Evaluates a value of the expected return of the portfolio on the Efficient Frontier which is optimal with respect to the investors (Return) Utility function which is a function of the expected return.
0.001
then the risk will be returned to within 0.001
etc, of the `exact' solution.Once the expected return is known the corresponding value of the risk of the portfolio can be evaluated using the method FindRisk.
Notes on the Efficient Frontier input parameters
A set of points on the Efficient Frontier should be evaluated using methods from the Markowitz class, in particular:
Note: Alternatively you may choose to use the complex type PointsOnEfficientFrontier, and the related methods from the portfolio class in order to find the set of points on the efficient frontier for which it is evaluated.
The parameters of the Investors Utility Function
The (Return) Utility function is given by a set of points which lie on the utility curve. The (Return) utility function is assumed to take the same range of values of the expected return parameter as the range of the expected return over which the Efficient Frontier is defined. It is essential within the formation of this approach that the (Return) Utility function is a function of the expected return. In particular, if we are given a value of the return then there corresponds a unique value of the risk. In practice, since we are applying a Cubic spline method in order to interpolate the (Return) Utility function from the finite set of points it is enough to ensure that from this set of points there does not exist two distinct points with have the same value of the return.
Advantages of a General Utility Function
A more general Utility function allows the investor to express the likely fact that as the expected return increase they may except a higher level of risk. In the case when the (Return) Utility function returns a constant value of the risk this methods reduced to the case considered in FindReturn.
Exception Type | Condition |
---|---|
SolveFrontierException | Thrown if no value is found for the given input parameters. |
InterpolationException | Thrown when there does not correspond a points on the interpolation function corresponding to the parameters given. |
SolveFrontier Class | WebCab.Libraries.Finance.Portfolio Namespace | SolveFrontier.FindReturn Overload List | FindReturn(double, double[], double[]) - this is a special case of this method which corresponds to the case where the (Return) Utility function is a constant function which states that the investor will accept of given maximum risk and is not influence by the corresponding level of expected return.