In investing, it’s widely accepted that higher risk can lead to higher returns. But some assets carry risks that are hard to foresee while offering only limited rewards. Cryptocurrencies are notably volatile, yet certain tokens show better risk-return profiles under extreme conditions when compared to traditional assets. However, research findings are based on historical data. Investors should always consider their own risk tolerance before making any financial decision.
“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 in his shirt.”
— Nassim Nicholas Taleb, The Black Swan
Volatility Does Not Fully Capture Risk
When quantifying financial risk, many rely on the concept of “volatility”—a statistical measure of how much an asset’s returns vary over time. It’s commonly calculated as the standard deviation of logarithmic returns. For example, if a stock has a daily volatility of 1%, on roughly two-thirds of trading days, its price will move between -1% and +1%.
But volatility and standard deviation assume that returns follow a “normal distribution”—the classic bell curve. This works well when price movements result from many small, independent random factors. Under these conditions, the central limit theorem suggests returns should converge toward a normal distribution.
In a normal distribution, events lying three or even six standard deviations from the mean are considered extremely rare. However, financial markets frequently experience moves far larger than these models predict. These unexpected shocks are often called “black swan” events, a term popularized by Taleb, especially after the 2008 financial crisis.
Such events occur more frequently than standard models anticipate and can severely impact investment returns. Statistically, they indicate that the distribution of returns has “heavy tails”—meaning extreme outcomes are more likely than a normal distribution would predict.
What causes these heavy-tail events in finance? There are many possible explanations, including information asymmetry, insider trading, excessive leverage, market concentration, or even outright manipulation—none of which contribute to healthy, efficient markets.
Let’s explore how we can measure the frequency and impact of these tail events across different asset classes.
Measuring Heavy-Tail Risk
To quantify heavy-tail risk, analysts often use two metrics: the Mild Outlier Probability (MOP) and Extreme Outlier Probability (EOP). These measure how often an asset experiences moderate or severe price movements beyond typical daily fluctuations.
These metrics are derived using methods based on interquartile range (IQR), as described in research by P. Jordanova et al. Values that fall just outside the IQR boundaries are considered mild outliers, while those further out are classified as extreme outliers.
What does this feel like in practice?
A mild outlier might be a day when the S&P 500 drops 3%—enough to make headlines and stir anxiety among investors.
An extreme outlier could be a sudden 10% market crash, leaving investors shocked and scrambling to reassess their portfolios.
If we chart these outlier events (red for negative, green for positive), we can visually identify periods of unusual market stress. Those familiar with U.S. stock market history may recognize many of these dates.
It’s important to note that higher volatility doesn’t always mean higher tail risk. Predictable volatility (like that of Bitcoin) can be managed, but it’s the unexpected extreme moves that cause the most financial damage.
Now, let’s compare tail risk across asset classes—including cryptocurrencies.
A Look at Cryptocurrency Tail Risk
The following analysis compares MOP and EOP across multiple asset types:
- U.S. stocks
- Chinese stocks
- Fixed income (U.S. 20-year Treasury bonds)
- Physical assets (gold and real estate investment trusts)
- Cryptocurrencies
In the chart, the size of each circle represents volatility, and the position indicates tail risk (higher and farther right means more tail risk). Here are the key takeaways:
1. Cryptocurrencies Are Highly Volatile with Heavy Tails
This aligns with general intuition. Major cryptocurrencies like Bitcoin and XRP show both high volatility and high tail risk compared to most traditional assets. For example, Bitcoin has an Extreme Outlier Probability of nearly 4%—meaning大约every three to four weeks, it experiences a severe price swing.
These moves are often driven by events like regulatory rumors, exchange hacks, or large-scale liquidations.
2. Some Cryptocurrencies Have Milder Tail Risk Than Traditional Assets
Surprisingly, privacy-focused coins like Monero (XMR) and Dash (DASH) exhibit lower tail risk than the S&P 500—and far less than the Chinese stock market, which shows tail risk similar to some mid-cap crypto tokens.
