Does Efficient Market Hypothesis make anticipated monetary policies useless? Since the market perfectly captures all the information, is it true that any anticipated monetary policy has no impact on equity prices? Or the “information” has an immediate impact but the “event” itself has no impact.
We begin our story at time $t-1$, where we have a Goldilocks economy (not too hot nor too cold). At time $t$, the economy gets worse. At time $t+1$, it becomes obvious that the central bank will cut the policy rate by 25 basis points at the next meeting and that this is sufficient to move the economy back to where it was at $t-1$. At time $t+2$, the central bank cuts the policy rate by 25 basis points. If markets are semi-strong efficient and the worsening of the economy is public information (along with the monetary policy action), then we would expect stocks to fall on $t$, rise on $t+1$ to the same level as $t-1$, and be unchanged on $t+2$ (assuming nothing else is happening in the economy). 

However, this does not make monetary policy useless in this situation. If the monetary policy authority, meeting on $t+2$, left rates unchanged (instead of cutting them), then we would expect equities to fall on $t+2$. While there are many monetary policy channels, in most of them, the changing of the policy rate actually improves the economy. This can raise equity prices by boosting firm cash flows. 

When the central bank cuts rates, this isn't useless, even if expected, because it caused the economy to be better, which also boosted the value of financial assets. Yes, if the rate change is fully anticipated, there is no effect seen on the day of the rate change, but that is not because it is useless. Rather, it is because it is already priced into the value of financial assets before the rate change actually occurs.