Assuming we're dealing with rational investors, the stock price is equal to the present value of all future dividends(supposedly discounting at the nominal or real interest rates should give the same present value).
Imagine the Central Bank increases the real money supply, from an initial state of equilibrium, and this increase is unexpected by the investors of the stock market.
Now we have the consequences of monetary expansion in the 'physical' economy:
- In the short run, the expansion causes the nominal interest rate to decrease and the output to increase. However, in the medium run, the output reverts back to the natural level, and assuming for simplicity that the output growth rate is zero, the nominal interest rate also increases when compared to initial medium run equilibrium.
- In the short run, real interest rate decrease. In the medium run it increases to the natural level, and remains equal to initial levels.
In a book I'm reading on macroeconomics, it's stated that since in the short run the output (and dividends) increase, and the nominal interest rate decreases, the stock prices will go up, because the monetary expansion was unexpected.
My question is: shouldn't the rational investor know that changes in the nominal interest rate are only short term, with the longer term effect being in the opposite direction, and hence it's not clear cut that stocks' price should go up? Or should they always go up? Is it due to expected inflation that counteracts the higher expected nominal interest rate?