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
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.']);
%
% 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