QQ chart

[Kavita.bhangdia]

Hi David,
apologies but I am having a hard time interpreting a QQ plot.

Please can you help me with the same? How do you know the skewnss, kurtosis and fat tails looking at QQ plot

Thanks,
Kavita

 

[brian.field]

If the QQ plot is linear, then this suggests that the actual data and the specified distribution are in line....meaning the the specified distribution is a good candidate for the data. At the lower left and upper right ends of the QQ plot, you need to pay attention to the slope of the line. If I remember correctly, a steep slope at these places implies fatter tails in the data than assumed in the specified distribution. You can also get a sense of the mean or location of the appropriate candidate distribution by looking at the intercept of the QQ line. Similarly, the slope of the QQ line provides an indication of the spread or variance/standard deviation of the appropriate candidate distribution.

So, assume we have a random sample of data that are taken from a normal(0,1) distribution and we compare this data to a normal(0,1) distribution.
The QQ plot should be linear with a slope of 1 and pass through the point (0,0).

 

[Kavita.bhangdia]

Hi Brian,
That helps a lot.. Thanks!

Kavita

 

[brian.field]

Sure - do you have the GARP
books? This information is in chapter one of topic 5, market risk.

 

[Kavita.bhangdia]

Hi Brian,
No I do not have the GARP books... But i did download the Kevin dowd book from internet.. I could not find the information though. May be it was a old edition.
I am pretty much sticking to BT as the study material.

Thanks,
Kavita

 

[brian.field]

Going through some questions now @Kavita.bhangdia - if you look at the question set for Dowd, question 74.2's solution mentions that SKEW CAN BE VISUALIZED AND MANIFESTS AS AN ARCHED PATTERN.

 

[David Harper CFA FRM]

The first question in the 2016 P2 exam is about QQ plot (see below). Note that you need to be mindful of axes: what GARP here called "Normal Quantiles" (per assigned Dowd) is aka "Theoretical Normal Quantiles" and their Empirical is aka "sample." In the example below, the straight line includes the point [x = -4, y = -4] such that the normal "theoretical" quantile expects only 0.00317% = NORM.S.DIST(-4, true) of the sorted actual data to be less than the -4.0 standard deviations below mean if the actual sample is perfectly normal. But in the actual empirical sample, that same proportion of the actual data (ie, 0.00317%) falls about about the -5 standard deviations (this is standardized). In short, for a an extremely small given probability (p%), the actual data is more standard deviations away from (below) the mean compared to the normal, which indicates a fat tail. It takes a little bit of time to grok, but it's really helpful reinforcement of the quantile-probability relationship. As Dowd says, VaR is just a quantile; e.g., -1.645 quantile = 5% probabilty. Also, keep in mind, any theoretical distribution can be used. Thanks,

 

[Kavita.bhangdia]

Hi David,

If the actual data is more standard deviations away from from the normal, then it should be thin tailed and not fat tailed? I am having trouble visualising this..

Please correct me if I am wrong..

Thanks
Kavita

 

[Deepak Chitnis]

Hi @Kavita.bhangdia, actual data or real world data is far different than normal data or distribution. It has fat tails (skewed) and heavy peakdness (kurtosis>3). In actual data standard deviation away from normal means that it has more volatility. So it performs fat tails and heavy peakdness. Hope that helps.
Thank you

 

[ami44]

Hi David,

If the actual data is more standard deviations away from from the normal, then it should be thin tailed and not fat tailed? I am having trouble visualising this..

Hi Kavita,

I made you a drawing with the pdf of a normal distribution and a student t distribution with 4 degrees of freedom.



I marked the 2.28% quantile for both distributions.
As you can see, for the student t distribution with the fat tail, the same quantile is further away from the middle than it is for the normal distribution.

 

[Kavita.bhangdia]

Thanks Ami44.. that was most helpful.. you couldn't have been more clearer..

Regards,
Kavita

 

[Kavita.bhangdia]

Hello David,
How do we check for Skegness (positive or negative) by looking at Qq plot..?

Thanks
Kavita

 

[Deepak Chitnis]

Hi @Kavita.bhangdia, please refer to http://emp.byui.edu/BrownD/Stats-intro/dscrptv/graphs/qq-plot_egs.htm great explanation. Hope it will help you.
Thank you

 

[Kavita.bhangdia]

Thanks Deepak Chitnis, that was a really good link.

Regards,
Kavita

 

[David Harper CFA FRM]

I agree with @Kavita.bhangdia, this is a really good link, thank you @Deepak Chitnis