**"Fat tails" in finance**

"Fat
tails" is a statistical phenomenon,
it appears in financial data tas well as in
other fields that involve human activity.

You should understand that this phenomenon has no mathematical solution, i.e. we cannot eliminate this phenomenon using some smart or very smart algorithms. Take it as "Memento mori" - the fact we have to accept whether we like it or not. This is the environment we live in.

Briefly "fat tails" phenomena may be
formed
this way: the power of accidental factor (or we think that this factor is
accidental) is
much more higher than your common
sense says you.

Here are some
examples:

**#1 impossible big
drop:** I would like to start with a classical example, example that
is responsible (as I understand) for the name "fat tails".

We ask ourselves: how often this huge drop may happen in the future, from statistical point of view?

**#2 impossible big win/loss
ratio:** This is a model calculated with Timing Solution software. The Efficiency test shows us the
information regarding trades around these vertical lines; we
make 14 long winning trades versus 2 loss trades, 87% winning trades:

Let's analyze this
phenomenon from the point of view of the normal distributed statistics which is
based on one simple idea: we dice a coin; if it is a
head - I win; if tail - I lose. I diced that coin 11 times, and I win 10 times
losing just one time. Would you like to use this coin for your play? Definitely yes, this coin
has provided much more winning cases for me, you would expect that it will work
the same way for you, why not?. But... Common sense tells us that something is wrong with that coin, it likes
"heads" more than "tails". This is not an occasional fact; the probability
that it is not some chance is 100x(1-1/2^9)=99.8%.

Now let's go back to our stock market example. Can we use the above strategy to trade using our own trading account? Would you put your money on it? Your common sense should tell you: there is some pitfall there. And your common sense is right: in our example we analyze the price chart since 2012 when the market was in a very strong trend.

If we extend the analyzed period to cover uptrend and downtrend zones, our results become not so impressive - 32 ups versus 24 downs:

You see, in these two examples we tried to apply standard statistical formula to estimate financial parameters and in both cases we failed in our estimations. This is why I wrote this class - be careful when somebody uses standard statistical formula.

One more example: somebody has invented a trading system that makes 100 trades, and 70 of them are winning trades. With the probability of 99.5%, this is not an occasional fact. However, it does not mean that the next 100 trades will be so good.