estimateFrontierByRisk
Estimate optimal portfolios with targeted portfolio risks
Syntax
Description
[
estimates optimal portfolios with targeted portfolio risks for
pwgt
,pbuy
,psell
]
= estimateFrontierByRisk(obj
,TargetRisk
)Portfolio
, PortfolioCVaR
, or
PortfolioMAD
objects. For details on the respective
workflows when using these different objects, see Portfolio Object Workflow, PortfolioCVaR Object Workflow,
and PortfolioMAD Object Workflow.
[
adds name-optional name-value pair arguments for pwgt
,pbuy
,psell
]
= estimateFrontierByRisk(___,Name,Value
)Portfolio
or
PortfolioMAD
objects.
Examples
Obtain Portfolios with Targeted Portfolio Risks for a Portfolio Object
To obtain efficient portfolios that have targeted portfolio risks, the estimateFrontierByRisk
function accepts one or more target portfolio risks and obtains efficient portfolios with the specified risks. Assume you have a universe of four assets where you want to obtain efficient portfolios with target portfolio risks of 12%, 14%, and 16%. This example uses the default 'direct'
method to estimate the optimal portfolios with targeted portfolio risks.
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 = estimateFrontierByRisk(p, [0.12, 0.14, 0.16]); display(pwgt);
pwgt = 4×3
0.3984 0.2659 0.1416
0.3064 0.3791 0.4474
0.0882 0.1010 0.1131
0.2071 0.2540 0.2979
Use Portfolio Object to Solve for Portfolio Weights to Achieve Min/Max Objective
To obtain efficient portfolios for a Portfolio
object that has targeted portfolio risks, estimateFrontierByRisk
accepts one or more target portfolio risks and obtains efficient portfolios with the specified risks.
Load the stock price data and set portfolio constraints so that the total weight of the portfolio must equal 1
and the maximum allocation to for any one stock is 50%, while the minimum is 5%.
T = readtable('dowPortfolio.xlsx');
| Dates | DJI | AA | AIG | AXP | BA | C | CAT | DD | DIS | GE | GM | HD | HON | HPQ | IBM | INTC | JNJ | JPM | KO | MCD | MMM | MO | MRK | MSFT | PFE | PG | T | UTX | VZ | WMT | XOM |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 1/3/2006 | 1.0847e+04 | 28.7200 | 68.4100 | 51.5300 | 68.6300 | 45.2600 | 55.8600 | 40.6800 | 24.1800 | 33.6000 | 17.8200 | 39.7900 | 36.1400 | 28.3500 | 80.1300 | 24.5700 | 59.0800 | 37.7800 | 38.9800 | 32.7200 | 75.9300 | 52.2700 | 30.7300 | 26.1900 | 22.1600 | 56.3800 | 22.7000 | 54.9400 | 26.7900 | 44.9000 | 56.6400 |
2 | 1/4/2006 | 1.0880e+04 | 28.8900 | 68.5100 | 51.0300 | 69.3400 | 44.4200 | 57.2900 | 40.4600 | 23.7700 | 33.5600 | 18.3000 | 39.0500 | 35.9900 | 29.1800 | 80.0300 | 24.9000 | 59.9900 | 37.5600 | 38.9100 | 33.0100 | 75.5400 | 52.6500 | 31.0800 | 26.3200 | 22.8800 | 56.4800 | 22.8700 | 54.6100 | 27.5800 | 44.9900 | 56.7400 |
3 | 1/5/2006 | 1.0882e+04 | 29.1200 | 68.6000 | 51.5700 | 68.5300 | 44.6500 | 57.2900 | 40.3800 | 24.1900 | 33.4700 | 19.3400 | 38.6700 | 35.9700 | 28.9700 | 80.5600 | 25.2500 | 59.7400 | 37.6700 | 39.1000 | 33.0500 | 74.8500 | 52.5200 | 31.1300 | 26.3400 | 22.9000 | 56.3000 | 22.9200 | 54.4100 | 27.9000 | 44.3800 | 56.4500 |
