WebCab Portfolio Web Services for .NET v5.0 Demo

CapitalMarket.CalculateEfficientFrontier Method (Double[][], Double[], Int32, Double)

Constructs the Efficient Frontier over its extire range of expected returns.

public void CalculateEfficientFrontier(
   double[][] covarianceMatrix,
   double[] expectedReturns,
   int numberInterpolationPoints,
   double precision
);

Parameters

covarianceMatrix
The covariance matrix of the assets from which the (optimal) portfolio can be constructed. The dimensions of the (symmetric) covariance matrix will be n X n, where n is the number of assets from which the (optimal) portfolio can be constructed.
expectedReturns
The array of the expected returns of the assets from which the portfolios can be constructed. Where the k-th term will correspond to the percentage return (i.e. 1 percent = 1) or the absolute return of the k-th asset from the set of assets from which the Portfolios (on the Efficient Frontier) can be constructed.
numberInterpolationPoints
The number of interpolation points for which the Efficient Frontier is calculated. Note that these interpolation points lie within the interval bound by the minimum and maximum expected returns set and be equally dispersed within this interval. Moreover, in all case one of the interpolation points will lie of the minimum expected return set and another will lie on the maximum expected return set.
precision
This parameters allow the level of the precision required to be set, where the small the parameters the (generally) higher the precision. This variable should be chosen between the range 1E-1 and 1E-6. Note as with most numerical procedures the higher the precision the more computationally intensive the algorithm will become. The precision must be set to be a positive number less than 1, and we suggest that a value of 1E-3 should be used initially. Further details are provided within the Programmer's guide chapter of the PDF documentation.

Remarks

This method calls CalculateEfficientFrontier by setting the range of the expected returns over which the Efficient Frontier is evaluated to be the entire range over which the (constrained) Efficient Frontier exists.

For more details concerning the issues effecting the constraints, efficiency, number of interpolation points to use and so on...; we refer the reader to the documentation for the method CalculateEfficientFrontier. As mentioned above the only difference with the aforementioned method at that here the range of expected returns have been set as detail below.

Range of Expected Returns

The range over which the (constrained) Efficient Frontier is evaluated can be evaluated by using the methods MinFrontierReturn, MaxFrontierReturn; in order to evaluate the minimum and maximum of the continuous range of the expected return over which the Efficient Frontier exists for the given set of assets considered. Note that with this procedure we have set the range over which the Efficient Frontier is constructed to be equal to this largest possible range.

See Also

CapitalMarket Class | Portfolio Namespace | CapitalMarket.CalculateEfficientFrontier Overload List