Equation and Importance of CML

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 The Equation for the CML:

We now know the intercept and slope of the CML. Since the CML is the tradeoff between expected return and risk for efficient portfolios, and risk is being measured by the standard deviation, the equation for the CML is shown as Equation 9-1:

where:

 E (Rp) = the expected return on any efficient portfolio on the CML 
 RF = the rate of return on the risk-free asset 
 E (RM) = the expected return on the market portfolio M 
 σM = the standard deviation of the returns on the market portfolio 
 σp = the standard deviation of the efficient portfolio being considered 

In words, the expected return for any portfolio on the CML is equal to the risk-free rate plus a risk premium. The risk premium is the product of the market price of risk and the amount of risk for the portfolio under consideration.

Important Points About the CML:

 The following points should be noted about the CML: 

1. Only efficient portfolios consisting of the risk-free asset and portfolio M lie on the CML. Portfolio M, the market portfolio of risky securities, contains all securities weighted by their respective market values—it is the optimum combination of risky securities and is, by definition, an efficient portfolio. The risk-free asset has no risk. Therefore, all combinations of these two assets on the CML are efficient portfolios.

 2. As a statement of equilibrium, the CML must always be upward-sloping, because the price of risk must always be positive. Remember that the CML is formulated in a world of expected return, and risk-averse investors will not invest unless they expect to be compensated for the risk. The greater the risk, the greater the expected return. 

3. On a historical basis, for some particular period of time such as a year or two, or four consecutive quarters, the CML can be downward-sloping; that is, the return on RF exceeds the return on the market portfolio. This does not negate the validity of the CML; it merely indicates that returns actually realized differ from those that were expected. Obviously, investor expectations are not always realized. (If they were, there would be no risk.) Thus, although the CML must be upward-sloping ex ante (before the fact), it can be, and sometimes is, downward-sloping ex post (after the fact). 

4. The CML can be used to determine the optimal expected returns associated with different portfolio risk levels. Therefore, the CML indicates the required return for each portfolio risk level.



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