plotFrontier
Plot efficient frontier
Syntax
Description
[ estimates the efficient frontier
with default number of 10 portfolios on the frontier, and plots the
corresponding efficient frontier for prsk,pret]
= plotFrontier(obj)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.
[
estimates the efficient frontier with a specified number of portfolios
(prsk,pret]
= plotFrontier(obj,NumPortfolios)NumPortfolios) on the frontier, and plots the
corresponding efficient frontier.
[
estimates efficient portfolio risks and returns with
prsk,pret]
= plotFrontier(obj,PortfolioWeights)PortfolioWeights, and plots the efficient frontier with
those portfolios. This syntax assumes that you provide valid efficient portfolio
weights as input. PortWeights is a
NumAssets-by-NumPortfolios
matrix.
[
plots the efficient frontier with the given risks and returns. This syntax
assumes that you provide valid inputs for efficient portfolio risks and returns.
prsk,pret]
= plotFrontier(obj,PortfolioRisks,PortfolioReturns)PortfolioRisks and
PortfolioReturns are vectors with the same size.
Note
plotFrontier handles multiple input formats as
described above. Given an asset universe with
NumAssets assets and an efficient frontier with
NumPortfolios portfolios, remember that portfolio
weights are
NumAsset-by-NumPortfolios
matrices and that portfolio risks and returns are
NumPortfolios-by-1 column
vectors.
Examples
Given a portfolio p, plot the efficient frontier.
load CAPMuniverse p = Portfolio('AssetList',Assets(1:12)); p = estimateAssetMoments(p, Data(:,1:12),'missingdata',true); p = setDefaultConstraints(p); plotFrontier(p);
Given a portfolio p, plot the efficient frontier and specify an axes object using the Parent name-value argument.
% Define the Portfolio object.
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(AssetMean=m,AssetCovar=C);
p = setDefaultConstraints(p); Plot 20 efficient portfolios for the Portfolio object on the left y-axes using the Parent name-value argument.
fig = figure;
ax = newplot(fig);
yyaxis(ax,'left')
[~,~,h1] = plotFrontier(p,20,Parent=ax);Plot 20 efficient portfolios for the associated PortfolioCVaR object on the right y-axes using the Parent name-value argument.
% Create PortfolioCVaR object AssetScenarios = mvnrnd(m,C,1000); pCVaR = PortfolioCVaR(Scenarios=AssetScenarios,ProbabilityLevel=0.95); pCVaR = setDefaultConstraints(pCVaR); % Plot yyaxis(ax,'right') [~,~,h2] = plotFrontier(pCVaR,20,Parent=ax); h2.Color = 'r'; h2.LineStyle = ':'; xlabel(ax,'Portfolio Returns Risk') legend('Standard Deviation','CVaR')
Given a portfolio p, plot the efficient frontier and specify an axes object using an optional first input argument.
% Define the Portfolio object. 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(AssetMean=m,AssetCovar=C); p = p.setDefaultConstraints; % Add an initial portfolio to a copy of the Portfolio object. pInit = p; pInit.InitPort = 1/4*ones(4,1);
Plot both Portfolio objects efficient frontiers using different axes.
figure ax1 = axes('Position',[0.1 0.1 0.7 0.7]); ax2 = axes('Position',[0.65 0.65 0.28 0.28]);
Plot the efficient frontier for the Portfolio object without the initial portfolio (p) in ax2.
[~,~,h] = plotFrontier(ax2,p)
h =
Line (Efficient Frontier) with properties:
Color: [0.0660 0.4430 0.7450]
LineStyle: '-'
LineWidth: 2
Marker: 'none'
MarkerSize: 6
MarkerFaceColor: 'none'
XData: [0.0769 0.0831 0.0994 0.1217 0.1474 0.1750 0.2068 0.2487 0.2968 0.3500]
YData: [0.0590 0.0725 0.0859 0.0994 0.1128 0.1262 0.1397 0.1531 0.1666 0.1800]
Show all properties
Plot the efficient frontiers for the Portfolio object with initial portfolio (pInit) in ax1.
