Page 279 - DCOM504_SECURITY_ANALYSIS_AND_PORTFOLIO_MANAGEMENT

Security Analysis and Portfolio Management

Notes Now, if the expected return of asset A is in equilibrium, then an investor should be
indifferent between augmenting his or her portfolio with a quantity of A and simply
levering up the existing market portfolio position. If this were not the case, then either the
investor would not be willing to hold A, or A would dominate the portfolio entirely. We
can calculate the same Risk-Return Trade-off for buying dx quantity of the market portfolio
P instead of security A. Risk-Return Trade-off for P = dE /dv = [E – R ]/2 var(m) .
m m f
The equations are almost the same, except that the cov(A,m) is replaced with var(m). This
is because the covariance of any security with itself is the variance of the security.
These Risk-reward Tradeoffs must be equal:
[E – R ]/2 cov(A,m) = [E – R ]/2 var(m)
A f m f
Thus, [E – R ] = [cov(A,m)/var(m)][E – R ]
A f m f
The value cov(A,m)/var(m) is also known as the of A with respect to m. is a famous
statistic in finance. It is functionally related to the correlation and the covariance between
the security and the market portfolio in the following way:

i i,m
i,m 2
m m
2. A Model of Expected Returns: In the preceding example, notice that we used the expression
expected returns. That is, we found an equation that related the expected future return of
asset A (in excess of the riskless rate) to the expected future return of the market (in excess
of the riskless rate). This expected return is the return that investors will demand when
asset prices are in the equilibrium described by the CAPM. For any asset i, the CAPM
argues that the appropriate rate at which to discount the cash flows of the firm is that same
rate that investors demand to include the security in their portfolio:
E[R ] = R + (E[R ] – R )
i f i m f
!

Caution One surprising thing about this equation is what is not in it. There is no measure
of the security’s own standard deviation. The CAPM says that you do not care about the
volatility of the security. You only care about its beta with respect to the market portfolio!
Risk is now re-defined as the quantity of exposure the security has to fluctuations in the
market portfolio.

Task Make a technical assessment of CAPM and discuss its advantages and
disadvantages in the changed world scenario.

11.4 Security Market Line (SML)

The CAPM equation describes a linear relationship between risk and return. Risk, in this case, is
measured by beta. We may plot this line in mean and ß space: The Security Market Line (SML)
expresses the basic theme of the CAPM i.e., expected return of a security increases linearly with
risk, as measured by ‘beta’. The SML is an upward sloping straight line with an intercept at the
risk-free return securities and passes through the market portfolio. The upward slope of the line
indicates that greater excepted returns accompany higher levels of beta. In equilibrium, each
security or portfolio lies on the SML. The next figure shows that the return expected from

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