Back in 1933 the US had experienced years of deflation and nominal interest rates were close to zero.  FDR sharply devalued the dollar over a period of 10 months, and stock prices closely tracked the value of foreign exchange during this period of monetary stimulus.  Last year the Japanese did the same, and Marcus Nunes has a great post showing that the results were pretty similar.  Here are some of his graphs:

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That certainly looks like a positive correlation.  Some people will say; “QE only helps the asset markets, it doesn’t boost NGDP.”  I don’t know how something could dramatically impact stock prices without impacting nominal spending, but in any case NGDP growth picked up in Japan last year.
Others will ask; “What makes you think higher NGDP growth will lead to higher RGDP growth?” This does:
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Again, that’s pretty similar to what occurred in 1933.  Another complaint is that currency depreciation is a “beggar-thy-neighbor” policy, which doesn’t work at a global level.  The worry is that it simply steals jobs from other countries.  And yet after the devaluation of 1933 US imports actually grew faster than our exports. Marcus shows that the same thing happened last year in Japan:
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Marcus explains why:

This is indicative that the income effect of the expansionary policy was stronger than the terms of trade effect of the exchange devaluation. In other words, it reflects an increase in domestic demand.

Marcus Nunes is the master of graphical analysis, and his post has four other nice graphs. Strongly recommended.