Six Sigma Event

Introduction

Any event that is extremely rare, beyond the sixth standard deviation in a normal distribution, is known as a six sigma event. The probability of such an event happening would be about [2* 10^(-9)] or twice in a billion. It can also be compared to flipping an unbiased coin a large number of times in a row and getting heads or tails each time.

 

Source: Wikipedia

The Six Sigma methodology relies on the concept of a normal distribution.

In this distribution, the mean (μ) is located at the center (0), and the horizontal axis measures the distance from the mean in standard deviation units (σ or sigma). A larger standard deviation indicates a wider spread of values.

For instance, in the green curve, μ is at 0 and σ is 1. The upper and lower specification limits (USL and LSL) are positioned 6σ away from the mean. With a normal distribution, values far from the mean are extremely rare, approximately 1 in a billion on both ends.

Even if the mean shifts slightly to the right or left by 1.5 standard deviations (a 1.5 sigma shift, marked in red and blue), there's still a safety margin. The Six Sigma methodology relies on the concept of a normal distribution. In this distribution, the mean (μ) is located at the center (0), and the horizontal axis measures the distance from the mean in standard deviation units (σ or sigma). A larger standard deviation indicates a wider spread of values. For instance, in the green curve, μ is at 0 and σ is 1.

The upper and lower specification limits (USL and LSL) are positioned 6σ away from the mean. With a normal distribution, values far from the mean are extremely rare, approximately 1 in a billion on both ends. Even if the mean shifts slightly to the right or left by 1.5 standard deviations (a 1.5 sigma shift, marked in red and blue), there's still a safety margin.

 

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Six sigma in finacial markets

In the financial markets, anything which is not ordinary, like a huge fall or sudden rise in the price of stock/market, is a six sigma event. An example of six sigma event can be 2008 financial crisis.
 

Technically, six sigma implies the six standard deviations away from the mean of a probability distribution, Here, sigma (σ) is the common notation for a standard deviation. Also, the underlying distribution is implicitly a normal (Gaussian) distribution.

 

Here’s a table to indicate the odds against a “k-sigma” event for various “k” (tries).

 

Sigma	Odds
1	4: 1
2	41: 1
3	381: 1
4	19,000: 1
5	1,90,000: 1
6	9,00,000,000: 1