Visualisation of N-Asset Portfolio in Matlab

Many of you who wished to use the Matlab’s Financial Toolbox for portfolio visualization most probably realised that something was wrong. Not every time the annualised risk and return for different time-series matched with what was expected. Below you can find an improved piece of code which does the job correctly.

The input sampling of your financial time-series now can be specified directly as daily, weekly, monthly, or quarterly and the risk-return diagram will be displayed with annualised results. Otherwise, you have an option, instead of annualised value, specify another time-horizon. All smooth and easy.

% Specialised plotting function for visualisation of portfolios
% based on the Financial Toolbox's portfolio objects
% 
% Modified by Pawel Lachowicz, 2014/03/01
%
% Remarks: Essential corrections introduced in the calculation and plotting
% of the annualised risk and returns coded incorrectly by the team at 
% The MathWorks, Inc.

function plotportfolio(varargin)

    plottitle = varargin{1};  % plot title, e.g. 'Efficient Frontier'
    plotfreq =  varargin{2};  % frequency of raw data (dt; or 'daily', etc.)
    plotfreq2=  varargin{3};  % e.g. ’annualised’
    plotfreq3=  varargin{4};
    plotlegend = [];

    switch plotfreq2
        case 'annualised'
            switch plotfreq
                case 'daily'
                    periods=252;
                case 'weekly'
                    periods=52;
                case 'monthly'
                    periods=12;
                case 'quarterly'
                    periods=4;
            end
        otherwise
            periods=plotfreq3;
    end

    for i = 5:nargin
        plotinfo = varargin{i};

        plottype = plotinfo{1};
        plotrsk  = plotinfo{2};
        plotret  = plotinfo{3};
        if numel(plotinfo) > 3
            plotlabel = plotinfo{4};
        else
            plotlabel = [];
        end
        if numel(plotinfo) > 4
            plotstyle = plotinfo{5};
            if isempty(plotstyle)
                plotstyle = 'b';
            end
        else
            if strcmpi(plottype,'line')
                plotstyle = 'b';
            else
                plotstyle = 'g';
            end
        end
        if numel(plotinfo) > 5
            plotline = plotinfo{6};
            if isempty(plotline)
                plotline = 1;
            end
        else
            if strcmpi(plottype,'line')
                plotline = 2;
            else
                plotline = [];
            end
        end

        % line plot
        if strcmpi(plottype,'line')
            hold on;
            for k = 1:size(plotrsk,2)
                plot(plotrsk(:,k)*sqrt(periods),((plotret(:,k)+1).^periods-1), ...
                     plotstyle, 'LineWidth', plotline);
                if i == 2 && k == 1
                    hold on
                end
                if ~isempty(plotlabel) && ~isempty(plotlabel{k})
                    plotlegend = [ plotlegend, {plotlabel{k}} ];
                end
            end

        % scatter plot
        else
            if any(plotstyle == '.')
                scatter(plotrsk*sqrt(periods),((plotret(:,k)+1).^periods-1),'or','Filled');
            else
                scatter(plotrsk*sqrt(periods),((plotret(:,k)+1).^periods-1),'og','Filled');
            end			
            if i==2
                hold on
            end
            if ~isempty(plotlabel)
                for k = 1:numel(plotrsk)
                    if ~isempty(plotlabel{k})
                        text(plotrsk(k)*sqrt(periods)+0.005, ...
                            ((plotret(k)+1).^periods-1), plotlabel{k},'FontSize', 9);
                    end
                end
            end
        end
    end

    if ~isempty(plotlegend)
        legend(plotlegend,'Location','SouthEast');
    end
    if(plotfreq2=='annualised')
        xlabel('Annualised Volatility');
        ylabel('Annualised Expected Returns');
    else
        xlabel('Volatility');
        ylabel('Returns');
    end
    grid on

end

Now, you can call it with various parameters of your interest, matching the data directly, for instance:

plotportfolio('Portfolio',dt,'annualised',[], ... 
    {'line', prsk, pret}, ...
    {'scatter',CashRsk,CashRet, {'Cash'}}, ...
    {'scatter', sqrt(diag(p.AssetCovar)), p.AssetMean, p.AssetList,'.r'});