Capital Market Line (CML) - Assignment

THE CAPITAL MARKET LINE
All investors are assumed to have identical (homogeneous) expectations. Hence, all of
them will face the same efficient frontier depicted in Fig. 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. This portfolio of all risky securities is referred to as
the market portfolio M. Each security will be held in the proportion which the market value
of the security bears to the total market value of 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 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 the following equation.
Re = Rf + [ Re – Rf] σe
σm
Where the subscript e denotes an efficient portfolio.
The risk free return Rf represents the reward for waiting. It is, in other words, the
price of time. The term [(Rm – Rf/σ m] 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, σ 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.

THE SECURITY MARKET LINE
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 describe 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 earlier that the total risk of a security as measured by standard deviation
is compared 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 trends to
become zero and the only relevant risk is systematic risk measured by beta (β). Hence, it is
argued that the correct measure of a security‘s risk is beta.
It follows that the expected return of a security or of a portfolio should be related to
the risk of that security or portfolios as measured by β. Beta is a measure of the security‘s
sensitivity to change in market return. Beta value greater than one indicates higher sensitivity
to market changes, whereas beta value less than one indicates lower sensitivity to market
changes. A β value of one indicates that the security moves at the same rate and in the same
direction as the market. Thus, the β of the market may be taken as one.
The relationship between expected return and β of a security can be determined
graphically. Let us consider and XY graph where expected returns are plotted on the Y axis
and beta coefficients are plotted on the X axis. A risk free asset has an expected return
equivalent to Rf and beta coefficient of zero. The market portfolio M has a beta coefficient of
one and expected return equivalent R m. A straight line joining these two points is known as
the security market line (SML). This is illustrated in Fig. 1
The security market line provides the relationship between the expected return and
beta of a security or portfolio. This relationship can be expressed in the form of the following
equation:
Rm – Rf + βi (Rm - Rf )
A part of the return on any security or portfolio is a reward for bearing risk and the
rest is the reward for waiting, representing the time value of money. The risk free rate, R f
(which is earned by a security which has no risk) is the reward for waiting. The reward for
bearing risk is the risk premium. The risk premium of a security is directly proportional to the
risk as measured by β. The risk premium of a security is calculated as the product of beta and
the risk premium of the market which is the excess of expected market return over the risk
free return, that is, [Rm - Rf ].

Thus,
Expected return on a security = Risk free return + (Beta x Risk premium of market)
Fig. 1 Security Market Line