Consider the single index model of investment returns in which for any security i: R =...

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Consider the single index model of investment returns in which for any security i: R₁ = a₁ + R₁₂ R₁ + E₂ where E(e;)=0, E(ee;)=0 for ij, E(R)=0 and R, is the return on the market. (0) Assuming that this model applies, derive expressions for the mean investment return on security i, and the mean investment return on a portfolio P. containing n securities, with a proportion x, invested in security i. [3] (ii) Show that Cip=xCy, where Cup and C are the covariance of investment j=1 returns between security and portfolio P and securities i and respectively. [2] (iii) State a general expression for the variance of portfolio P in terms of the covariances Cij [1] (iv) Use your results from (ii) and (iii) to show that: dop 1 Bip = where Pip - dx, Op CIP and comment briefly on this result. [7] Consider the single index model of investment returns in which for any security i: R₁ = a₁ + R₁₂ R₁ + E₂ where E(e;)=0, E(ee;)=0 for ij, E(R)=0 and R, is the return on the market. (0) Assuming that this model applies, derive expressions for the mean investment return on security i, and the mean investment return on a portfolio P. containing n securities, with a proportion x, invested in security i. [3] (ii) Show that Cip=xCy, where Cup and C are the covariance of investment j=1 returns between security and portfolio P and securities i and respectively. [2] (iii) State a general expression for the variance of portfolio P in terms of the covariances Cij [1] (iv) Use your results from (ii) and (iii) to show that: dop 1 Bip = where Pip - dx, Op CIP and comment briefly on this result. [7]

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i For any security i the mean investment return is ERi i The mean retu... View the full answer