WebCab Portfolio for COM v5.0 Demo

SolveFrontier Class

Within this class we provide methods by which the optimal portfolio can be selected from the Efficient Frontier when the investor describes his investment preferences.

For a list of all members of this type, see SolveFrontier Members.

System.Object
   SolveFrontier

public class SolveFrontier

Remarks

The investors preferences can be given in terms of one of the following:

  1. Maximum Risk - The optimal portfolio is selected from the Efficient Frontier by knowing its total risk.
  2. Expected Return - The optimal portfolio is selected from the Efficient Frontier by knowing its expected return.
  3. (Risk) Investors Utility Function - The optimal portfolio(s) is selected from the Efficient Frontier by using the given (Risk) investors Utility function which is a function of the risk.
  4. (Return) Investors Utility Function - The optimal portfolio(s) is selected from the Efficient Frontier by using the given (Return) investors Utility function which is a function of the expected return.

Remark: Since the Efficient Frontier is monotonically increasing in the risk and expected return a given value of the risk or expected return will determine a unique portfolio if the given Efficient Frontier takes the given values of the expected return and risk at some point. However, knowledge of the investors Utility function does not guarantee the existence of a corresponding optimal portfolio.

Selecting a Portfolio from the Efficient Frontier when its risk or expected return is known

Once we are provided with either the maximum risk or the expected returns we are able to select the corresponding portfolio from the Efficient Frontier using one of:

  1. Solve for a given maximum risk using FindReturn - The maximum risk which the investor will accept is given and then the weights and the expected return of the Efficient Frontier is returned. Once the Efficient Frontier is known you are able to evaluate the (possibly constrained) weights of the corresponding portfolio by calling the method EfficientFrontier or its stateful version EfficientFrontier, if the Efficient Frontier be been pre-evaluation.
  2. Solve for a given expected return using FindRisk - The expected return of the portfolio which the investor requires is given and then the risk of the corresponding Efficient Frontier is returned. That is, the portfolio with the lowest risk from the given expected return required. If you require to know the corresponding weights of the asset of this portfolio then you can use the method EfficientFrontier or its stateful version EfficientFrontier, if the Efficient Frontier be been pre-evaluation.

Selecting a Portfolio from the Efficient Frontier when the Utility function in known

Depending on whether you are provided of the Utility function which is a function of the expected return or the risk you should use of the following methods in order to evaluate the risk or expected return of the optimal portfolio(s) (if it exists) on the Efficient Frontier:

  1. (Risk) Utility Function - Use FindRisk in order to evaluate the risk of the optimal portfolio (if it exists) on the Efficient Frontier.
  2. (Return) Utility Function - Use FindReturn in order to evaluate the return of the optimal portfolio (if it exists) on the Efficient Frontier.

Once the expected return or the risk of the Efficient Frontier is known you will be able to evaluate the asset weights and other properties of the optimal portfolio. The advantage here over the methods provided within the Markowitz class is that we are able to provide a Utility function which is a function of the risk or the return rather than only of the return.

Internal Interpolation Algorithm used

Within this class we use cubic spline interpolation in order to interpolate the Efficient Frontier around the finite set of points at which it is evaluated using the method EfficientFrontier

Internal Equation Solver Algorithm used

Internally within this class we use the Interval bisection method which allows the solution of equations of one variable to be found. In this instance since the Efficient Frontier is a continuous function defined over a finite interval (of risk and return) this approach will always produce a solution to a given degree of accuracy.

Finding the Asset Weights when the Risk and Expected Return is known

Whether you know the expected risk which to the investor will accept or the expected return desired you will determine a unique portfolio on the Efficient Frontier constructed from the available assets. Here we details how you are able to find the assets weights of this given portfolio on the Efficient Frontier.

If the expected return which the investor requires is known then the weights of the corresponding portfolio can be evaluated using EfficientFrontier. If the risk is known then the corresponding unique expected return should be evaluated using the method FindReturn. Once the corresponding expected return is known the same procedure can be applied using EfficientFrontier, in order to find the corresponding weights of the portfolio with the given maximum risk.

Requirements

Namespace: WebCab.COM.Finance.Portfolio

Assembly: WebCab.COM.PortfolioDemo (in WebCab.COM.PortfolioDemo.dll)

See Also

SolveFrontier Members | WebCab.COM.Finance.Portfolio Namespace