WebCab Portfolio for COM v5.0 Demo

CapitalMarket.Weight2Risk Method 

Evaluates the total risk of a portfolio on the CML when the weighting of the Market Portfolio within the portfolio selected for the CML is known.

public double Weight2Risk(
   double weighting,
   double equityRisk
);

Parameters

weighting
The weighting of the Market Portfolio within the CML portfolio. The weighting corresponds to the multiple of the base capital which is invested within the market portfolio. Recall that all portfolios on the CML consist of a weighting in the market portfolio which can be constructed using the method MarketPortfolio and cash. The weighting in cash can be negative, that is money can be borrowed from the market in order to increase that amount of the Market Portfolio which is controlled by the underlying capital base. In this instance the weighting of the Market Portfolio will increase above 1 since more than 100 percent of the available (base) capital has been invested within the Market Portfolio.
equityRisk

Return Value

The total risk in decimal format (i.e. 1 percent = 0.01) of the portfolio on the CML which has a given weighting of the Market Portfolio.

Remarks

Further Explanation

Note that we are required to provide the risk of the Market Portfolio within the application of this method. This constant can be evaluated by using MarketPortfolioRisk, which in turn requires that the Market Portfolios asset weights are known. The weights of the assets within the Market Portfolio can be evaluated using the MarketPortfolio. The evaluation of these (possibly constrained) weights requires that the Efficient Frontier has already been evaluated using CalculateEfficientFrontier, before which the constraints on the asset should have been set (if applicable) using SetConstraints.

Completeness of the Methods: Weight2Risk, RiskCML, WeightCML, ReturnCML

The portfolio on the CML can be selected from knowledge of its total risk, expected return or weight of the Market Portfolio. Then using the above mentioned methods we are able to evaluate the other quantities which are not given. For example, if the expected return of the portfolio is known then the weight of the market portfolio can be evaluated using WeightCML and the risk can be evaluated using RiskCML. If on the other hand the total risk of the portfolio is known then the corresponding expected return of the portfolio can be evaluated by ReturnCML, and then using this deduced value we are able to evaluated the weight of the Market Portfolio using WeightCML. For completeness we include the method Weight2Risk which evaluates the risk of a portfolio on the CML when the weight of the Market Portfolio within the CML portfolio is known. From knowledge of the risk of the CML portfolio we able to evaluate the corresponding value of the expected return using the method ReturnCML.

Therefore, using the three `...CML' methods along with `weight2Risk', which one of: total risk, expected return or weight of Market Portfolio, is used in order to selected the portfolio from the CML we are able to deduce the other two quantitative properties.

Remarks on time units and the percentage convention used

Within the application of this method you are required to provide the risk in decimal format (i.e. 1 percent = 0.01) of the Market Portfolio which will be quoted within respect to a given period of time, such as `per year', `per month' and so on. Moreover, the returned value of the total risk of the portfolio on the CML will also be expressed with respect to the same unit of time and in decimal format (i.e. 1 percent = 0.01).

Remarks concerning Constraints on the level of Cash Borrowed or Lent

As mentioned in the introduction of this class often in practice a given fund will have limits regarding:

  1. Maximum level of cash which should be help within the portfolio
  2. Maximum level of borrowing (i.e. gearing) which the portfolio use
We provide further motivation concerning the rational for such limits within the PDF documentation.

Within the context of our implementation these restrictions would translate into constraints on the level of cash, that is the weighting of the Market Portfolio within the portfolio on the CML. Within the class we are able to deal with such constraints of the level of cash borrow or lent from/to the market. In particular, within such instances we are able to evaluated the corresponding optimal portfolio's expected return, risk and Market Portfolio Weighting for the following schema:

  1. Express in terms of Weightings: Translated the restrictions on the borrow and lending into statements concerning the maximum and minimum weighting and the Market Portfolio.
  2. Evaluate the range of Total Risk: Evaluate the corresponding range of the Total Risk of the range of portfolios on the CML which have the given range of Market Portfolio weightings found in the previous step. We are able to evaluate this range by apply this method and observing that the Total Risk is monotonically increasing in risk as the Market Portfolio weighting increases.
  3. Evaluate the range of the Expected Return: Evaluate the corresponding range of the expected returns of the range of portfolios on the CML which have given range of Market Portfolio weightings. Since (by the previous step) the portfolios with a range of Market Portfolio Weightings corresponds to the collection of portfolios on the CML for a given range of the total risk, and the fact that the expected return increase monotonically as the total risk increase by using ReturnCML we are able to evaluate the range of expected returns which determines the portfolios with given constraints on the cash levels within the portfolio.

Remark: The key reason why this approach works is that if the weighting of the Market Portfolio increases continuously monotonically increases, the corresponding total risk and expected returns of the portfolio also continuously monotonically increases.

The only thing that needs to be established is how we can translate statements concerning the limits on borrowing and lending, and statements concerning the weighting of the market portfolio. We will illustrate how this is done by the following example:

Example: We know that the Market Portfolio of a collection of assets has an expected return of 10 percent per year and a risk of 20 percent per year. According to the CAPM if the portfolio manager can only leverage his portfolio by 20 percent, and must also never hold more than 30 percent of the funds capital in cash then what is the range of total risk and expected return of the (optimal) portfolios which the fund manager can hold?

Solution: Since the optimal portfolio will consist of the Market Portfolio with either excess money lent to the market or money borrowed from the market in order to purchase more baskets of the Market Portfolio. The optimal portfolios will can be constructed will range from borrowing 20 percent of the capital base and purchasing further baskets of the Market Portfolio, to lending 30 percent of the capital base and holding the remaining 70 percent of the capital base within the Market Portfolio. Therefore, the Weighting of the Market Portfolio can range from 1.2 (maximum gearing) to 0.7 (maximum lending). This completes step 1, in the above schema to evaluate range of the risk and expected return we just perform step 2 and 3, as describe above.

Note: We implement this exact instance as an examples called CapitalMarketClient_CashConstraints.

See Also

CapitalMarket Class | WebCab.COM.Finance.Portfolio Namespace | WeightCML - allows the Market Portfolios weight to be evaluated for a portfolio on the CML with a given expected return. | ReturnCML - allows the expected return of a portfolio on the CML to be evaluated when the total risk of the portfolio is known. | RiskCML - allow the risk of a portfolio on the CML to be evaluated when the expected return of the portfolio is known.