[R-SIG-Finance] VaR again

[Megh Dal]

Hi Brian, Thank you so much for this kind reply. I understand that, in VaR calculation all Kurtosis, skewness need to be incorporated and therefore some other fat-tailed distribution like t-dist can be better alternative of Normal distribution. However here my purpose is little bit different. Here my goal is not to calculate VaR most accurately using some complex distribution/modelling (however you also agree that a sophisticated model does not guarantee a better estimate) rather to get a overall view of total risk of my portfolio and contribution of each component on that.

Here you suggested to calculate VaR in percentage. however I am not sure how to do it in current scenario because, Currency exposure is not "explicit" here. Am I missing something detail here? Can you please be more specific? Any reproducible example and/or web resources will be truly helpful to me.

Thanks,


--- On Wed, 4/29/09, Brian G. Peterson <brian at braverock.com> wrote:

> From: Brian G. Peterson <brian at braverock.com>
> Subject: Re: [R-SIG-Finance] VaR again
> To: "megh" <megh700004 at yahoo.com>
> Cc: r-sig-finance at stat.math.ethz.ch
> Date: Wednesday, April 29, 2009, 6:26 PM
> megh wrote:
> > Hi all Gurus, I have a problem to quantify the
> riskiness of a typical
> > position wherein this position is in some foreign
> country. Let me be more
> > specific on my problem.
> > 
> > Say I am a British investor and taken a position in
> NYSE, say in ATT (AT&T).
> > Therefore apart from the risk due to fluctuation in
> stock quote of that, I
> > am exposed of additional risk due to fluctuation in
> USD/GBP exchange rate. I
> > intend to calculate the VaR of this position in GBP.
> Here I used monte carlo
> > simulation approach to find that, which is as follows,
> please see the R code
> > :
> > 
> > # calculation of risk on an unit position
> > att <- 25.67                                       
>                              # last traded price of AT&T
> in USD
> > usdgbp <- 0.68366                                  
>                          # last quote for USDGBP   vcv <-
> matrix(c(5.33727E-05, 2.56709E-05, 2.56709E-05,0.000176556),
> 2)                                                          
>                                      # VCV matrix for
> AT&T and USDGBP
> > 
> > # We simulate 1-day ahead stock price and ex. rate
> assumig a Bi-variate
> > normal dist. with above VCV structure
> > library(mnormt)
> > simu <- exp(rmnorm(10000,
> c(log(25.67),log(0.68366)), vcv))
> > simu.pos.val <- apply(simu, 1, function(X)
> X[1]*X[2])                 #
> > Simulated value of my position in USD
> > abs(quantile(simu.pos.val, 0.05) - att*usdgbp)        
>       # VaR (in GBP)
> > in terms of Maximum possible loss
> > 
> > Upto this point I am OK. However next thing
> automatically comes is that what
> > is contribution of Stock and Ex. rate in total risk,
> i.e. Dissecting the
> > risk. Can anyone please guide me how to do this for
> n-asset portfolio (of
> > this kind) under MCS framework?
> > 
> > Thanks
> >   
> 
> My first comment is that your Monte Carlo simulation makes
> the
> assumption that the simulation is normally distributed. 
> Currency
> markets are almost all much fatter tailed than that.  You
> might want to
> consider a different VaR method that takes the fat tails
> into account.
> Many people believe that because Monte Carlo VaR methods
> are
> "non-parametric" that there are no distributional
> assumptions built in,
> but a quick glance at your code should make it obvious that
> this is not
> true, and how dangerous it is.
> 
> Next, If you want to separate the two components, and do it
> for a large
> portfolio that may be mixed in different currencies  and
> instrument
> types, you should be calculating VaR in percentages, using
> returns.
> Then you calculate the market risk to the
> portfolio/instrument and the
> currency risk to the portfolio/instrument separately. You
> can always
> turn the aggregate number back to dollars/pounds/whatever
> if you
> need/want to.  To get a univariate VaR number, you can
> aggregate the
> positions by weight and calculate a univariate return for
> the portfolio
> in a given currency, from which VaR may be taken (but see
> below on
> portfolio VaR).
> 
> I think it is rather important to look at the actual
> observed (or
> estimated) variance, skewness, and kurtosis of each
> instrument in
> working out the VaR for that instrument, via simulation or
> any other
> method.  Then, you can separately work out the currency
> risk to your
> portfolio once you aggregate the risks of each position in
> a given currency.
> 
> Finally, if you are doing this in a portfolio context, the
> co-moments of
> the instruments have a massive effect on the total
> portfolio risk.
> There is a large literature on "Portfolio VaR" or
> "Component VaR" that
> discusses this and its solution. Component VaR is
> subadditive, so you
> can dissect the risk as you ask for above.
> 
> Regards,
> 
>    - Brian
> 
> 
> -- Brian G. Peterson
> http://braverock.com/brian/
> Ph: 773-459-4973
> IM: bgpbraverock