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Back testing

11 messages · leo sea, Daniel Cegiełka, Brian G. Peterson +4 more

Original
Christofer Bogaso
# 
Hi,

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.

Thanks,
leo sea
# 
Hi
I am also interested in in ES backtesting.
Good idea
Thanks

T?l?chargez Outlook pour Android<https://aka.ms/ghei36>
Brian G. Peterson
#
On Wed, 2020-06-10 at 15:08 +0530, Christofer Bogaso wrote:
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.

To the best of my knowledge, the most widely used and cited approaches
are outlined here:

https://dlu-umich.github.io/docs/Research_Insight_Backtesting_Expected_Shortfall_December_2014.pdf

Generally, I like the overall methodology presented by this paper.  The
only complexity is the need to store (or be able to recalculate) the
full distribution of the tail.  I don't see this as a giant roadblock,
since the tail distribution contains additional information of interest
anyway, the shape of the tail is useful in model validation and
fitting, and disk is cheap.

The models presented in the reference above, while not to my knowledge
directly implemented in R, should be able to be constructed from data
in the recent R packages by Ardia et. al. GAS:

https://journal.r-project.org/archive/2018/RJ-2018-064/RJ-2018-064.pdf

and MSGARCH:

https://www.sciencedirect.com/science/article/pii/S0169207018300840

Regards,

Brian
Daniel Cegiełka
# 
?r., 10 cze 2020 o 19:23 Brian G. Peterson <brian at braverock.com> napisa?(a):
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).

Best regards,
Daniel
Brian G. Peterson
#
On Wed, 2020-06-10 at 20:08 +0200, Daniel Cegie?ka wrote:
VaR and ES (CVaR, ETL) are mathematically related to each other, since
ES is the mean loss when the loss exceeds the VaR quantile.

Confusingly, one of the permissible tests of a bank's ES model under
Basel is the 'VaR test' which measures the number of VaR exceeding
events, and the degree of the loss eceeding VaR to evaluate whether the
*ES* model is likely valid.  This test has been widely criticized, and
should likely be avoided as anything other than a quick check of
possible suitability.

Regards,

Brian
Alexios Ghalanos
#
On 6/10/20 11:08 AM, Daniel Cegie?ka wrote:
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).

Regards,

Alexios
Daniel Cegiełka
# 
?r., 10 cze 2020 o 21:14 alexios galanos <alexios at 4dscape.com> napisa?(a):
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 habit. Such
imprecise use of the names often leads to misunderstanding.

Daniel
2 days later
Christofer Bogaso
# 
Thanks Brian, the resources are really helpful.

However I am not sure if I fully understood the implementation part of
the MSCI's approach. It basically defines different test-statistics
r.g. Z1, Z2, etc. For Z1, it asserts that under null, the expected
value for Z1 will be zero. I failed to see what distribution would it
take under H0, so that I can complete the significance testing and/or
defining some confidence interval under null.

Ideally, with realised daily PnL and forecasted ES, we will have a
time series of Z1 - if my understanding is perfect. To carry out if
E[Z1] = 0, can I do some t-test or some non-parametric test for
testing mean =0?

I think, this should be valid as only assumption was that PnL has to
be independent, may not be identically distributed. My only concern
is, can I use an ordinary significance table for t-test? I am little
concerned because, testing would be done on Z1's values, which are
calculated values, not the original dataset. So a non-parametric test
may be more appropriate.

Any pointer on above thinking is highly appreciated.
On Wed, Jun 10, 2020 at 5:21 PM leo sea <leosea at outlook.com> wrote:
1 day later
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-Universit?t Halle-Wittenberg
Chair of Finance & Banking
 
Gro?e Steinstra?e 73 | D-06108 Halle | Germany
Tel 0049 345 5523452
?r., 10 cze 2020 o 21:14 alexios galanos <alexios at 4dscape.com>
napisa?(a):
napisa?(a):
any
loss
the
ES,
that
ES
for
name
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
questions should go.
questions should go.
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Alexios Ghalanos
# 
Hi Pit and thanks for sharing.

I was not aware of the Gneiting paper, but the Gneiting and Raftery 
(2007) paper discusses scoring rules and their mean interval score (MIS) 
has been used in the M4 competition (implemented in the greybox package).

Best,

Alexios
On 6/15/20 7:34 AM, Pit G?tz wrote:
1 day later
Sebastian Bayer
# 
Hi all,

We have been working on an ES backtest that only requires expected
shortfall forecasts (no quantiles or other inputs) besides the returns.
This is in striking contrast to all other available backtests.

The paper is going to be published in the next few days in JFEC. This is
the abstract:

This paper introduces novel backtests for the risk measure Expected
Shortfall (ES) following the testing idea
of Mincer and Zarnowitz (1969). Estimating a regression model for the ES
stand-alone is infeasible, and thus,
our tests are based on a joint regression model for the Value at Risk and
the ES, which allows for different
test specifications. These ES backtests are the first which solely backtest
the ES in the sense that they only
require ES forecasts as input variables. As the tests are potentially
subject to model misspecification, we
provide asymptotic theory under misspecification for the underlying joint
regression. We find that employing
a misspecification robust covariance estimator substantially improves the
tests? performance. We compare our
backtests to existing joint VaR and ES backtests and find that our tests
outperform the existing alternatives
throughout all considered simulations. In an empirical illustration, we
apply our backtests to ES forecasts for
200 stocks of the S&P 500 index.

You can find the last working paper version here:
https://arxiv.org/pdf/1801.04112.pdf
We also have an R package:
https://cran.r-project.org/web/packages/esback/index.html
Here's an example how to apply the backtest:
https://github.com/BayerSe/esback#examples

Regards

Am Mo., 15. Juni 2020 um 17:01 Uhr schrieb alexios galanos <
alexios at 4dscape.com>: