Modern Portfolio Analysis - Markowitz Model
Unit 2 SAPM Notes
Portfolio analysis and Management
MARKOWITZ MODEL INTRODUCTION
Dr. Harry M. Markowitz was the person who developed the first
modern portfolio analysis model. Markowitz used mathematical programming and
statistical analysis in order to arrange for the optimum allocation of assets
within portfolio. He infused a high degree of sophistication into portfolio
construction by developing a mean-variance model for the selection of portfolio.
Markowitz approach determines for the investors the efficient set of portfolio
through three importance variables - Return, standard deviation and coefficient
of correlation.
Markowitz model is called the “Full Covariance Model”. Through this method the investor can find out the efficient set of portfolio by finding out the trade off between risk and return, between the limits of zero and infinity. Markowitz theory is based on several assumptions these are:
ASSUMPTIONS OF MARKOWITZ’S MODEL
a)
The markets are efficient and absorb
all the information quickly and perfectly. So an investor can earn superior
returns either by technical analysis or fundamental analysis. All the investors
are in equal category in this regard.
b)
Investors
are risk averse. Before making any investments, all of them, have a common
goal-avoidance of risk. But practically this assumption does hold good. In a
country like India, majority of investors invests money on the basis of market
news without doing any technical and fundamental analysis.
c)
Investors are rational. They would
like to earn the maximum rate of return with a given level of income or money.
d)
Investors base their decisions solely
on expected return and variance (or standard deviation) of returns only.
e)
For a given risk level, investors
prefer high returns to lower returns. Similarly, for a given level of expected
return, they prefer less risk to more risk.
f)
The investor can reduce the risk if he
adds investments to his portfolio.
g)
Investors consider each investment alternative
as being represented by a probability distribution of expected returns over
some holding period.
h)
A portfolio of assets under the above
assumptions is considered to be efficient if no other portfolio of assets
offers higher expected return with the same (or lower) risk or lower risk with
the same (or higher) expected return.
PARAMETERS OF MARKOWITZ DIVERSIFICATION
Based on thorough and scientific research, Markowitz has set down
his own guidelines for diversification:
a)
The investments have different types
of risk characteristics. Some are systematic or market related risks and the
others are unsystematic or company related risks.
b)
His diversification involves a proper
number of securities not too less nor too many.
c)
The securities have no correlation or
negative correlation.
d)
Last is the proper choice of the
companies, securities or assets whose returns are not related and whose risks
are mutually off setting to reduce the overall risk.
Markowitz lays down three parameters for building up the efficient
set of portfolio:
a)
Expected returns.
b)
Standard deviation from mean to
measure variability of returns.
c)
Covariance or variance of one asset
return to other asset returns.
To generalize, higher the expected return, lower will be the
standard deviation or variance and lower is the correlation. In such a case,
better will be the security for investor choice. If the covariance of the
securities’ returns is negative or negligible, the total risk of the portfolio
of all securities may be lower as compared to the risk of the individual
securities in isolation.
By developing his model, Markowitz first did away with the
investment behaviour rule that the investor should maximize expected return.
This rule implied that the non-diversified single security portfolio with the
highest expected return is the most desirable portfolio. Only by buying that
single security can expected return be maximized. The single security portfolio
can be much preferred if the higher return turns out to be the actual return.
However, in real world, there are conditions of so much uncertainty that most
risk averse investors, joint with Markowitz in adopting diversification of
securities.