A portfolio P consists of n assets, with a proportion x, invested in asset i, i=1,2,...,...

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A portfolio P consists of n assets, with a proportion x, invested in asset i, i=1,2,..., (so that Σx, =1) Derive a formula for the portfolio beta, pp, in i=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 de fining this model and show that: var(Rp.)= var(R₁) + var(p) where Ep denotes the component of the portfolio return that is independent of movements in the market. (ii) Explain why the specific risk var(Ep) 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." [Total 11] A portfolio P consists of n assets, with a proportion x, invested in asset i, i=1,2,..., (so that Σx, =1) Derive a formula for the portfolio beta, pp, in i=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 de fining this model and show that: var(Rp.)= var(R₁) + var(p) where Ep denotes the component of the portfolio return that is independent of movements in the market. (ii) Explain why the specific risk var(Ep) 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." [Total 11]

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i To derive the formula for the portfolio beta Bp we need to calculate the weighted average of individual betas for each asset The proportion invested ... View the full answer