Does Cryptocurrency Have More Black Swan Events than Other Assets?
“If you hear a “prominent” economist using the word ‘equilibrium,’ or ‘normal distribution,’ do not argue with him; just ignore him, or try to put a rat down his shirt.”
― Nassim Nicholas Taleb, The Black Swan
Volatility does not measure the true risk
Usually, when people quantify financial risk, they use a concept called “volatility”. It is just a fancy word for “fluctuation”, or dispersion of returns. Usually, it is measured by the standard deviation of stock return (log return to be exact). It reflects the typical daily change of stock price. For example, if we say the daily volatility of the stock market is 1%, then for 2/3 of the days, the stock fluctuation is within -1% and 1%, and you can only see a jump larger than 2% less than 1 in 20 days.
However, volatility (computed as standard deviation of returns) is only a good measure for “normal distribution”. The distribution of its daily return looks like a bell shape. If the up and down of an asset is determined by many independent random factors, then according to the central limit theorem, the distribution of its return converges to the normal distribution.
The normal distribution has many good properties. Typically, it is quite safe to bet your money against a 3-standard-deviation event (default of a high-grade bond), and it is safe to bet your life against a 6-standard-deviation event (e.g. encountering a car accident).
However, you may have noticed that it is more often for the market to have some big, nasty movements that far exceeds your expectation, which people have been using the term “black swan” event, to describe, which was brought to popularity by Nassim Taleb in his book The Black Swan: The Impact of the Highly Improbable, especially after the shockwave of the 2008 financial crisis. These events are more often than people may expect, and their repercussion has a significant impact on the investment returns.
Alternatively, we can call these black swan event “heavy-tail” events, because the distributions that generate these large unexpected values typically have thicker tails than normal distribution. In the following sections, we refer to these events as “heavy-tail events”, or simply “tail events”.
What are the causes of these events in the financial world? There are myriad of possible explanations, but almost none of them are benign: Asymmetry of information, insider trading, over-leverage, too much concentration of the assets, or even blatant market manipulation? None of these are good for the long-term health of the financial market.
Now let’s see how we can quantify these tail events and measure their prevalence across different asset classes.
How To Measure Heavy-tailedness
In short, we use the probability of two types of tail events (mild and extreme) to measure the degree heavy-tailed ness. The more often we see these two types of events, the more “manipulated” the assets are.
We employ the definition of mild outlier probability (MOP) and extreme outlier probability (EOP) using the methods described in Measuring heavy-tailedness of distributions by P. Jordanova et. al. In short, they use quartiles and inter-quartile range (IQR)to define several boundaries. Values fell into the leftmost boundary are left extreme outliers, and values fell between the two left boundaries are left mild outliers. Vice versa for the right counterparts, as shown in the plot below.
Intuitively, what do these two types of outliers (mild and extreme) mean? Here is an example. Probably you have been used to the lukewarm ups and downs of S&P, typically less than 1% every trading day for a few months. One day you catch a glimpse of MSNBC or open up Yahoo finance and you see a whopping 3% market drop, and every stock pundits and commentators are making a big fuss out of this, showing glittering numbers, choppy charts and pictures of NYSE traders wrapping their hands around heads, panicking. This is what a “mild outlier” feels like. If, however, you see a 10% market crash, and cannot comprehend what it means to your portfolio right away. Moreover, everyone silently checks to see if their 401k accounts have just turned into 201k… then we’ve got an “extreme outlier”.
If we mark these tail events (red as negative outliers, and green as positive outliers) in the price chart of SPY in the last 4 year, they look like the plot below. If you are familiar with the US Equity market, probably you can still remember the days marked by those red segments.
Of course, nobody likes these nasty surprises. Unfortunately, when the price of an asset is only determined by a few factors, especially when those factors are opaque to the public and in the hands of few, they tend to be more devastating. Therefore, by measuring the frequency of the occurrence of these types of events, we can get a good idea on how each asset perform in terms of tail risks. Note that higher volatility does not necessarily mean higher tail risks, because if you can expect the magnitude of the fluctuation, then there are almost no nasty surprises. For example, nowadays nobody would complain about 3~5% Bitcoin fluctuation at all, but they curse over a 3~5% S&P 500 drop. It is the unforeseeable outliers that do the most damage.
Now let’s take a look a the tail risks of different assets, especially cryptocurrencies.
Tail risks of cryptocurrency in perspective
In the plot below, we demonstrate volatility, mild outlier probability (MOP) and extreme outlier probability (EOP) all together across multiple asset classes including
- US stock market
- Chinese stock market
- Fixed income (US 20-year treasury bond)
- Physical assets (Gold and REIT)
- Cryptocurrency
The size of the circles indicates the volatility, and the locations of the dots indicate the tail risks (right-top means more heavy-tailedness). Let us go through several key observations from this plot.
