expected returns of the individual securities comprising the portfolio, the weights being
the respective proportion of each security in the portfolio.
The variance (s^2 ) of the portfolio return can be computed by repeated application of the
procedure used in the two security situation above. The portfolio of two securities can be
regarded as a single new security and combined with the third security, and the process
repeated till all n securities have been included in the portfolio.
At this stage we may ask whether the gains from diversification will continue to be
realized, till the portfolio return variance (s^2 ) reduces to zero. A little reflection will show
that this is not so. For if it was so, and then the portfolio consisting of all securities in the
market (technically called the market portfolio) which is the most diversified portfolio
imaginable would not have any risk. Yet we know that the market index does fluctuate
quite substantially though less than an individual security does. This suggests that there
is a minimum level of risk below which we cannot get by merely diversifying our
portfolio.
In general, as the number of securities in a portfolio increases, say up to 20 or 25, the
diversification reduces the portfolio risk (s^2 ) rapidly. However, soon thereafter, the
marginal reduction to portfolio risk of any further diversification becomes very small (Fig
2). Thus, a diversified portfolio of about 25 securities
Fig 2 Reduction of Risk through Diversification.
Selected from different industries more or less represents a market portfolio. Consider
for example, the BSE Sensex index which comprises a mere 30 securities, but is deemed
to represent the entire market. Again, it is for the reason that both the Sensex Index with
its 30 securities and the BSE National Index comprising 100 securities are actually very