This example shows how to generate a MEX function and C source code from MATLAB code that performs portfolio optimization using the Black Litterman approach.
There are no prerequisites for this example.
hlblacklitterman FunctionThe hlblacklitterman.m function reads in financial information regarding a portfolio and performs portfolio optimization using the Black Litterman approach.
type hlblacklittermanfunction [er, ps, w, pw, lambda, theta] = hlblacklitterman(delta, weq, sigma, tau, P, Q, Omega)%#codegen
% hlblacklitterman
% This function performs the Black-Litterman blending of the prior
% and the views into a new posterior estimate of the returns as
% described in the paper by He and Litterman.
% Inputs
% delta - Risk tolerance from the equilibrium portfolio
% weq - Weights of the assets in the equilibrium portfolio
% sigma - Prior covariance matrix
% tau - Coefficiet of uncertainty in the prior estimate of the mean (pi)
% P - Pick matrix for the view(s)
% Q - Vector of view returns
% Omega - Matrix of variance of the views (diagonal)
% Outputs
% Er - Posterior estimate of the mean returns
% w - Unconstrained weights computed given the Posterior estimates
% of the mean and covariance of returns.
% lambda - A measure of the impact of each view on the posterior estimates.
% theta - A measure of the share of the prior and sample information in the
% posterior precision.
% Reverse optimize and back out the equilibrium returns
% This is formula (12) page 6.
pi = weq * sigma * delta;
% We use tau * sigma many places so just compute it once
ts = tau * sigma;
% Compute posterior estimate of the mean
% This is a simplified version of formula (8) on page 4.
er = pi' + ts * P' * inv(P * ts * P' + Omega) * (Q - P * pi');
% We can also do it the long way to illustrate that d1 + d2 = I
d = inv(inv(ts) + P' * inv(Omega) * P);
d1 = d * inv(ts);
d2 = d * P' * inv(Omega) * P;
er2 = d1 * pi' + d2 * pinv(P) * Q;
% Compute posterior estimate of the uncertainty in the mean
% This is a simplified and combined version of formulas (9) and (15)
ps = ts - ts * P' * inv(P * ts * P' + Omega) * P * ts;
posteriorSigma = sigma + ps;
% Compute the share of the posterior precision from prior and views,
% then for each individual view so we can compare it with lambda
theta=zeros(1,2+size(P,1));
theta(1,1) = (trace(inv(ts) * ps) / size(ts,1));
theta(1,2) = (trace(P'*inv(Omega)*P* ps) / size(ts,1));
for i=1:size(P,1)
theta(1,2+i) = (trace(P(i,:)'*inv(Omega(i,i))*P(i,:)* ps) / size(ts,1));
end
% Compute posterior weights based solely on changed covariance
w = (er' * inv(delta * posteriorSigma))';
% Compute posterior weights based on uncertainty in mean and covariance
pw = (pi * inv(delta * posteriorSigma))';
% Compute lambda value
% We solve for lambda from formula (17) page 7, rather than formula (18)
% just because it is less to type, and we've already computed w*.
lambda = pinv(P)' * (w'*(1+tau) - weq)';
end
% Black-Litterman example code for MatLab (hlblacklitterman.m)
% Copyright (c) Jay Walters, blacklitterman.org, 2008.
%
% Redistribution and use in source and binary forms,
% with or without modification, are permitted provided
% that the following conditions are met:
%
% Redistributions of source code must retain the above
% copyright notice, this list of conditions and the following
% disclaimer.
%
% Redistributions in binary form must reproduce the above
% copyright notice, this list of conditions and the following
% disclaimer in the documentation and/or other materials
% provided with the distribution.
%
% Neither the name of blacklitterman.org nor the names of its
% contributors may be used to endorse or promote products
% derived from this software without specific prior written
% permission.
%
% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
% CONTRIBUTORS "AS IS" AND 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 COPYRIGHT OWNER OR
% CONTRIBUTORS 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.
%
% This program uses the examples from the paper "The Intuition
% Behind Black-Litterman Model Portfolios", by He and Litterman,
% 1999. You can find a copy of this paper at the following url.