Cryptocurrencies are indeed highly volatile and heavy-tailed
This matches our intuition. As we can see from all those big red dots on the top-right part of the plot, main-stream cryptocurrencies like Bitcoin (BTC) and Ripple (XRP) indeed have higher volatility and higher MOP and EOP than most of the conventional assets.
For example, we have a whopping 4% EOP for Bitcoin. It is such a big number, that almost every 3 to 4 weeks, we can hear some ground shaking market events for Bitcoin. A skyrocketing new high, a 20% bloodbath dump, an ETF regulation rumor hype, or some exchange wallet hack scandal, you name it.
However, not all cryptocurrencies are created equal. We have some surprisingly docile creatures.
Some cryptocurrencies have better tail-risk profiles than conventional assets
For example, some “privacy” cryptocurrency like Monero (XMR) and Dash (DASH) are actually less heavy-tailed than conventional investments like the S&P 500 index, let alone the super swingy Chinese stocks, which laughably share similar tail-risk profile as some other risky cryptocurrencies. This is probably due to the facts that these “privacy” cryptos are more “traded” than “hoarded”. This can be verified by their much higher rank in trading volume relative to their market cap amongst cryptocurrencies. More market participants, more liquidity, less manipulation, fewer tail events.
Therefore, arguably, compared to big crypto giants like Bitcoin and Ripple, Monero and Dash are actually more suitable entry-level coins for new investors if they are trying to dip their toes into the torrents of cryptocurrency world. At least, these data would assure them so sleep sound at night.
Note that these “privacy” cryptos are actually higher in volatility, which is the random risk that you can normally observe and hence can hedge or diversify, yet lower in heavy-tailedness, which is the kind of nasty events that wipe out a significant chunk of your assets or blow up your leveraged position entirely.
In addition, the cryptocurrency market is evolving rapidly.
Cryptocurrency is becoming more mature
Bitcoin has more than 10 years of history. Now there are thousands of exchanges supporting Bitcoin trading. We dedicated two data points to Bitcoin in our plot above, one for the Pre-2015 Bitcoin, the other for Post-2015 Bitcoin. As illustrated, we have seen a big drop in EOP for Bitcoin, which is an encouraging trend to continue. Hopefully, cryptocurrencies will soon become main-stream investments, despite all the historical booms and busts.
In the future, we will see more crypto exchanges, more legal ways to enter the crypto markets, and even institution-supported stable coins and crypto funds — everything for a new ecosystem is on its way.
Are the high tail-risks of cryptocurrencies justified?
Don’t let the high risk of cryptocurrency scare you away. Take a closer look at the return-risk trade-off from the plot above. In the plot, size indicates the average daily return. For taking a similar level of tail-risk, investors can be rewarded very handsomely even with the recent cryptocurrency crash.
Risk is not necessarily a bad thing for investors, if higher risk means higher reward. Random risks can be justified. However, it is risks that are not properly compensated, or asymmetric risks, that are truly detrimental to investors: you get a relatively meager return for some unforeseeable events to wipe your assets away. In Taleb’s words, these investments are not “anti-fragile”.
In the plot above, simply look at the size of the Monero dot vs the S&P dot: They locate similarly on the MOP-&-EOP chart, yet there is a staggering difference between their sizes (returns). Remember what happened in the US stock market in 2008 and what happened in Chines stock market in 2015: distorted market leading to tremendous losses, followed by heavy-handed government intervention, paid eventually by the taxpayers. Cryptocurrencies, on the other hand, as wild and unregulated as they are, reward its investors much more generously, as long as you are not scared off in the process.
Conclusion
Compared to other conventional assets like stock, bond, and physical assets, cryptocurrency usually has higher volatility and higher tail risks. However, some of the cryptocurrencies (e.g. Monero and Dash) share similar tail-risk profile as US equity index, and they reward investors with a much higher expected return, eclipsing other conventional investment vehicles. In addition, in the past ten years, the tail risk profile of Bitcoin is also on the decline, potentially a sign of a more mature market.
About the Author: SophonTech Inc. is a technology-driven company that provides solutions to cryptocurrency software and quantitative research.
Contributor and Editorial Credit: H. Zheng
Legal Disclaimer: SophonTech Inc. is not an investment advisor, and makes no representation regarding the advisability of investing in any security, fund, token, derivatives, physical assets or any other investment vehicles. All SophonTech Inc. materials have been created solely for informational purposes based upon public information from sources generally believed to be reliable. The data and analysis demonstrated do not represent the results of actual trading/investing.
