File
kyles_lambda.m
Name
kyles_lambda
Synopsis
kyles_lambda - Calculates the Kyle's lambda (price impact liquidity measure).
Introduction
NOTE: PART OF A SET OF 2 RELATED FILES:
This approach is motivated by Kyles (1985) model in which liquidity is measured by a linear-regression estimate of the volume required to move the price of a security by one dollar. Sometimes referred to as Kyles lambda, this measure is an inverse proxy of liquidity, with higher values of lambda implying lower liquidity and market depth. The authors estimate this measure on a daily basis by using all transactions during normal trading hours on each day. The aggregate measure of market liquidity (MLI) is then given by the daily cross-sectional average of the estimated price impact coefficients.
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.']);
num_days = size(returns,1);
num_securities = size(returns,2);
lambdas = zeros(num_securities,1);
% Loop through all the securities
for security = 1:num_securities
y = returns(:,security);
t = modified_sign(y);
X = [ones(num_days,1) t.*log(prices(:,security).*volumes(security))];
betas = regress(y,X);
lambdas(security) = betas(2);
end
% Aggregate measure of market liquidity
mli = mean(lambdas);
Examples
NOTE: Numbers used in the examples are arbitrary valid values.
They do not necessarily represent a realistic or plausible scenario.
First row of prices will only be used to generate returns, and then dropped. Calculate returns as price at i minus price at time i-1 / price at time i.
volumes = ...
[180, 250, 700;
900, 400, 220;
970, 590, 110;
430, 260, 290;
110, 600, 310];
price_raw = ...
[ 44, 82, 55;
39, 81, 67;
36, 79, 13;
28, 40, 72;
23, 26, 10;
18, 13, 65];
returns = (price_raw(2:end, :) ./ price_raw(1:(end-1), :)) - 1
prices = price_raw(2:end,:);
mli = kyles_lambda(returns, prices, volumes)
References