There’s a strong relationship between starting valuations and subsequent annualized ten-year returns. Higher starting valuations consistently lead to lower returns, and vice versa. There are minor variations in the observations, but no serious exceptions.

I might be looking at this wrong, but doesn't this stand to simple reason without even looking at any actual numbers? Let's say there's an expected long-term return, call it 10% for ease of this illustration. If you look at windowed periods (of 10 years, or 20, or whatever) and the first portion of the period has averaged higher than 10%, then doesn't it stand to reason that the probability is that the remainder of the period might be under 10% at some point to roughly keep within that average expected return over the long period?

Furthermore, if this were NOT the case, if a higher than expected average happened near the start of a period, and the future returns DO NOT go lower to maintain that long term average. Then wouldn't it cause two things:
1. The long term average increases and the premise was incorrect.
2. Possibly, to maintain that status forever, the returns keep going up and up with time. (but I haven't thought through this part)