The market is a conversation, not a calculation. There is no equation for its "proper" valuation because there is no equation for an asset's "proper" price. We have markets because these calculations, the economic calculation problem [1], are hard.
Financial theory has a habit of magicking uncertainty into variables that look like constants but aren't. With option theory, it's the volatility curve. With CAPM [2], it's the risk-free rate curve and general market risk premia (also beta). In the discounted cash flow model [3], it's the discount rate and future payout curve.
These models sort of work a lot of the time, but not always and not as well as we'd like them to. Unfortunately for the precision-minded, the bridge between the quantitative models are people doing their people things.
Note that I'm not saying it's all voodoo. There are models. But understanding them takes appreciating their constraints, assumptions and strengths.
Shiller Price/Earnings[1], probably. It looks at the previous 10 years of earnings to do a P/E to try to even out the earnings and get a better picture. But I'd imagine even just normal P/E ratio would be better...
On a grand scale, it's hard to tell, as the market is so big. When you break it down, there is the stock market, then there's the derivative market, the bond market, the housing market, foreign markets, crypto markets, and on and on. You also have to look at previous crashes and see what sticks out from past lessons.
With the stock market, you can look at average P/E ratios over time for the Nasdaq and get somewhat of an estimate. To dig a little deeper, you can look at individual sectors index, such as the Nasdaq Biotechnology Index - NBI
Derivatives market - Deutsch Bank last year was facing a semi crisis mode due to having too big of an open derivatives position. What was it? Idk, I didn't dig too deep. Derivatives markets are still, well, derived from an underlying product. So in theory, if you find the product, you find the bubble. Something like soymeal futures last year, is a good example.
Bond market - falling due to increasing rates. 1981-82 was caused by interest rate hikes, to fight inflation, but they were like 15-17%. We're struggling to get the glorified 2% inflation. Granted this is all what's reported to us, who really knows.
Foreign markets - A lot of countries for the past couple years have been in the shitter, in terms of GDP - Russia, Canada, Mexico, Brazil, Australia, etc. Then there are countries who have cooled off - UK, Germany, China, etc. However, the US and India just keep charging up the hill. Also, a lot of it is based on speculation. China a couple weeks ago announced that they had tied last years GDP growth, when analysts thought they were gonna miss. Regardless, this is still one piece to a massive puzzle. If you look at participation rate through out the world, http://data.worldbank.org/indicator/SL.TLF.CACT.ZS?page=2 it's been falling. This could be explained by an aging population of basically all WW2 countries - http://www.worldatlas.com/articles/countries-with-the-larges.... As well all know fine and well here, this may not be a big problem YET due to automation. In other words, it's hard to truly tell where and which pillar could break, that could really push this beast downward.
Crypto markets - the fun new kid on the block. Super entertaining to watch people hodl and meme about it, but is still no where near the size needed to cause a correction.
A few other interesting things I've seen floating around:
The VIX is at an all time low. Someone commented somewhere that they believe this is due to too many people believing there's gonna be a crash soon. As such, they're holding more cash than usual.
Around $4.2 trillion is now tied up in index funds. As such, if there is a panic in the index fund market, it could cause a crash. Idk about the validity of this one though, market makers could easily prop it, and buy on the panic and sell when it's cooled off.
