Table of Contents


File

dar.m

Name

dar

Synopsis

ar_shift - Calculates the standardized AR shift from AR based on Kritzman et al. (2010)

Introduction

NOTE: PART OF A SET OF 2 RELATED FILES:

Kritzman, Li, Page, and Rigobon (2010) propose to measure systemic risk via the Absorption Ratio (AR), which they define as the fraction of the total variance of a set of asset returns explained or absorbed by a fixed number of eigenvectors. The absorption ratio captures the extent to which markets are unified or tightly coupled. When markets are tightly coupled, they become more fragile in the sense that negative shocks propagate more quickly and broadly than when markets are loosely linked. The authors apply their AR analysis to several broad markets, introduce a standardized measure of shifts in the AR, and analyze how these shifts relate to changes in asset prices and financial turbulence.

The authors also propose a technical indicator of AR movements which they find to be a leading indicator of trouble for asset prices. This is known as the standardized AR shift.

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

absorption_ratios
Name:
absorption_ratios
Description:

The fraction of the total variance of a set of asset returns explained or absorbed by a fixed number of eigenvectors. In the paper absorption ratios are given for 1 year.

Type:
float
Range:
(0,1]
Dimensions:

Tx1 matrix

  1. Rows represent each of T periods at which rolling AR was calculated.

fraction
Name:
fraction
Description:

Number of days in the short term absorption ratio over number of days in the long term absorption ratio. In the paper 15/252 if we consider a year having 252 absorption ratios.

Type:
float
Range:
(0,1)
Dimensions:

scalar


Outputs

ar_shift
Name:
ar_shift
Description:

Number of days used to create short term moving average of absorption ratio over number of days used in creating a long term moving average. The paper uses 15/252 assuming a year has 252 absorption ratios.

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_rows, num_cols] = size(absorption_ratios);
   if (num_rows ~= 1) && (num_cols ~=1)
    error('The absorption_ratios is a 1-d vector');
   end

   num_days = length(absorption_ratios);
   num_days_short_term = round(fraction*num_days);

   % Calculate the AR shift
   % For the short term absorption ratio take the last num_days_short_term days
   numerator = mean(absorption_ratios(end-num_days_short_term+1:end)) ...
   - mean(absorption_ratios);
   denominator = std(absorption_ratios);
   ar_shift = numerator/denominator;

Examples

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

 absorption_ratios = [.23, .25, .11, .50, .9]';

 fraction = .2;

 ar_shift = dar(absorption_ratios, fraction);

References

Kritzman, et al. (2010). Principal components as a measure of systemic risk. SSRN eLibrary.

Bisias et al. (2012). A survey of systemic risk analytics (Working paper #0001). Washington, DC: Office of Financial Research, 98-100.