in sterling are more often than not good for shares. But it does not follow that you should rush out to buy on the grounds that sterling will fall further. It certainly could do so, simply because exchange rates are volatile - although they've been less so recently than in the more distant past.
But the mere fact that sterling has fallen recently tells us nothing about its chances of continuing to do so. This is because, at the time horizons longer than a few moments, there is no momentum in currencies. One measure of this is simply the correlation between exchange rate moves in one month and the next. For sterling's index since 1990, this correlation has been 0.02, implying that moves in one month are independent of those the previous month. Another test is to look at variance ratios. If there's momentum in prices, longer-term volatility will be higher than short-term volatility as price moves feed on themselves. But this is not the case for sterling's index. The standard deviation of annual changes in it since 1990 has been 6.9 percentage points, almost exactly the same as the 6.8 per cent annualised volatility of monthly changes.
We cannot, therefore, say that sterling will fall simply because it has done so recently.
Nor can we do so because of any other reason. The sad fact is that exchange rate moves, at the time horizons that matter for investors, are largely unpredictable except by using information, such as orders flows, which is not readily available to most retail investors.
Of course, it's easy to tell a story in which sterling falls. But stories and futurological opinions about exchange rates are too weak a foundation for sensible investment strategies.
All we can say is that - except in circumstances that are more often imagined than observed - a further fall in sterling probably would be good for equities. In this sense, investors shouldn't worry about the pound.