4 | 1/6/2006 | 1.0959e+04 | 29.0200 | 68.8900 | 51.7500 | 67.5700 | 44.6500 | 58.4300 | 40.5500 | 24.5200 | 33.7000 | 19.6100 | 38.9600 | 36.5300 | 29.8000 | 82.9600 | 25.2800 | 60.0100 | 37.9400 | 39.4700 | 33.2500 | 75.4700 | 52.9500 | 31.0800 | 26.2600 | 23.1600 | 56.2400 | 23.2100 | 54.5800 | 28.0100 | 44.5600 | 57.5700 |
5 | 1/9/2006 | 1.1012e+04 | 29.3700 | 68.5700 | 53.0400 | 67.0100 | 44.4300 | 59.4900 | 40.3200 | 24.7800 | 33.6100 | 21.1200 | 39.3800 | 36.2300 | 30.1700 | 81.7600 | 25.4400 | 60.3800 | 38.5500 | 39.6600 | 33.8800 | 75.8400 | 53.1100 | 31.5800 | 26.2100 | 23.1600 | 56.6700 | 23.3000 | 55.2000 | 28.1200 | 44.4000 | 57.5400 |
6 | 1/10/2006 | 1.1012e+04 | 28.4400 | 69.1800 | 52.8800 | 67.3300 | 44.5700 | 59.2500 | 40.2000 | 25.0900 | 33.4300 | 20.7900 | 40.3300 | 36.1700 | 30.3300 | 82.1000 | 25.1000 | 60.4900 | 38.6100 | 39.7000 | 33.9100 | 75.3700 | 53.0400 | 31.2700 | 26.3500 | 22.7700 | 56.4500 | 23.1600 | 55.2400 | 28.2400 | 44.5400 | 57.9900 |
7 | 1/11/2006 | 1.1043e+04 | 28.0500 | 69.6000 | 52.5900 | 68.3000 | 44.9800 | 59.2800 | 38.8700 | 25.3300 | 33.6600 | 20.6100 | 41.4400 | 36.1900 | 30.8800 | 82.1900 | 25.1200 | 59.9100 | 38.5800 | 39.7200 | 34.5000 | 75.2200 | 53.3100 | 31.3900 | 26.6300 | 23.0600 | 56.6500 | 23.3400 | 54.4100 | 28.5800 | 45.2300 | 58.3800 |
8 | 1/12/2006 | 1.0962e+04 | 27.6800 | 69.0400 | 52.6000 | 67.9000 | 45.0200 | 60.1300 | 38.0200 | 25.4100 | 33.2500 | 19.7600 | 41.0500 | 35.7700 | 30.5700 | 81.6100 | 24.9600 | 59.6300 | 37.8700 | 39.5000 | 33.9600 | 74.5700 | 53.2300 | 31.4100 | 26.4800 | 22.9000 | 56.0200 | 23.2400 | 53.9000 | 28.6900 | 44.4300 | 57.7700 |
9 | 1/13/2006 | 1.0960e+04 | 27.8100 | 68.8400 | 52.5000 | 67.7000 | 44.9200 | 60.2400 | 37.8600 | 25.4700 | 33.3500 | 19.2000 | 40.4300 | 35.8500 | 31.4300 | 81.2200 | 24.7800 | 59.2600 | 37.8400 | 39.3700 | 33.6500 | 74.3800 | 53.2900 | 31.4000 | 26.5300 | 22.9900 | 56.4900 | 23.2700 | 54.1000 | 28.7500 | 44.1000 | 59.0600 |
10 | 1/17/2006 | 1.0896e+04 | 27.9700 | 67.8400 | 52.0300 | 66.9300 | 44.4700 | 60.8500 | 37.7500 | 25.1500 | 33.2000 | 18.6800 | 40.1100 | 35.5600 | 31.2000 | 81.0500 | 24.5200 | 58.7400 | 37.6400 | 39.1100 | 33.7700 | 73.9900 | 52.8500 | 31.1600 | 26.3400 | 22.6300 | 56.2500 | 23.1300 | 54.4100 | 28.1200 | 43.6600 | 59.6100 |
11 | 1/18/2006 | 1.0855e+04 | 27.8100 | 67.4200 | 51.8400 | 66.5800 | 44.4100 | 60.0400 | 37.5400 | 24.9700 | 33.0800 | 18.9800 | 40.4200 | 35.7100 | 31.2100 | 81.8300 | 21.7200 | 59.6100 | 37.2400 | 38.9100 | 34.1600 | 74.0700 | 52.8900 | 30.9900 | 26.1800 | 22.3600 | 56.5400 | 23.1100 | 54.0800 | 27.8300 | 43.8800 | 58.7800 |
12 | 1/19/2006 | 1.0881e+04 | 28.3300 | 66.9200 | 51.6600 | 66.4200 | 44.0200 | 60.6600 | 37.6900 | 26.0000 | 32.9500 | 19.1000 | 39.8300 | 35.8800 | 31.7700 | 81.1400 | 21.5300 | 59.6000 | 37.0300 | 39.0100 | 34.3600 | 73.8100 | 52.6800 | 31.2600 | 26.3600 | 23.2700 | 56.3900 | 23.1800 | 54.4100 | 28.0700 | 44.4900 | 59.5700 |
