Obtaining Efficient Portfolios for Target Returns
This example shows how to obtain efficient portfolios that have targeted portfolio returns using the estimateFrontierByReturn
function.
The estimateFrontierByReturn
function accepts one or more target portfolios returns and obtains efficient portfolios with the specified returns. For example, assume that you have a universe of four assets where you want to obtain efficient portfolios with target portfolio returns of 6%, 9%, and 12%:
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 = estimateFrontierByReturn(p, [0.06, 0.09, 0.12]); display(pwgt)
pwgt = 4×3
0.8772 0.5032 0.1293
0.0434 0.2488 0.4541
0.0416 0.0780 0.1143
0.0378 0.1700 0.3022
Sometimes, you can request a return for which no efficient portfolio exists. Based on the previous code, suppose that you want a portfolio with a 5% return (which is the return of the first asset). A portfolio that is fully invested in the first asset, however, is inefficient. estimateFrontierByReturn
warns if your target returns are outside the range of efficient portfolio returns and replaces it with the endpoint portfolio of the efficient frontier closest to your target return. The best way to avoid this situation is to bracket your target portfolio returns with estimateFrontierLimits
and estimatePortReturn
(see Obtaining Endpoints of the Efficient Frontier and Obtaining Portfolio Risks and Returns).
pret = estimatePortReturn(p, p.estimateFrontierLimits); display(pret)
pret = 2×1
0.0590
0.1800
This result indicates that efficient portfolios have returns that range between 5.9% and 18%.
If you have an initial portfolio, estimateFrontierByReturn
also returns purchases and sales to get from your initial portfolio to the target portfolios on the efficient frontier. For example, given an initial portfolio in pwgt0
, to obtain purchases and sales with target returns of 6%, 9%, and 12%:
pwgt0 = [ 0.3; 0.3; 0.2; 0.1 ]; p = setInitPort(p, pwgt0); [pwgt, pbuy, psell] = estimateFrontierByReturn(p, [0.06, 0.09, 0.12]); display(pwgt)
pwgt = 4×3
0.8772 0.5032 0.1293
0.0434 0.2488 0.4541
0.0416 0.0780 0.1143
0.0378 0.1700 0.3022
display(pbuy)
pbuy = 4×3
0.5772 0.2032 0
0 0 0.1541
0 0 0
0 0.0700 0.2022
display(psell)
psell = 4×3
0 0 0.1707
0.2566 0.0512 0
0.1584 0.1220 0.0857
0.0622 0 0
If you do not have an initial portfolio, the purchase and sale weights assume that your initial portfolio is 0
.
See Also
Portfolio
| estimateFrontier
| estimateFrontierLimits
| estimatePortMoments
| estimateFrontierByReturn
| estimatePortReturn
| estimateFrontierByRisk
| estimatePortRisk
| estimateFrontierByRisk
| estimateMaxSharpeRatio
| setSolver
Topics
- 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 Using Financial Toolbox
- Portfolio Optimization with Semicontinuous and Cardinality Constraints
- Black-Litterman Portfolio Optimization Using Financial Toolbox
- Portfolio Optimization Using Factor Models
- Portfolio Optimization Using Social Performance Measure
- Diversify Portfolios Using Custom Objective
- Portfolio Object
- Portfolio Optimization Theory
- Portfolio Object Workflow