Basic expected shortfall (ES) report on failures and severity
returns a basic report on the given
S = summary(
esbacktestbyde data. The
report includes the number of observations, number of failures, observed
confidence level, and so on. See
S for details.
Unlike other ES backtesting classes, the
does not require VaR data or ES data inputs.
internally computes VaR and ES data based on distribution information to
determine the severity information reported by the
esbacktestbydeObject and Run ES Backtest Summary Report
esbacktestbyde object for a t model with 10 degrees of freedom, and then run a basic ES backtest summary report.
load ESBacktestDistributionData.mat rng('default'); % For reproducibility ebtde = esbacktestbyde(Returns,"t",... 'DegreesOfFreedom',T10DoF,... 'Location',T10Location,... 'Scale',T10Scale,... 'PortfolioID',"S&P",... 'VaRID',["t(10) 95%","t(10) 97.5%","t(10) 99%"],... 'VaRLevel',VaRLevel); summary(ebtde)
ans=3×11 table PortfolioID VaRID VaRLevel ObservedLevel ExpectedSeverity ObservedSeverity Observations Failures Expected Ratio Missing ___________ _____________ ________ _____________ ________________ ________________ ____________ ________ ________ ______ _______ "S&P" "t(10) 95%" 0.95 0.94812 1.3288 1.4515 1966 102 98.3 1.0376 0 "S&P" "t(10) 97.5%" 0.975 0.97202 1.2652 1.4134 1966 55 49.15 1.119 0 "S&P" "t(10) 99%" 0.99 0.98627 1.2169 1.3947 1966 27 19.66 1.3733 0
esbacktestbyde object contains a copy of the data
ESData properties) and all combinations of
portfolio ID, VaR ID, and VaR levels to be tested.
Unlike other ES backtesting classes,
esbacktestbyde does not require VaR data or ES
esbacktestbyde internally computes VaR and ES data
based on distribution information to determine the severity
information reported by
summary. For more
information on creating an
S— Summary report
Summary report, returned as a table. The table rows correspond to all combinations of portfolio ID, VaR ID, and VaR levels to be tested. The columns correspond to the following:
'PortfolioID' — Portfolio ID for
the given data
'VaRID' — VaR ID for each of the
'VaRLevel' — VaR level
'ObservedLevel' — Observed
confidence level, defined as the number of periods without
failures divided by number of observations
'ExpectedSeverity' — Expected
average severity ratio, that is, the average ratio of ES to
VaR over the periods with VaR failures
'ObservedSeverity' — Observed
average severity ratio, that is, the average ratio of loss
to VaR over the periods with VaR failures
'Observations' — Number of
observations, where missing values are removed from the
'Failures' — Number of failures,
where a failure occurs whenever the loss (negative of
portfolio data) exceeds the VaR
'Expected' — Expected number of
failures, defined as the number of observations multiplied
by 1 minus the VaR level
'Ratio' — Ratio of number of
failures to expected number of failures
'Missing' — Number of periods
with missing values removed from the sample
'ObservedSeverity' ratios are
NaN) when there are no VaR
failures in the data.
 Du, Z., and J. C. Escanciano. "Backtesting Expected Shortfall: Accounting for Tail Risk." Management Science. Vol. 63, Issue 4, April 2017.
 Basel Committee on Banking Supervision. "Minimum Capital Requirements for Market Risk". January 2016 (https://www.bis.org/bcbs/publ/d352.pdf).