Table of Contents


File

return_smoothing.m

Name

return_smoothing

Synopsis

return_smoothing - Calculates the smoothing weights and the parameter ksi for a hedge fund

Introduction

It is a well documented empirical fact that returns to hedge funds and other alternative investments are often highly serially correlated, and Getmansky, Lo, and Makarov (2004) explore several sources of such serial correlation and show that the most likely explanation is illiquidity exposure and smoothed returns. The authors propose an econometric model of return smoothing coefficients; they find that these vary considerably across hedge- fund style categories and posit that they may be a useful proxy for quantifying illiquidity exposure. Their argument for why this is the case goes as follows: for illiquid securities, prices are not readily available and often, linear extrapolation methods of pricing are used, resulting in more persistent and smoother returns. Even when quotes are obtained from broker/dealers, the phenomenon still exists because broker/dealers also often use linear extrapolation pricing methods; furthermore, averaging quotes from multiple broker/dealers can lead to smoother profiles. Thus, hedge funds which invest in more illiquid securities/areas should exhibit a higher serial correlation in their reported returns.

The authors model this return smoothing and develop a measure to quantify the effect. This is discussed in detail in Bisias et al. (2012), Section F.6, and specifically in equations (A.93) - (A.95). This code estimates smoothing weights and the parameter ksi.

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

hedge_fund_returns
Name:
hedge_fund_returns
Description:

The returns of the hedge fund.

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

Tx1 matrix

  1. Rows represent dates.

factor_returns
Name:
factor_returns
Description:

The returns of a benchmark factor (like S&P 500).

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

Tx1 matrix

  1. Rows represent dates.

lag
Name:
lag
Description:

The number of past years incorporated into the smoothing process.

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

scalar


Outputs

thetas
Name:
thetas
Description:

The individual weightings assigned to each of the past years returns.

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

Nx1 matrix


ksi
Name:
ksi
Description:

The sum of the squares of the smoothing weights or thetas.

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.']);




n = length(hedge_fund_returns);

% The first lag entries are ignored 
y = hedge_fund_returns(lag+1:end);
% Let's form the matrix X
X = ones(n-lag,lag+2);
for i=0:lag
    X(:,i+2)= factor_returns(lag+1-i:n-i);
end

gammas = regress(y,X);

thetas = gammas(2:end)/sum(gammas(2:end));

ksi = thetas'*thetas;

Examples

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

 hedge_fund_returns = ...
 [ 0.2; -0.1; 0.1;-0.01; 0.15;-0.11;-0.09; 0.18];
 factor_returns = ...
 [ 0.10; 0.10;-0.09;-0.07;-0.08; 0.06;-0.21; 0.16]

 lag = 2;

 [thetas, ksi] = return_smoothing(hedge_fund_returns, ...
 factor_returns, lag)

References

Getmansky, M., Lo, A. W., & Makarov, I. (2004). An econometric model of serial correlation and illiquidity in hedge fund returns. Journal of Financial Economics, 74(3), 529-609.

Bisias et al. (2012). A survey of systemic risk analytics (Working paper #0001). Washington, DC: Office of Financial Research, 129-133.