Perfect Negative Correlation
(p = -1.0) In this case, portfolio standard deviation is the difference (non-negative value) caused by the standard deviation of returns on individual assets weighted by their respective shares in the portfolio. Portfolio variance is given by the Equation (3.12):
This equation shows that when the correlation coefficient between asset returns is negative unity. It is possible to combine them in it manner that will eliminate all risk. The portfolio contains two risk asset, but the portfolio risk (standard deviation) can bee reduced to zero, for such a minimum variance portfolio can he directly obtained from Equation (3.14):
When two assets with perfect negative correlation between their returns are combined in different proportions, the relationship between risk and return of these portfolios forms a V-shaped image with its tip resting on the axis of return. The clockwise movement of the risk return relationship along this image implies that with gradual increase in the weight of an asset with high-risk and high-return, and with simultaneous decrease in the overall risk, the expected return from the portfolio increases. The process continues till the risk is completely eliminated (point T), After that, higher expected returns, with increase in the weight of the riskier asset, come with higher portfolio risk only.
When the risk-return relationship far various combinations of two assets under the assumption of perfect positive correlation is combined with the corresponding relationship for perfect negative correlation, a triangle ATB is formed. Points A and B, which are common to the two cases, represent pure or undiversified portfolio, Since the correlation coefficient takes values between positive unity to negative unity, this triangle specifies the limits for diversification. All portfolios represented by the three line segments are feasible but some are more efficient than others. The risk-return relationship for all other values of correlation coefficient will lie in this space only.