% http:%papers.ssrn.com/sol3/papers.cfm?abstract_id=334304
%
% For more details on the Black-Litterman model you can also view
% "The BlackLitterman Model: A Detailed Exploration", by this author
% at the following url.
% http:%www.blacklitterman.org/Black-Litterman.pdf
%
The %#codegen directive indicates that the MATLAB code is intended for code generation.
Generate a MEX function using the codegen command.
codegen hlblacklitterman -args {0, zeros(1, 7), zeros(7,7), 0, zeros(1, 7), 0, 0}
Before generating C code, you should first test the MEX function in MATLAB to ensure that it is functionally equivalent to the original MATLAB code and that no run-time errors occur. By default, codegen generates a MEX function named hlblacklitterman_mex in the current folder. This allows you to test the MATLAB code and MEX function and compare the results.
Call the generated MEX function
testMex();
View 1 Country P mu w* Australia 0 4.328 1.524 Canada 0 7.576 2.095 France -29.5 9.288 -3.948 Germany 100 11.04 35.41 Japan 0 4.506 11.05 UK -70.5 6.953 -9.462 USA 0 8.069 58.57 q 5 omega/tau 0.0213 lambda 0.317 theta 0.0714 pr theta 0.929 View 1 Country P mu w* Australia 0 4.328 1.524 Canada 0 7.576 2.095 France -29.5 9.288 -3.948 Germany 100 11.04 35.41 Japan 0 4.506 11.05 UK -70.5 6.953 -9.462 USA 0 8.069 58.57 q 5 omega/tau 0.0213 lambda 0.317 theta 0.0714 pr theta 0.929 Execution Time - MATLAB function: 0.018389 seconds Execution Time - MEX function : 0.011486 seconds
cfg = coder.config('lib'); codegen -config cfg hlblacklitterman -args {0, zeros(1, 7), zeros(7,7), 0, zeros(1, 7), 0, 0}
Using codegen with the specified -config cfg option produces a standalone C library.
By default, the code generated for the library is in the folder codegen/lib/hbblacklitterman/.
The files are:
dir codegen/lib/hlblacklitterman/. hlblacklitterman_terminate.h .. hlblacklitterman_terminate.o .gitignore hlblacklitterman_types.h buildInfo.mat interface codeInfo.mat inv.c codedescriptor.dmr inv.h compileInfo.mat inv.o defines.txt pinv.c examples pinv.h hlblacklitterman.a pinv.o hlblacklitterman.c rtGetInf.c hlblacklitterman.h rtGetInf.h hlblacklitterman.o rtGetInf.o hlblacklitterman_data.c rtGetNaN.c hlblacklitterman_data.h rtGetNaN.h hlblacklitterman_data.o rtGetNaN.o hlblacklitterman_initialize.c rt_nonfinite.c hlblacklitterman_initialize.h rt_nonfinite.h hlblacklitterman_initialize.o rt_nonfinite.o hlblacklitterman_ref.rsp rtw_proj.tmw hlblacklitterman_rtw.mk rtwtypes.h hlblacklitterman_terminate.c
hlblacklitterman.c Functiontype codegen/lib/hlblacklitterman/hlblacklitterman.c/*
* File: hlblacklitterman.c
*
* MATLAB Coder version : 5.1
* C/C++ source code generated on : 17-Aug-2020 20:29:13
*/
/* Include Files */
#include "hlblacklitterman.h"
#include "inv.h"
#include "pinv.h"
#include "rt_nonfinite.h"
/* Function Definitions */
/*
* hlblacklitterman
* This function performs the Black-Litterman blending of the prior
* and the views into a new posterior estimate of the returns as
* described in the paper by He and Litterman.
* Inputs
* delta - Risk tolerance from the equilibrium portfolio
* weq - Weights of the assets in the equilibrium portfolio
* sigma - Prior covariance matrix
* tau - Coefficiet of uncertainty in the prior estimate of the mean (pi)
* P - Pick matrix for the view(s)
* Q - Vector of view returns
* Omega - Matrix of variance of the views (diagonal)
* Outputs
* Er - Posterior estimate of the mean returns
* w - Unconstrained weights computed given the Posterior estimates
* of the mean and covariance of returns.
