# Project #18923 - Optimal Portfolio Choice III

Please see problem 4.4 in the attachment

Consider a financial market with only two risky assets S1 and S2, whose returns we denote by R1 and R2. For i = 1, 2, let μi denote the expected return on the risky asset Si, σi2 its variance and ρ the correlation between the two assets. In other

words, μi = E(Ri), σi2 = var(Ri) and ρ = cov(Ri,Rj). Consider an individual σ1 σ2

investor who optimizes her portfolio P according to the mean-variance criterion and denote by wi, i = 1, 2, her portfolio weights on the two risky assets. We shall assume that short sales are not allowed.

1. What are the expected value μP and the variance σP2 of the return RP on the investor’s portfolio P ?

2. What additional constraint do the portfolio weights wi (i = 1, 2) need to satisfy when no short sales are allowed? What is then the equation of the minimum variance frontier of portfolios composed of the two risky assets S1 and S2 only?

3. Show that the minimum variance frontier can be represented by one part of a hyperbola in a (σ(R), E(R)) space. (hint: do not forget that short sales are not allowed)

4. Intheaboveframework,assumethatμ1 =4,μ2 =1,σ1 =4,andσ2 =1. Compute the variance of the minimum variance portfolio obtained when ρ = 0 and ρ = 0.5.

4.5. OPTIMALPORTFOLIOCHOICEIV 23 5. What happens to the minimum variance portfolio when the two assets are

perfectly positively correlated, i.e. ρ = 1? What is its variance in this case?

 Subject Business Due By (Pacific Time) 12/06/2013 12:00 am
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