##### Active member
183 0
HI all, there's something mathematical that really confused me: leptokurtosis has more peaked shape than normal distribution, but why when it is more peaked it has fatter tails??? when I read the dynamic hedging book, it says that lower volatility has more peaked shape distribution but higher volatility has fatter tails and less peaked shape of distribution. However, mathematically leptokurtic distribution suggests that extreme stock price movements are more likely to happen than a normal distribution because of the fat tails risk, so which means the shape of leptokurtic distribution signals higher volatility than normal distribution, which goes against what Taleb says in the book, right?

cheers

#### Shakone

##### Senior member
2,458 665
HI all, there's something mathematical that really confused me: leptokurtosis has more peaked shape than normal distribution, but why when it is more peaked it has fatter tails??? when I read the dynamic hedging book, it says that lower volatility has more peaked shape distribution but higher volatility has fatter tails and less peaked shape of distribution. However, mathematically leptokurtic distribution suggests that extreme stock price movements are more likely to happen than a normal distribution because of the fat tails risk, so which means the shape of leptokurtic distribution signals higher volatility than normal distribution, which goes against what Taleb says in the book, right?

cheers

No, not really.

#### numbertea

##### Well-known member
257 9
The distribution is clustered on the mean of the sample with volatility present in the outlying areas that will put off most conservative investors. The overall volatility is not necessarily impacted by the kurtosis level.

Cheers

##### Active member
183 0
No, not really.

thanks.

but why not? Reasonally and mathematically speaking, the lower the peak, the fatter and longer the tails to ensure the area of the shape is 1, and that is what Taleb means: lower volatility leads to high peaked distribution with thinner tails but higher volatility with lower peak has fatter and longer tails.

However, mathematical definition of leptokurtic distribution tells that the higher the peak the fatter the tails and that indicates that movement should have higher volatility, right?

##### Active member
183 0
The distribution is clustered on the mean of the sample with volatility present in the outlying areas that will put off most conservative investors. The overall volatility is not necessarily impacted by the kurtosis level.

Cheers

thanks mate. is kurtosis level relavant to the volatility of volaitlity? I thought kurotisis is a bit related to volatility.

#### Shakone

##### Senior member
2,458 665
thanks.

but why not?

The reason that I didn't give a fuller answer yesterday, is because every time you come back with more and more questions, it occurs to me that you aren't really putting in enough effort to answer some of these questions yourself.

A) Can you plot a normal distribution (like a bell curve) for a chosen mean and variance? Yes or no?

B) Can you plot a leptokurtic distribution?

C) How is volatility related with distribution? i.e. if I have a normally (or lognormally) distributed asset, with a particular volatility, what does its distribution look like?

The plots can be done in EXCEL manually (takes a little bit of time, but not too much and not that hard) or a math program like mathematica will plot this sort of thing very quickly and easily for you. I'd suggest if you can't do A), that you forget Taleb and any other questions and go and learn how to do it.

The above A, B and C gives you the right steps for you to find the answer for yourself! Are you willing to do that?

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##### Active member
183 0
The reason that I didn't give a fuller answer yesterday, is because every time you come back with more and more questions, it occurs to me that you aren't really putting in enough effort to answer some of these questions yourself.

A) Can you plot a normal distribution (like a bell curve) for a chosen mean and variance? Yes or no?

B) Can you plot a leptokurtic distribution?

C) How is volatility related with distribution? i.e. if I have a normally (or lognormally) distributed asset, with a particular volatility, what does its distribution look like?

The plots can be done in EXCEL manually (takes a little bit of time, but not too much and not that hard) or a math program like mathematica will plot this sort of thing very quickly and easily for you. I'd suggest if you can't do A), that you forget Taleb and any other questions and go and learn how to do it.

The above A, B and C gives you the right steps for you to find the answer for yourself! Are you willing to do that?

thanks for your advice mate, I will try, but to be honest, I have never plotted bell curve in a spreadsheet, how to do that?:smart:

#### Shakone

##### Senior member
2,458 665
thanks for your advice mate, I will try, but to be honest, I have never plotted bell curve in a spreadsheet, how to do that?:smart:

You can lead a horse to water...

Even google will have links to show you how to do that, 10-15 minutes tops. So as I suspected, you're not making enough effort to understand this stuff at all. Good luck, but I can't help people that won't help themselves.

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##### Active member
183 0
You can lead a horse to water...

Even google will have links to show you how to do that, 10-15 minutes tops. So as I suspected, you're not making enough effort to understand this stuff at all. Good luck, but I can't help people that won't help themselves.

understand, thanks a lot mate.

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