Robert Shiller rightly deserves his Nobel Prize as perhaps the world's leading expert on asset bubbles. (I beat him by a year on the housing bubble in the United States.) But I think he gets the story badly wrong in making the case that there is currently a serious bubble in the U.S. stock market.
Shiller's rationale is that the price-to-earnings ratio is well above its historic average. Furthermore, he points to the large stock plunges the last three times the price to earnings ratio approached current levels in 1929, 2000, and 2007.
There are two reasons I find the case less than compelling. First, it seems very plausible that people feel more comfortable investing in the stock market today than was the case thirty or forty years ago. This can be explained by the existence of index funds and the growth of defined contribution pensions. As a simple factual matter, a much larger percent of the population has stock holding today than was the case forty years ago, even if the distribution of holdings is still quite skewed.
The implication is that people if people view the market as less risky now than in the past, stock would command a lower risk premium than it had historically. This would justify a higher price-to-earnings ratio. This could mean that something like the ratio of 27 that Shiller calculates, compared to a long-term average of 17, could be reasonable. The ratio of 44 he calculated for 2000 clearly was not. (Note that the 2000 ratio is more than 60 percent higher than the current ratio.)
Btw, the tumble from 2007 peak was associated with a small detail: the collapse of the housing bubble and the ensuing financial crisis. I had warned of the market peak back then not because I thought stock prices were inherently too high, but that no one on Wall Street anticipated the devastation that would follow the collapse of the housing bubble.
The other reason why the current PEs in the stock market might be justified is that interest rates are well below their historic averages. With the nominal rate on 10-year Treasury bonds at just over 2.0 percent and the inflation rate around 1.6 percent, the real interest rate is roughly 0.5 percent. This compares to a long-period average in the range of 2.5-3.0 percent.
With the alternatives to holding stock offering returns that are far lower than they have in the past, it makes sense that people would be willing to accept a much lower return on their stock. The current PE should still allow a premium in the range of 4.0 percentage points relative to bonds, which is roughly the long period average. Of course if we had reason to expect that the real returns on bonds would rise sharply in the near future, then this argument would not carry much weight, but there does not appear to be any good story as to why real bond yields should be headed much higher in the near future.
In short, stocks do look high in the sense that people should expect lower returns in the future than the historic yield on stock, and they certainly should not expect to see anything like the run-up from 2009-2014. However, there is no reason to expect a sharp downturn barring a major downturn in the economy for reasons not currently in sight.