[Fwd: Performance Analytics internal multivariateMoments calculations]

-------- Forwarded Message --------
Subject:     Re: [Fwd: [R-SIG-Finance] Performance Analytics internal 
multivariateMoments calculations]
Date:     Tue, 23 May 2017 02:10:21 +0000
From:     Dries Cornilly <dries.cornilly at kuleuven.be>
To:     Brian G. Peterson <brian at braverock.com>



Also, Joe Byers did not run in the same issue. He is confusing the 
kurtosis and the excess kurtosis.

The function ?kurtosis.MM? in ?mVaR.MM? does not return the excess 
kurtosis, but rather m4 / sd^4 and hence the -3 still needs to be 
done. His example where he claims that GVaR and MVaR should return the 
same is not correct. He uses 0 as fourth order moment in the input, 
which is only valid for a degenerate distribution. The input for 
equality should rather be
GVaR(w, Mean, Stdev, .95)
MVaR(w, Mean, Stdev, 0, 3 * Stdev^4, .95) # note the difference in 
fourth moment.
For a Gaussian the excess kurtosis is zero, or equivalently, the 
standardised fourth moment (m4 / sd^4) is equal to 3, but the fourth 
moment of a Gaussian is not equal to zero, it is equal to a function 
of the variance.

Additionally, he will generate problems when using the skewness input 
as in his ?corrected? version. The function ?mVaR.MM? takes the raw 
third order central moment(s) and standardises in the function itself, 
whereas his altered function will standardise again on the already 
standardised input and hence give a wrong result.

Regards
Dries


On 22 May 2017 at 20:32:04, Dries Cornilly (dries.cornilly at kuleuven.be 
<mailto:dries.cornilly at kuleuven.be>) wrote:

I showed it to Joshua this morning and it seemed like a pure integer
problem.

library(PerformanceAnalytics)
X <- matrix(1:12, ncol = 3)
M3.MM(X) # this one behaves strangely (at this time, X is still filled
with integers)
M3.MM(X * 1.0)  # multiplying by 1.0 to cast to double provides a zero
coskewness matrix at it should

However, I do have some code replicating the modified VaR and modified
Expected shortfall using simplified formulas (coming from a working
paper of Doug Martin if I recall correctly). I was going to suggest to
replace it since the output is identical and it seems more stable to
compute. When I have the alternative moment estimators using the
unique elements, it might be a good idea to replace the inside of mVaR
and mES using the multivariate moments to work with the vector of
unique elements (and extract the unique elements if the full matrices
are given). This will be a good memory improvement, especially when
computing the portfolio moments for mVaR and mES and the derivatives
needed for the component VaR and component ES.


Regards
Dries


On 22 May 2017 at 16:20:22, Brian G. Peterson (brian at braverock.com
<mailto:brian at braverock.com>) wrote:

Looks like Joe Byers ran into the same issue you found earlier today.

-- 
Brian G. Peterson
http://braverock.com/brian/
Ph: 773-459-4973
IM: bgpbraverock

-------- Forwarded Message --------
From: Joe W. Byers via R-SIG-Finance <r-sig-finance at r-project.org>
Reply-to: "Joe W. Byers" <ecjbosu at aol.com>
To: r-sig-finance at r-project.org
Subject: [R-SIG-Finance] Performance Analytics internal
multivariateMoments calculations
Date: Mon, 22 May 2017 15:59:59 -0400

All,


I have carved on all methods in MultivariateMoments.R so I can all
them
directly

I am working on the modified var calculations.  I ran the mVaR.MM on
my
data and the results were odd.  I reran setting skewness and kurtosis
to
0 to compare with GVAR.MM.  Still questions.  I have the following
example

#test for sigfinance
w = 1000000;
Mean = 0.0001898251;
Stdev = 0.01612464;
ExKurtosis = 3.946156;
Skewness = -0.1373454;

GVaR = GVaR.MM(w,Mean,Stdev, .95)
GVaR
MVaR = mVaR.MM(w,Mean,Stdev, 0,0, .95);
#shoud be equal to GVaR
GVaR==MVaR
MVaR

mVaR.MM does not return the GVaR.MM.  I found the exkurt was not zero
as
I think it should be.  I remove the - 3 from that line and exkurt
became
zero and mVaR.MM == GVaR results.  I have included this modified
version
of mVaR.MM below and continued the test.  Is this an issue or am I
missing something?


#corrected exkurt calc
mVaR.MM1 = function(w, mu, sigma, M3, M4, p ){
   skew = skewness.MM(w,sigma,M3);
   exkurt = kurtosis.MM(w,sigma,M4); #removed -3
   z = qnorm(1-p);
   zc = z + (1/6)*(z^2 -1)*skew
   Zcf = zc + (1/24)*(z^3 - 3*z)*exkurt - (1/36)*(2*z^3 - 5*z)*skew^2;
   return ( -multivariate_mean(w,mu) - Zcf*StdDev.MM(w,sigma) )
}

#call revised mVAR.MM with m3 and m4 equal 0
MVaR1 = mVaR.MM1(w,Mean,Stdev, 0,0, .95);
#shoud be equal to GVaR
GVaR==MVaR1
MVaR1

#with m3 and m4 not zero
MVaR1 = mVaR.MM1(1, Mean, Stdev, Skewness, ExKurtosis, .95);
MVaR1

MVaR1 = mVaR.MM1(w, Mean, Stdev, Skewness, ExKurtosis, .95);
MVaR1

This result still looks strange and would appreciate any thoughts,
with
1 or w weights, I get the same just scaled.  Note this is real
commodity
data with all statistics generated by table.Stats.

Thanks

Joe


-- 
*Joe W. Byers*

[[alternative HTML version deleted]]