0.70 0.30 23.00 11.80 10.28 2.20
0.65 0.35 23.50 12.10 10.49 0.90
0.615 0.385 23085 12.31 10.66 0.00
0.60 0.40 24.00 12.40 10.74 0.40
0.55 0.45 24.50 12.70 11.03 1.70
0.50 0.50 25.00 13.00 11.36 3.00
0.45 0.55 25.50 13.30 11.72 4.30
0.40 0.60 26.00 13.60 12.11 5.60
0.35 0.65 26.50 13.90 12.52 6.90
0.30 0.70 27.0 0 14.20 12.96 8.20
0.25 0.75 27.50 14.50 13.43 9.50
0.20 0.80 28.00 14.80 13.91 10.80
0.15 0.85 28.50 15.10 14.41 12.10
0.10 0.90 29.00 15.40 14.93 13.40
0.05 0.95 29.50 15.70 15.46 14.70
0.00 1.00 30.00 16.00 16.00 16.00
The tabulated values and the graphs demonstrate the impact of correlation in returns on
the variability of portfolio return.
If the return on the two securities are perfectly correlated (that is, correlation coefficient =
1.0), the portfolio return moves along the straight line joining points X and Y. as we
move from X to Y, for every 1% increase in the expected return, the risk of the portfolio
goes up by 0.6%. In effect, there is no reduction in risk on account of diversification,
when the returns across the securities are perfectly correlated, since the volatility (as
measured by s) of the portfolio return is the weighted average of the volatility of the
individual securities.
If the returns are imperfectly correlated (say, correlation coefficient = 0.5), the portfolio
return moves along a curve, reaching level of risk (s) which is below the weighted
average risk. For a given value of expected portfolio return, the risk with imperfect
correlation is always below the risk when there is perfect correlation.
If the returns are perfectly negatively correlated (that is, correlation coefficient = -1.0),
the risk can be reduced to zero. By investing about 61.5% of money in X and the rest in
security Y, an investor can derive risk-free return (s = 0.0) of 23.85%. For most other
portfolios, for a specified value of expected return, the risk in this case would be much
lower than the risk when there is perfect correlation in returns.
It is clear from the above, that whenever the two security returns are less than perfectly
correlated, an investor gains through diversification, the gains can often reduce the risk of
the portfolio below the risk of securities comprising the portfolio.
In general, an investor is likely to have many securities in his portfolio. The computation
of the expected return of the portfolio as usual is merely the weighted average of the