WebCab Portfolio for .NET v5.0 Demo

CapitalMarket.ReturnCML Method 

Find the corresponding value of the expected return of the portfolio on the Capital Market Line (CML) when the total risk is known.

public double ReturnCML(
   double risk,
   double equityRisk,
   double equityExpected,
   double marketRate
);

Parameters

risk
The total risk in decimal format (i.e. 1 percent = 0.01) of the portfolio on the CML for which the expected return is being evaluate.
equityRisk
The risk given in decimal format (i.e. 1 percent = 0.01) of the market portfolio which can be evaluated using the method MarketPortfolioRisk.
equityExpected
The expected return from the Market Portfolio given in decimal format (i.e. 1 percent = 0.01). The expected return of the Market Portfolio can be evaluated using the method MarketPortfolioExpectedReturn.
marketRate
The fixed rate at which the investor can borrow or lend money from the market given in decimal format (i.e. 1 percent = 0.01). Recall, that the CAPM assumes that the investor can borrow or lend cash at some prevailing market rate. Though in practice the lending and borrowing costs in general will differ, for large market players such as investment banks these two rates will be approximately the same and be approximately equal to the overnight rate offered between investment banks (i.e. LIBOR or similar). Smaller players can also obtain similar lending and borrow rates through the use of structured products such as REPOs and similar, offered by investments banks. Therefore, for most market participants this assumption is reasonable and does not lead to significant errors. Please note, that this rate refers to the rate the investor will receive on any cash held within the portfolio as well as the rate at which they are able to borrow cash from the market.

Return Value

Expected return of a portfolio on the CML which has a given total risk.

Remarks

Further Explanation

In order to evaluate the expected return total we are required to provide the total risk of the portfolio on the CML, the total risk and expected return of the Market Portfolio and the prevailing market rate at which cash can be borrowed or lent to the market. The market rate at which cash can by borrow or lend should be known but the expected return and the total risk of the Market Portfolio should be evaluated using MarketPortfolioExpectedReturn and MarketPortfolioRisk respectively. In order to evaluate these constants you will need to construct the Market Portfolio itself by using MarketPortfolio, which in turn depends firstly the asset weights constraints (if applicable) being set using SetConstraints before the Efficient Frontier is constructed using CalculateEfficientFrontier.

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

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 weighting 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 notation convention used

Within the application of this method you are required to provide a number of of parameters which are quoted within respect to a given period of time, such as `per year', `per month' and so on. Within the application of this method it is important to point out that the time unit used for each of these parameters should correspond. For instance the risk of the desired portfolio, risk of the Market Portfolio, expected return of the Market Portfolio and the market rate at which money can be lent or borrowed which are each given in decimal format (i.e. 1 percent = 0.01) should be given with respect to the same unit of time. Moreover, the returned value of the expected return 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).

See Also

CapitalMarket Class | WebCab.Libraries.Finance.Portfolio Namespace | RiskCML - allow the risk of a portfolio on the CML to be evaluated when the expected return of the portfolio is known. | WeightCML - allows the Market Portfolios weight to be evaluated for a portfolio on the CML with a given expected return. | Weight2Risk - allows the risk of a portfolio on the CML to be evaluated when the weight of the Market Portfolio within the CML portfolio is known.