What Causes Asset Bubbles?

As we showed yesterday, the price of bitcoin has finally surpassed "Tulips" in the global bubble race.

Overnight the former Bridgewater analysts Howard Wang and Robert Wu, who make up Convoy Investments, released their thoughts on what happens next... and most importantly, what causes asset bubbles...

When we see a dramatic rise in asset prices, there is often an internal struggle between the two types of investors within us.

The first is the value investor, “is this investment getting too expensive?”


The second is the momentum investor, “am I missing out on a trend?”

I believe the balance of these two approaches, both within ourselves and across a market, ultimately determines the propensity for bubble-like behavior. When there is a new or rapidly evolving market, our conviction in the value investor can weaken and the momentum investor can take over. Other markets that structurally lack a basis for valuation are even more susceptible to momentum swings because the main indicator of future value is the market’s perception of recent value. In this commentary, I quantify the balance of value vs. momentum in a market to explore how that tug of war can result in incredible asset bubbles.

The balance of value vs. momentum determines a market’s serial correlation

I believe the outcome of the tug of war between value and momentum in any market can be largely captured by a statistical measure called serial correlation – how likely is the recent past to determine the near future? A value of -1 means future returns are the exact opposite of recent past returns, a value of 0 means they are independent of each other, and a value of 1 means recent past returns are perfectly predictive future returns. After a dramatic price change, value investing would generally expect a reversion to the mean, suggesting a negative serial correlation. Momentum investing would expect that trend to continue, implying a positive serial correlation. A value focused investor base tends to lower serial correlation while a momentum focused investor base tends to increase serial correlation. The balance of the two determines the aggregate level of serial correlation in a market.

In reality, most markets see a relatively even balance between value and momentum and their returns are serially uncorrelated most of the time. Of course, every market will also experience periods when investors lose conviction in value and momentum dominates. A rise in serial correlation can occur when investors don’t have an established framework of value in new and opaque markets such as the complex structured products in the years leading up to the 2008 Financial Crisis. Investors didn’t trust in their own independent valuation of their portfolio and relied on recent price climbs as an indicator of future returns. Serial correlation can also rise in rapidly evolving markets such as technology in the late 90s. During those periods, the industry is dramatically reshaped and investors lose faith in their traditional value framework and again rely on recent price changes as the main metric for future price changes.

While the logic around serial correlation is basically common sense, below I quantify why serial correlation is so statistically important and just how powerful it can be in creating asset bubbles.

What’s so important about serial correlation?

As I discussed in my tail risk letter, despite markets being pretty random and chaotic, most of the time they actually closely follow normal distributions because of the Central Limit Theorem – if you aggregate a large number of transactions each being relatively independent from others, the average of these transactions will follow a normal distribution curve and have well defined statistical characteristics. As a result, massive bubble-like price increases or crashes are predictably rare.

Key to the normality of markets is a close to zero serial correlation of prices across time. Losing this critical condition can produce abnormally large losses or gains. For example, in 2008 a minor group of leveraged players in the markets were squeezed and were forced to sell. This selling pressure lowered the market prices which in turn forced another group of participants who were previously above water to sell, which in turn lowered prices and again brought a new group of people into trouble. This highly serially correlated behavior caused huge losses because a large portion of the market was now basically acting as one.  In the opposite direction, a bubble tends to form when a group of people buying something raises the price enough to inspire another group of people to buy, which further raises the price to continue the cycle. Here, the serial correlation between participants produces abnormally large gains.

A quantitative measure for bubble behavior

Before we examine how serial correlation causes asset bubbles, we need a systematic definition because asset bubbles can be subjective and difficult to define. After all, market prices will always fluctuate up and down; what is normal randomness and at what point does it become a bubble?

Below, I lay out a relatively straightforward metric – it is not a comprehensive measure of bubble behavior and is meant to be a naïve illustration. Take any average 3 year period in a market, what is the price path of its best and worst year? We could then look at all 3 year periods for the market and average the paths of those best and worst years to get a systematic pattern of how rapidly a market tends to rise and fall. Below, I averaged the price path of the best and worst years over all 3 year periods for stocks since 1920.

Over an average 3 year period since 1920, stock’s best year rose 45% and its worst year fell by -20%. So how does this stack up against a theoretical normal distribution? Is this kind of price increase statistically normal or is it higher than expected (i.e. more bubble-like)? Below, I simulated 10000 3-year periods of a normally distributed theoretical market with the same return and risk as stocks, and then I similarly aggregated and averaged the path of its best and worst year in each of those 10000 3-year periods. In this simulation, I explicitly defined the serial correlation of the market price from one period to the next to be completely independent (zero serial correlation).

