# Thread: kurtosis, leptokurtic, platykurtic, excess kurtosis

1. ## kurtosis, leptokurtic, platykurtic, excess kurtosis

kurtosis, leptokurtic, platykurtic, excess kurtosis

Date: August 27, 2008 05:04AM

Hi everybody,

It taken time for me to read over again the study note about the skew and kurtosis (ss2) but i still get some confusing as following. Pls help me make it clear.

1. Why the computed kurtos for all normal distributions is three? I don't understand why it must be three.

2. Is that right if i say leptokurtic and platykurtic are excess kurtosis?

3. Why it is said that "value of sample skew in excess of 0.5 in absolute value indicate significant levels of skewness"?

Thanks a lot for your kindly help.

Thu Thuy

2. Date: August 27, 2008 06:37AM

1. For CFA exam it just is. If you want to go into it the why (not needed for exam unless chnaged) you'd need to do some calculus iirc (my maths degree is a long time ago I can't do it know).

3. Date: August 27, 2008 08:50AM

2. Leptokurtic has a kurtosis greater than 3. Platykurtic has a kurtosis less than 3.

A normal distribution has an excess kurtosis of 0 or kurtosis of 3.

*The way I remember it is kurtosis of normal =3, excess of 0.
If you lept in the air . . . ie. higher . . . it would be leptokurtic.

3. Positive skew looks like you pulled the tail out longer to the right and has Mean > Median > Mode

4. Date: August 27, 2008 09:16AM

3 is correction factor...

to make kurtos for normal distribution to zero...3 has to be substracted.....

think kurtosis as fourth standardized moment ....

5. Date: August 27, 2008 10:20AM

I just have two more questions would like to ask you about the skew and kurtosis relation.

1. If a normal distribution has skewness of zero >>> Has it leptokurtic or platykurtic?

2. It is said that greater positive kurtosis and more negative skew in return distributions indicates increased risk.

Does it mean the more leptokurtic and more negative skew indicates increased risk?

Platykurtic is negative excess kurtosis, right?

3. The more leptokurtic, the flatter tail it is. And the more high-risk of investment?

Thu Thuy

6. Date: August 27, 2008 12:30PM

I think Platykutic is more flat and Leptokurtic taller.

7. Date: August 27, 2008 01:12PM

1. If a normal distribution has skewness of zero >>> Has it leptokurtic or platykurtic?

skewness of zero?? then no kurtosis is present...

regarding second question...

For example, when looking at past stock returns, analysts will want to determine the likelihood of extreme returns (or losses) in the future. If past stock data results in a platykurtic distribution, analysts will expect more volatility in future returns. This means that there is a higher probability than usual for extreme price movements to occur.

8. Date: August 27, 2008 01:12PM

Leptokurtic and negative skew do not neccessarily go together, they are different things.

Leptokurtic is slender and more peaked (taller). It also has a greater % of small and very large deviations, so there are lots of outliers. This would generally be considered more risky.

9. Date: August 27, 2008 01:19PM

kurtosis is used by many analysts in pairs trading. they will keep an eye on standard deviation from last 3-4 year's data. and then they ll decide when to go short or long based on this.

10. Date: September 3, 2008 09:07AM

It makes more sense if you look at the pictures in the books. The tails are fatter for the leptokurtic because there are more outliers (small infrequent gains/losses, large frequent gains/losses)

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