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Speeding Up Optimization Problems with Parallel Computing

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Speeding Up Optimization Problems with Parallel Computing


Stuart Kozola


Files from the webinar: Speeding up optimization problems with parallel computing

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function [portStd, portRet, portWts, portIndx] = computebestportfolioPCT(expRet,expCov,portSize,targetRet)
% Oren Rosen
% 4/14/2009
% Copyright 2008 The MathWorks, Inc.
% This function implements a custom portfolio optimization routine:
% Find the weights that minimize portfolio standard deviation with
% constraints that require a given target portfolio return and a maximum
% number of non-zero weights (cardinality constraint).
% Inputs:
% expRet    - Column vector of expected returns of equity universe.
% expCov    - Square matrix of expected covariance of equity universe.
% portSize  - Maximum number of non-zero weights. Less than the number of
%             equities in the universe.
% targetRet - Target return for complete portfolio.
% Outputs:
% portStd   - Standard deviation of optimal portfolio.
% portRet   - Total return of optimal portfolio (should match targetRet).
% portWts   - Vector of optimal weights. Length equal to universe size.
% PortIndx  - Vector of integers dictating which equities are included in
%             the portfolio.
% The implementation of this routine is done with nested optimization
% routines. The outer layer uses a custom genetic algorithm based on a bit
% string data type. The bit string has length equal to the number of
% equities in the universe, and a 1 (or 0) represents that an equity is
% included (not included) in the current portfolio. The portfolio
% cardinality constraint is built into the genetic algorithm evolution
% functions:
% generateinitpopNcK(...)
% crossoverNcK(...)
% mutationNcK(...)
% The genetic algorithm determines which equities are included in the best
% portfolio. Within the fitness function, the quadratic programming solver
% "quadprog" is used to find the optimal weights for the current choice of
% equities.
% NOTE: This version is meant to be used with a demonstration of the GA/PCT
% features. Note the addition of the last 2 options in the calls below to 
% "gaoptimset". It is identical in all other ways to the version in the 
% MLScript directory.

% Generate initial population for GA
univSize = length(expRet);
iPop = generateinitpopNcK(univSize,portSize);

% Start with default options
options = gaoptimset;

% Set population options
options = gaoptimset(options,'PopulationSize' ,univSize-portSize+1 );
options = gaoptimset(options,'InitialPopulation' , iPop);

% Set evolution options
options = gaoptimset(options,'CrossoverFraction' ,0.9 );
options = gaoptimset(options,'CrossoverFcn' ,@crossoverNcK);
options = gaoptimset(options,'MutationFcn' ,@mutationNcK);
options = gaoptimset(options,'Vectorize' ,'off');

% Set diaplay options
options = gaoptimset(options,'Display' ,'off');

% *** Set options for PCT Demo ***
options = gaoptimset(options,'UseParallel','always');
options = gaoptimset(options,'Generations',4); % Limit generations

% Maximum portfolio standard deviation is the largest individual stock
% standard deviation. This will be used in the GA fitness function below.
maxPortStd = sqrt(max(diag(expCov)));

% Run GA
[portBits,fval,gaExit] = ga(@rankport,univSize,[],[],[],[],[],[],[],options);

% Output of GA is logical vector of the best equities to
% include in the portfolio. Use this data to run quadprog
% one more time to insure that we get the correct weights.

% Extract subsets of expected return and covariance
portBits = logical(portBits);
subCov = expCov(portBits,portBits);
subRet = expRet(portBits);

% Calculate optimal weights, compute portfolio statistics
[subWts,subVar,mvExit] = minvar(subCov,subRet,targetRet);
portRet = subWts'*subRet;
portStd = sqrt(subVar);

% Build full weight vector and index vector for optimal portfolio
indices = 1:univSize;
portIndx = indices(portBits);
portWts = zeros(univSize,1);
portWts(portIndx) = subWts;

    % *****************************************************************%
    % Fitness function for GA
    % The input "x" is a bit string that represents which stocks to include
    % in the current portfolio. The fitness of this portfolio is measured
    % as the minimum portfolio standard deviation possible given the target
    % return constraint and the current choice of equities.
    function risk = rankport(x)
        % Use the current bit-string "x" to extract subsets of the equities
        % expected returns and covariance.
        x = logical(x);
        subCov = expCov(x,x);
        subRet = expRet(x);
        % "minvar" is a user defined m-function. It is essentially a
        % wrapper for "quadprog" and calculates the weights for the
        % current portfolio that minimizes portfolio variance. If a
        % different measure of risk is desired, replace this function.
        [weights,fval,mvExit] = minvar(subCov,subRet,targetRet);
        % Risk is measure in this routine as portfolio standard deviation.
        % If the optimization routine in "minvar" failed, set risk to a
        % high valuec so that this choice of portfolio is flagged as
        % un-optimal. This could happen simply because the expected returns
        % for the current choice of stocks are inadequete to achieve the
        % target return.
        if( mvExit == 1 )
            risk = sqrt(fval);
            risk = 10*maxPortStd;
    % *****************************************************************%

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