13 | 1/20/2006 | 1.0667e+04 | 27.6700 | 65.5500 | 50.4900 | 64.7900 | 41.9500 | 58.9800 | 37.3400 | 25.4900 | 31.7000 | 18.9000 | 38.7600 | 34.5700 | 31.2800 | 79.4500 | 20.9100 | 58.2800 | 36.0700 | 38.2100 | 35.0100 | 72.2100 | 52.1800 | 31.2000 | 25.7700 | 23.0300 | 55.7400 | 23.0100 | 53.4600 | 27.6400 | 43.7100 | 58.6300 |
14 | 1/23/2006 | 1.0689e+04 | 28.0300 | 65.4600 | 50.5300 | 65.3000 | 42.2400 | 59.2300 | 37.3700 | 25.2900 | 31.6300 | 20.6000 | 38.2900 | 34.7800 | 30.8800 | 79.5000 | 20.5200 | 58.6600 | 36.2800 | 38.6000 | 34.8600 | 72.6500 | 52.0900 | 30.8000 | 25.7100 | 23.1900 | 55.5500 | 22.7700 | 52.9400 | 27.6900 | 43.9500 | 59.2800 |
15 | 1/24/2006 | 1.0712e+04 | 28.1600 | 65.3900 | 51.8900 | 65.9200 | 42.2500 | 59.5300 | 37.0900 | 25.7600 | 31.3200 | 21.7300 | 39.0300 | 35.2500 | 30.9100 | 78.9500 | 20.4500 | 56.9000 | 36.1300 | 38.9800 | 35.0000 | 71.2100 | 51.7400 | 30.7600 | 25.6400 | 22.9100 | 55.7700 | 22.9600 | 54.8600 | 27.6000 | 44.4100 | 59.0500 |
16 | 1/25/2006 | 1.0710e+04 | 28.5700 | 64.6700 | 51.9700 | 65.1900 | 42.4500 | 60.2300 | 37.0500 | 25.2100 | 31.1300 | 22.4800 | 38.5700 | 34.7900 | 31.6400 | 79.0100 | 20.3800 | 56.0800 | 36.4800 | 39.2100 | 34.3200 | 70.0600 | 51.4900 | 31.1400 | 25.7600 | 23.1400 | 56.3500 | 23.4700 | 55.4000 | 28.0300 | 44.6500 | 58.3200 |
⋮ |
Setup a portfolio of ten stocks.
symbol = T.Properties.VariableNames(3:12)'; dailyReturn = tick2ret(T{:,3:12}); p = Portfolio('AssetList',symbol,'RiskFreeRate',0.01/252);
Estimate the mean and variance of portfolio based on daily returns using estimateAssetMoments
.
p = estimateAssetMoments(p,dailyReturn);
Set the total weight of portfolio to 1
where the LowerBudget
= 1
and the UpperBudget
= 1
.
p = setBudget(p,1,1)
p = Portfolio with properties: BuyCost: [] SellCost: [] RiskFreeRate: 3.9683e-05 AssetMean: [10x1 double] AssetCovar: [10x10 double] TrackingError: [] TrackingPort: [] Turnover: [] BuyTurnover: [] SellTurnover: [] Name: [] NumAssets: 10 AssetList: {'AA' 'AIG' 'AXP' 'BA' 'C' 'CAT' 'DD' 'DIS' 'GE' 'GM'} InitPort: [] AInequality: [] bInequality: [] AEquality: [] bEquality: [] LowerBound: [] UpperBound: [] LowerBudget: 1 UpperBudget: 1 GroupMatrix: [] LowerGroup: [] UpperGroup: [] GroupA: [] GroupB: [] LowerRatio: [] UpperRatio: [] MinNumAssets: [] MaxNumAssets: [] ConditionalBudgetThreshold: [] ConditionalUpperBudget: [] BoundType: []
Set the maximum allocation for any one security to 50%, and set the minimum for any one security to 5%.
p.LowerBound = repmat(0.05,[10,1]); p.UpperBound = repmat(0.5,[10,1]);
Calculate the portfolio weights for the maximum Sharpe ratio using estimateMaxSharpeRatio
.
w1 = estimateMaxSharpeRatio(p)
w1 = 10×1
0.0500
0.0500
0.0500
0.0500
0.0500
0.0500
0.0500
0.4357
0.0500
0.1643
Estimate moments of portfolio returns using estimatePortMoments
.
