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.
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
dataset
object to obtain shares and shares to be traded. checkFeasibility
| estimateScenarioMoments
| PortfolioMAD