# Tail Risk

Tail risk it is the risk of an asset or portfolio of assets moving more than three standard deviations from its current price. Technically, tail risks arise when the possibility that an investment will move more than three standard deviations from the mean is greater than what is shown by a normal distribution (see the chart below). To simplify, tail risks are very unlikely events which entail very serious consequences.

The standard deviation is a measure of how much an investment’s returns can vary from its average return. The higher standard deviation, the more volatile and risky the asset is. The probability that a return will change by three standard deviations is very, very low. This is why tail risk is often described as the risk of rare events, or the risk of black swans.

## Fat Tails

Financial analysts often assume that the distribution of returns follows a normal pattern. According to the assumption of normal distribution, the probability of returns moving more than three standard deviations from the mean is merely 0.03 percent. However, the financial variables hardly follow a normal pattern. In reality, the distribution is not normal, but skewed and has fatter tails relative to the normal distribution. Fat tails increase the tail risk, i.e. the probability of returns moving more than three standard deviations from the mean. The term ‘fat tails’ derives from the fact that the tails are fatter, i.e. extreme observations occur more frequently than the normal distribution would suggest. In other words, tail events are very rare in a normal distribution, but market tails are in fact fatter, and rare event are more frequent than many people realize. Especially in the stock markets, extreme price movements are not as seldom as the normal curve would predict. Therefore, models assuming a normal distribution, like those used by the Long-Term Capital Management, understate the true level of risk. Investors should always remember that risk is significantly higher than the normal distribution suggests.

A chart below illustrates the idea of "fat tails" – we can see percentage gold price changes in the period May 14, 2011 - Oct 10, 2011.

The above histogram presents real changes in the price of gold, while the red line is the theoretical distribution of the price change, if it were normal, with the mean and standard deviation computed using the sample. We can see that near the mean, the values resemble the normal distribution quite well, yet at the edge the values are far too high to be normally distributed.

## Tail Risk and Gold

Gold has low or negative correlation with other assets. Therefore, it is a portfolio diversifier and a safe haven against tail risks, like financial crises. During crises asset prices can move downward more than three standard deviations from their mean, reducing the worth of the portfolio. However, gold usually shines during financial crises, therefore it protects the investors’ wealth against tail risks. Hence, gold is a safe haven, which protects investors during crises, but not necessarily in normal times of high confidence in the fundamentals of the economy. However, gold is not a safe haven against any particular asset class; rather it is protection against systemic risks – an insurance against a current monetary system based on the fiat U.S. dollar.

We encourage you to learn more about gold – not only how it is affected by tail risk, but also how to successfully use the shiny metal as an investment or portfolio diversifier and how to profitably trade it. A great way to start is to sign up for our gold newsletter today. It's free and if you don't like it, you can easily unsubscribe.

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