Estimate Efficient Portfolios for Entire Efficient Frontier for Portfolio Object
There are two ways to look at a portfolio optimization problem that depends on what
you are trying to do. One goal is to estimate efficient portfolios and the other is to
estimate efficient frontiers. This section focuses on the former goal and Estimate Efficient Frontiers for Portfolio Object focuses on the latter goal. For information on
the workflow when using Portfolio
objects, see Portfolio Object Workflow.
Obtaining Portfolios Along the Entire Efficient Frontier
The most basic way to obtain optimal portfolios is to obtain points over the
entire range of the efficient frontier. Given a portfolio optimization problem in a
Portfolio
object, the estimateFrontier
function computes
efficient portfolios spaced evenly according to the return proxy from the minimum to
maximum return efficient portfolios. The number of portfolios estimated is
controlled by the hidden property defaultNumPorts
which is set to
10
. A different value for the number of portfolios estimated
is specified as input to estimateFrontier
. This example
shows the default number of efficient portfolios over the entire range of the
efficient frontier:
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 = estimateFrontier(p); disp(pwgt)
0.8891 0.7215 0.5540 0.3865 0.2190 0.0515 0 0 0 0 0.0369 0.1289 0.2209 0.3129 0.4049 0.4969 0.4049 0.2314 0.0579 0 0.0404 0.0567 0.0730 0.0893 0.1056 0.1219 0.1320 0.1394 0.1468 0 0.0336 0.0929 0.1521 0.2113 0.2705 0.3297 0.4630 0.6292 0.7953 1.0000
pwgt = estimateFrontier(p, 4); disp(pwgt)
0.8891 0.3865 0 0 0.0369 0.3129 0.4049 0 0.0404 0.0893 0.1320 0 0.0336 0.2113 0.4630 1.0000
Starting from the initial portfolio, estimateFrontier
also returns
purchases and sales to get from your initial portfolio to each efficient portfolio
on the efficient frontier. For example, given an initial portfolio in
pwgt0
, you can obtain purchases and
sales:
pwgt0 = [ 0.3; 0.3; 0.2; 0.1 ]; p = setInitPort(p, pwgt0); [pwgt, pbuy, psell] = estimateFrontier(p); display(pwgt) display(pbuy) display(psell)
pwgt = 0.8891 0.7215 0.5540 0.3865 0.2190 0.0515 0 0 0 0 0.0369 0.1289 0.2209 0.3129 0.4049 0.4969 0.4049 0.2314 0.0579 0 0.0404 0.0567 0.0730 0.0893 0.1056 0.1219 0.1320 0.1394 0.1468 0 0.0336 0.0929 0.1521 0.2113 0.2705 0.3297 0.4630 0.6292 0.7953 1.0000 pbuy = 0.5891 0.4215 0.2540 0.0865 0 0 0 0 0 0 0 0 0 0.0129 0.1049 0.1969 0.1049 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0521 0.1113 0.1705 0.2297 0.3630 0.5292 0.6953 0.9000 psell = 0 0 0 0 0.0810 0.2485 0.3000 0.3000 0.3000 0.3000 0.2631 0.1711 0.0791 0 0 0 0 0.0686 0.2421 0.3000 0.1596 0.1433 0.1270 0.1107 0.0944 0.0781 0.0680 0.0606 0.0532 0.2000 0.0664 0.0071 0 0 0 0 0 0 0 0
0
. See Also
Portfolio
| estimateFrontier
| estimateFrontierLimits
| estimatePortMoments
| estimateFrontierByReturn
| estimatePortReturn
| estimateFrontierByRisk
| estimatePortRisk
| estimateFrontierByRisk
| estimateMaxSharpeRatio
| setSolver
Related Examples
- Obtaining Endpoints of the Efficient Frontier
- Obtaining Efficient Portfolios for Target Returns
- Obtaining Efficient Portfolios for Target Risks
- Efficient Portfolio That Maximizes Sharpe Ratio
- Plotting the Efficient Frontier for a 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