setTrackingError

Set up maximum portfolio tracking error constraint

Syntax

obj = setTrackingError(obj,TrackingError)

obj = setTrackingError(___,TrackingPort,NumAssets)

Description

obj = setTrackingError(obj,TrackingError) sets up a maximum portfolio tracking error constraint for a Portfolio object. For details on the workflow when using a Portfolio object, see Portfolio Object Workflow.

obj = setTrackingError(___,TrackingPort,NumAssets) sets up a maximum portfolio tracking error constraint using optional arguments for TrackingPort and NumAssets.

Examples

Set up a Tracking Error Constraint

Create a Portfolio object.

AssetMean = [ 0.05; 0.1; 0.12; 0.18 ];
AssetCovar = [ 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('mean', AssetMean, 'covar', AssetCovar, 'lb', 0, 'budget', 1)

p = 
  Portfolio with properties:

                       BuyCost: []
                      SellCost: []
                  RiskFreeRate: []
                     AssetMean: [4×1 double]
                    AssetCovar: [4×4 double]
                 TrackingError: []
                  TrackingPort: []
                      Turnover: []
                   BuyTurnover: []
                  SellTurnover: []
                          Name: []
                     NumAssets: 4
                     AssetList: []
                      InitPort: []
                   AInequality: []
                   bInequality: []
                     AEquality: []
                     bEquality: []
                    LowerBound: [4×1 double]
                    UpperBound: []
                   LowerBudget: 1
                   UpperBudget: 1
                   GroupMatrix: []
                    LowerGroup: []
                    UpperGroup: []
                        GroupA: []
                        GroupB: []
                    LowerRatio: []
                    UpperRatio: []
                  MinNumAssets: []
                  MaxNumAssets: []
    ConditionalBudgetThreshold: []
        ConditionalUpperBudget: []
                     BoundType: []

Estimate the Sharpe ratio for the Portfolio object p and define the tracking error.

x0 = estimateMaxSharpeRatio(p);
te = 0.08;
p = setTrackingError(p, te, x0);
display(p.NumAssets);

     4

display(p.TrackingError);

    0.0800

display(p.TrackingPort);

    0.6608
    0.1622
    0.0626
    0.1143

Input Arguments

obj — Object for portfolio

object

Object for portfolio, specified using a Portfolio object. For more information on creating a portfolio object, see Portfolio.

Data Types: object

TrackingError — Upper bound for portfolio tracking error

nonnegative and finite scalar

Upper bound for portfolio tracking error, specified using a nonnegative and finite scalar.

Given an upper bound for portfolio tracking error in TrackingError and a tracking portfolio in TrackingPort, the tracking error constraint requires any portfolio in Port to satisfy

(Port - TrackingPort)'*AssetCovar*(Port - TrackingPort) <= TrackingError^2.

For more information, see Tracking Error Constraints.

Data Types: double

TrackingPort — Tracking portfolio weights

finite vector

Tracking portfolio weights, specified using a vector. TrackingPort must be a finite vector with NumAssets > 0 elements.

If no TrackingPort is specified, it is assumed to be 0. If TrackingPort is specified as a scalar and NumAssets exists, then TrackingPort undergoes scalar expansion.

Data Types: double

NumAssets — Number of assets in portfolio

scalar

Number of assets in portfolio, specified using a scalar. If it is not possible to obtain a value for NumAssets, it is assumed that NumAssets is 1.

Data Types: double

Output Arguments

obj — Updated portfolio object

object for portfolio

Updated portfolio object, returned as a Portfolio object. For more information on creating a portfolio object, see Portfolio.

Note

The tracking error constraints can be used with any of the other supported constraints in the Portfolio object without restrictions. However, since the portfolio set necessarily and sufficiently must be a non-empty compact set, the application of a tracking error constraint can result in an empty portfolio set. Use estimateBounds to confirm that the portfolio set is non-empty and compact.

More About

Tracking Error

Tracking error is a measure used in portfolio management to assess how closely a portfolio's performance aligns with that of a benchmark index.

Tracking error is the standard deviation of the difference between the returns of the portfolio and the returns of the benchmark index. It provides a statistical measure of the variability of the portfolio's excess returns relative to the benchmark.

Tips

You can also use dot notation to set up a maximum portfolio tracking error constraint.

obj = obj.setTrackingError(TrackingError, NumAssets);

To remove a tracking portfolio, call this function with an empty argument ([]) for TrackingError.

obj = setTrackingError(obj, [ ]);

Version History

Introduced in R2015b