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The discrepancy between
normality and reality !
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Six Sigma Events have
nothing to do with the Six Sigma Practice, This concept has been
around since the inception of Probabilistic Risk Modeling, much
before the name was borrowed to to sell business
books!
A Six Sigma Event was coined
from observation of the normal distribution to describe
extreme movements in market prices that contradict normal distribution assumptions.
A six sigma event is characterized by a price drop of six times the
volatility (or standard deviations) of the asset , thus the name
six-sigma, sigma being the Greek letter representing volatility.
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According to normal distribution assumptions, This type of events
should happen EXTREMELY rarely.
We've actually seen quite a few in the past decade!
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- Crash of '87.
- .....
- Mexican Crisis. Tequila Effect.
- Russian Devaluation .
- Asian Crisis.
- Technology bubble....
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The following table draws the probability that an event will occur
according to the normal distribution versus the number of
standard deviations and Value-at-risk
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No of
Standard Deviations |
Probability
of Occurrence |
Value
at Risk |
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1 |
94 |
600'000 |
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... |
... |
... |
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1.65 |
95 |
1'000'000 |
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1.96 |
97.5 |
1'200'000 |
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2.99 |
99 |
1'410'000 |
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6 |
99.99996 |
> 3 Mio |
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From this, a
six sigma event assumes a 99.99996 %
probability of occurrence. For a daily horizon this translates into one event happening once
every 2'500'000 days. All the recent market slumps i.e. '87 Crash, Mexican
Tequila effect, Russian Devaluation, Asian Crisis and Internet
speculative bubble, .. have all been
six sigma events and they've all happened in the past two decades.
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