[risk1, ret1] = estimatePortMoments(p,w1)
risk1 = 0.0090
ret1 = 0.0013
Calculate portfolio weights given a target risk.
TargetRisk = 0.01
TargetRisk = 0.0100
Use estimateFrontierByRisk
to estimate optimal portfolios with targeted portfolio risks.
w3 = estimateFrontierByRisk(p,TargetRisk)
w3 = 10×1
0.0500
0.0500
0.0500
0.0500
0.0500
0.0500
0.0500
0.3419
0.0500
0.2581
Estimate moments of portfolio returns using estimatePortMoments
, where risk3
is estimates for standard deviations of portfolio returns for each portfolio and ret3
is estimates for means of portfolio returns for each portfolio.
[risk3,ret3] = estimatePortMoments(p,w3)
risk3 = 0.0100
ret3 = 0.0013
Obtain Portfolios with Targeted Portfolio Risks for a Portfolio
Object with BoundType
, MinNumAsset
, and MaxNumAsset
Constraints
When any one, or any combination of the constraints from 'Conditional'
BoundType
, MinNumAssets
, and MaxNumAssets
are active, the portfolio problem is formulated as mixed integer programming problem and the MINLP solver is used.
Create a Portfolio
object for three assets.
AssetMean = [ 0.0101110; 0.0043532; 0.0137058 ]; AssetCovar = [ 0.00324625 0.00022983 0.00420395; 0.00022983 0.00049937 0.00019247; 0.00420395 0.00019247 0.00764097 ]; p = Portfolio('AssetMean', AssetMean, 'AssetCovar', AssetCovar); p = setDefaultConstraints(p);
Use setBounds
with semicontinuous constraints to set xi = 0
or 0.02
<= xi
<= 0.5
for all i = 1
,...NumAssets
.
p = setBounds(p, 0.02, 0.7,'BoundType', 'Conditional', 'NumAssets', 3);
When working with a Portfolio
object, the setMinMaxNumAssets
function enables you to set up the limits on the number of assets invested (as known as cardinality) constraints. This sets the total number of allocated assets satisfying the Bound constraints that are between MinNumAssets
and MaxNumAssets
. By setting MinNumAssets
= MaxNumAssets
= 2, only two of the three assets are invested in the portfolio.
p = setMinMaxNumAssets(p, 2, 2);
Use estimateFrontierByRisk
to estimate optimal portfolios with targeted portfolio risks.
[pwgt, pbuy, psell] = estimateFrontierByRisk(p,[0.0324241, 0.0694534 ])
pwgt = 3×2
0.0000 0.5000
0.6907 0.0000
0.3093 0.5000
pbuy = 3×2
0.0000 0.5000
0.6907 0.0000
0.3093 0.5000
psell = 3×2
0 0
0 0
0 0
The estimateFrontierByRisk
function uses the MINLP solver to solve this problem. Use the setSolverMINLP
function to configure the SolverType
and options.
p.solverTypeMINLP
ans = 'OuterApproximation'
p.solverOptionsMINLP
ans = struct with fields:
MaxIterations: 1000
AbsoluteGapTolerance: 1.0000e-07
RelativeGapTolerance: 1.0000e-05
NonlinearScalingFactor: 1000
ObjectiveScalingFactor: 1000
Display: 'off'
CutGeneration: 'basic'
MaxIterationsInactiveCut: 30
ActiveCutTolerance: 1.0000e-07
IntMainSolverOptions: [1x1 optim.options.Intlinprog]
NumIterationsEarlyIntegerConvergence: 30
ExtendedFormulation: 0
NumInnerCuts: 10
NumInitialOuterCuts: 10
Obtain Portfolios with Targeted Portfolio Risks for a Portfolio Object Using the Direct Method and Solver Options
To obtain efficient portfolios that have targeted portfolio risks, the estimateFrontierByRisk
function accepts one or more target portfolio risks and obtains efficient portfolios with the specified risks. Assume you have a universe of four assets where you want to obtain efficient portfolios with target portfolio risks of 12%, 14%, and 16%. This example uses the default'direct'
method to estimate the optimal portfolios with targeted portfolio risks. The 'direct'
method uses fmincon
to solve the optimization problem that maximizes portfolio return, subject to the target risk as the quadratic nonlinear constraint. setSolver
specifies the solverType
and SolverOptions
for fmincon
.
