For the last few years (and this year in particular!) it has felt a bit like financial markets have gone mad: The economy is struggling, but stocks are reaching all-time highs (while some of the top winners are bleeding cash). Digital currencies seem to have a shot at becoming the new gold. Investors trying to value companies on fundamentals have been underperforming for years. Working from home seems to have renewed thinking about the Internet as a ‘New Economy’. A new generation of stock-trading apps have ‘gamified’ the trading of stocks. And so on.
Of course, many people have noticed that 2020 is not normal—and I’m not just talking about the coronavirus pandemic, but also that market sentiment seems to be getting out of hand with 2020 seeing a revival of the SPAC; bankrupt companies getting a new lease on life; and with the IPO market getting increasingly frenzied with loss-making companies doubling on their first day as if there simply wasn’t enough stock to go around. Mind-boggingly, it looks like everything (except for the traditional safe havens) is rallying.
At the same time, surrounded by this weirdness and New World-thinking, there are plenty of people who suggest that we must be close to the end of this market cycle:
The Financial Times, for example, quoted Jeremy Grantham, the founder of the investment group GMO, in an article on the ‘everything rally’, where he
reckons [that] markets have smashed past the “full bull” stage and are in a late-bubble “melt-up” phase that rivals the two biggest bubbles of the past century. … There is as much craziness now as there was in late 1999 or 1929 … It is bewildering, impressive, and for financial historians like me, exciting. This is the real thing … It looked like we were in a bubble mode this summer, but the real craziness has come out in the last few months.
Similarly, Matt Maley, chief market strategist at Miller Tabak & Co., is quoted in Bloomberg (via an Almost Daily Grant’s) that “The action in these [IPO] names is definitely a concern for us … Experience tells us that froth in the IPO market tends to be a ‘leading indicator’ for an important top.”
Intuitively, it feels like these people must be right: Surely, the current rally just cannot go on? Yet, haven’t people been saying this for years, while the market has just kept on going up?
Indeed, if we look to the US market, the Dow Jones Industrial Average is up 85 % in the last 5 years and having increased almost 12 % this November (its best monthly showing since 1987). Similarly, the NASDAQ 100 is up almost 200 % since the end of 2015 and increasing 11 % last month. Internationally, the MSCI World Index also increased over 12 % during the same period (making November its best-performing month since 1975), with the index up almost 80 % in the last 5-year period . How (the reasonable among us ask) can we reconcile these stellar market performances with the vague feeling that it all—surely—should have ended long ago?
What I’m going to argue in this post is that these observations are not as conflicting as they might first appear: It is possible for financial markets to post increasingly stellar results long, long after contrarian investors have started feeling uneasy. For example, if history is any guide, markets never crash when things are looking down. Instead, crashes happen when the market is at its peak—suggesting that Mr. Maley’s experience might not be too far off: That irrational exuberance can be a harbinger of more painful times to come. As it happens, there might be a simple explanation for these somewhat contradictory observations, where, the higher markets go, the more unstable they also become, with the risk of a crash increasing alongside.
This dynamic starts to make sense once we start thinking of financial markets as complex systems, with behaviours that emerge from the interactions of multiple independent agents using the markets as a vehicle for capital exchange. Complex systems such as these are also nonlinear, meaning that their overall behaviour emerges from the rolling interaction of its component parts. For example, if you were to break a financial market down and to place all of its component money flows and buyers and sellers and their different motivations and economic contents into separate buckets, you wouldn’t be able to recreate the market’s behaviour by just putting them all together again. In this way, a market is more like an organism: Just putting different parts of an animal together does not a living, breathing thing make. Therefore, while it’s valuable to form a bottom-up understanding of a complex system (by dissecting its parts), this understanding must be paired with a top-down understanding of its behaviour as well. When it comes to financial markets, this requires us to understand the processes that the market is home to, and how small fluctuations in these can be amplified by the system to generate out-sized effects.
Speculative bubbles are hurricanes, but in in financial markets
At their most simple, the speculative bubbles that sometimes occur in financial markets can be understood as runaway processes that, once started, can drive valuations increasingly far away from fundamentals. Once you start looking into the mechanisms of how bubbles are born and how they grow, you’ll also start to realise that they are a form of ‘self-organising system’. While the physics underlying the emergence of such systems can be devilishly complex, I find that they can be relatively easy to understand conceptually. For example, self-organised systems can be found everywhere—ranging from the ‘convection cells’ that arise in heated fluids or in organised storm systems like tornadoes or hurricanes, to processes like life itself (in the form of organisms). Therefore, if we can understand the emergence of such diverse systems, we can start to build a mental model of the emergence of self-sustaining systems like bubbles in financial markets as well.