This may be because these cryptocurrencies are used more for transactions than speculation, leading to higher liquidity, more participants, and less market manipulation. For new investors entering the crypto space, these assets might offer a less stressful experience.
It’s worth noting that although these privacy coins are still volatile, that volatility is often more predictable—and thus easier to hedge or diversify—compared to unexpected tail events that can wipe out leveraged positions.
3. The Crypto Market Is Maturing
Bitcoin is now over a decade old. Thousands of exchanges support its trade, and institutional involvement is growing. When comparing pre-2015 and post-2015 Bitcoin data, we see a noticeable decline in extreme outlier probability—a sign of a maturing market.
As more regulated exchanges enter the space, and with the rise of institutional-grade custody and financial products, crypto is gradually becoming more integrated into mainstream finance.
Is Crypto’s Tail Risk Justified?
High risk often scares people away from crypto. But if we consider risk in terms of return per unit of risk taken, the story becomes more nuanced.
In the chart above, the circle size represents average daily return. Some cryptocurrencies—even those with significant tail risk—have offered substantially higher returns than traditional assets with similar tail risk profiles.
Compare Monero with the S&P 500, for example. Both have similar tail risk, but Monero’s average daily return is much higher. In traditional markets, events like the 2008 crash or the 2015 Chinese market turmoil led to massive losses, often followed by government bailouts. Crypto, by contrast, tends to reward those who stay calm during periods of high volatility.
In the words of Taleb, a well-structured portfolio is “anti-fragile”—it benefits from volatility and unexpected events. Cryptocurrencies, despite their risks, may offer exactly that kind of potential when managed wisely.
Conclusion
Cryptocurrencies generally show higher volatility and heavier tail risk than traditional assets like stocks, bonds, and commodities. However, some crypto assets—such as Monero and Dash—display tail risk profiles similar to major U.S. stock indices while offering significantly higher returns.
Moreover, Bitcoin’s tail risk has decreased over the past decade, suggesting that the market is maturing. As liquidity, regulation, and institutional participation grow, crypto may become a more stable asset class.
For investors, the key is not to avoid risk altogether, but to understand it, diversify appropriately, and use strategies that allow for both safety and growth. 👉 Explore advanced portfolio strategies
Frequently Asked Questions
What is a “black swan” event in financial markets?
A black swan event is an extreme, unexpected occurrence that has a severe impact on financial markets. These events are often inappropriately rationalized after the fact with the benefit of hindsight. Examples include the 2008 global financial crisis and the 2020 market crash triggered by the COVID-19 pandemic.
How can investors protect themselves from tail risk?
Diversification is the first line of defense. Including non-correlated assets—such as gold, Treasury bonds, or even certain cryptocurrencies—can help. Some also use options or tail-risk hedging strategies that profit from market crashes. Always avoid over-leveraging, especially in volatile markets.
Are all cryptocurrencies equally risky?
No. While major cryptocurrencies like Bitcoin and Ethereum are highly volatile, some alternative coins exhibit lower tail risk. Assets with stronger liquidity, real-world use cases, and higher trading volumes often show more stable price behavior over time.
Is crypto tail risk decreasing over time?
Evidence suggests that Bitcoin’s tail risk has diminished compared to its early years. As regulatory clarity improves and institutional adoption grows, the entire crypto market may become less prone to extreme price swings.
Can traditional risk management models be applied to crypto?
Standard models like Value at Risk (VaR) often assume normal distribution and can underestimate tail risk in crypto. It’s better to use stress testing, scenario analysis, and heavy-tailed distributions when modeling cryptocurrency risk.
What role does leverage play in tail risk?
Leverage magnifies losses during tail events. Many sudden crypto price crashes are accelerated by the liquidation of leveraged positions. Using minimal or no leverage is one way to reduce exposure to tail risk.