portfolio return not only depends on the variability of the security returns, but also
on the correlation coefficient.
The s of portfolio return will be 13.6% only when the two securities X and Y
move in perfect tandem with each other, that is, when the correlation coefficient
between returns on X and returns on Y is +1. So long as X and Y have a
correlation coefficient of less than +1, the s the portfolio return will be less than
13.6%. For example, if the correlation coefficient is only 0.5, then the s of the
portfolio will be only 12.1%.
The fact that the portfolio s is only 12.1% as against the weighted average s of
13.6% implies there has been some gain from diversification. Let us see why this
is so. If we invest all our money in Y, the expected return is 30% and the risk is
16%; while if we invest all our money in X, the expected return is 20% and risk is
10%. We have assumed 6% additional risk for 10% additional return. This
implies that if there were no gains from diversification, as we move our money
from X to Y, on an average, for every 1% additional returns, we have to take 0.6%
additional risk. For example, if the correlation coefficient is +1, since the s of
portfolio return is nothing but the weighted average of the sās of security returns,
there is no gain from diversification, because every 1% increase in return is
accompanied with the average 0.6% increase in risk. It can be shown that except
in this extreme case of a correlation coefficient of +1, investing in two securities
does result in gains because the increase in risk for every 1% increase in return is
below the average increase in risk. In our illustration above, the return rose from
20% to 26% and the risk from 10% to 12.1% implying that there was only a 0.35%
increase in risk for every 1% increase in return. Gains from diversification allow
us to get additional return with less than commensurate increase in the risk level.
Let us extend our understanding of how an investor stands to gain through
diversification by investing in securities with imperfectly correlated returns, by
examining Table 1, which contains the expected return and risk for varying
composition of portfolio. The portfolios are also graphically displayed Fig 1, in
which the risk (s) is on the horizontal axis and the expected return is on the
vertical axis. The three curves in the figure are for three different degrees of
correlation between the securities.