The unholy trinity of bubbles: valuation, volatility, and volume

Are we currently in the midst of an AI-fueled stock market bubble? In my prior post (“No, we are not in a bubble yet”), I defined bubbles and gave my top bubble symptoms. Here, I want to continue by studying the aggregate stock market itself. What can we learn from prices and trading? How can we tell if these are consistent with a bubble?

Spoiler alert: No bubble yet.

The three Vs

When it comes to stock market bubbles, V is not for Vendetta but rather for the three Vs of bubbles:

• Valuation: A rise in stock prices to an unreasonably high level
• Volatility: High aggregate return volatility and high return dispersion
• Volume: High trading volume measured in turnover; short holding periods

This unholy trinity of high valuation, high volume, and high volatility is always bad news, not just during bubble periods. I would say that a “speculative stock” is a stock that has all three of the Vs, and on average they have low subsequent returns. But during bubbles, we see all three Vs go up for the whole market.

Now, the bad news is that some of these Vs might be present in non-bubble periods. For example, when there is huge negative economic news (the GFC or the onset of COVID-19), we also see lots of price volatility and volume. So just as you need multiple symptoms to diagnose a disease, you need multiple symptoms to diagnose a bubble. The three Vs are a necessary but not sufficient condition for a bubble.

Let me start by giving the classic symptoms as summarized by Brunnermeier and Oehmke (2012) including the three Vs (my bolding):

An initial displacement—for example, a new technology or financial innovation—leads to expectations of increased profits and economic growth. This leads to a boom phase that is usually characterized by low volatility, credit expansion, and increases in investment. Asset prices rise, first at a slower pace but then with growing momentum. During the boom phase, the increases in prices may be such that prices start exceeding the actual fundamental improvements from the innovation. This is followed by a phase of euphoria during which investors trade the overvalued asset in a frenzy. Prices increase in an explosive fashion. At this point investors may be aware, or at least suspicious, that there may be a bubble, but they are confident that they can sell the asset to a greater fool in the future. Usually, this phase will be associated with high trading volume. The resulting trading frenzy may also lead to price volatility as observed, for example, during the internet bubble of the late 1990s. At some point, sophisticated investors start reducing their positions and take their profits. During this phase of profit taking there may, for a while, be enough demand from less sophisticated investors who may be new to that particular market.

Valuation

The first obvious bubble ingredient is prices that rise over time. Anyone who works in asset management knows The Iron Law of Return-Chasing Flows: Money chases trailing returns. This phenomenon gives rise to a positive feedback loop where rising prices beget inflows beget rising prices. Shiller (2005) calls this feedback loop a “naturally occurring Ponzi scheme,” one that attracts new buyers:

It would appear, by extrapolation from examples like those given in the previous section, that speculative feedback loops that are in effect naturally occurring Ponzi schemes do arise from time to time without the contrivance of a fraudulent manager. Even if there is no manipulator fabricating false stories and deliberately deceiving investors in the aggregate stock market, tales about the market are everywhere. When prices go up a number of times, investors are rewarded sequentially by price movements in these markets, just as they are in Ponzi schemes … The path of a naturally occurring Ponzi scheme—if we may call speculative bubbles that—will be more irregular and less dramatic, since there is no direct manipulation, but the path may sometimes resemble that of a Ponzi scheme when it is supported by naturally occurring stories.

One could view this return chasing as the product of naïve extrapolation. I am trying to predict what will happen in the future, I measure returns over the past five years and notice that stocks have high returns, so I buy stocks. Extrapolative expectations are one root cause of bubbles.

In addition to looking at rising prices, another argument is that bubble dynamics involve accelerating price rises. That is the argument of Greenwood, Shleifer, and You (2019), who find that price acceleration (defined as price increase this year is bigger than price increase last year) is an important bubble indicator.

Moving on to the level of overvaluation, what does it mean for stock prices to be unreasonably high? You may have your own definition, but one example would be the price should be 100, but instead it is 200, with expected returns going forward being commensurately lower.

Here’s another definition of “unreasonably high:” Stock prices rise to a valuation level that cannot be justified by rational forecasts of subsequent cash flows. Then they double, while your rational forecast of cash flows stays constant.

Not specific enough for you? Well, here’s a strategy for identifying bubbles you could try:

1. Spend four years getting a Ph.D. in economics from MIT and then get a job as a finance professor at the University of Chicago.
2. Carefully analyze historical data on prices, earnings, and dividends, and decide that the U.S. stock market is overvalued or equivalently has “very low” or “negative” expected returns. Publish this assertion in the top academic finance journal (Lamont (1998)).
3. Over the subsequent three years, watch in amazement as the S&P index doubles and the Nasdaq 100 triples.

