Portfolio Optimization Demo (with Distributed Arrays and SPMD)

This demo calculates returns the risk-return relationship in the stock portfolio that is optimal in the mean-variance sense. covMat and expRet are the covariance and mean returns of a collection of stocks and muVec is a vector of desired returns.

The covariance matrix (covMat) is calculated using distributed arrays. To calculate the covariance matrix we must process a large data set comprising several thousand time points for each stock. For this exercise, for demostration purposes, we use a reduced dataset so as to fit all the data in a single computer running four local workers. However, for higher-fidelity simulations one would require higher number of data points for a larger number of stocks. This can quickly breach the limits of a single desktop computer.

Once the covariance matrix is computed, since it is N x N where N is just the number of stocks, it can be held in a single computer's memory and used locally.

Clear out all old variables
Opening a matlabpool
Loading in historical stock data
Calculating the covariance matrix
Calculating range and points along the efficency frontier
Find the frontier for the stock portfolio
Visualization
Close the matlabpool

Clear out all old variables

clear all

Opening a matlabpool

if matlabpool('size') == 0
    matlabpool open 2
else
    warning('MATLAB:poolOpen', 'matlabpool already open')
end

Starting matlabpool using the parallel configuration 'local'.
Waiting for parallel job to start...
Connected to a matlabpool session with 2 labs.

Loading in historical stock data

numFiles = 4; % number of files to use
numStocks = 200; % number of stocks to use
numPoints = 10;  % number of points on the efficency frontier

x = Exercise2_loadReturns(numFiles,numStocks);

  1 ans =
          144004         200
  2 ans =
          144004         200

Calculating the covariance matrix

spmd
    [n,m] = size(x);
    display(size(x));

    % calculating the covariance and expected return
    expRet = sum(x)/m;
    expRet = gather(expRet);

    x = bsxfun(@minus,localPart(x),sum(localPart(x),1)./m);  % Remove mean
    x = codistributed(x, codistributor('1d',1));

    covMat = (x' * x) / (m-1);
    covMat = gather(covMat,1);

end

Calculating range and points along the efficency frontier

expRet = expRet{1}; % getting data back from workers
covMat = covMat{1}; % getting data back from workers

retRange = [min(expRet(expRet > 0)) max(expRet)];
rangeFudge = abs(diff(retRange))/20;  % a little above and below the range
retRange = retRange + [rangeFudge -rangeFudge];
muVec = linspace(retRange(1), retRange(2), numPoints); % points along frontier

Find the frontier for the stock portfolio

This function uses a parfor. You can combine parfor and spmd in the same program along with serial code. View code for Exercise2_task_optim

[risk, ret] = Exercise2_task_optim(covMat, expRet, muVec);

Visualization

fig2 = figure;
Exercise2_plot_optim(fig2, risk, ret);

Close the matlabpool

if matlabpool('size') ~= 0
    matlabpool close
else
    warning('MATLAB:poolClose', 'matlabpool already closed')
end

Sending a stop signal to all the labs...
Waiting for parallel job to finish...
Performing parallel job cleanup...
Done.