Two risky portfolios exist for investing: one is a bond portfolio with a beta of

Question

Two risky portfolios exist for investing: one is a bond portfolio with a beta of 0.6 and an expected return of 7.1% and the other is an equity portfolio with a beta of 1.2 and an expected return of 15.8%. If these portfolios are the only two available assets for investing, what combination of these two assets will give the following investors their desired level of expected return? What are the betas of each investor's combination of the bond and equity portfolio?

a. Bart: Desired expected return 15%

b. Lisa: Desired expected return 13%

c. Maggie: Desired expected return 11%

Explanation / Answer

a).

let weightage of equity portfolio is x

15 = 7.1(1-x)+x15.8

15 = 7.1x+15.8-15.8x

15 = 7.1+8.7x

x = weightage of equity portfolio = (15-7.1)/(15.8-7.1) = (Desired return-bond return)/(equity return-bond return) = .9080

(1-x) = weightage of bond portfolio = 1-.9080 = .092

beta = .9080*1.2+.092*.6 = 1.1448

b)

let weightage of equity portfolio is x

13 = 7.1(1-x)+x15.8

13 = 7.1x+15.8-15.8x

13 = 7.1+8.7x

x = weightage of equity portfolio = (13-7.1)/(15.8-7.1) = (Desired return-bond return)/(equity return-bond return) = .6781

(1-x) = weightage of bond portfolio = 1-.6781 = .3219

beta = .6781*1.2+.3219*.6 = 1.0068

c).

11 = 7.1(1-x)+x15.8

11 = 7.1x+15.8-15.8x

11 = 7.1+8.7x

x = weightage of equity portfolio = (11-7.1)/(15.8-7.1) = (Desired return-bond return)/(equity return-bond return) = .44827

(1-x) = weightage of bond portfolio = 1-.44827 = .55173

beta = .44827*1.2+.55173*.6 = 0.86896

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