[R-SIG-Finance] Back testing Expected Shortfall

[Pit Götz]

Hello everyone,

I work at a university in 
germany and we are also currently working on forecasting ES and (of 
course) backtesting of said forecasts.

Over the last few months some students, who are writing their masters
thesis at our chair, had to some litarature research.
Thats why I wanted to give you a very brief overview of their findings:

The
 most widely applied ES backtests seems to be the backtest by McNeil, 
Frey and Embrechts (2000), implemented for example in the rugarch 
package.
(the test was already mentioned here by Alexios)

In addition to the already mentioned tests and the paper by Acerby and
Szekely I wanted to add the following:


A
 Hitsequence based backtest was introduced for by Du, Escanciano (2017).
 As far as I am concerned, this test has not yet been implemented in a 
package, but their code is available online. In a broader view, this 
test is a special case of a spectral measure test by Costanzino, Curran 
(2014), which was then extended to a Basel-Like traffic light approach 
in 2018 (Not sure about the availability of code).

In
 Emmer et al. (2015) it is suggested, that a suitable ES forecast can be
 approximated by only 4 different VaR forecasts. This also suggests, 
that you can backtest ES, forecasted by a model that forecasts both, ES 
and VaR, such as GARCH, by backtesting th 4 different VaR forecasts.
However this approach seems to need more empirical valuation.

I
 also wanted to mention the paper by Gneiting (2011), showing that the 
ES lacks elicitability property. This can lead to complications, when 
you try to backtest the ES itself as a point forecast.However, this 
property can be used to construct a model comparison like backtest as in
 Fissler et al. (2015).

More reacently, a 
quantile regression based approach has been suggested by Coupier, 
Leymarie (2020). I have not yet read said paper and therefore I can not 
tell you anything about it.

I hope that this message gives you some new insights and some usefull
information.

Best regards,
Pit




Research Associate
Martin-Luther-Universität Halle-Wittenberg
Chair of Finance & Banking
 
Große Steinstraße 73 | D-06108 Halle | Germany
Tel 0049 345 5523452

 
>>> Daniel Cegiełka <daniel.cegielka using gmail.com> 10.06.20 21.49 Uhr >>>
śr., 10 cze 2020 o 21:14 alexios galanos <alexios using 4dscape.com>
napisał(a):
>
>
>
> On 6/10/20 11:08 AM, Daniel Cegiełka wrote:
> > śr., 10 cze 2020 o 19:23 Brian G. Peterson <brian using braverock.com>
napisał(a):
> >>
> >> On Wed, 2020-06-10 at 15:08 +0530, Christofer Bogaso wrote:
> >>> I was looking for an idea how banks backtest their models for
> >>> Expected
> >>> Shortfall. Backtesting VaR is well documented but I failed to get
any
> >>> practical idea about backtesting ES.
> >>>
> >>> Any pointer towards the best practice will be really helpful.
> >>
> >> If you are using Normal VaR, then you know the Expected Shortfall
> >> estimate too.
> >>
> >> If you are using a different mechanism, then of course the mean
loss
> >> when the loss exceeds the VaR may be significantly different than
the
> >> Normal ES.
> >>
> >> So, to backetesting...  the newest Basel standard replaces VaR with
ES,
> >> and requires that banks justify their use of a particular ES model
that
> >> they are using to calculate required regulatory capital.
> >
> > In my opinion, there is one aspect that introduces some confusion.
ES
> > (CVaR) is now common, but many people, perhaps out of habit, maybe
for
> > historical reasons, still use the term VaR instead of the correct
name
> > (ES).
>
> Not sure I follow. VaR and ES are different measures. VaR is a
> quantile while ES is the average loss conditional on that quantile
> (i.e. the expected loss conditional that the loss is greater than
> the quantile of the loss distribution).

I agree that these names should not be confused. However, I
encountered that the _name_ "VaR" is used for ES. In my opinion, this
is due to a mental shortcut, or it's a historical > Alexios
>
> >
> > Best regards,
> > Daniel
> >
> >
> >> Regards,
> >>
> >> Brian
> >>
> >>
> >> --
> >> Brian G. Peterson
> >> ph: +1.773.459.4973
> >> im: bgpbraverock
> >>
> >> _______________________________________________
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> >
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questions should go.
> >

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