That was my strategy in the 1990s, although not one I would recommend.

Let me offer four possible definitions of “unreasonably high” stock prices:

• Price > 1.5X fundamental value.

  – Extreme version: Price > 2X fundamental value.
  – Super-extreme version: Price > 3X fundamental value.

• The expected return on stocks over T-bills is less than half its normal level. So expected excess returns are not 6%, say, they are 3% or lower.

  – Extreme version: Expected return on stocks < T-bills.
  – Super-extreme version: Expected return on stocks < zero.

• A rational investor will lower his allocation to equities to half what it normally is. So if the investor is usually 60/40 equity/bonds, he switches to 30/70.

  – Extreme version: Zero allocation to equities.
  – Super-extreme version: Negative allocation to equities.

• An English-speaking adult, when asked if the market is overvalued, replies “yes.”

  – Extreme version: “Hell, yes.”
  – Super-extreme version: “You will never find a more wretched hive of scum and villainy.”¹

Volatility

Price volatility is associated with both overvaluation generally and bubbles specifically. Shiller (2005) describes the “gambler’s excitement” of bubbles, and you can’t have excitement unless prices are going up and down. Price volatility is also a characteristic of speculative assets, that is, overpriced assets with very high volume, purchases motivated by quick resale, and very short holding periods. Classic examples of notably overvalued assets exhibiting notably high volatility include cryptocurrency and the Chinese stock market. Lottery-loving speculators want to buy risky assets, not boring safe assets.

Price volatility typically goes up in bubbles, for example in the Chinese stock market bubbles of 2007 and 2015. The volatility of individual stocks in China is always quite high, but during these bubbles it was even higher. More generally, Greenwood, Shleifer, and You (2019) find that an increase in return volatility is a valuable bubble indicator in U.S. and international equities.

Another aspect of bubble-related volatility is price dispersion, that is, some assets go up more than others. What happened in the U.S. in 2000 and 2021 was not that all assets went up, it was rather that some specific types of assets went up a lot, so that the return gap between winners and losers widened. This widening is related to stock-specific volatility. In bubbles, we generally see risky stocks go up the most and safe stocks go up the least as the bubble inflates (with this pattern reversing when the bubble deflates). In addition to market-wide volatility and stock-specific volatility, another type of volatility that rises is “factor volatility;” that is, common price risk related to a characteristic such as firm size, firm valuation, or industry category.

The exact timing of volatility increases—whether volatility mostly goes up on the way up, or on the way down—is unclear.

Volume

Like high volatility, high volume is associated with overpricing both in normal times and bubble times. Volume indicates disagreement, excitement, and attention. You can’t have a speculative motive for trade (the plan to resell the asset to a greater fool) if you don’t have volume.

Here’s Bagehot (1873) on the speculative motive:

owners of savings … rush into anything that promises speciously, and when they find that these specious investments can be disposed of at a high profit, they rush into them more and more. … So long as such sales can be effected the mania continues; when it ceases to be possible to effect them, ruin begins.

We typically see elevated volume in stock market bubbles, often characterized as “mania” or “frenzied trading” (Barberis, Greenwood, Jin, and Shleifer (2018)). In the tech stock bubble peaking in 2000, volume went up for all stocks, but went up more for internet stocks (Ofek and Richardson (2003)). In my paper with Richard Thaler studying tech stock carveouts during the bubble, we found extremely high volume for overpriced subsidiaries, with turnover around 40% per day, implying holding periods of less than a week (Lamont and Thaler (2003)).

Short holding periods are also a common explanation for why overvaluation occurs in bubbles. Who cares whether the underlying asset is overvalued if you are just planning to hold for three days?

As with volatility, often it is the case the volume goes up as the bubble inflates but goes up even more when the bubble deflates.

Where are we today?

• Valuation: stocks don’t look cheap, but it is not obvious they are grossly overvalued. Fundamentals are strong and perhaps justify current valuations.
• Volatility: Realized and implied aggregate volatility are modest, with implied volatility arguably too low.²
• Volume: Does not appear higher than recent history.

What’s the next item on our checklist? In future posts, I’ll explore two more definitions of “unreasonably high:”

• The stock market is unreasonably high when a preponderance of wise economics/finance professors say it is too high.
• The stock market is unreasonably high when in a survey, a large majority of market participants says that it is too high.

Endnotes

1. Kenobi, Obi-wan, Star Wars: Episode IV—A New Hope (1977).
2. BIS, Markets count on a smooth landing, March 2024.

References