Table of Contents


File

systemic_liquidity_indicator.m

Name

systemic_liquidity_indicator

Synopsis

systemic_liquidity_indicator - calculates the Q-stats for each fund and the systemic liquidity indicator.

Introduction

Chan, Getmansky, Haas, and Lo (2006a, 2006b) consider the broader impact of hedge funds on systemic risk by examining the unique risk/return profiles of hedge funds at both the individual-fund and aggregate-industry levels and propose three new risk measures for hedge fund investments. The first measure is an autocorrelation-based measure used to proxy hedge fund illiquidity exposures similar to that in Getmansky, Lo, and Makarov (2004)

Autocorrelation-Based Measures: For a given monthly return series of a hedge fund, the first 6 autocorrelation coefficients are estimated. The Q statistic, proposed by Ljung & Box in Ljung and Box (1978) is then calculated.

In terms of defining an overall measure of systemic risk (or illiquidity) in the hedge fund sector, the authors propose using a cross-sectional weighted average of hedge funds rolling first-order autocorrelations (systemic liquidity indicator).

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

funds_returns
Name:
funds_returns
Description:

A matrix of monthly fund returns.

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

TxK matrix

  1. Rows represent each of T periods. T >= 7.
  2. Columns represent returns for each of K funds.

assets_under_management
Name:
assets_under_management
Description:

Assets under management for the different funds.

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

Kx1 matrix

  1. Rows represent each of K funds

Outputs

q_stats
Name:
q_stats
Description:

The q-statistics for the different funds' returns.

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

Kx1 matrix

  1. Rows represent each of K funds

sys_liquidity_ind
Name:
sys_liquidity_ind
Description:

The systemic liquidity indicator

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.']);

%
% Paramaters:
% funds_returns The monthly returns of the funds. A nxk matrix.  Rows are 
% the different periods  Columns are the different funds. 
% assets_under_management The assets under management for the different
% funds A kx1 vector
% Outputs:
% q_stats The q-statistics for the different funds' returns. A kx1 vector
% sys_liquidity_ind The systemic liquidity indicator

num_funds = size(funds_returns,2);
q_stats = zeros(num_funds,1);

for i=1:num_funds
    % Find the Ljung-Box statistic
    [h pval stat] = lbqtest(funds_returns(:,i),'lags',6);
    q_stats(i) = stat;

    rho = autocorr(funds_returns(:,i), 1);
    % 1st order autocorrelation
    rhos(i) = rho(2);
end

sys_liquidity_ind = rhos*assets_under_management/sum(assets_under_management);

Examples

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

 funds_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;
  0.0287, 0.1352, 0.0291;
  -0.0523, 0.0700, 0.0020;
  0.0614, 0.0151, 0.0919];

 assets_under_management = ...
 [453.7977;
  432.3915;
  133.1710];

 [q_stats sys_liquidity_ind] = systemic_liquidity_indicator( ...
 funds_returns, assets_under_management);

References

Chan et al. (2006a). Do hedge funds increase systemic risk?. Economic Review-Federal Reserve Bank of Atlanta, 91(4), 49.

Chan et al. (2006b). Systemic risk and hedge funds. The Risks of Financial Institutions. Chicago, IL: University of Chicago Press, 235-330.

Bisias et al. (2012). A survey of systemic risk analytics (Working paper #0001). Washington, DC: Office of Financial Research, 133-134.