kurtosis, leptokurtic, platykurtic, excess kurtosis

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.

  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).
  1. 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

3 is correction factor… to make kurtos for normal distribution to zero…3 has to be substracted… think kurtosis as fourth standardized moment …

Thank you all for your valuable comments. 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?

I think Platykutic is more flat and Leptokurtic taller.

  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.

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.

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.

Standard deviation, skewness, and kurtosis are only related in pretty complicated ways. In general, you should think that a distribution can have any combination of those. Negative skewness is bad for the risk manager because it means that you will have a higher percentage of large losses than large gains. A classic example of negative skewness is selling way OTM call options. You collect nickels and hand out sawbucks. Positive kurtosis is bad because it means you have more extreme events than predicted by a normal distribution and your variance estimate. Almost all financial data has excess kurtosis but stock returns are classic. There are simply more big gainers and losers than a normal distribution would predict. Nobody uses the words “platykurtic” or “leptokurtic”.

lepto = fatter tails = more risk.

JoeyDVivre Wrote: ------------------------------------------------------- > Nobody uses the words “platykurtic” or > “leptokurtic”. Greek people might.

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)

chrismaths Wrote: ------------------------------------------------------- > JoeyDVivre Wrote: > -------------------------------------------------- > ----- > > Nobody uses the words “platykurtic” or > > “leptokurtic”. > > Greek people might. If you call a Greek woman leptokurtic, what happens?

You get skewed.



JoeyDVivre Wrote: ------------------------------------------------------- > Nice… Nice? Really? Topic off . So funny! Over imagination… :smiley:

FYI: “nice” there is an American expression that just means “I thought that was funny and clever”