The effect of Monetary Policy on Asset Price Inflation
My understanding of the effect of easing monetary policy on asset prices is that it can work through a more direct channel. 

If markets are efficient and risk neutral then generally the value of an asset $i$ is equal to the net present value of the expected cash flows generated by that project:
$$ P_i = NPV(i) = \sum_{\tau=0}^{\infty} \frac{E[C_\tau]}{\Pi_{\ell=0}^{\tau}(1+r_{\ell})} $$
Monetary policy directly lowers the denominator of the the fraction in the sum, so it raises the value of the sum. In English, by reducing the rate at which we discount future investment the present value of the asset's cash flows become more valuable. If monetary policy can also improve the economy more generally, it can also increase the expected size of the cash flows, further increasing the value of the asset (it also raises the numerator).