The Shiller CAPE seems very dangerous in 2 situations. One is when a market is 'expensive' and then goes through a profit boom
Lets say a index is a 1000, the 10y avg profit is 50 (20 Shiller PE). Then something happens and profits soar. The index might go to 1500 but the avg profit only to 55. The PE goes to 27 and the person thinks 'you know, this is too expensive, I'm out'. But what they are missing is the fact that the "true" PE might not have risen all that much once you account for the profit boom, its possible that the market is still cheap. As years passes and more of the profit boom becomes part of the 10 year average profit (and the less of the old and low profits are part of the 10t average), all of the sudden the Shiller PE changes and signals that the market is not that expensive. This could be what is going on right now in the US, although it depends on whether the Trump agenda adavances. Pop example: imagine analyzying AAPL by looking at 10y avg earnings, you would be thinking is overvalued for like decades
Another situation is where there is a collapse in profits and the Shiller PE keeps telling you to buy. Lets say the same index is at 1000 with 10y average profits at 50 (20 Shiller PE). Then there is a economic depression, profits start to collapse. Stock investors (a lot smarter than academics) will take the index down to 400. A dumb investor will look at a 400 index vs 10y avg profit at 45 and think 'this market is a 9 times earnings, time to buy', but he doesnt get it that the index is only that low because smart investors see that the old profits are gone and there is a new reality where profits will be much lower. This was the Greece scenario where CAPE investors got killed as the index dropped 95% and profits dissapeared. Pop example: Imagine analyzing VRX by looking at 10y avg earnings, you would miss out that the future will have a lot lower profitability
The Shiller PE has this implicit 'mean reversion' in the profit mentality that can be very dangerous. In the Greece scenario is not that bad because at least you can only lose what you put in when you invest in equities and usually, in most capitalistic economies, that profit mean reversion tends to happen (although it will fail in the tail scenarios like it did in Greece and Venezuela). But when we are talking about profit booms, it can easly lead someone to stay out of market during a huge exponential run.
Stocks are a forward looking market, it is not appropriate to use a backward looking, slow to adjust indicator created by an academic that is not experienced with the stock market