"I can show, really precisely, that there are two warranted prices for a share. The one I prefer is based on such fundamentals as earnings and growth rates, but the bubble is rational in a certain sense. The expectation of growth produces the growth, which confirms the expectation; people will buy it because it went up. But once you are convinced that it is not growing anymore, nobody wants to hold a stock because it is overvalued. Everybody wants to get out and it collapses, beyond the fundamentals."

– Nobel Laureate Franco Modigliani, New York Times, March 30, 2000

The word “bubble” is tossed around quite a bit in the financial markets, but it’s rarely used correctly. See, the thing that defines a bubble isn’t that valuations are extremely high, or that expected returns are extremely low. Instead, what defines a bubble is that investors drive valuations higher without simultaneously adjusting expectations for returns lower. That is, investors extrapolate past returns based on price behavior, even though those expectations are inconsistent with the returns that would equate price with discounted cash flows.

In March 2000, at the height of the technology bubble, I noted: “Over time, price/revenue ratios come back in line. Currently, that would imply an 83% plunge in tech stocks. If you understand values and market history, you know we’re not joking.” The following month, I discussed Modigliani’s quote above, and detailed the dynamics he was describing. The collapse of the 2000 bubble would ultimately erase half the value of the S&P 500, and would take the tech-heavy Nasdaq 100 down an implausibly precise 83%.

The defining feature of a bubble is inconsistency between expected returns based on price behavior and expected returns based on valuations. If investors pay $150 today for a security that will deliver a single $100 payment a decade from now, but they also fully understand that they’ll lose 4% annually on the deal, without extrapolating past gains into the future, then we might say the security is overvalued, and we might question why investors would accept that trade, but we can’t call it a bubble.

But if investors pay $150 today for that security, because they look back in the rear-view mirror, decide that it “always goes up” over time, and convince themselves that expected future returns are always positive, then you’ve got a bubble. Discounting the future $100 cash flow of the security using any positive expected return would produce a price less than $100. So the positive returns expected by investors are inconsistent with the returns that would equate price with discounted cash flows. The size of the bubble is the fraction of the market price that represents expectational “hot air.”

Likewise, the willingness of investors to embrace “passive investments” like ETFs and asset-backed securities based on past performance, with little concern about the valuations, yields, or credit risk of the securities inside, is a the very soap from which bubbles repeatedly emerge. Amid the current enthusiasm for special purpose acquisition companies (SPACS), investors might recall the bubble in “incubators” at the 2000 peak, the “conglomerates” of the late-1960’s Go-Go bubble, and even the South Sea Company in the early 1700’s, along with similar companies formed at the time “for carrying on an undertaking of great advantage, but nobody to know what it is.”

If investors price the S&P 500 at levels that are highly likely to produce negative returns for a decade, as they did in 1929 and 2000, and as I believe they are doing at present, yet investors continue to press stock prices higher on the expectation that they will provide historically normal levels of future return regardless of valuations, then you have the sort of inconsistency that defines a bubble.