[R-SIG-Finance] VaR.Beyond() etc.

[Brian G. Peterson]

Murali Menon wrote:
> I see that the definition of VaR.Beyond() in the PerformanceAnalytics 
> package includes a parameter called periods, to determine the expected 
> shortfall across various time horizons. However, it is not used within 
> the function, at least not in PerformanceAnalytics_0.9.6, which is what 
> I have. Has this been remedied?
>  
> Likewise, does it make sense to have a multiperiod VaR method as well?

First of all, we're including new CVaR/ES functions in 
PerformanceAnalytics 0.9.7 that provide more functionality than the 
original VaR.Beyond function provides, including an implementation of a 
Modified Cornish Fisher Expected Shortfall that we developed for an 
upcoming paper in the Journal of Risk (to appear Winter 2008).

PerformanceAnalytics 0.9.7 will be released as soon as we finish the 
documentation for a few of the new functions.

> I'm not sure how to incorporate the notion of horizons into the 
> computation or I'd have done this myself. Is there any paper that helps 
> to explain the concept?

There are multiple papers on this topic, which I'll look up later if I 
have time, but I'll summarize some of the relevant approaches here.

The simplest methods incorporate some sort of decay function.  If you 
are assuming a normal distribution, as Gaussian parametric VaR and ES 
do, then you would multiply the single period VaR number by the square 
root of the number of periods to scale over, as is commonly done with 
variance.  This is the method that was implemented in an earlier version 
of the VaR.Beyond function, although I believe I took it out because it 
was having issues. (I'm also unconvinced of the accuracy of this 
approach, although it is most likely true if you assume a Gaussian 
distribution)

Another major method looks at conditional or unconditional risk against 
one or more factors over some period, and scales the risk metric that 
way.  (I think this is likely the most accurate, but also the most 
difficult approach)

A third method is typically based on Monte Carlo simulation, where the 
multiperiod risk can be taken directly as a quantile of the simulated 
results.  (This is the method most often employed by banks as part of 
their approach for calculating regulatory capital, in my experience.)

There have also been papers about using GARCH models to scale risk 
measure to multiple periods, but I recall reading a paper by Embrechts 
and McNeil that called that methodology into question.

Regards,

   - Brian