The first thing that we need to understand to understand self-organising systems is that they’re powered by the flow of energy. Energy flows from regions of high energy to regions of low energy (like from a hot reservoir to a cold reservoir), and wherever this flow is strong enough (because the gradient is large enough), a self-organising system (an ‘organism of physics’) can emerge. The emergence of such a self-organising system ultimately helps dissipate the underlying energy gradient faster than the alternative where no self-organised system was present. These systems can also persist for as long as the underlying flow of energy remains strong enough, and they only ‘die’ when the underlying energy flow has been depleted.
Thermodynamics textbooks commonly use the example of a convection cell arising in a heated fluid when discussing self-organising systems, but I find weather phenomena to be more intuitive. (Both convection cells and weather systems are also examples of heat engines, which are powered by temperature differences.) To give a brief introduction to the weather, the sun shining on something like the Earth’s oceans creates a temperature gradient, where the ocean surface is relatively hot, and the atmosphere’s higher layers are much colder. This heating of the surface causes water at the surface to vaporise. The heat-energy contained in this moisture is then absorbed by the hot air at the ocean’s surface, and the hot air begins to rise. As the air rises, it starts to cool down, eventually releasing the moisture as rain and some of the latent heat-energy that it has been carrying is released into space. While the now-dry and cold air will start falling towards the surface again and the cycle repeats for as long as the underlying gradient persists, the ultimate result of this process is that the high-quality energy from sunlight is lost into space as low-quality heat. A hurricane is simply an extreme version of this process, where the heat-energy of the rising, moisture-laden air is high enough to create an updraft so powerful that it reaches a high-enough wind-speed for the process to be classified as a hurricane. In other words, a hurricane is just an extreme form of atmospheric mixing and an efficient way for the temperature gradient between the hot surface and the cold atmosphere to be dissipated.
So, that’s all very well and good (I hear you ask), but what does this have to do with bubbles in financial markets?
Quite a lot, I think!
Let me explain:
While hurricanes form in the atmosphere and ‘feed’ on a temperature gradient that exists between the hot surface and the colder layers of air above, speculative market bubbles form in financial markets where they feed on energy in the form of money flows.
To be more precise, let us map the dynamic of a financial-market bubble onto the dynamic of an atmospheric heat engine like a hurricane: First, while the hurricane forms from a strong-enough temperature gradient between the surface and the atmosphere, market bubbles form from a strong-enough money-gradient between the economy and the market. Second, while the hurricane feeds on the underlying temperature gradient (sucking more air in) and, as a result, dissipates heat into space, the financial-markets bubble feeds on money entering the market (sucking more money in) and dissipates the gradient by reducing the purchasing power of the currency (in market units). Third, while the hurricane dies down when the underlying temperature gradient is weakened, the market bubble dies when the underlying money-flows have been depleted.
From this, we have the beginnings of a simple model for the formation and persistence of speculative bubbles in markets, where, (1) they form when economy money-flows favour financial markets over other parts of the economy (creating a strong flow of money into the market); (2) they pick up steam as they start growing by attracting more money into the market, which allows them to persist; and (3) they deflate (gently or catastrophically) when there is not enough money entering the market for them to continue to grow.
With this model in hand, let us look at some dynamics that can favour the emergence (and growth) of bubbles in financial markets.
Misallocated money flows can cause asset values to increasingly deviate from fundamentals
From the first part of our simple model, we see that market bubbles are formed when money-flows favour the market instead of other parts of the economy. (Of course, money-flows favouring non-market assets can lead to bubbles forming in non-market parts of the economy.) Normally, you’d think that the sum total of money-flows in the economy would balance themselves out, where too much money flowing into one part of the economy would incentivise less money to flow into those parts in the future. There are, however, circumstances when this is not the case, and where both economic and social factors can incentivise the disproportionate flow of money into one part of the economy and creating the conditions for a bubble to start to form.
First, uncertainty can play an important part in the misallocation of economy money-flows by making some assets seem more attractive than they are: While all assets have a ‘fundamental value’ (i.e. what the asset would be worth given perfect knowledge of life, the universe, and everything), nobody has perfect-enough knowledge of the asset or the future to be able to value assets with perfect accuracy. This makes the fundamental value of an asset more of an idealisation and an approximation, rather than something that can ever be known in real life. This value can also be thought of as an ‘equilibrium value’, which the real-time value of an asset—even if imperfect—would fluctuate around; updating bit by bit as more information about the asset or the future gradually becomes available. Therefore, these approximate fundamental values serve as good placeholders for the never-to-be-fully-known real fundamental valuation of an asset.
