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 ]; p = Portfolio; p = setAssetMoments(p, m, C); p = setDefaultConstraints(p); pwgt = estimateFrontierLimits(p); disp(pwgt)
0.8891 0 0.0369 0 0.0404 0 0.0336 1.0000
The estimatePortMoments
function shows the
range of risks and returns for efficient
portfolios:
[prsk, pret] = estimatePortMoments(p, pwgt); disp([prsk, pret])
0.0769 0.0590 0.3500 0.1800
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 ]; p = Portfolio; p = setAssetMoments(p, m, C); 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 = 0.8891 0 0.0369 0 0.0404 0 0.0336 1.0000 pbuy = 0.5891 0 0 0 0 0 0 0.9000 psell = 0 0.3000 0.2631 0.3000 0.1596 0.2000 0.0664 0
0
.
See Also
Portfolio
| estimateFrontier
| estimateFrontierLimits
| estimatePortMoments
| estimateFrontierByReturn
| estimatePortReturn
| estimateFrontierByRisk
| estimatePortRisk
| estimateFrontierByRisk
| estimateMaxSharpeRatio
| setSolver
Related Examples
- Estimate Efficient Portfolios for Entire Efficient Frontier for Portfolio Object
- Creating the Portfolio Object
- Working with Portfolio Constraints Using Defaults
- Estimate Efficient Frontiers for Portfolio Object
- Asset Allocation Case Study
- Portfolio Optimization Examples
- Portfolio Optimization with Semicontinuous and Cardinality Constraints
- Black-Litterman Portfolio Optimization
- Portfolio Optimization Using Factor Models
- Portfolio Optimization Using a Social Performance Measure
- Diversification of Portfolios