Working with Tracking Error Constraints Using Portfolio Object

Tracking error constraints are optional constraints (see Tracking Error Constraints) that measure the risk relative to a portfolio called a tracking portfolio. Tracking error constraints can be set using the Portfolio object or the setTrackingError function.

The tracking error constraint is an optional quadratic constraint that enforces an upper bound on tracking error, which is the relative risk between a portfolio and a designated tracking portfolio. For more information, see Tracking Error Constraints.

The tracking error constraint can be set using the Portfolio object or the setTrackingPort and setTrackingError functions. The tracking error constraint depends on a tracking portfolio, which is assumed to be zero if not set when the tracking error constraint is set. The tracking error constraint has properties TrackingError, for the upper bound on tracking error, and TrackingPort, for the portfolio against which tracking error is computed.

Note

The initial portfolio in the Portfolio object property InitPort is distinct from the tracking portfolio in the Portfolio object property TrackingPort.

Setting Tracking Error Constraints Using the Portfolio Function

The properties for the tracking error constraints are set using the Portfolio object. Suppose that you have a tracking portfolio of 10 assets in a variable x0 and you want to ensure that the tracking error of any portfolio on the efficient frontier is no more than 8% relative to this portfolio. To set this constraint:

x0 = [ 0.12; 0.09; 0.08; 0.07; 0.1; 0.1; 0.15; 0.11; 0.08; 0.1 ]; 
p = Portfolio('TrackingError', 0.08, 'TrackingPort', x0);
disp(p.NumAssets);
disp(p.TrackingError);
disp(p.TrackingPort);
    10

    0.0800

    0.1200
    0.0900
    0.0800
    0.0700
    0.1000
    0.1000
    0.1500
    0.1100
    0.0800
    0.1000

If the NumAssets or TrackingPort properties are not set before or when the tracking error constraint is set, various rules are applied to assign default values to these properties (see Setting Up a Tracking Portfolio).

Setting Tracking Error Constraints Using the setTrackingError Function

You can also set properties for portfolio tracking error using the setTrackingError function to specify both the upper bound for tracking error and a designated tracking portfolio. Suppose that you have a tracking portfolio of 10 assets in a variable x0 and want to ensure that tracking error is no more than 8%. Given a Portfolio object p, use setTrackingError to set the tracking error constraint with and without the initial portfolio being set previously:

x0 = [ 0.12; 0.09; 0.08; 0.07; 0.1; 0.1; 0.15; 0.11; 0.08; 0.1 ];
p = Portfolio('TrackingPort', x0);
p = setTrackingError(p, 0.08);

disp(p.NumAssets);
disp(p.TrackingError);
disp(p.TrackingPort);  
    10

    0.0800

    0.1200
    0.0900
    0.0800
    0.0700
    0.1000
    0.1000
    0.1500
    0.1100
    0.0800
    0.1000

or

x0 = [ 0.12; 0.09; 0.08; 0.07; 0.1; 0.1; 0.15; 0.11; 0.08; 0.1 ];
p = Portfolio('TrackingPort', x0);
p = setTrackingError(p, 0.08, x0);

disp(p.NumAssets);
disp(p.TrackingError);
disp(p.TrackingPort);  
    10

    0.0800

    0.1200
    0.0900
    0.0800
    0.0700
    0.1000
    0.1000
    0.1500
    0.1100
    0.0800
    0.1000

If the NumAssets or TrackingPort properties are not set before or when the tracking error constraint is set, various rules are applied to assign default values to these properties (see Setting Up a Tracking Portfolio).

setTrackingError implements scalar expansion on the argument for the tracking portfolio. If the NumAssets property is already set in the Portfolio object, a scalar argument for TrackingPort expands to have the same value across all dimensions. In addition, setTrackingError lets you specify NumAssets as an optional argument. To clear tracking error from your Portfolio object, use the Portfolio object or setTrackingError with empty inputs for the properties to be cleared.

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