Macroeconomics questions model

Question 5.4 A modeller has developed a two-factor model to explain the returns obtained from security i It has the form: R; = 2+1.3/ +0.812+ 6; However, he is concerned that the two indices 1 and 2 may be correlated and so decides to re-express the model in terms of orthogonal factors. He therefore regresses Index 1 on Index 2 and obtains the following equation for the line of best fit: / =0.8+0.3/2 Use this information to re-express the two-factor model in terms of two orthogonal factors / and 12.Question (i) A portfolio P consists of n assets, with a proportion x; invested in asset i, i =1,2,...,n (so that > >; =1). Derive a formula for the portfolio beta, Ap, in 1=1 terms of the individual betas for each asset. [2] (ii) The annual returns Rp on this portfolio can be assumed to conform to the single-index model of asset returns. Write down an equation defining this model and show that: var( Rp ) = Bp var( Ry ) + var(Ep) where ap denotes the component of the portfolio return that is independent of movements in the market. [3] (iii) Explain why the specific risk var(8p) is sometimes referred to as the "diversifiable risk", giving an algebraic justification for your answer. [4] (iv) Discuss the following statement: "A portfolio with a beta of zero is equivalent to a risk-free asset. " [2] [Total 11]