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CML & SML

The capital market line (CML) shows the relationship between risk and return for all efficient portfolios. It is formed by investors combining the market portfolio with a risk-free asset. The CML is a straight line represented by the equation: Expected Return = Risk-Free Return + (Risk Premium) * (Amount of Risk). All efficient portfolios lie along this line, and it provides a measure of risk-return for these portfolios based on their standard deviation. The security market line (SML) extends this relationship to include both efficient and inefficient portfolios/securities based on their systematic risk or beta rather than total risk.

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197 views2 pages

CML & SML

The capital market line (CML) shows the relationship between risk and return for all efficient portfolios. It is formed by investors combining the market portfolio with a risk-free asset. The CML is a straight line represented by the equation: Expected Return = Risk-Free Return + (Risk Premium) * (Amount of Risk). All efficient portfolios lie along this line, and it provides a measure of risk-return for these portfolios based on their standard deviation. The security market line (SML) extends this relationship to include both efficient and inefficient portfolios/securities based on their systematic risk or beta rather than total risk.

Uploaded by

moinmemon1763
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© Attribution Non-Commercial (BY-NC)
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Capital Market Line:

Rational investors would choose a combination of Rf and S (S represents the point on the efficient frontier of risky portfolios where the straight line emanating from Rf is tangential to the efficient frontier). If all investors attempt to purchase the securities in S and ignore securities not included in S, prices of securities would be revised. On the one hand, prices of securities included in S would rise and hence their expected returns will fall. This would shift S, along with other points which share securities with S, downward: On the other hand, prices of securities not included in S will fall, leading to an increase in their expected return. Consequently, points representing portfolios in which these securities are included will shift upward. As this process continues, the efficient frontier of risky securities will flatten. Finally, the set of prices reached would be such that every security will enter at least one portfolio on the linear segment KML. Of course, the market portfolio would itself be a point on that linear segment. Portfolios which have returns that are perfectly positively correlated with the market portfolio are referred to as efficient portfolios. Obviously, these are portfolios that lie on the linear segment. All investors are assumed to have identical (homogenous) expectations. Hence, all of them will face the same efficient frontier. Every investor will seek to combine the same risky portfolio B with different levels of lending or borrowing according to his desired level of risk. Because all investors hold the same risky portfolio, then it will include all risky securities in the market. All investors will hold combinations of only two assets, the market portfolio and a riskless security. All these combinations will lie along the straight line, representing the efficient frontier. This line formed by the action of all the investors mixing the market portfolio with the risk free asset is known as the capital market line (CML). All efficient portfolios of all investors will lie along this capital market line. The relationship between the return and risk of any efficient portfolio on the capital market line can be expressed in the form of following equation.
e=

Rf + [ ]

where the subscript e denotes an efficient portfolio. The risk free return Rf represents the price of risk or risk premium, i.e. the excess return earned per unit of risk or standard deviation. It measures the additional return for an additional unit of risk. When the risk of the efficient portfolio, e , is multiplied with this term, we get the risk premium available for the particular efficient portfolio under consideration. Thus, the expected return on an efficient portfolio is: (Expected Return) = (Price of time) + (Price of risk) (Amount of risk) The CML provides a risk return relationship and a measure of risk for efficient portfolios. The appropriate measure of risk for an efficient portfolio is the standard deviation of return of the portfolio. There is a linear relationship between the risk as measured by the standard deviation and the expected return for these efficient portfolios. For efficient portfolios (which

includes the market portfolio) the relationship between risk and return is depicted by the straight line RfMZ. The equation for this line, called the capital market line (CML), is: E(Rj) = Rf +

Security Market Line (SML):


The CML shows the risk-return relationship for all efficient portfolios. They would all lie along the capital market line. All portfolios other than the efficient ones will lie below the capital market line. The CML does not subscribe the risk-return relationship of inefficient portfolios or of individual securities. The capital asset pricing model specifies the relationship between expected return and risk for all securities and all portfolios, whether efficient or inefficient. We have seen that the total risk of a security as measured by standard deviation is composed of two components: systematic risk and unsystematic risk or diversifiable risk. As investment is diversified and more and more securities are added to a portfolio, the unsystematic risk is reduced. For a very well diversified portfolio, unsystematic risk tends to become zero and the only relevant risk is systematic risk measured by beta (). Hence, it is argued that the correct measure of a securitys risk is beta. It follows that the expected return of a security or of a portfolio should be related

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