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Basic expected shortfall (ES) report on failures and severity


S = summary(ebts)



S = summary(ebts) returns a basic report on the given esbacktestbysim data, including the number of observations, number of failures, observed confidence level, and so on (see S for details).


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Create an esbacktestbysim object.

load ESBacktestBySimData
rng('default'); % for reproducibility
ebts = esbacktestbysim(Returns,VaR,ES,"t",...
       'VaRID',["t(10) 95%","t(10) 97.5%","t(10) 99%"],...

Generate the ES summary report.

S = summary(ebts)
S =

  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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esbacktestbysim (ebts) object, which contains a copy of the given data (the PortfolioData, VarData, ESData, and Distribution properties) and all combinations of portfolio ID, VaR ID, and VaR levels to be tested. For more information on creating an esbacktestbysim object, see esbacktestbysim.

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 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

  • '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


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

Introduced in R2017b

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