That being said, the approximate fundamental value has two significant flaws in being sensitive to both the uncertainty of the inputs and the value of money in the economy:
The quality of the inputs matter because the output of the valuation formula is very sensitive to even slight changes in the input values. This is because the value of an asset is determined based on cash flows, where the value of an asset is the present value of all the future cash flows to result from the asset. Since these cash flows can never be known, they must be estimated, meaning that the more accurate the estimates are, the more accurate the final valuation will be. During periods of great social or technological change, the uncertainty surrounding these estimates is however greatly increased. This uncertainty ultimately reduces the accuracy of the estimated cash flows, allowing the resultant approximate value to start deviating from its underlying fundamental value by an amount that scales with the underlying uncertainty. (It can help to think of this amount as an ‘uncertainty component’ of the valuation.) The positive skew of asset-price returns (limited downside and unlimited upside) and the human tendency to overestimate the impact of changes in the short run and to underestimate the impact in the long run (Amara’s law) also implies that these deviations from fundamental values are likely to be positive.
(Importantly, the uncertainty component emerges naturally from use of the discounted cash flow formula, making it natural for asset prices to deviate from their fundamental values. Indeed, given the underlying uncertainty of the inputs and their future values, the situation where an asset is valued at its fundamental value should be considered exceptional, as this would represent a very unlikely event. The larger the uncertainty around future cash flows, the larger the deviation from fundamentals will become. This also means that we shouldn’t be surprised to see valuations start to deviate significantly from fundamentals during periods of great social, technological, or economic change, as this would cause the uncertainty component would start to make up an ever-greater proportion of the asset’s valuation. In this way, the sensitivity of the formula to the uncertainty of inputs helps to explain why asset prices are more likely to deviate from fundamentals during times when New Economy-type thinking is prevalent, as this is when the uncertainty of the inputs would be at its highest.)
Economically, the discount rate also plays a role: When we value a risk-free asset, we adjust the cash flows for growth using the risk-free growth rate and then discount these back to the present using the risk-free discount rate. To adjust the formula for risk, we then simply add in a risk premium in the form of a risk-adjusted growth rate and a risk-adjusted discount rate. However (as the famous mathematician John von Neumann realised in the 1950s), in a perfectly balanced economy, the growth rate would equal the interest rate (and thus the discount rate). In this situation, the discounted cash flow formula would break down, as the risk-adjusted growth rate would equal the risk-free rate, meaning that we’d be dividing by zero and asset values would go up to infinity. In economics, this is known as the ‘growth stock paradox’. At the point where this happens (where the risk-adjusted growth rate is equal to or larger than the discount rate), the value of money isn’t enough to stabilise the economy.
When the value of money isn’t enough to stabilise the economy, money-flows can be diverted and misallocated because it becomes favourable to borrow money and to use this borrowed money to buy assets earning a more effective rate of return. Like the uncertainty dynamic described above, this destabilising dynamic also allows values to deviate from fundamentals as it encourages the misallocation of money; allowing more of it to become concentrated in a small part of the economy. Wherever this happens (and for whatever reason), self-organising systems in the form of asset-price bubbles have the potential to form as the underlying money-flows become strong enough to push asset-values away from fundamentals and to sustain this mis-valuation over time.
Historically, the onset of many bubbles in financial markets has also been traced back to misbalanced economic growth rates and interest rates in this way, perhaps most famously (and disastrously) in the 1920s. Of course, plenty of additional examples abound, like the Japanese land bubble in the late 1980s; the dot-com bubble in the late 1990s; the US housing bubble in the late 2000s; the Chinese stock-market bubble of the early 2010s; and so on. Today, it’s possible that we’re seeing a similar dynamic at play—perhaps triggered by the favourable tax implications of Donald Trump’s win of the US Presidency in 2016 and exacerbated by the uncertainty surrounding the economic impact of COVID-19 and the work-from-home trend.
Investor herding allows market returns to accelerate during bubbles
While uncertainty can make some assets seem more attractive than they really are (and favour the allocation of money to these) and misaligned interest rates can cause money to lose its value (and pool more locally in the economy), the local herding of investors into some areas is an additional factor that can help create (and feed) asset-price bubbles by strengthening the underlying money-flows.