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); p = setSolver(p, 'fmincon', 'Display', 'off', 'Algorithm', 'sqp', ... 'SpecifyObjectiveGradient', true, 'SpecifyConstraintGradient', true, ... 'ConstraintTolerance', 1.0e-8, 'OptimalityTolerance', 1.0e-8, 'StepTolerance', 1.0e-8); pwgt = estimateFrontierByRisk(p, [0.12, 0.14, 0.16]); display(pwgt);
pwgt = 4×3
0.3984 0.2659 0.1416
0.3064 0.3791 0.4474
0.0882 0.1010 0.1131
0.2071 0.2540 0.2979
Obtain Portfolios with Targeted Portfolio Risks for a PortfolioCVaR Object
To obtain efficient portfolios that have targeted portfolio risks, the estimateFrontierByRisk
function accepts one or more target portfolio risks and obtains efficient portfolios with the specified risks. Assume you have a universe of four assets where you want to obtain efficient portfolios with target portfolio risks of 12%, 20%, and 30%.
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 ]; rng(11); p = PortfolioCVaR; p = simulateNormalScenariosByMoments(p, m, C, 2000); p = setDefaultConstraints(p); p = setProbabilityLevel(p, 0.95); pwgt = estimateFrontierByRisk(p, [0.12, 0.20, 0.30]); display(pwgt);
pwgt = 4×3
0.5363 0.1387 0
0.2655 0.4991 0.3830
0.0570 0.1239 0.1461
0.1412 0.2382 0.4709
The function rng
() resets the random number generator to produce the documented results. It is not necessary to reset the random number generator to simulate scenarios.
Obtain Portfolios with Targeted Portfolio Risks for a PortfolioMAD Object
To obtain efficient portfolios that have targeted portfolio risks, the estimateFrontierByRisk
function accepts one or more target portfolio risks and obtains efficient portfolios with the specified risks. Assume you have a universe of four assets where you want to obtain efficient portfolios with target portfolio risks of 12%, 20%, and 25%. This example uses the default 'direct'
method to estimate the optimal portfolios with targeted portfolio risks.
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 ]; rng(11); p = PortfolioMAD; p = simulateNormalScenariosByMoments(p, m, C, 2000); p = setDefaultConstraints(p); pwgt = estimateFrontierByRisk(p, [0.12, 0.20, 0.25]); display(pwgt);
pwgt = 4×3
0.1611 0 0
0.4774 0.2137 0.0047
0.1126 0.1384 0.1200
0.2488 0.6480 0.8753
The function rng
() resets the random number generator to produce the documented results. It is not necessary to reset the random number generator to simulate scenarios.
Obtain Portfolios with Targeted Portfolio Risks for a PortfolioMAD Object Using the Direct Method and Solver Options
To obtain efficient portfolios that have targeted portfolio risks, the estimateFrontierByRisk
function accepts one or more target portfolio risks and obtains efficient portfolios with the specified risks. Assume you have a universe of four assets where you want to obtain efficient portfolios with target portfolio risks of 12%, 20%, and 25%. This example uses the default 'direct'
method to estimate the optimal portfolios with targeted portfolio risks. The 'direct'
method uses fmincon
to solve the optimization problem that maximizes portfolio return, subject to the target risk as the quadratic nonlinear constraint. setSolver
specifies the solverType
and SolverOptions
for fmincon
.
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 ]; rng(11); p = PortfolioMAD; p = simulateNormalScenariosByMoments(p, m, C, 2000); p = setDefaultConstraints(p); p = setSolver(p, 'fmincon', 'Display', 'off', 'Algorithm', 'sqp', ... 'SpecifyObjectiveGradient', true, 'SpecifyConstraintGradient', true, ... 'ConstraintTolerance', 1.0e-8, 'OptimalityTolerance', 1.0e-8, 'StepTolerance', 1.0e-8); plotFrontier(p);
pwgt = estimateFrontierByRisk(p, [0.12 0.20, 0.25]); display(pwgt);
pwgt = 4×3
0.1613 0 0
0.4777 0.2139 0.0037
0.1118 0.1381 0.1214
0.2492 0.6480 0.8749
Input Arguments
obj
— Object for portfolio
object
Object for portfolio, specified using Portfolio
,
PortfolioCVaR
, or PortfolioMAD
object. For more information on creating a portfolio object, see
Note
If no initial portfolio is specified in
obj.InitPort
, it is assumed to be
0
so that pbuy =
max(0,pwgt)
and psell =
max(0,-pwgt)
. For more information on setting an
initial portfolio, see setInitPort
.
