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Capital Market Line:
Rational investors would choose a combination of R f and S (S
represents the point on theefficient frontier of risky portfolios
where the straight line emanating from R f is tangential tothe
efficient frontier). If all investors attempt to purchase the
securities in S and ignoresecurities 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 shiftS, along with other points which share
securities with S, downward: On the other hand, pricesof 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 shiftupward. 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 oneportfolio on the linear segment
KML. Of course, the market portfolio would itself be a pointon 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 portfoliosthat lie on the linear
segment.
All investors are assumed to have identical (homogenous)
expectations. Hence, all of themwill face the same efficient
frontier. Every investor will seek to combine the same
riskyportfolio 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
inthe market. All investors will hold combinations of only two
assets, the market portfolio anda riskless security. All these
combinations will lie along the straight line, representing
theefficient frontier. This line formed by the action of all the
investors mixing the marketportfolio with the risk free asset is
known as the capital market line (CML). All efficientportfolios of
all investors will lie along this capital market line. The
relationship between thereturn and risk of any efficient portfolio
on the capital market line can be expressed in theform of following
equation.
e = R f + [ ]
where the subscript e denotes an efficient portfolio. The risk
free return R f represents theprice of risk or risk premium, i.e.
the excess return earned per unit of risk or standarddeviation. It
measures the additional return for an additional unit of risk. When
the risk of theefficient portfolio, e , is multiplied with this
term, we get the risk premium available for theparticular efficient
portfolio under consideration. Thus, the expected return on an
efficientportfolio 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 standarddeviation and the expected return for these
efficient portfolios. For efficient portfolios (which
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includes the market portfolio) the relationship between risk and
return is depicted by thestraight line R f MZ. The equation for
this line, called the capital market line (CML), is:
E(R j) = R f +
Security Market Line (SML):The CML shows the risk-return
relationship for all efficient portfolios. They would all liealong
the capital market line. All portfolios other than the efficient
ones will lie below thecapital market line. The CML does not
subscribe the risk-return relationship of inefficientportfolios or
of individual securities. The capital asset pricing model specifies
the relationshipbetween expected return and risk for all securities
and all portfolios, whether efficient orinefficient. We have seen
that the total risk of a security as measured by standard deviation
iscomposed of two components: systematic risk and unsystematic risk
or diversifiable risk. Asinvestment is diversified and more and
more securities are added to a portfolio, theunsystematic risk is
reduced. For a very well diversified portfolio, unsystematic risk
tends tobecome zero and the only relevant risk is systematic risk
measured by beta (). Hence, it isargued that the correct measure of
a securitys risk is beta. It follows that the expected returnof a
security or of a portfolio should be related
