Table of Contents


File

turbulence_var.m

Name

turbulence_var

Synopsis

turbulence_var - calculates the value-at-risk of a portfolio using only data from turbulent periods. Turbulence is defined at a q-percentile based on Kritzman et al. (2010)

Introduction

NOTE: PART OF A SET OF 2 RELATED FILES:

Kritzman and Li (2010) define financial turbulence as a condition in which asset prices, given their historical patterns of behavior, behave in an uncharacteristic fashion, including extreme price moves, decoupling of correlated assets, and convergence of uncorrelated assets. They quantify turbulence via the Mahalanobis distance (see Merton (1937)), which measures the statistical unusualness of a set of returns given their historical pattern of behavior. Their measure is very general and can be applied across asset classes for which time-series return data are available.

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

asset_returns
Name:
asset_returns
Description:

Time series returns for different asset classes.

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

TxK matrix

  1. Rows represent dates.
  2. Columns represent returns for each of K asset classes.

q
Name:
q
Description:

The percentile at which we define the lower bound for turbulence.
In the paper q = 0.75.

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

scalar


portfolio
Name:
portfolio
Description:

The portfolio weights per asset class.

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

1xK matrix

  1. Columns represent asset classes..

Outputs

var
Name:
var
Description:

The value-at-risk of the portfolio consisting of only turbulent periods.
Default used is 5% or .05.

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.']);


% Parameters:
% asset_returns A matrix of asset returns. Rows are different dates.
% Columns are different assets.
% portfolio The portfolio weights
% q The percentile
% Output:
% var the turbulence value-at-risk of the portfolio

[turbulence_series, threshold, turbulent_periods] = turbulence(asset_returns,q);

% Find the portfolio returns only at the turbulent periods
portfolio_returns = portfolio'*asset_returns(turbulent_periods,:);

% Find the variance-at-risk i.e. the 5% percentile
var = prctile(portfolio_returns,5);

Examples

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

 asset_returns = ...
 [ 0.0595, 0.1211,-0.0806; 
  -0.1091, 0.0897,-0.0254; 
   0.0901, 0.0714,-0.0915; 
   0.1086, 0.0033,-0.1173;
   0.0614, 0.0151, 0.0291];

 q = .75;

 portfolio = [.33,.33,.33]

 var = turbulence_var(asset_returns,portfolio, q)

References

Kritzman, M., & Li, Y. (2010). Skulls, financial turbulence, and risk management. Financial Analysts Journal, 66(5), 30-41.

Bisias et al. (2012). A survey of systemic risk analytics (Working paper #0001). Washington, DC: Office of Financial Research, 80-81.