estimatePortSharpeRatio

This example shows how to find efficient portfolios that satisfy the target returns and then find the Sharpe ratios corresponding to each of the portfolios.

To obtain efficient portfolios that have targeted portfolio returns, the estimateFrontierByReturn function accepts one or more target portfolio returns and obtains efficient portfolios with the specified returns. Assume you have a universe of four assets where you want to obtain efficient portfolios with target portfolio returns of 6%, 9%, and 12%. Use estimatePortSharpeRatio to obtain the Sharpe ratio for the collection of portfolios (pwgt).

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

pwgt is a NumAssets-by-NumPorts matrix where NumAssets is the number of asset in the universe and NumPorts is the number of portfolios in the collection of portfolios.

psharpe = estimatePortSharpeRatio(p,pwgt) 

psharpe = 3×1

    0.7796
    0.8519
    0.7406

psharpe is a NumPorts-by-1 vector, where NumPorts is the number of portfolios in the collection of portfolios.

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 semi-continuous constraints to set xi=0 or 0.02<=xi<=0.5 for all i=1,...NumAssets.

p = setBounds(p, 0.02, 0.5,'BoundType', 'Conditional', 'NumAssets', 3);                    

When working with a Portfolio object, the setMinMaxNumAssets function enables you to set up cardinality constraints for a long-only portfolio. This sets the cardinality constraints for the Portfolio object, where the total number of allocated assets satisfying the nonzero semi-continuous constraints 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 estimatePortSharpeRatio to estimate Sharpe ratio of given portfolio weights for a Portfolio object.

pwgt = estimateFrontierByReturn(p, [ 0.0072321, 0.0119084 ]);
psharpe = estimatePortSharpeRatio(p,pwgt)

psharpe = 2×1

    0.2230
    0.1715

The estimatePortSharpeRatio function uses the MINLP solver to solve this problem. Use the setSolverMINLP function to configure the SolverType and options.

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