[~,~,hInit] = plotFrontier(ax1,pInit)
hInit = 2×1 graphics array: Scatter (Initial Portfolio) Line (Efficient Frontier)
Modify the plot properties.
h.LineStyle = '--'; hInit(1).MarkerFaceColor = 'r';
Create a Portfolio object for 12 stocks based on CAPMuniverse.mat.
load CAPMuniverse p0 = Portfolio('AssetList',Assets(1:12)); p0 = estimateAssetMoments(p0, Data(:,1:12),'missingdata',true); p0 = setDefaultConstraints(p0);
Use setMinMaxNumAssets to define a maximum number of 3 assets.
pWithMaxNumAssets = setMinMaxNumAssets(p0, [], 3);
Use setBounds to define a lower and upper bound and a BoundType of 'Conditional'.
pWithConditionalBound = setBounds(p0, 0.1, 0.5,'BoundType', 'Conditional');
Use plotFrontier to compare the different portfolio objects.
figure; plotFrontier(p0); hold on; plotFrontier(pWithMaxNumAssets); hold on; plotFrontier(pWithConditionalBound); hold off; legend('p0', 'with Max 3 assets invested', ' with each asset weight 0 or [0.1, 0.5]', 'location', 'best');
![Figure contains an axes object. The axes object with title Efficient Frontier, xlabel Standard Deviation of Portfolio Returns, ylabel Mean of Portfolio Returns contains 3 objects of type line. These objects represent p0, with Max 3 assets invested, with each asset weight 0 or [0.1, 0.5].](../examples/finance/win64/PlotEfficientFrontierPortObjBoundMaxNumExample_01.png)
Define a target return and use estimateFrontierByReturn to compare the three portfolio objects.
targetRetn = 2.0e-3; pwgt0 = estimateFrontierByReturn(p0, targetRetn); pwgtWithMaxNumAssets = estimateFrontierByReturn(pWithMaxNumAssets, targetRetn); pwgtConditionalBound = estimateFrontierByReturn(pWithConditionalBound, targetRetn);
The following table shows the final allocation for specified target return among the three portfolio objects. You can see that the small positions in 'AAPL'and 'HPQ' are avoided in pwgtConditionalBound, and only three assets are invested in pwgtWithMaxNumAssets.
result = table(p0.AssetList',pwgt0,pwgtWithMaxNumAssets,pwgtConditionalBound)
result=12×4 table
Var1 pwgt0 pwgtWithMaxNumAssets pwgtConditionalBound
________ ________ ____________________ ____________________
{'AAPL'} 0.076791 -5.2042e-17 0.1
{'AMZN'} 0 0 0
{'CSCO'} 0 0 0
{'DELL'} 0 0 0
{'EBAY'} 0 0 0
{'GOOG'} 0.44841 0.47297 0.44255
{'HPQ' } 0.022406 0 0
{'IBM' } 0.31139 0.34763 0.31592
{'INTC'} 0 0 0
{'MSFT'} 0.14101 0.1794 0.14153
{'ORCL'} 0 0 0
{'YHOO'} 0 0 0
Given a PortfolioCVaR p, plot 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 ];
m = m/12;
C = C/12;
AssetScenarios = mvnrnd(m, C, 20000);
p = PortfolioCVaR;
p = setScenarios(p, AssetScenarios);
p = setDefaultConstraints(p);
p = setProbabilityLevel(p, 0.95);
plotFrontier(p);
Given a PortfolioMAD p, plot 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 ];
m = m/12;
C = C/12;
AssetScenarios = mvnrnd(m, C, 20000);
p = PortfolioMAD;
p = setScenarios(p, AssetScenarios);
p = setDefaultConstraints(p);
plotFrontier(p);
Input Arguments
Name-Value Arguments
Output Arguments
More About
Tips
You can also use dot notation to plot the efficient frontier.
[prsk, pret] = obj.plotFrontier;
