Negative Perfect Correlation

The anticipate return on the portfolio is the leaden come of expected returns on the component securities with portfolio proportions (w) as weights: (1) The departure of the two-asset portfolio is: (2) Recall that the covariance of a variable with itself is the variance of that variable, that is: . Therefore, another way to express the variance of the portfolio is as fol economic crisiss: (3) cigarette be positive or negative. equivalence 3 reveals that portfolio variance is reduced if the covariance term is negative. The correlation coefficient is slight than 1, making the portfolio standard deviation less than the weighted norm of the component standard deviations. Because the portfolios expected return is the weighted average of its component expected returns, whereas its standard deviation is less than the weighted average of the component standard deviations, portfolios of less than perfectly gibe assets always offer better risk-return opportunities than the individual component securities on their own. The lower the correlation between the assets, the greater is the gain in efficiency. Therefore, other things equal, we will always prefer to add to our portfolio assets with low or, even better, negative correlation with our existing position. How low can portfolio standard deviation be?

The lowest possible take to be of the correlation coefficient is -1, representing perfect negative correlation. In this case, the equation preceding(prenominal) simplifies to: 2 solutions: (1) : (2) From both (1) and (2) we get: and Since , (1) holds for: and (2) holds for: . (1) gives for . It is increase in and consequently decreasing when falls. Now: increases when falls, i.e.: . (2) gives for and is decreasing in and hence increasing when falls. Conclusion: it is possible to reduce the risk to zero: it is the benefit of the perfect negative correlation. Participant| Income| Years of Education| #1| 125,000... If you want to get a full essay, order it on our website: Orderessay

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