During periods of low uncertainty (when data is plentiful and accurate), investors are afforded the luxury of independence of thought, courtesy to their access to diverse sources of information. As a result, the insight they generate is likely to be accurate, which allows for the efficient functioning of the market as investors collate their individual pieces of information into the market ‘library’ as they’re hoping to profit. As a result, the market valuation of an asset is likely to be a good approximation of its fundamental value, as the approximation has been derived from a large collection of heterogenous and independent sources of high-quality information. (The market acting as a repository of collective information is also further reminiscent of how Benjamin Graham likened the market to a ‘weighing machine’ in the long run. This also makes it unlikely for an individual investor to be able to ‘beat’ the market, as the market ‘knows’ more in aggregate than any individual investor does.) In this efficient market, investors will also use any new information that they come across to improve on their estimated fundamental valuation of asset, meaning that the approximate fundamental valuations of an asset will evolve as the market’s collective understanding of it evolves. This allows valuations to remain true to fundamentals for as long as enough data is available.
When the level of uncertainty is high and data is scarce, investors however often have to make do with lower-quality sources of information—like looking over their shoulder to observe the behaviour of other investors. When this happens (and the behaviour of one investor influences the behaviour of another investor), an ‘imitation game’ is initiated that reduces the heterogeneity of the market. This decreasing heterogeneity can exacerbate the misallocation of money flows as the misallocation of money in an uncertain environment begets more misallocation in an uncertain environment.
In the short term, the increasing misallocation of money-flows means that investor returns will accelerate as investor herding in an uncertain environment begets increasingly irrational exuberance, where the more money is going into the market, the greater the investor returns to result, and the more other investors will be incentivised to join in—adding more money into the market to push returns up further, and so on. (This dynamic also helps the bubble to achieve an ‘autocatalytic’ state, where the bubble sucks up more investor monies the longer it persists; allowing market valuations to grow ever-more-divergent from the underlying fundamentals.) This makes autocatalysis an important component of the bubble dynamic, since it’s symptomatic of a state where growth begets even more growth, allowing returns to compound faster and faster. As a result, we should expect returns to scale with the duration of a bubble: expecting returns to increase slowly at first, but growing more and more for as longer as the bubble goes on.
Counter-intuitively, the autocatalytic process also means that the greatest returns are earned at the point where the bubble is at its most unstable, as it’s growing at a pace faster than the underlying money-flows can support. A Swiss professor, Didier Sornette, has further shown in a book called Why Stock Markets Crash that bubble-induced increases in market capitalisations can be tracked mathematically by fitting a power-law trendline to the underlying data. Diagnostically, an accelerating power-law exponent could therefore be symptomatic of an underlying autocatalytic process, meaning that a bubble can be suspected to be underway in such markets.
In the long term, the increasing misallocation of money flows into local parts of the economy will however burn itself out as the autocatalytic process supporting the bubble’s growth will eventually require more energy than what is available to the system. Theoretically, if we were to treat the bubble as an abstract ‘heat engine’—but at work in financial markets—we would be able to calculate the theoretical upper bound of the price-appreciation trend based on simple thermodynamic formulae (much like how we can calculate the maximal wind speed of a hurricane using temperature and moisture data). In reality, the numbers we’d need to plug into these equations (including the total energy available to feed the system) would however be hard to know, even as it would be interesting to see more economists try. Experience however tells us that the total amount of money available to feed financial market bubbles is always much larger than you’d think at first glance—allowing bubble-induced market returns to keep compounding for much longer than any sensible person would think. While this is what underlies the warning to short sellers that “the market can stay irrational for longer than you can stay solvent”, understanding how bubbles die and how markets collapse could however be helpful for short-sellers to time their positions better and to minimise losses in the lead-up to the market’s final growth-spurt.
Structural instabilities lead to crashes in financial markets
Market returns increase faster the closer the market gets to the point where the market’s continued growth requires more energy than what is available to the system. This point would more accurately be called a ‘critical point’ as the closer the market gets to this point, the more unstable the market becomes. That market returns scale with increasing proximity to this point suggests that investors are compensated for the risk that they’re shouldering: As the risk of a crash increases, the greater the return that investors will require to assume the risk of staying invested in the market. As further discussed in Why Stock Markets Crash, this dynamic also suggests that it’s rational for investors to stay invested throughout a bubble as the returns are attractive and the risk of the bubble ending in a crash is less than 1 (meaning that there is a probability that a crash will not happen and the market will gently deflate instead; giving investors ample time to exit). Indeed, data available to Sornette when he wrote Why Stock Markets Crash in 2003, suggests that 60 % of autocatalytic bubbles end in crashes—with the remaining 40 % of bubbles ending in ‘deflation’. (It can however be argued that deflations are slow-motion crashes, as both events commonly see market capitalisations decrease by 30 – 70 % from the market peak.) Importantly, both deflations and crashes however see market capitalisations returning to something closer to their underlying fundamental values.
