# Tail Risk Explained: Managing Rare Events Leading to Portfolio Losses

![Tail Risk: The possibility that an asset performs far above or below its average past performance.](https://www.investopedia.com/thmb/6Cg2M1cf47Nc81VMHR9pILBN3vQ=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/tailrisk.asp-final-23b01c67c985407d96ebd297736e6c8a.png)

*— Investopedia / Tara Anand*

## What Is Tail Risk?

Tail risk represents the probability that investment returns deviate more than three standard deviations from the mean—a situation not adequately captured by a normal distribution. These events, although rare, can significantly impact portfolios, necessitating strategies to mitigate potential losses.

### Key Takeaways

*   Tail risk arises when an investment's potential to deviate more than three standard deviations from the mean exceeds expectations under a normal distribution.
*   Traditional financial models often assume asset returns follow a normal distribution, yet market returns may exhibit skewness and fat tails.
*   Tail events, or extreme market moves, challenge the assumptions of conventional financial theories like modern portfolio theory.
*   Hedging against tail risk can involve using derivatives or diversification to mitigate potential negative impacts on a portfolio.
*   Recognizing different probability distributions, such as leptokurtic distributions, helps investors understand the frequency of extreme market events.

## Delving Deeper Into Tail Risk

Traditional portfolio strategies typically follow the idea that market returns follow a normal distribution. However, the concept of tail risk suggests that the distribution of returns is not normal, but [skewed](https://www.investopedia.com/terms/s/skewness.asp), and has fatter tails.

The fat tails indicate that there is a probability, which may be larger than otherwise anticipated, that an investment will move beyond three [standard deviations](https://www.investopedia.com/terms/s/standarddeviation.asp). Distributions that are characterized by fat tails are often seen when looking at [hedge fund](https://www.investopedia.com/terms/h/hedgefund.asp) returns, for example.

The chart below depicts three curves of increasing right-skewness, with fat tails to the downside, and which differ from the symmetrical [bell curve](https://www.investopedia.com/terms/b/bell-curve.asp) shape of the normal distribution.

![Right skewness](https://www.investopedia.com/thmb/sgvPbYJjwzcJgoviy4hMgqw3HIo=/640x0/filters:no_upscale():max_bytes(150000):strip_icc()/Clipboard01-5c684fb046e0fb0001f0e38b.jpg)

*Right skewness.*

## How Normal Distributions Influence Asset Returns

When creating a portfolio, it is assumed that returns will follow a normal distribution where 99.7% stay within three standard deviations of the mean. This means that the probability of returns moving more than three standard deviations beyond the mean is 0.3%.

The assumption that market returns follow a normal distribution is key to many financial models, such as Harry Markowitz's [modern portfolio theory (MPT)](https://www.investopedia.com/terms/m/modernportfoliotheory.asp) and the Black-Scholes-Merton [option pricing model](https://www.investopedia.com/terms/o/optionpricingtheory.asp). However, this assumption does not properly reflect market returns, and tail events have a large effect on market returns.

> **Fast Fact**
>
> Tail risk is highlighted in Nassim Taleb's bestselling financial book "The Black Swan".

## Examining Alternative Distributions With Fat Tails

Stock market returns often have [excess kurtosis](https://www.investopedia.com/terms/e/excesskurtosis.asp), meaning their tails are heavier than those of a normal distribution. The normal distribution curve has a [kurtosis](https://www.investopedia.com/terms/k/kurtosis.asp) equal to three, and, therefore, if a security follows a distribution with kurtosis greater than three, it is said to have fat tails.

A [leptokurtic distribution](https://www.investopedia.com/terms/l/leptokurtic.asp), or heavy/fat-tailed distribution, depicts situations in which extreme outcomes have occurred more than expected. Compared to the normal distribution, these curves have excess kurtosis. Therefore, securities that follow this distribution have experienced returns that have exceeded three standard deviations beyond the mean more than 0.3% of the observed outcomes.

The graph below depicts the normal distribution (in green) as well as increasingly leptokurtic curves (in red and blue), which exhibit fat tails.

![A graph showing 3 different kurtosis](https://www.investopedia.com/thmb/L0CduuSN08gTNvMYlMk5avZnmUU=/1053x0/filters:no_upscale():max_bytes(150000):strip_icc()/kurtosis-5764c7f25f9b58346a2433c3-5c3cf61b46e0fb0001d45eef.jpg)

*Kurtosis describes the different kinds of peaks that probability distributions can have. —  ThoughtCo*

## Hedging Against Tail Risk

Though rare, tail events can lead to big losses, so investors should hedge against them. Hedging against tail risk aims to enhance returns over the long term, but investors must assume short-term costs. Investors may look to diversify their portfolios to hedge against tail risk.

For example, if an investor is long [exchange-traded funds (ETFs)](https://www.investopedia.com/terms/e/etf.asp) that track the Standard & Poor's 500 Index (S&P 500), the investor could hedge against tail risk by purchasing [derivatives](https://www.investopedia.com/terms/d/derivative.asp) on the Cboe Volatility Index, which is [inversely correlated](https://www.investopedia.com/terms/i/inverse-correlation.asp) to the S&P 500.

## The Bottom Line

Tail risk represents a critical consideration in portfolio management, highlighting the chance of significant losses due to rare, extreme market events. While traditional models assume returns follow a normal distribution, real-world data often exhibit fat tails, indicating a higher probability of extreme outcomes.

Investors should recognize the limitations of normal distribution assumptions and consider hedging strategies, such as diversification and derivatives, to protect against potential tail events. By understanding and addressing tail risk, investors can better manage potential vulnerabilities and aim for more stable long-term returns.

> **Article Sources**
>
> 1.  Markowitz, Harry. "[Portfolio Selection](https://www.math.hkust.edu.hk/~maykwok/courses/ma362/07F/markowitz_JF.pdf)." _The Journal of Finance,_ vol. 7, no. 1, March 1952, pp. 77-91.
>     
> 2.  Black, Fischer, and Myron Scholes. "[The Pricing of Options and Corporate Liabilities](https://www.cs.princeton.edu/courses/archive/fall09/cos323/papers/black_scholes73.pdf)." _The Journal of Political Economy_, vol. 81, no. 3, May-June 1973, pp. 637-654.
>     
> 3.  Nassim Nicholas Taleb. "[The Black Swan: The Impact of the Highly Improbable](https://www.google.com/books/edition/The_Black_Swan/gWW4SkJjM08C)." Random House Publishing Group, 2007.
>     
> 4.  Cboe. "[Vix Volatility Products](https://www.cboe.com/tradable_products/vix/)."