File
delta_co_var.m
Name
delta_co_var
Synopsis
delta_co_var - Calculates the marginal contribution (delta CoVaR) of an institution to systemic risk.
Introduction
NOTE: PART OF A SET OF 2 RELATED FILES:
Adrian and Brunnermeier (2010) propose to measure systemic risk via the conditional value-at-risk (CoVaR) of the financial system, conditional on institutions being in a state of distress. An institutions contribution to systemic risk is defined as the difference between CoVaR conditional on the institution being in distress and CoVaR in the median state of the institution. The CoVaR systemic risk measure is able to identify the risk on the system by individually systemically important institutions, which are so interconnected and large that they can cause negative risk spillover effects on others, as well as by smaller institutions that are systemic when acting as part of a herd. Furthermore, CoVaR is a measure which does not rely on contemporaneous price movements and thus can be used to anticipate systemic risk. The CoVaR measure captures institutional externalities such as too big to fail, too interconnected to fail, and crowded trade positions.
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
Outputs
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.']);
% Default value quantile = 0.05
if nargin < 4
quantile = 0.05;
end
if nargin < 3
lagged_factors_returns = [];
end
num_periods = size(output_returns,1);
median_percentile = 0.5;
% Calculate the median state of the input institution
X = [ones(num_periods,1) lagged_factors_returns(1:end-1,:)];
y = input_returns;
betas = quantile_regression(y,X,median_percentile,0);
if nargin<3
% lagged_factors_returns is empty
median_input_state = betas(1);
else
median_input_state = [1 lagged_factors_returns(end,:)]*betas;
end
% Calculate the distressed state of the input institution
betas = quantile_regression(y,X,quantile,0);
if nargin < 3
% lagged_factors_returns is empty
distressed_input_state = betas(1);
else
distressed_input_state = [1 lagged_factors_returns(end,:)]*betas;
end
% Quantile regression of the output_institution or system on lagged factors
% and input institution
X = [ones(num_periods,1) input_returns lagged_factors_returns(1:end-1,:)];
y = output_returns;
betas = quantile_regression(y,X,quantile,0);
% Definition of delta_co_var equation (9)
dcovar = betas(2)*(distressed_input_state - median_input_state);
Examples
NOTE: Numbers used in the examples are arbitrary valid values.
They do not necessarily represent a realistic or plausible scenario.
output_returns = [-0.01, 0.03, -0.02, 0.05, 0.03, 0.03]';
input_returns = [0.01, 0.04, -0.02, -0.03, 0.004, 0.03]';
lagged_factors_returns = [0.07, 0.11, 0.10, 0.16, 0.08, 0.12, 0.01]';
quantile = 0.05;
dcovar = delta_co_var(output_returns, input_returns, ...
lagged_factors_returns, quantile);
References
Adrian, T., & Brunnermeier, M. K. (2011). CoVaR (No. w17454). National Bureau of Economic Research.