Postprocessing Results to Set Up Tradable Portfolios

After obtaining efficient portfolios or estimates for expected portfolio risks and returns, use your results to set up trades to move toward an efficient portfolio. For information on the workflow when using PortfolioMAD objects, see PortfolioMAD Object Workflow.

Setting Up Tradable Portfolios

Suppose that you set up a portfolio optimization problem and obtained portfolios on the efficient frontier. Use the dataset object from Statistics and Machine Learning Toolbox™ to form a blotter that lists your portfolios with the names for each asset. For example, suppose that you want to obtain five portfolios along the efficient frontier. You can set up a blotter with weights multiplied by 100 to view the allocations for each portfolio:

m = [ 0.05; 0.1; 0.12; 0.18 ];
C = [ 0.0064 0.00408 0.00192 0;
0.00408 0.0289 0.0204 0.0119;
0.00192 0.0204 0.0576 0.0336;
0 0.0119 0.0336 0.1225 ];

pwgt0 = [ 0.3; 0.3; 0.2; 0.1 ];

p = PortfolioMAD;
p = setAssetList(p, 'Bonds','Large-Cap Equities','Small-Cap Equities','Emerging Equities');
p = setInitPort(p, pwgt0);
p = simulateNormalScenariosByMoments(p, m, C, 20000);
p = setDefaultConstraints(p);

pwgt = estimateFrontier(p, 5);

pnames = cell(1,5);
for i = 1:5
pnames{i} = sprintf('Port%d',i);
end

Blotter = dataset([{100*pwgt},pnames],'obsnames',p.AssetList);
display(Blotter)

Blotter = 

                          Port1     Port2     Port3     Port4     Port5     
    Bonds                 88.154    50.867    13.611         0    1.0609e-12
    Large-Cap Equities    4.0454    22.571    41.276     23.38    7.9362e-13
    Small-Cap Equities    4.2804    9.3108    14.028    17.878    6.4823e-14
    Emerging Equities     3.5202    17.252    31.084    58.743           100

Note

Your results may differ from this result due to the simulation of scenarios.

This result indicates that you would invest primarily in bonds at the minimum-risk/minimum-return end of the efficient frontier (Port1), and that you would invest completely in emerging equity at the maximum-risk/maximum-return end of the efficient frontier (Port5). You can also select a particular efficient portfolio, for example, suppose that you want a portfolio with 15% risk and you add purchase and sale weights outputs obtained from the “estimateFrontier” functions to set up a trade blotter:

m = [ 0.05; 0.1; 0.12; 0.18 ];
C = [ 0.0064 0.00408 0.00192 0;
0.00408 0.0289 0.0204 0.0119;
0.00192 0.0204 0.0576 0.0336;
0 0.0119 0.0336 0.1225 ];

pwgt0 = [ 0.3; 0.3; 0.2; 0.1 ];

p = PortfolioMAD;
p = setAssetList(p, 'Bonds','Large-Cap Equities','Small-Cap Equities','Emerging Equities');

p = setInitPort(p, pwgt0);
p = simulateNormalScenariosByMoments(p, m, C, 20000);
p = p.setDefaultConstraints;

[pwgt, pbuy, psell] = estimateFrontierByRisk(p, 0.15);

Blotter = dataset([{100*[pwgt0, pwgt, pbuy, psell]}, ...
{'Initial','Weight', 'Purchases','Sales'}],'obsnames',p.AssetList);
display(Blotter)

Blotter = 

                          Initial    Weight        Purchases    Sales 
    Bonds                 30         6.0364e-18         0           30
    Large-Cap Equities    30             50.179    20.179            0
    Small-Cap Equities    20              13.43         0       6.5696
    Emerging Equities     10             36.391    26.391            0

If you have prices for each asset (in this example, they can be ETFs), add them to your blotter and then use the tools of the dataset object to obtain shares and shares to be traded.