David,

I HAVE NOT BEEN ABLE TO COME UP WITH THE NUMBERS THAT HE GOT FOR 3.47 AND 3.48

Hi Frank,

Me neither! See attached XLS. In prepping the notes, 3.46 & 3.48 frustrated me b/c i could not get his answer. But we’ve since discovered more than a few errors in Gujarati so I gave up… There is an errata, but strangely, even it is incorrect, it says “Table 3-3. Sample var (Y) should be 368,871 instead of 368,872” which is wrong!

Here is my XLS from this:
gujarat sample skew & kurt

Note: I was satisfied that i could reconcile with Excel’s SKEW() and KURT(). Note: under Gujarati, I got 0.467 and 1.546.

Also note: re: 3.47 and 3.48, I assume you realize, are not the skew and kurtosis per se: they must be divided by, respectively, the sample standard dev ^3 and ^4. This is called normalizing the moments.

The key takeaway is that sample skew (e.g.) is sample third moment divided by cube of sample standard deviations.

mean: 1st moment
variance: 2nd moment (such that std dev is a normalized 2nd moment)
skew: function of [3rd moment], not 3rd moment per se; i.e., a normalized 3rd moment
kurt: function of [4th moment], not 4th moment per se; i.e., a normalized 4th moment

wikipedia is helpful on this.

So you can see, the general form is

nth moment / standard dev ^ (n)

David

Thank you David.  The spread sheet will not open.

Frank

Hi Frank,

The link is to an editgrid, which seems to be working.
The editgrid is pretty universal https://wiki.editgrid.com/display/helpcentre/Supported+Browsers
can you check your browser?

David

David,

In you screen cast you show Skewness as u^3/SD^3 and Kurtosis as u^4/SD^4. 
When I do it that way I don’t get the same numbers as when I to it the long way ie (x-u)^3/SD^3

Frank

do you refer to p 53 and 54? if so, just ignore the u^3 (notice, i didn’t speak to them, u^3 is shorthand for 3rd moment). if you don’t mean 53 and p 54, i don’t know what you mean. It is as we have above, in the XLS. And in Gujarati 3.39 and 3.40.

if you have a doubt like this, sometimes it may help to look at the XLS:
https://www.editgrid.com/bt/frm_2008/gujarati_3-3

David

David,

It was 52 or 53.  I did go to the spread sheet and could not do it.  It would have been a nice short cut.  I understand the notation now.  Thank you

frank

Hi David,
Gujarati Pg.67 says leptokurtic Kurtosis has slim or long tail. You mentioned in recent AIMs discussions as leptokurtic having fat tails? Which is true? Pls. give one real world example each for leptokurtic and platykurtic.

Thanks for the briefcasts. We should appreciate(you) that it must be very tough to be so detailed on all three parts of Risk subject(i.e. Market, Credit and Rest all).

Also, if possible, can you pls. briefcast on Metalgesellschaft, I mean, audio,video and excel with assumed numbers.
Thanks
Regars
mudaltiru

Hi mudaltiru,

Re kurtosis, you raise an excellent point (a prior discussion thread here)

Traditionally (for as long as I can remember), we say “asset returns tend to be non-normal with fat tails. They exhibit leptokurtosis.” You will see the authors (e.g., Jorion) refer to leptokurtosis = fat tails. What really matters for us is that asset returns tend to follow distribution with leptokurtosis; i.e., kurtosis > 3 or excess kurtosis > 0

I currently believe that “fat tails” is an ambiguous term. Gujarati is correct that leptokurtosis = long tails.

But (IMO) the most accurate is: Leptokurtosis = HEAVY TAILS (as fat/skinny can be interpreted wrongly; wrong is a vertical perspective). One my favorite authors for his precision is Kevin Dowd, and he uses “heavy tails.”

A good example of leptokurtosis is student’s t (the distribution we use to test the sample mean when the population variance is unknown). Compare the normal at 99% confidence to the student’s t:

Normal @ 99% = NORMSINV(99%) = 2.33 standard deviations
Student’s t @ 99% = TINV(1%, 20 degrees of freedom; just for example) = 2.85 standard deviations

The excess kurtosis of the student’s t = 6/(20-4) = 0.375 or kurtosis = 3.375.
The student’s t always gives leptokurtosis and, here is the point: the 1% significance deviation is 2.85 versus 2.33. The issue is not fat versus skinny but rather, the student’s t implies gives greater deviation for the same significance. You can see the tail is skinnier but at the same time, it has more density (is heavier) in the extremes.

Thanks for your kind feedback. I am really glad you appreciate the service at BT
Also, I love the name “briefcasts.” That is a wonderful term!!

Yes, I will add Metal. to the briefcast schedule.

David