What we find is that the average path of rise and fall for stocks actually closely tracks that of a normal distribution with zero serial correlation. Stocks on average have a relatively close to normal distribution and develop major bubbles at a predictably rare rate. To put a single number around the propensity of a market to develop bubbles, I took the ratio of the actual average market rise against the rise predicted by a normal distribution. A ratio of 1 would mean the market is not inclined to form more bubbles than a normal distribution and a higher number would mean a greater propensity for bubble-like behavior. Stocks have about a 1.1 bubble score – it is fairly normally distributed but experiences the rare bubbles that are bigger than statistically predicted.  

Serially correlated markets are prone to massive bubbles

Losing serial independence has an enormous impact on market returns. Below, I did similar Monte Carlo simulations on theoretical return streams with the same return and risk as stocks but explicitly built in varying degrees of serial correlation. On one end, I looked at a distribution with negative serial correlation, meaning that a rise in price would be more likely followed by a fall in price, which is more of a value investor mentality. On the other end, I looked at a distribution with a positive serial correlation, meaning that a rise in price would be more likely followed by a further rise in price, which is more of a momentum investor mentality. 

Below, I put numbers around the visual above.

What we see is that differing levels of serial correlation produce enormously different outcomes. Remember these return streams all share the same expected return and risk – the only thing I’m varying is the serial correlation. If the stock market was serially negatively correlated, we’d see smaller ups and downs than reality. If the stock market was serially positively correlated, we’d see much bigger ups and downs. Towards the extreme end, we’d routinely see 500% annual price increases if the market was 0.9 serially correlated. In reality, the stock market is likely somewhere between 0 and 0.1 serially correlated. This suggests a relatively even balance between value and momentum in the market. Common sense logic agrees with this number as we see the market mostly being normally distributed with rare periods of bubble and panic behavior when prices do become serially correlated.

Below, I show the same table for bonds since 1920. Similar to stocks, we also see a roughly 1.1 bubble score for bonds and somewhere between a 0 and 0.1 serial correlation.

Bitcoins exhibit highly serially correlated behavior

Below, I show the same chart of aggregate rise and falls of Bitcoins over all 3 year periods since 2010 relative to a theoretically normal distribution with the same return and volatility as Bitcoins. Bitcoins have a bubble score of 21.2 and have a dramatically higher propensity for bubble-like behavior. Its average rises and falls have been far more dramatic than predicted by a normal distribution with similar return and volatility. On average, its best year in any 3year period would see an 82X price multiple and its worst year would see a -75% price drop. A market like Bitcoin that had serial correlation of 0 would see far smaller ups and downs and be boring by comparison, as shown in the muted grey line.

Below I show a similar table of actual Bitcoin vs. simulated distributions of varying levels of serial correlation. The magnitude of Bitcoin’s ups and downs suggests a very uneven balance of momentum vs. value in the market. The serial correlation in the market is far higher than that of traditional markets like stocks and bonds. Serial correlation has exponential power to create speculative bubbles. If Bitcoin was 0.9 serially correlated, we’d see even more outrageous levels of price growth (prices multiplying by hundreds of thousands of times per year). There is essentially no limit to how big a bubble serially correlated behavior can create. Of course, in reality, the level of serial correlation is capped by the availability of capital in the world and some bound on human irrationality (hopefully).  What we are seeing in the Bitcoin market is likely getting close to that limit, which is what makes this market so fascinating to me.

Why do markets become so serially correlated?

Unlike stocks, bonds and real estate, the Bitcoin market sees momentum consistently dominate value. While investors in stocks, bonds and real estate can always come back to dividends, interest and rent payments as anchor points around valuation, Bitcoins have no income and no intrinsic basis of value. Its only source of value is other people’s perception of its value. To borrow Warren Buffett’s framework of a market being a popularity contest in the short run and a weighing machine in the long run, Bitcoins structurally have no weighing machine. It’s only long-term value is its popularity. As a result, the markets are stuck with Bitcoin’ recent value as the only indicator of its future value, producing an enormous feedback loop that amplifies its ups and downs relative to a more balanced market. 

More broadly speaking, when there isn’t a clear framework around value, momentum can take over. This is true of existing markets that experience a dramatic change such as tech stocks during the late 90s or the new and complex structured product markets in the 2000s. Other markets like Tulips that produce no income tend to rely even more on momentum and as a result create even bigger bubbles. While dramatic in magnitude, there is nothing structurally different about Bitcoin’s price rise. It is simply an extreme case of an echoing chamber of serially correlated actions. This type of groupthink behavior is deeply ingrained in the human psyche.

Arise of Bitcoin’s magnitude is rare and we go through centuries without experiencing one. It provides an once-in-alifetime opportunity to make money, to lose money and to learn. As an investor, I’ve always been more interested in the weighing machine than the popularity contest, so I’ll be on the sidelines for this one. Enough smart people have failed in these extreme, irrational markets that I distrust my own ability to navigate the risks. Instead, I look forward to my front row seat as a student of this historical moment. I leave you with the following chart1 and quote: “I can calculate the movement of stars, but not the madness of men.”

Look back at the chart on the first page, the bubble that broke Newton is barely a blip compared to the recent Bitcoin price rise.

Source: Convoy Investments