source of risk in planet Delta – the weather – and it affected the two securities in
exactly opposite directions. Such a situation seldom occurs in real life. More
often than not, in practice, there are several sources of risk some of which affect
only one of the securities, some affect both in opposite directions and some others
affect them in the same direction. Clearly it is important to know what is the net
effect of all these multiple causes which affect the security returns. Do the
securities move in the same direction or in opposite directions? In either case, what
is the strength of the coefficient (denoted by the symbol ?) to answer these
questions? The correlation coefficient ranges from -1 to +1. If the two returns
move exactly opposite to each other, the correlation coefficient is -1, if they move
exactly in step with each other, then it is +1; if the two returns are entirely
unrelated to each other, it is zero. A positive correlation coefficient which is less
than +1 indicates that the two returns have a tendency to move in the same
direction, but are not always inexact step with each other. This kind of imperfect
correlation is most commonly observed, since two different securities belonging to
two different firms can hardly b expected to move in perfect harmony with each
other. Positive correlation between two securities implies, for example, that when
the market as a whole booms, both the securities would register a rise in prices, or
when the market crashes, both the securities would show a decline in prices.
Let us, next, move from Planet Delta to Planet Earth and consider a more realistic
example.
Consider two securities X and Y with the following attributes:Expected return on Security X = 20%
Expected return on Security Y = 30%
s of Security X = 10%
s of Security Y = 16%Coefficient of Correlation
Between the Returns of X and Y = -1, 0.5, +1 (three scenarios).We shall evaluate the impact on the gains from diversification, for the three
different values of the correlation coefficients.Let us first analyze the case where we hold a portfolio with 40% invested in X and
60% invested in Y. The expected portfolio return is nothing but the weighted
average of the expected returns from each security in the portfolio, the weights
being the proportion of investment in each security. Therefore, the expected
portfolio return will be 26% (being 20 X 0.4 + 30 X 0.6).
Is the s of portfolio return the same as the weighted average of the s ‘s of the
security returns? That is, would the s of portfolio return be 13.6% (being 10 X 0.4
- 16 X 0.6)? These questions cannot be answered because the variability of