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 0.5 and an expected return of 8%, and the other is an equity portfolio with a beta of 1.2 and an expected return of 15%. If these portfolios arc the only two available assets for investing, what combination of these two assets will give the following investors their desired level of expected returns? What are the betas of each investor's combination of the bond and equity portfolio? a. Bart: desired expected return of 14% b. Lisa: desired expected return of 12%

Explanation / Answer

a. Bart: expected return of 14%

Let X be invested in Bond and(1-X) be invested in equity

So, X*8 + (1-X)*15 = 14

8X + 15 - 15X =14

7X = 1

X = 1/7 = 0.1429 and 1-X = 1-0.1429 = 0.8571

So the Bart should invest 14.29% in Bonds and 85.71% in equity

The beta for Bart is = 0.1429 *0.5 + 0.8571* 1.2 = 1.09985 = 1.10

b. Lisa: expected return of 12%

Let X be invested in Bond and(1-X) be invested in equity

So, X*8 + (1-X)*15 = 12

8X + 15 - 15X =12

7X = 3

X = 3/7 = 0.4286 and 1-X = 1-0.1429 = 0.5714

So the Lisa should invest 42.86% in Bonds and 57.14% in equity

The beta for Lisa is = 0.4286 *0.5 + 0.5714* 1.2 = 0.8999 = 0.90

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