Of Course QE Has Significantly Boosted Stock Prices
They first have an empirical argument by asserting that valuation levels really aren't high, but that's because they use a misleading measure, namely current stock prices compared to projected future earnings. But such projections tends to be systematically over-optimistic as official "analysts" wants to fool people in to buying stocks, something their firms profits from. Furthermore, their last data was from december 2012. Since then, the S&P 500 has risen by more than 26%.
If you instead look at stock prices compared to actually reported earnings, you can see that they are about 50% higher than the historical average.
And as they noted themselves later, stock prices aren't just boosted through higher valuations, they're also boosted by increasing corporate profits. Their assertion that this effect is however supposedly small rests on the faulty assumtion that this only happens because of lower interest expenses. A more important causal channel is by raising product prices more than wages/salaries. As a result, corporate profits are at an all time high of national income.
Another argument they use, that the negative reaction on stock prices from warnings about taper was transitory only proves the point further. A key reason it was transitory was because there was no actual taper.
They further use the "theoretical" argument that lower interest rates will only have a small effect on the discount rate that investors use when calculating the present value of future earnings and dividends because investors will expect interest rates to rise eventually. That argument fails on two grounds. One is that it is dubious whether we should really expect interest rates to rise soon as the economies become increasingly addicted to cheap money. Another is that the whole point of QE is to bring down long-term yields, something that secures a lower discount rate for all earnings/dividends the coming decade.
Finally, they argue that most of the money coming in to the stock market from bonds, but from institutional investors. But that proves nothing as it is likely that low bond yields have made them prefer stocks over bonds.