Obtaining Endpoints of the Efficient Frontier
Often, you might be interested in the endpoint portfolios for the efficient frontier. Suppose
that you want to determine the range of returns from minimum to maximum to refine a
search for a portfolio with a specific target return. Use the estimateFrontierLimits
function to obtain the endpoint portfolios:
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 ]; m = m/12; C = C/12; AssetScenarios = mvnrnd(m, C, 20000); p = PortfolioMAD; p = setScenarios(p, AssetScenarios); p = setDefaultConstraints(p); pwgt = estimateFrontierLimits(p); disp(pwgt)
0.8875 0.0000 0.0373 0.0000 0.0386 0.0000 0.0366 1.0000
Note
The endpoints of the efficient frontier depend upon the Scenarios in the
PortfolioMAD
object. If you change the Scenarios, you are
likely to obtain different endpoints.
Starting from an initial portfolio, estimateFrontierLimits
also returns
purchases and sales to get from the initial portfolio to the endpoint portfolios on the
efficient frontier. For example, given an initial portfolio in pwgt0
,
you can obtain purchases and
sales:
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 ]; m = m/12; C = C/12; AssetScenarios = mvnrnd(m, C, 20000); p = PortfolioMAD; p = setScenarios(p, AssetScenarios); p = setDefaultConstraints(p); pwgt0 = [ 0.3; 0.3; 0.2; 0.1 ]; p = setInitPort(p, pwgt0); [pwgt, pbuy, psell] = estimateFrontierLimits(p); display(pwgt) display(pbuy) display(psell)
pwgt = 0.8927 0.0000 0.0334 0.0000 0.0422 0.0000 0.0317 1.0000 pbuy = 0.5927 0 0 0 0 0 0 0.9000 psell = 0 0.3000 0.2666 0.3000 0.1578 0.2000 0.0683 0
0
.
See Also
PortfolioMAD
| estimateFrontier
| estimateFrontierLimits
| estimateFrontierByReturn
| estimatePortReturn
| estimateFrontierByRisk
| estimatePortRisk
| estimateFrontierByRisk
| setSolver
Related Examples
- Estimate Efficient Portfolios Along the Entire Frontier for PortfolioMAD Object
- Creating the PortfolioMAD Object
- Working with MAD Portfolio Constraints Using Defaults
- Estimate Efficient Frontiers for PortfolioMAD Object
- Asset Returns and Scenarios Using PortfolioMAD Object