Table of Contents


File

systemic_expected_shortfall.m

Name

systemic_expected_shortfall

Synopsis

systemic_expected_shortfall - Calculates the systemic expected shortfall for a firm.

Introduction

NOTE: PART OF A SET OF 3 RELATED FILES:

Acharya, Pedersen, Philippon, and Richardson (2010) argue that each financial institutions contribution to systemic risk can be measured as its systemic expected shortfall (SES), i.e., its propensity to be undercapitalized when the system as a whole is undercapitalized. SES is a theoretical construct and the authors use the following 3 measures to proxy it:

  1. The outcome of stress tests performed by regulators. The SES metric of a firm here is defined as the recommended capital that it was required to raise as a result of the stress test in February 2009.
  2. The decline in equity valuations of large financial firms during the crisis, as measured by their cumulative equity return from July 2007 to December 2008.
  3. The widening of the credit default swap spreads of large financial firms as measured by their cumulative CDS spread increases from July 2007 to December 2008.

Given these proxies, the authors seek to develop leading indicators which predict an institutions SES; these leading indicators are marginal expected shortfall (MES) and leverage (LVG).

License

=============================================================================

Copyright 2011, Dimitrios Bisias, Andrew W. Lo, and Stavros Valavanis

COPYRIGHT STATUS: This work was funded in whole or in part by the Office of Financial Research under U.S. Government contract TOSOFR-11-C-0001, and is, therefore, subject to the following license: The Government is granted for itself and others acting on its behalf a paid-up, nonexclusive, irrevocable, worldwide license to reproduce, prepare derivative works, distribute copies to the public, perform and display the work.
All other rights are reserved by the copyright owner.

THIS SOFTWARE IS PROVIDED "AS IS". YOU ARE USING THIS SOFTWARE AT YOUR OWN RISK. ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHORS, CONTRIBUTORS, OR THE UNITED STATES GOVERNMENT BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

=============================================================================

Inputs

mes_training_sample
Name:
mes_training_sample
Description:

MES or value per firm defined as avg equity return during 5% worst days for overall market during training period.

Type:
float
Range:
(-inf,+inf)
Dimensions:

Fx1 matrix

  1. Rows represent firms

lvg_training_sample
Name:
lvg_training_sample
Description:

Leverage per firm defined on the last day of the period of training data.

Type:
float
Range:
(0,+inf)
Dimensions:

Fx1 matrix

  1. Rows represent firms

ses_training_sample
Name:
ses_training_sample
Description:

Cumulative return per firm for date range after mes/lvg_training_sample.

Type:
float
Range:
(-inf,+inf)
Dimensions:

Fx1 matrix

  1. Rows represent firms

mes_firm
Name:
mes_firm
Description:

The current firm MES used to calculate the firm SES value.

Type:
float
Range:
(-inf,+inf)
Dimensions:

scalar


lvg_firm
Name:
lvg_firm
Description:

The current firm leverage used to calculate the firm SES value.

Type:
float
Range:
(0,+inf)
Dimensions:

scalar


Outputs

ses
Name:
ses
Description:

The systemic risk that firm i poses to the system at a future time t.

Type:
float
Range:
(-inf,+inf)
Dimensions:

scalar


Code

% Run warning message
warning('OFRwp0001:UntestedCode', ...
    ['This version of the source code is very preliminary, ' ...
     'and has not been thoroughly tested. Users should not rely on ' ...
     'these calculations.']);


num_firms = length(mes_training_sample);

% Regressors
X = [ones(num_firms,1) mes_training_sample lvg_training_sample];

% Regress systemic expected shortfall on marginal expected shortfall and
% leverage
betas = regress(ses_training_sample, X);

b = betas(2);
c = betas(3);
ses = (b*mes_firm + c*lvg_firm)/(b+c);

Examples

NOTE: Numbers used in the examples are arbitrary valid values.
They do not necessarily represent a realistic or plausible scenario.

 mes_training_sample = [ -.023, -.07, .01 ]';
 lvg_training_sample = [  1.8, 1.5, 2.2 ]';
 ses_training_sample = [ .3, .4, -.2 ]';
 mes_firm = .04;
 lvg_firm = 1.7;

 ses = systemic_expected_shortfall(mes_training_sample, ...
 lvg_training_sample, ses_training_sample, mes_firm, lvg_firm);

References

Acharya, Pedersen, Philippon, & Richardson. (2010). Measuring systemic risk.

Bisias et al. (2012). A survey of systemic risk analytics(Working paper #0001). Washington, DC: Office of Financial Research, 114-116.