Data Types: object
TargetRisk
— Target values for portfolio risk
vector
Target values for portfolio risk, specified as a
NumPorts
vector.
Note
If any TargetRisk
values are outside the range
of risks for efficient portfolios, the target risk is replaced with
the minimum or maximum efficient portfolio risk, depending on
whether the target risk is below or above the range of efficient
portfolio risks.
Data Types: double
Name-Value Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name
in quotes.
Example: [pwgt,pbuy,psell] =
estimateFrontierByRisk(p,‘method’,‘direct’)
Method
— Method to estimate frontier by risk for Portfolio
or PortfolioMAD
objects
'direct'
(default) | character vector with value 'direct'
or
'iterative'
Method to estimate frontier by risk for Portfolio
or PortfolioMAD
objects, specified as the
comma-separated pair consisting of 'Method'
and a
character vector with one of the following values:
'direct'
— Construct one optimization problem to maximize the portfolio return with target risk as the nonlinear constraint, and solve it directly usingfmincon
, instead of iteratively exploring the efficient frontier. For an example of using the'direct'
option, see Obtain Portfolios with Targeted Portfolio Risks for a Portfolio Object Using the Direct Method and Solver Options and Obtain Portfolios with Targeted Portfolio Risks for a PortfolioMAD Object Using the Direct Method and Solver Options.'iterative'
— One-dimensional optimization usingfminbnd
to find the portfolio return between min and max return on the frontier that minimizes the difference between the actual risk and target risk. Then the portfolio weights are obtained by solving a frontier by return problem. Consequently, the'iterative'
method is slower than the'direct'
.
Data Types: char
Output Arguments
pwgt
— Optimal portfolios on efficient frontier with specified target risks
matrix
Optimal portfolios on the efficient frontier with specified target returns
from TargetRisk
, returned as a
NumAssets
-by-NumPorts
matrix.
pwgt
is returned for a Portfolio
,
PortfolioCVaR
, or PortfolioMAD
input object (obj
).
pbuy
— Purchases relative to initial portfolio for optimal portfolios on efficient frontier
matrix
Purchases relative to an initial portfolio for optimal portfolios on the
efficient frontier, returned as
NumAssets
-by-NumPorts
matrix.
Note
If no initial portfolio is specified in
obj.InitPort
, that value is assumed to be
0
such that pbuy =
max(0,pwgt)
and psell =
max(0,-pwgt)
.
pbuy
is returned for a Portfolio
,
PortfolioCVaR
, or PortfolioMAD
input object (obj
).
psell
— Sales relative to initial portfolio for optimal portfolios on efficient frontier
matrix
Sales relative to an initial portfolio for optimal portfolios on the
efficient frontier, returned as a
NumAssets
-by-NumPorts
matrix.
Note
If no initial portfolio is specified in
obj.InitPort
, that value is assumed to be
0
such that pbuy =
max(0,pwgt)
and psell =
max(0,-pwgt)
.
psell
is returned for Portfolio
,
PortfolioCVaR
, or PortfolioMAD
input object (obj
).
Tips
You can also use dot notation to estimate optimal portfolios with targeted portfolio risks.
[pwgt,pbuy,psell] = obj.estimateFrontierByRisk(TargetRisk);
or
[pwgt,pbuy,psell] = obj.estimateFrontierByRisk(TargetRisk,Name,Value);
Version History
Introduced in R2011a
See Also
estimateFrontier
| estimateFrontierByReturn
| estimateFrontierLimits
| setInitPort
| rng
| setBounds
| setMinMaxNumAssets
Topics
- Estimate Efficient Portfolios for Entire Efficient Frontier for Portfolio Object
- Estimate Efficient Frontiers for Portfolio Object
- Estimate Efficient Portfolios for Entire Frontier for PortfolioCVaR Object
- Estimate Efficient Frontiers for PortfolioCVaR Object
- Estimate Efficient Portfolios Along the Entire Frontier for PortfolioMAD Object
- Estimate Efficient Frontiers for PortfolioMAD Object
- Portfolio Optimization Examples Using Financial Toolbox
- Black-Litterman Portfolio Optimization Using Financial Toolbox
- Portfolio Optimization Using Factor Models
- Add Risk Constraint to a Custom Objective Problem
- Portfolio Optimization Theory
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