MBA (Finance) – IV Semester, Investment and Portfolio Management, Unit 4.2
Risk and Return With Different Correlation
All the graphs show the portfolio risks under varying levels of correlation co-efficients. All the figures can be assembled together and placed in a single figure. The following figure expresses the relationship between expected returns and standard deviations of returns for various correlation coefficients.
Risk and Return With Different Correlation
The four figures indicate the relationship between risk and return.
All the graphs show the portfolio risks under varying levels of
correlation co-efficients. All the figures can be assembled together and placed
in a single figure. The following figure expresses the relationship between
expected returns and standard deviations of returns for various correlation
coefficients.
Two Security Portfolios with
Different Correlation Coefficients
In the figure, portfolio return is given on the vertical axis and
portfolio risk on the horizontal axis. Point A represents 100 per cent holdings
of X and point B represents 100 per cent holdings of Y. The intermediate points
along the line segment AB represent portfolios containing various combinations
of two securities.
The straight line r = + 1 shows that the portfolio risk increases
with the increase in portfolio return. Here, the combination f two securities
could not reduce the portfolio risk-because of their positive correlation.
Again, the ratio of smaller standard deviation to larger deviation is less than
the correlation coefficient.
1 > 4/10 = 1 > .4 which indicates that benefit cannot be
derived by combining both the securities. In this case if an investor wish to
minimize his risk, it would be better for him to invest all the money in
security X where the risk is comparatively lower.
The rxy = 0 line is a hyperbola.
Along the line segment ACB, the r = 0. CB contains portfolios that a superior
to those along the line segment AC. Markowitz says that all portfolios along
the ACB line segment are feasible but some are more efficient than others. The
line segment ADB indicates (r = -1) perfect inverse correlation and it is
possible to reduce portfolio risk to zero. Portfolios on the line segment DB
provides superior returns than on the line segment AD. For example, take two
points on both the line segments K and J. The point K is superior to the point
J because with the same level of risk the investor earns more return on point K
than on pointy.
Thus, Markowitz diversification can lower the risk if the
securities in the portfolio have low correlation coefficients.
