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