Postprocessing Results to Set Up Tradable Portfolios

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

Suppose that you set up a portfolio optimization problem and obtained portfolios on the efficient frontier. Use the dataset object 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                 88.232     50.89    13.581         0      0  
    Large-Cap Equities    4.2697    25.147    45.859    30.299      0  
    Small-Cap Equities    3.9151    6.7146    9.6576    9.5949      0  
    Emerging Equities     3.5828    17.249    30.903    60.106    100  

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              0         0           30
    Large-Cap Equities    30         50.597    20.597            0
    Small-Cap Equities    20         12.416         0       7.5843
    Emerging Equities     10         36.987    26.987            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. For an example, see Asset Allocation Case Study.