WebCab Portfolio for COM v5.0 Demo

Markowitz.OpimalPortfolioMaxRange Method 

This method constructs the optimal portfolios with respect to the investors utility function over the entire range for which the Efficient Frontier exists.

public double[,] OpimalPortfolioMaxRange(
   double[,] covarianceMatrix,
   double[] expectedReturns
);

Parameters

covarianceMatrix
The covariance matrix of the collection of assets from which the (optimal) portfolio can be constructed.
expectedReturns
The array of the expected returns of the assets in absolute or relative terms from which the portfolios can be constructed. Where the k-th term corresponds to the expected return of the k-th asset. Note that the units used for the expected return will determine the units of the returned result. It is also important to point out that within any application the units for the expected returns should be used consistently throughout.

Return Value

A array of dimension two where each of the array elements contains the weights of the assets of an optimal portfolio on the Efficient Frontier selected with respect to the Investors Utility function. For the n-th array element, the k-th terms cooresponds to the weight of the k-th asset within the n-th optimal portfolio found. If no optimal portfolio was found (i.e. no portfolio was selected from the Efficient Frontier by the investors utility function intersecting) then this method will return an empty array of dimension 2.

Remarks

That is, we call the method OptimalPortfolio, where the minimum and maximum range of the expected returns are set in accordance with the methods MaxFrontierReturn and MinFrontierReturn.

Remarks:

  1. Care must be taken to ensure that the investors Utility function is given over all values of the expected return for which the Efficient Frontier exists.
  2. Once you have called this method which evaluates the optimal portfolios over the entire range you will be able to select the relevant range of the expected return in which the desired optimal portfolio exists before before a more exact construct is carried out using the method OptimalPortfolio.

For further details concerns the construction of the optimal portfolios we refer the reader to the documentation of OptimalPortfolio.

Exceptions

Exception TypeCondition
PortfolioExceptionThrown if the number of optimal portfolios found is more than 100. In this instance the investors utility function is probably very close if not identical to the Efficient Frontier over at least a section of the range of the expected returns considered. To address this issue to utility function should be refined so that it is more clearly distinguishable from the Efficient Frontier. Since it is very likely that modulo interpolation errors the utility function is identical to the Efficient Frontier over a section of the expected returns considered which causes the method at present in principal to fail. Anyway, once the Investors Utility function has been refined you will be able to re-apply this method.

See Also

Markowitz Class | WebCab.COM.Finance.Portfolio Namespace