The structural instability that builds up in a market undergoing the autocatalytic growth of a bubble can also be exacerbated investor herding, further increasing the risk of a crash. This is because as investors herd (because they’re starved for high-quality data and are forced to play the imitation game), they organise into increasingly homogenous clusters. The larger theses clusters become, the larger the risk then becomes that a large group of investors will have the same ‘sell!’-reaction to an unexpected piece of news, with such a large sell-order also carrying the risk of oversaturating the market’s ability to absorb the order, causing the market to crash catastrophically. As such, crashes happen when the incoming money-flows are too weak to compensate for the market outflows, forcing the market to return to a ‘lower level of complexity’ (as outlined in a previous post on this blog). Whenever we see market returns accelerating beyond reason, we should therefore brace ourselves and be ready for something to happen. Some parties simply cannot go on indefinitely, even if it’s uncertain exactly how they will end.
The dependence of catastrophic market crashes on the underlying autocatalytic behaviour of the bubble also means that the nature of crashes is not part of the ‘normal’ behaviour of markets. Indeed, autocatalytic processes birth ‘outlier’ phenomena (which are not normal, by definition). Instead, ‘normal’ in financial markets is the ‘random walk’ that features in investing classics as Burton Malkiel’s A Random Walk Down Wall Street. The random walk of markets is the result of investors making random trading decisions like model adjustments or investing/redeeming client cash flows. These decisions (which are noisy and non-informational) altogether cause market values to fluctuate randomly up and down; sometimes deviating positively and sometimes negatively from fundamentals, allowing value investors to capitalise on the stock market’s tendency to regress to the mean over moderate time-spans. The autocatalytic behaviours described above are however very different and do not form part of the market’s random walk. This means that they can both persist for a very long time and that they can see rapid reversals.
One of the main theses of the book Why Stock Markets Crash is further that autocatalytic behaviours underlying the growth of bubbles allows the death of the bubble to be timed with a fair degree of accuracy. While the random movements that result from ‘normal’ market behaviours are truly random (and therefore impossible to predict), the autocatalytic process underlying the growth of bubbles is much more predictable. As a result, bubble-induced corrections are not the ‘black swans’ that have been popularised by Nassim Taleb, but are instead much more predictable outlier phenomena. Indeed, Sornette claims that the appearance of log-periodicity in the accelerating power-law curve applied to autocatalytic markets allows observers to determine the timing of the market’s critical point, as the log-periodic oscillations contain information about the market’s underlying homogeneity and implied instability. However, again, this information might not be useful to investors, if we were to assume that they are compensated for the risks that they’ve assumed by staying invested.
Yet, something about this sits uneasily with me (as it does with Sornette, as outlined in the introduction to his book) as we live in a very strange time in history when an increasing proportion of the social contract requires us to stay invested in the market to pay for our future spending in the form of education, healthcare, and pensions. This need to stay invested (and the dearth of safer investment opportunities offering us enough compensation to accept the risk of not investing in markets) creates interesting regulatory problems, as it’s becoming increasingly expected of regulators to avoid any catastrophic market meltdowns. Understanding the mechanisms underlying the accelerating returns in markets is therefore crucially important, as this allows investors to make decisions that fit their long-term risk-appetite.
Financial markets are organised and complex—and risky
All things considered, a growing emphasis on the riskiness of financial markets would ultimately allow us to develop much healthier social attitudes in terms of the risks that come with staying invested in financial markets over long periods of time—as well as better recognising the increasing need of stimulating capital investments in other part of the economy to ensure the economy (and its cumulative investments) are as safe and diverse as can be. Indeed, if there is one message you should take away from this blog post it’s this: That complex systems like financial markets can be extremely unpredictable in the long term, as their behaviour unfurls over time, feeding on inputs that reach far into the past. As mentioned above, financial markets share these characteristics with other complex systems like the weather, and while the either can typically be forecast with a reasonable degree of accuracy, this accuracy declines the further we look into the future. Of course, this also applies to financial markers, and it means that the age-old wisdom of diversifying our investments remains sound—regardless of how attractive current market returns may happen to be. For some of us, this understanding will be little more than a curiosity (but hopefully one to help us with our own work and investments), but for others, it will help us to make the most of the opportunities (and challenges) that undoubtedly lie ahead.
Finally, this understanding will however also help us make better sense of recent events and developments, where loss-making companies are generating unprecedented returns for brave investors and the working-from-home trend seems to have renewed New Economy-type thinking and enthusiasm. Furthermore, this understanding also helps us to make sense of the anecdotal wisdom of more wizened investors as the only thing that doesn’t change in financial markets are the human agents who stay invested in them. After a few market cycles, you start seeing the patterns in markets in remarkably new ways.