1 A portfolio consists of two assets A and B Their respectiv

1. A portfolio consists of two assets A and B. Their respective mean returns are E(RA) = 15% and E(RB) = 10%. Their variances are 2 A = 81 and 2 B = 49. Sixty per cent of the portfolio consist of asset A. (a) Assuming Cov(RA, RB) = 50, calculate the mean and the variance of the return to the whole portfolio. (b) Assuming that the covariance between the two assets is at its maximum possible value, calculate the return to the whole portfolio. (c) What is the minimum variance that a portfolio consisting of both assets with Cov(RA, RB) = 50 can achieve? (d) Show that the variance of the portfolio (its risk) can be driven to 0 if the two assets are perfectly negatively correlated.

Solution

Mean of the portfolio = 15 * 0.60 + 10 * (1 - 0.60) [Weighted average mean of all the assets in portfolio]

   = 9 + 4

   = 13 %

Variance of the porfolio = 81 * 0.60 + 49 * 0.40 [Weighted average variance of all the assets in portfolio]

   = 48.6 + 19.6

= 68.2

Standard deviation of portfolio = Under root of 68.2

   = 8.26 (approx)