I think you have to look at the concept of spurious regression.
A key idea useful to interpreting correlations like this is the idea of "spurious regression". Any two time series X and Y each of which has a trend (even if it's a "random trend" !) will appear to have a high negative or positive correlation. (This is because, if there's a trend, all the values above the mean and all the values below the mean will tend to be on opposite sides of the time series, for both series. A high correlation then tells you that the above the mean values of one series coincide with the above(or below) the mean values of the other series...which is not very surprising.) A high correlation in this setup is an interesting finding if it's a correlation of the 'de-trended' series, or of the 'differenced' series.
Also, plot the series since then. The stock market has gone through upturns and downturns that do not seem to be related to the monetary base in any way.