unconditionalT
Unconditional expected shortfall (ES) backtest by Acerbi-Szekely with critical values for t distributions
Description
runs the unconditional expected shortfall (ES) backtest by Acerbi-Szekely (2014)
using precomputed critical values and assuming that the returns distribution is
t with 3 degrees of freedom.TestResults
= unconditionalT(ebt
)
adds an optional name-value pair argument for TestResults
= unconditionalT(ebt
,Name,Value
)TestLevel
.
Examples
Run an Unconditional t
ES Backtest
Create an esbacktest
object.
load ESBacktestData ebt = esbacktest(Returns,VaRModel1,ESModel1,'VaRLevel',VaRLevel)
ebt = esbacktest with properties: PortfolioData: [1966x1 double] VaRData: [1966x1 double] ESData: [1966x1 double] Time: [1966x1 double] PortfolioID: "Portfolio" VaRID: "VaR" VaRLevel: 0.9750
Generate the TestResults
report for the unconditional t
ES backtest that assumes the returns distribution is t
with 3 degrees of freedom.
TestResults = unconditionalT(ebt,'TestLevel',0.99)
TestResults=1×9 table
PortfolioID VaRID VaRLevel UnconditionalT PValue TestStatistic CriticalValue Observations TestLevel
___________ _____ ________ ______________ ________ _____________ _____________ ____________ _________
"Portfolio" "VaR" 0.975 accept 0.018566 -0.38265 -0.42986 1966 0.99
Input Arguments
ebt
— esbacktest
object
object
esbacktest
(ebt
) object, which
contains a copy of the given data (the PortfolioData
,
VarData
, and ESData
properties) and all combinations of portfolio ID, VaR ID, and VaR levels
to be tested. For more information on creating an
esbacktest
object, see esbacktest
.
Name-Value Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name
in quotes.
Example: TestResults =
unconditionalT(ebt,'TestLevel',0.99)
TestLevel
— Test confidence level
0.95
(default) | numeric value between 0.5
and
0.9999
Test confidence level, specified as the comma-separated pair
consisting of 'TestLevel'
and a numeric value
between 0.5
and 0.9999
.
Data Types: double
Output Arguments
TestResults
— Results
table
Results, returned as a table where the rows correspond to all combinations of portfolio ID, VaR ID, and VaR levels to be tested. The columns correspond to the following information:
'PortfolioID'
— Portfolio ID for the given data.'VaRID'
— VaR ID for each of the VaR data columns provided.'VaRLevel'
— VaR level for the corresponding VaR data column.'UnconditionalT'
— Categorical array with categories 'accept' and 'reject' indicating the result of the unconditional t test.'PValue'
— P-value of the unconditional t test, interpolated from the precomputed critical values under the assumption that the returns follow a standard normal distribution.Note
p-values <
0.0001
are truncated to the minimum (0.0001
) and p-values >0.5
are displayed as a maximum (0.5
).'TestStatistic'
— Unconditional t test statistic.'CriticalValue'
— Precomputed critical value for the corresponding test level and number of observations. Critical values are obtained under the assumption that the returns follow a t distribution with 3 degrees of freedom.'Observations'
— Number of observations.'TestLevel'
— Test confidence level.
Note
For the test results, the terms 'accept'
and 'reject'
are used for convenience.
Technically, a test does not accept a model; rather, a test
fails to reject it.
More About
Unconditional Test by Acerbi and Szekely
The unconditional test (also known as the second Acerbi-Szekely test) scales the losses by the corresponding ES value.
The unconditional test statistic is based on the unconditional relationship
where
X
t is the portfolio outcome, that
is, the portfolio return or portfolio profit and loss for period
t.
P
VaR is the probability of VaR
failure defined as 1-VaR level.
ES
t is the estimated expected
shortfall for period t.
I
t is the VaR failure indicator on
period t with a value of 1 if
X
t < -VaR, and 0
otherwise.
The unconditional test statistic is defined as:
The critical values for the unconditional test statistic, which form the basis
for table-based tests, are stable across a range of distributions. The esbacktest
class runs the
unconditional test against precomputed critical values under two distributional
assumptions: normal distribution (thin tails) using unconditionalNormal
and t distribution with 3
degrees of freedom (heavy tails) using unconditionalT
.
References
[1] Acerbi, C., and B. Szekely. Backtesting Expected Shortfall. MSCI Inc. December, 2014.
Version History
Introduced in R2017b
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