- The Notion of Non-diversifiable or Market Risk while diversification does
reduce risk, even a very highly diversified portfolio does not become risk free.
The well-diversified portfolio that we can think of is the one which contains all the
securities in the stock market (technically known as the market portfolio). Even
this portfolio reveals substantial variability as is evident from the fluctuations in
the market index. This risk is clearly undiversifiable and is known as market risk. - The Notion of Beta The above discussion indicates that the most important
source of risk is the market risk because it cannot be eliminated through
diversification. The modern Portfolio Theory, therefore, argues that the riskiness
of a security should be measured by its vulnerability to market risk. If the market
were to go down by 1%, would the security go down by 0.5%, by 1% or by 2%?
This sensitivity of the security to the movements of the market is known as the
beta coefficient of the security. - The Notion of Trade off between Risk and Return The modern portfolio
theory also demonstrates that if the securities are correctly priced, the return on
each security would be commensurate with its risk as measured by its beta. The
graphical depiction of the resulting straight line relationship between return and
beta is known as the security market line. A similar straight line relationship,
called the capital market line, exists between return and risk (as measured by
variability) of well-diversified portfolio.
The rest of this chapter is devoted to an exposition of MPT. We shall in the
process make the above notions more precise and rigorous.
What is Risk?
Let us go back to the example at the beginning of this chapter where we looked at
the returns over the last five years on shares M and N:
Share M: 30%, 28%, 34%, 32% and 31%
Share N: 26%, 13%, 48%, 11% and 57%
We concluded intuitively that share N was riskier because its return fluctuated
much more. While both had an average return of 31%, N’s returns deviated to a
greater extent from this average than M’s did. Statisticians measure this kind of
deviation or fluctuation by either the standard deviation or the variance. In MPT,
the variability or riskiness of securities is measured by the standard deviation of
the security returns. Standard deviation is usually denoted by the Greek letter s
(pronounced sigma). The variance is nothing but the square of the standard
deviation and hence denoted by s^2 (pronounced sigma square). The mathematical
definitions of standard deviation and variance have been explained in Appendix 5,
but the average reader need not know these definitions at all. All that is important