= (0.60 x 14) + (0.40 x 20) = 8.40 + 8 = 16.40% Measure of variance (risk) of a Portfolio Risk of a portfolio is the variance of returns of the portfolio from its expected return. The variance or standard deviation is a measure of the variation of possible of returns from the expected rate of return. The variance of a portfolio depends not only on the variances of the securities making up the portfolio, but also on the relationship among those securities called and coefficient of variation. (Variance equation) Covariance: Covariance is the statistical measure of the degree to which two securities returns move together relative to their individual means over time. That is the extent to which their returns co-move or co-vary from their respective averages. When the two returns move together in the same direction, they have positive co-variance; when they move in opposite directions they have negative co-variance; when their movements do not affect each other then they have Thus, if returns of securities in a portfolio exhibit positive covariance then the zero co-variance. investment does not reduce overall risk of the investor. On the other hand, if they have negative covariance they reduce the overall risk of the investor. The equation for co-variance between the returns of securities X and Y (covXY) is; Where Rx and Ry = expected returns of securities X and Y and = the average returns of securities X and Y = the probability of occurrence of an event The riskiness or standard deviation of a two–security portfolio is determined by; Portfolio Variance - P= P Where = the weight (proportion) of total funds invested in security X = Variance of returns of security X σ2x = the weight (proportion) of total funds invested in security Y = variance of returns of security Y σ2y
= (0.60 x 14) + (0.40 x 20) = 8.40 + 8 = 16.40% Measure of variance (risk) of a Portfolio Risk of a portfolio is the variance of returns of the portfolio from its expected return. The variance or standard deviation is a measure of the variation of possible of returns from the expected rate of return. The variance of a portfolio depends not only on the variances of the securities making up the portfolio, but also on the relationship among those securities called and coefficient of variation. (Variance equation) Covariance: Covariance is the statistical measure of the degree to which two securities returns move together relative to their individual means over time. That is the extent to which their returns co-move or co-vary from their respective averages. When the two returns move together in the same direction, they have positive co-variance; when they move in opposite directions they have negative co-variance; when their movements do not affect each other then they have zero co-variance. Thus, if returns of securities in a portfolio exhibit positive covariance then the investment does not reduce overall risk of the investor. On the other hand, if they have negative covariance they reduce the overall risk of the investor. The equation for co-variance between the returns of securities X and Y (covXY) is; Where Rx and Ry = expected returns of securities X and Y and = the average returns of securities X and Y = the probability of occurrence of an event The riskiness or standard deviation of a two–security portfolio is determined by; Portfolio Variance - P= P Where = the weight (proportion) of total funds invested in security X σ2x = Variance of returns of security X = the weight (proportion) of total funds invested in security Y σ2y = variance of returns of security Y
pbbf306-chapter-three.docx