Let's start from two principles.
First, QE is mildly effective - with the stress on both of those words. It is, says Scott Sumner of Bentley University, "likely to be only modestly successful". This is because cash is not quite a perfect substitute for Treasuries or mortgage-backed securities. Investors who get cash from the Fed will mostly just sit on it, but not entirely. Some of it will be used to buy other Treasuries or mortgage-backed securities or corporate bonds or equities. This will help reduce borrowing costs and so encourage people to buy houses and companies to invest. To this extent, QE does boost economic activity, relative to what would otherwise be the case. Economists at the Boston Fed estimate that $600bn of QE adds at most 1.2 per cent to GDP.
On top of this, there's an announcement effect. The Fed's promise to keep printing money until the labour market improves "substantially" should increase hopes of better times to come, which itself should encourage companies to step up their investment.
You might think this would be good for cyclical stocks and higher-beta ones, which should benefit from the increased appetite for risk that usually accompanies economic recovery. You'd be right, were it not for our second principle.
This is that the Fed is only printing money because it expects the economy to remain weak, and it will only continue to print money while it stays depressed. Such a weak economy does not favour equities. Good news about the size of QE will be bad news about the economy. This argues for investors having a defensive stance.
Combining these two principles suggests a case for a 'barbell'-type strategy - some cyclicals and speculative stocks to benefit if QE succeeds in bolstering the economy, but some defensives to insure us against the risk that a lot of QE might be needed, and from the fact that QE is only a weak tool.
The experience of the first two rounds of QE corroborates all this. During QE1, from November 2008 to June 2010, the Fed bought almost $1.6 trillion of bonds and the UK stock market rose 22 per cent. During QE2, from November 2010 to July 2011, the Fed's balance sheet expanded by another $600bn, but UK equities barely rose at all.
It seems, then, that our first principle - 'QE just about works' - applied to QE1, while our second - 'we need QE because the economy's weak' - applied to QE2.
But here's a curiosity. Although these two episodes look different, some sectors beat the market in both. These were the cyclical chemicals and industrials sectors, high-beta tech stocks, and beverages, food producers and tobacco - all defensives. This seems to support the case for a barbell strategy.
You might be surprised that miners aren't on this list. True, they did very well during QE1 - almost doubling in price. But they underperformed during QE2. A faltering economy is not good for commodity producers.
And there's one sector that underperformed in both periods - banks.
You might think this odd, given that cynics believe that part of the purpose of QE is to increase banks' profits. But I suspect there are two reasons offsetting this stimulus.
One is simply that any benefit to banks is discounted in advance and so banks lose during QE from the 'buy on rumour, sell on the fact' process. This could happen again, as banks have done especially well since July as hopes for a third bout of QE increased.
Secondly, anything that causes QE to be prolonged would be bad for banks. Ordinary slow growth would increase their bad debts, while the emergence of any new risks to the global economy would probably hit banks harder than others; banks are like the canary in the coal mine - the first to suffer badly from danger.
There might be a case for buying banks. But the mere fact of more QE is not it.
