Posted in: Ideas in Finance

The Dreaded Parabola and the Sandpile Collapse

Back when I was first scoping out topics for my PhD, I seriously considered doing something at the intersection of Complexity Theory and financial economics. Complexity theory had emerged out of the body of work that had earlier produced Chaos Theory. Both had, at times, elicited a great deal of excitement across many different fields, including economics. Most of that excitement has long since faded away. At the time, I read a lot of the chaos theory work that had been published in economics journals, along with various books on both chaos and complexity. For the general reader, it is hard to go past James Gleick’s Chaos: Making a New Science. There are good books about Complexity, but Gleick captures something of the milieu that escapes the authors of the other books I read.

At some point I came across Per Bak’s work on Complexity and, specifically, his Sandpile Model. In general, the idea is that placing random grains of sand on a grid will eventually produce sandpiles that grow higher and higher, steeper and steeper. Each new random grain added to a sandpile on one square of the grid might do nothing, or it may produce a collapse of that particular sandpile, or it might cause a cascade that has quite far-reaching effects across large sections of the grid. The possibility of applying this to financial markets is obvious. Each increment in price builds the sandpiles higher until they reach what Complexity theorists call criticality. Additional increments in price might have no noticeable effect or they may produce a collapse in one of the sandpiles (e.g., one stock) or, possibly, the collapse in one sandpile might produce a cascade across an entire industry or even the entire market.

Nothing can be built ever higher. How long it takes before a collapse depends on how broad the base is. On a defined grid, the sandpiles on a single square must grow steeply. The stock market can grow very steadily at a gentle pace for a long time. In fact, if that was all it ever did, stock market crashes or crashes in particular companies’ stocks would probably be very rare. Asset prices, however, sometimes accelerate very quickly. When the ascent is particularly steep, traders refer to the price as having gone parabolic. And traders know that like a sandpile, the steeper the ascent the more likely there will be a collapse.

The sandpile model depicts grains of sand dropped from above. The financial markets are supported by liquidity (money) flowing in and pushing up from below. Nothing can go straight up forever without more and more thrust. If you can fly an F35 fighter jet but you are unfamiliar with physical reality, you might tell onlookers as you hop into the cockpit that you’re going to fly it into low space orbit, maybe even to the moon. If they don’t know the plane’s capability, they might gather enthusiastically to see what you can do. So, you start the engine, take-off, and pull the nose straight up. You use every bit of power the engines have, and for a while your near vertical ascent has your audience thinking you might just do it. Then the engines begin to sputter and stall, and you begin to freefall. Your audience runs for cover, and you eject. This is what happens when liquidity dries up in markets. And the more steeply you have climbed, the steeper the fall can be.

If you search through the history of asset prices you can find many examples of parabolic growth followed by a significant setback. We don’t have to look very far. Between September 2024 and October 2025, Bitcoin went parabolic. Its price rose from around $50,000 to more than $120,000. It then slumped back to $60,000. Gold tripled in price from $2,000 an ounce to $5,600 between the beginning of 2024 and the beginning of 2026 before slipping back to $4,000. Silver was more extreme. One of the best examples is Korea’s stock market index (Kospi). From around 2,400 at the beginning of 2025, it skyrocketed to more than 9,000 before crashing back to 6,000. It lost almost 40% of its value in June and July 2026. Now, to the chart that caught my eye: Australian house prices.

Recently, the ABC put together the data and came up with a chart showing the mean price of dwellings in Australia from 2012 to now. From roughly $490,000 to more than $1.1 million. As we have noted in previous posts, liquidity in the form of credit flowing into the Australian housing market provides the metaphorical thrust for the jet. You can look at the ABC News chart. There are ups and downs. To illustrate the point, though, I have “stylised” the situation for the period from the year 2000 to depict the growth rate without the choppiness and to show the ascent in the average price of Australian houses without the occasional wobbles that have been experienced (e.g., in 2019). This is an approximation, but you can see the trend, with the average price being around $200,000 at the turn of the century, around $490,000 (as per the ABC data) in 2012, and around $1.1 million today:

The (literally) million-dollar question is how long the thrust (the liquidity) can keep powering this ascent higher. And how much more thrust will be needed to maintain the gradient of the ascent. Like a jet plane, more and more is required the higher you go. People have been predicting trouble for years. What they got wrong was that interest rates would fall fairly continuously for forty-five years, as we noted in a previous post. This allowed liquidity to continuously flow into the market. The danger is that, like a jet plane with its afterburners firing and nose pointed straight up, a little hiccup in thrust, a little disruption to the fuel supply, may be very consequential. There is something of a parabolic ascent in Australian house prices. It’s not as steep as other asset prices have experienced at times but are Australian house prices exempt from the dreaded parabola?

The Dreaded Parabola and the Sandpile Collapse

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