* lambda - A measure of the impact of each view on the posterior estimates.
* theta - A measure of the share of the prior and sample information in the
* posterior precision.
* Arguments : double delta
* const double weq[7]
* const double sigma[49]
* double tau
* const double P[7]
* double Q
* double Omega
* double er[7]
* double ps[49]
* double w[7]
* double pw[7]
* double *lambda
* double theta[3]
* Return Type : void
*/
void hlblacklitterman(double delta, const double weq[7], const double sigma[49],
double tau, const double P[7], double Q, double Omega,
double er[7], double ps[49], double w[7], double pw[7],
double *lambda, double theta[3])
{
double b_er_tmp[49];
double dv[49];
double posteriorSigma[49];
double ts[49];
double b_y_tmp[7];
double er_tmp[7];
double pi[7];
double unusedExpr[7];
double b;
double b_P;
double b_b;
double d;
double y_tmp;
int i;
int i1;
int ps_tmp;
/* Reverse optimize and back out the equilibrium returns */
/* This is formula (12) page 6. */
for (i = 0; i < 7; i++) {
b = 0.0;
for (i1 = 0; i1 < 7; i1++) {
b += weq[i1] * sigma[i1 + 7 * i];
}
pi[i] = b * delta;
}
/* We use tau * sigma many places so just compute it once */
for (i = 0; i < 49; i++) {
ts[i] = tau * sigma[i];
}
/* Compute posterior estimate of the mean */
/* This is a simplified version of formula (8) on page 4. */
y_tmp = 0.0;
b_P = 0.0;
for (i = 0; i < 7; i++) {
b = 0.0;
b_b = 0.0;
for (i1 = 0; i1 < 7; i1++) {
d = P[i1];
b += ts[i + 7 * i1] * d;
b_b += d * ts[i1 + 7 * i];
}
b_y_tmp[i] = b_b;
er_tmp[i] = b;
b = P[i];
y_tmp += b_b * b;
b_P += b * pi[i];
}
b_b = 1.0 / (y_tmp + Omega);
b = Q - b_P;
for (i = 0; i < 7; i++) {
er[i] = pi[i] + er_tmp[i] * b_b * b;
}
/* We can also do it the long way to illustrate that d1 + d2 = I */
y_tmp = 1.0 / Omega;
pinv(P, unusedExpr);
/* Compute posterior estimate of the uncertainty in the mean */
/* This is a simplified and combined version of formulas (9) and (15) */
b = 0.0;
for (i = 0; i < 7; i++) {
b += b_y_tmp[i] * P[i];
}
b_b = 1.0 / (b + Omega);
for (i = 0; i < 7; i++) {
for (i1 = 0; i1 < 7; i1++) {
b_er_tmp[i1 + 7 * i] = er_tmp[i1] * b_b * P[i];
}
}
for (i = 0; i < 7; i++) {
for (i1 = 0; i1 < 7; i1++) {
b = 0.0;
for (ps_tmp = 0; ps_tmp < 7; ps_tmp++) {
b += b_er_tmp[i + 7 * ps_tmp] * ts[ps_tmp + 7 * i1];
}
ps_tmp = i + 7 * i1;
ps[ps_tmp] = ts[ps_tmp] - b;
}
}
for (i = 0; i < 49; i++) {
posteriorSigma[i] = sigma[i] + ps[i];
}
/* Compute the share of the posterior precision from prior and views, */
/* then for each individual view so we can compare it with lambda */
inv(ts, dv);
for (i = 0; i < 7; i++) {
for (i1 = 0; i1 < 7; i1++) {
b = 0.0;
for (ps_tmp = 0; ps_tmp < 7; ps_tmp++) {
b += dv[i + 7 * ps_tmp] * ps[ps_tmp + 7 * i1];
}
ts[i + 7 * i1] = b;
}
}
b = 0.0;
for (ps_tmp = 0; ps_tmp < 7; ps_tmp++) {
b += ts[ps_tmp + 7 * ps_tmp];
}
theta[0] = b / 7.0;
for (i = 0; i < 7; i++) {
for (i1 = 0; i1 < 7; i1++) {
b_er_tmp[i1 + 7 * i] = P[i1] * y_tmp * P[i];
}
}
for (i = 0; i < 7; i++) {
for (i1 = 0; i1 < 7; i1++) {
b = 0.0;
for (ps_tmp = 0; ps_tmp < 7; ps_tmp++) {
b += b_er_tmp[i + 7 * ps_tmp] * ps[ps_tmp + 7 * i1];
