Term Structure, SKEW and Tail Risk

Tail Risk

In this lesson, you’ll learn about tail risk, a critical concept for understanding extreme market movements and their impact on options trading strategies. We’ll explore how price movements are measured using standard deviation and what happens when markets move beyond normal expectations.

The foundation of tail risk begins with normal distribution, also known as the Gaussian distribution, which creates a bell-shaped curve describing random variables in the market. Standard deviation measures how far prices disperse from the mean, with one standard deviation representing approximately 68.2% of results, two standard deviations covering 95.4%, and three standard deviations encompassing 99.7% of outcomes. These measurements help quantify market changes and understand price behavior patterns.

Understanding implied volatility is essential when applying these concepts to options trading. In a low implied volatility environment, prices tend to stay within one standard deviation from the mean. In a high implied volatility environment, the market expects larger price movements, with outcomes spanning two or three standard deviations away from the current stock price. For example, with 20% implied volatility on a $100 stock, you might expect a one standard deviation move between $80 and $120.

Tail risk events occur when asset prices move more than three standard deviations from the mean, beyond what normal distribution predicts. These events have small probability but significant impact, like the 2008 financial crisis and the COVID crisis. When analyzing tail risk, we use kurtosis, a statistical measure indicating whether data follows a fat tail distribution or leptokurtic distribution, where extreme outcomes occur more frequently than expected. Assets following this pattern show returns exceeding 3 standard deviations by more than 0.3% of observed outcomes.

The lesson distinguishes between left tail and right tail events. The left tail represents bearish market crashes, where investors use protective strategies like puts to protect the downside. The right tail signals bull market conditions. When building option strategies with our Q models, high implied volatility allows you to use much larger strikes and place strikes at the furthest wall, accounting for greater chances of stock movement between wider walls.

Video Chapters

  1. 00:00 – Introduction to tail risk and normal distribution
  2. 00:51 – Implied volatility and market expectations
  3. 02:10 – Standard deviation in practice with trading example
  4. 03:09 – Understanding tail risk events
  5. 03:34 – Kurtosis and fat tail distributions
  6. 04:24 – Left tail and right tail market movements

Key Takeaways

  1. Normal distribution creates a bell-shaped curve where one standard deviation represents 68.2% of outcomes, while three standard deviations cover 99.7%
  2. Tail risk events occur when prices move more than three standard deviations from the mean, like the 2008 financial crisis and COVID crisis
  3. Implied volatility environments determine strike placement—high volatility allows wider strikes in option strategies using Q models
  4. Left tail events represent bearish crashes requiring protective puts, while right tail events signal bull markets
Video Transcription

[00:00:00.10] - Speaker 1
In this lesson, we will cover the concept of Taylor risk. We will talk about the left and right tail, and we will talk about market movements in terms of standard deviation. This will then help us to understand better when we talk about tail risk strategies. First we need to talk about the concept of normal distribution. The normal distribution, also known as the Gaussian distribution, is a continuous probability distribution that describes many random variables.

[00:00:24.07] - Speaker 1
The normal distribution is described by a bell shaped curve. As you can see here in the chart, the distance from the midpoint is described in terms of standard deviation. The standard deviation is a measure of dispersion of the distribution around the mean. In this slide, we can see how a market change can be quantified using standard deviation. The standard deviation of prices shows us that while occurrences may seem random in the short term, the more occurrences we generate, the more consistent our results become.

[00:00:51.03] - Speaker 1
Here we see how thousands of occurrences typically start to create a bell curve around the median value. In the red square you can see the average value. But why is this an important concept for us who look at options? This idea goes hand by hand with implied volatility on the stock market. In fact, a low implied volatility environment tells us that the market does not expect the stock price to deviate much from the current stock price.

[00:01:13.27] - Speaker 1
This lack of implied volatility shows us how prices tend to stay within one standard deviation from the mean. If the market moves by only one standard deviation, we can see how the price moves into the green bell. So price movement tends to stay close to the mean. A high implied volatility environment tells us that the market expects the stock price to move away from the current price. This high implied volatility results in a range of outcomes with a large standard deviation away from the stock price.

[00:01:39.09] - Speaker 1
In our example, we can see how two or three standard deviations can lead the price very far from the mean. One standard deviation represents approximately 68.2% of the results in a distribution of occurrences based on the current implied volatility. Two standard deviations comprise approximately 95.4% of the results in a price distribution based on current implied volatility. Three standard deviations comprise approximately 99.7% of the outcomes in a price distribution based on current implied volatility. Let's put this into practice.

[00:02:10.15] - Speaker 1
In this example, the implied volatility of Our position is 20%. The price of the stock is at $100 based on volatility. Using the concept of normal distribution and standard deviation, we can try to predict the potential movement of the price 20% of implied volatility expects an implied movement of one standard deviation. So we might expect a one standard deviation move in the bell with a high of 120 and a low of 80. These are movements calculated using data and statistics.

[00:02:38.08] - Speaker 1
However, it is important to note that these types of movements cannot always be predicted by normal distributions. What we are trying to do is to improve our positioning using data and statistics, which is what we do every morning with our cue models. If we are trying to build an option strategy looking at data and statistics when the implied volatility is high, we can use much larger strikes. In the case of Q models, we can therefore use the furthest wall to place our strikes in our option strategy. When the implied volatility is high means that there is a greater chance of the stock moving up and down between the wider walls.

[00:03:09.05] - Speaker 1
This brings us to the next tail risk. These are events that occur when there is a chance that the price of an asset will move more than three standard deviations from the mean, so more than what is shown by a normal distribution. Tail risk include events that have a small probability of occurring and occur both on the upper and lower end of the normal distribution curve. These are events like the financial crisis of 2008 and the COVID crisis. In this section we will talk about this in more detail.

[00:03:34.18] - Speaker 1
Stock market returns tend to follow a normal distribution. Then there are tail risk movements and in this case we can use kurtosis. Kurtosis is a statistical measure that indicates whether the observed data follows a distribution with fat tails. Now if we look at the next chart, we see a leptokurtic or heavy tailed distribution, also known as fat tail. It describes a situation where extreme outcomes have occurred more than expected compared to the normal distribution.

[00:04:01.16] - Speaker 1
These curves have excess of kurtosis. Stocks that follow this distribution have seen returns exceeding 3 standard deviation above the mean by more than 0.3% of the observed outcomes. So assets with this distribution tends to have very high volatility. Finally, in the last two slides we will talk about the right and left tail. When we look at the left tail we are talking about bearish market crashes.

[00:04:24.05] - Speaker 1
In these cases, the investor uses protective strategies such as puts to protect the downside. And finally we see the right tail which is a signal of a bull market. We come to the end of the lesson on tear risk. We still have a few theoretical lessons to go before moving to the practical sect.