brian@braverock.com wrote:
> On Thursday 15 February 2007 06:49, Joe W. Byers wrote:
>   
>>> Hope it helps.
>>>       
>> This helps a bunch and is what I was thinking about doing to modify
>> this function.  I was also trying to be tactful about the assetsStat
>> functions is clearly wrong and all the risk stats that use these two
>> variables are incorrect.
>>     
>
> I also think the modifiedVaR calculation is wrong there, and doesn't take 
> the higher moments   Our functions have a Modified Cornish-Fisher VaR 
> calc that I think is more complete/correct.
>
>   
>>> We're working on packing all our previously released functions now,
>>> but writing .Rd files, standardizing parameter names and ordering,
>>> and collecting sample data, examples, and tests is taking time.
>>>       
>> Do you want some help? I might be able to help with docs, data (I have
>> a lot of energy data), and examples ( teach so I have some good ones ).
>>     
>
> I'll do a little more cleanup by Saturday morning at the latest, and post 
> the code and package tarball for you to take a look at.  In additiona to 
> all the analytics functions, have quite a few chart and (text) table 
> functions that collect performance statistics into groupings that we find 
> useful.
>
> I am wondering whether you've ever done any thinking about co-skewness or 
> co-kurtosis.  I had previously implemented and released functions for 
> these, but I'm now pretty much convinced that they are incorrect (which 
> also makes the standardized systematic functions that rely on them 
> incorrect).  Help sorting that out would be greatly appreciated.
>   
Brian, 
First, I looked at your code and the calculations look good.  My 
knowledge of the higher moment CAPM literature for these moments is that 
the co-skewness is the return on asset i * the square of the return on 
the portfolio. So your Ra and Ri may be reversed.  This I would clarify.

Second, I am not a theoretical statistician, so please bear that in mind 
with the following statements.  Skewness for a single asset is the third 
moment.  Co-skewness of 2 assets is also the third moment or could be 
the second moment of the covariances.  The co-skewness is 
mean((Ri-mean(Ri)*(Rj-mean(Rj)^2) but could also be the 
mean((Rj-mean(Rj)*(Ri-mean(Ri)^2), could it not?  This means that for 
every combination of assets there are 2 co-skewness terms and 2 
co-kurtosis terms.  A matrix of co-skewness or co-kurtosis may not be 
symmetric.  The higher moment CAPM uses asset j as the market and 
investors are concerned with minimizing systematic skewness and kurtosis 
meaning the first equation above it the co-skewness calculation.  
Investors want little negative skewness with the market and small 
positive kurtosis (see COVARIANCE, COSKEWNESS AND COKURTOSIS IN GLOBAL 
REAL ESTATE SECURITIES Kim Hiang LIOW and Lanz C.W.J. CHAN, Department 
of Real Estate, National University of Singapore).  I am not sure but 
these seem to a choice of direction is required in measuring the co 
moments.  The higher moment CAPM chooses the market return and 
systematic skewness and kurtosis.  A hedged portfolio will choose the 
hedging instrument to measure systematic skewness and kurtosis.

This is my thoughts and I have no empirical work on co-skewness or 
co-kurtosis, but we do have R and the ability to download security 
prices to look at these.  I know this probably does not help, but maybe 
we will get some additional comments.

Good luck
Joe

> Regards,
>
>   - Brian
>
>   


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