Question

Different investor weights. Two risky portfolios exist for investing: one is a bond portfolio with a beta of 0.5 and an expected return of 8.3%, and the other is an equity portfolio with a beta of 1.2 and an expected return of 16.4%. 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 is the beta of each investor's combined bond and equity portfolio?

**a. **Bart: desired expected return 15%

**b. **Lisa: desired expected return 13%

**c. **Maggie: desired expected return 11%

please show ALL work

please be sure to solve for w (weight) as well.

Answer #1

a. Bart E(r) = 15% = w*8.3% + (1-w)*16.4%

15% = 8.3w% + 16.4% -16.4w%

8.1w%=1.4%

w=.1728 or 17.28%

Bart should invest 17.28% of his wealth in Bond and 82.7% of his wealth in equity

Beta of Bart's portfolio = 0.1728*0.5+ 0.8271*1.2 = 1.07

Lisa E(r) = 13% = w%8.3% + (1-w)*16.4%

13% = 16..4% - 8.1w%

w = 3.4/8.1 =0.4197

Lisa should invest 41.9% of her wealth in bond and 58.1% of her wealth in equity

Beta of Lisa = 0.4197*0.5 + 0.5802*1.2 =.9060

Maggie E(r)= 11% = w%8.3% + (1-w)*16.4%

w=5.4/8.1 =0.6666

Maggie should invest 66.66% of her wealth in bond and 33.33% of her wealth in equity

Beta of Maggie = 0.6666*0.5+0.3333*1.2 = .7332

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