Page 304 - DCOM504_SECURITY_ANALYSIS_AND_PORTFOLIO_MANAGEMENT

Unit 12: Models

5. For a given risk level, investors prefer high returns to lower returns. Similarly, for a given Notes
level of expected return, investor prefer less risk to more risk.
Under these assumptions, a single asset or portfolio of assets is considered to be ‘efficient’ if no
other asset or portfolio of assets offers higher expected return with the same (or lower) risk or
lower risk with the same (or higher) expected return.

= W 2 2 + (1 – W ) 2 + 2 [W (1 – W ) r ] ½
p C C C E C C C E CE
E(R) = W E(R ) +(1 + W ) E(R )
P C C C E
Geographical representation of the Mean-Variance Criterion is presented in Figure 12.1, the
vertical axis denoting expected return while the horizontal axis measures the standard deviation
(or variance) of the returns. Given its expected return and standard deviation, any investment
option can be represented by a point on such a plane and the set of all potential options can be
enclosed by an area such as shown in Figure 12.1. The efficient frontier, given by the arc AB, is a
boundary of the attainable set. In Figure 12.1 the shaded area represents the attainable set of
portfolio considerations, with their own risks and expected returns. (Two different portfolios
may have the same expected return and risk). Any point inside the shaded area is not as efficient
as a corresponding point on the efficient frontier – the arc AB.

Figure 12.1: Markowitz Efficient Frontier

Example: The policy committee of CDME recently used reports from various security
analysts to develop inputs for the single-index model. Output derived from the single-index
model consisted of the following efficient portfolios:
Portfolio Expected Return (ER) Standard Deviation
1 8% 3%
2 10% 6%
3 13% 8%
4 17% 13%
5 20% 18%

1. If the prevailing risk-free rate is 6% which portfolio is the best?
2. If a SD of 12% were acceptable, what would the expected portfolio return be and how
would CDME Finance achieve it?

LOVELY PROFESSIONAL UNIVERSITY 299