}
ts[i + 7 * i1] = b;
}
}
b = 0.0;
for (ps_tmp = 0; ps_tmp < 7; ps_tmp++) {
b += ts[ps_tmp + 7 * ps_tmp];
}
theta[1] = b / 7.0;
for (i = 0; i < 7; i++) {
for (i1 = 0; i1 < 7; i1++) {
b_er_tmp[i1 + 7 * i] = P[i1] * y_tmp * P[i];
}
}
for (i = 0; i < 7; i++) {
for (i1 = 0; i1 < 7; i1++) {
b = 0.0;
for (ps_tmp = 0; ps_tmp < 7; ps_tmp++) {
b += b_er_tmp[i + 7 * ps_tmp] * ps[ps_tmp + 7 * i1];
}
ts[i + 7 * i1] = b;
}
}
b = 0.0;
for (ps_tmp = 0; ps_tmp < 7; ps_tmp++) {
b += ts[ps_tmp + 7 * ps_tmp];
}
theta[2] = b / 7.0;
/* Compute posterior weights based solely on changed covariance */
for (i = 0; i < 49; i++) {
b_er_tmp[i] = delta * posteriorSigma[i];
}
inv(b_er_tmp, dv);
for (i = 0; i < 7; i++) {
b = 0.0;
for (i1 = 0; i1 < 7; i1++) {
b += er[i1] * dv[i1 + 7 * i];
}
w[i] = b;
}
/* Compute posterior weights based on uncertainty in mean and covariance */
for (i = 0; i < 49; i++) {
posteriorSigma[i] *= delta;
}
inv(posteriorSigma, dv);
for (i = 0; i < 7; i++) {
b = 0.0;
for (i1 = 0; i1 < 7; i1++) {
b += pi[i1] * dv[i1 + 7 * i];
}
pw[i] = b;
}
/* Compute lambda value */
/* We solve for lambda from formula (17) page 7, rather than formula (18) */
/* just because it is less to type, and we've already computed w*. */
pinv(P, er_tmp);
*lambda = 0.0;
for (ps_tmp = 0; ps_tmp < 7; ps_tmp++) {
*lambda += er_tmp[ps_tmp] * (w[ps_tmp] * (tau + 1.0) - weq[ps_tmp]);
}
/* Black-Litterman example code for MatLab (hlblacklitterman.m) */
/* Copyright (c) Jay Walters, blacklitterman.org, 2008. */
/* */
/* Redistribution and use in source and binary forms, */
/* with or without modification, are permitted provided */
/* that the following conditions are met: */
/* */
/* Redistributions of source code must retain the above */
/* copyright notice, this list of conditions and the following */
/* disclaimer. */
/* */
/* Redistributions in binary form must reproduce the above */
/* copyright notice, this list of conditions and the following */
/* disclaimer in the documentation and/or other materials */
/* provided with the distribution. */
/* */
/* Neither the name of blacklitterman.org nor the names of its */
/* contributors may be used to endorse or promote products */
/* derived from this software without specific prior written */
/* permission. */
/* */
/* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND */
/* CONTRIBUTORS "AS IS" AND 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 COPYRIGHT OWNER OR */
/* CONTRIBUTORS 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. */
/* */
/* This program uses the examples from the paper "The Intuition */
/* Behind Black-Litterman Model Portfolios", by He and Litterman, */
/* 1999. You can find a copy of this paper at the following url. */
/* http:%papers.ssrn.com/sol3/papers.cfm?abstract_id=334304 */
/* */
/* For more details on the Black-Litterman model you can also view */
/* "The BlackLitterman Model: A Detailed Exploration", by this author */
/* at the following url. */
/* http:%www.blacklitterman.org/Black-Litterman.pdf */
/* */
}
/*
* File trailer for hlblacklitterman.c
*
* [EOF]
*/