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summary

Basic expected shortfall (ES) report on failures and severity

Description

example

S = summary(ebtde) returns a basic report on the given 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 esbacktestbyde object does not require VaR data or ES data inputs. esbacktestbyde internally computes VaR and ES data based on distribution information to determine the severity information reported by the summary function.

Examples

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Create an 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   

Input Arguments

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esbacktestbyde object contains a copy of the data (the PortfolioData, VaRData, and ESData properties) and all combinations of portfolio ID, VaR ID, and VaR levels to be tested.

Note

Unlike other ES backtesting classes, esbacktestbyde does not require VaR data or ES data inputs. 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 esbacktestbyde object, see esbacktestbyde.

Output Arguments

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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 VaR levels

  • '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 data

  • '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

    Note

    The 'ExpectedSeverity' and 'ObservedSeverity' ratios are undefined (NaN) when there are no VaR failures in the data.

References

[1] Du, Z., and J. C. Escanciano. "Backtesting Expected Shortfall: Accounting for Tail Risk." Management Science. Vol. 63, Issue 4, April 2017.

[2] Basel Committee on Banking Supervision. "Minimum Capital Requirements for Market Risk". January 2016 (https://www.bis.org/bcbs/publ/d352.pdf).

Introduced in R2019b