involves the selection of
securities. Each individual investor puts his
wealth in a combination of assets
depending on his wealth, income and his
The traditional theory of portfolio postulates
that selection of assets should be based on
lowest risk, as measured by its standard
deviation from the mean of expected
But how to gain highest returns from the
lowest risk?? is what led to the
development of Markowitz model.
Markowitz put forward this model in
It assists in the selection of the most efficient
by analyzing various possible portfolios of the
given securities. By choosing securities that do
not 'move' exactly together, the HM model
shows investors how to reduce their risk.
The HM model is also called Mean-Variance
Model due to the fact that it is based on
expected returns (mean) and the standard
deviation (variance) of the various portfolios.
started with the idea of risk aversion of
average investors and their desire to
maximise the expected return with the least
Markowitz model is thus a theoretical
framework for analysis of risk and return and
His framework led to the concept of efficient
An efficient portfolio is expected to yield the
highest return for a given level of risk or
lowest risk for a given level of return.
Assumptions of the
1. Risk of a portfolio is based on the
variability of returns from the said portfolio.
2. An investor is risk averse.
3. An investor prefers to increase
4. Analysis is based on single period model of
5. An investor either maximizes his portfolio
return for a given level of risk or maximizes
his return for the minimum risk.
6. An investor is rational in nature.
Parameters for building up the
efficient set of portfolio
1. Expected return.
2. Variability of returns as measured by
standard deviation from the mean.
3. Covariance or variance of one asset
return to other asset returns.
How to determine the efficient
In this figure, the shaded area
PVWP includes all the
possible securities an investor
can invest in. The efficient
portfolios are the ones that lie
on the boundary of PQVW.
This boundary PQVW is called
the Efficient Frontier.
All portfolios that lie below the
Efficient Frontier are not good
enough because the return
would be lower for the given
Portfolios that lie to the right
of the Efficient Frontier would
optimal portfolio is
found at the point of
tangency of the
efficient frontier with
curve. This point
marks the highest
level of satisfaction
the investor can
obtain. R is the point
where the efficient
frontier is tangent to
C3, and is an
Demerits of the HM Model
1. It requires lots of data to be included. An
investor must obtain variances of return,
covariance of returns and estimates of
return for all the securities in a portfolio.
2. There are numerous calculations
involved that are complicated because
from a given set of securities, a very
large number of portfolio combinations
can be made.
3. The expected return and variance will
also have to be computed for each of the
securities in the portfolio.
SHARPE’S SINGLE INDEX MODEL
The extension of Markowitz
model, overcoming of the
defects, is this model.
Sharpe showed that there is
along the efficient frontier a
unique portfolio that, when
combined with lending or
borrowing at the pure
interest rate, dominates all
other combinations of
Assumptions for Sharpe’s
(1)There exists a single pure interest
rate at which investors can lend and
borrow in unlimited amounts
(2) Investors have homogeneous
expectations regarding expected
returns, variances and correlations.
Equation for SIM
Ri =αi + β*Rm +ei
Ri = return on the stock
αi = component of security that is
of market performance
β =co-efficient in the market expected
change in Ri given a change in Rm
Rm =rate of return on market index
ei =random elements of αi.
Criticism of SIM
Single index model has been criticized
because of its assumption that stock
prices move together only because of
common co-movement with the
market. Many researchers have found
that there are influences beyond the
market like industry related factors
that cause securities to move together.
If investors are risk averse its suitable
for them to adopt Markowitz model, on
the other hand, though SIM is
criticized it is not possible by any other
models to simplify calculations using
Therefore, in choosing the portfolio of
investments, one has to analyze
carefully about the possibility of risk
and return and adopt the suitable