Question

Different investor weights.

Two risky portfolios exist for​ investing: one is a bond portfolio with a beta of 0.8 and an expected return of 6.1%  and the other is an equity portfolio with a beta of 1.2 and an expected return of 15.9% 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​%  The combination of these two assets that will give Bart an expected return of

15​% is __% in bonds and __% in stocks.(Round both answers to two decimal​places.)

b. Lisa: desired expected return 13​%  The combination of these two assets that will give Bart an expected return of

13​% is __% in bonds and __% in stocks.(Round both answers to two decimal​places.)

c.Maggie: desired expected return 11​%  The combination of these two assets that will give Bart an expected return of

11​% is __% in bonds and __% in stocks.(Round both answers to two decimal​places.)

Answer 1

Given :

	Beta	Expected Return
Bond portfolio	0.8	6.10%
Equity portfolio	1.2	15.90%

a) (i) Calculation of Weights of 2 assets which gives Bart desired expected return 15​%.

Let the Weight of Bonds be X
Weight of Equity = 1- X

where, ER(A) & ER(B) = Expected Return of Bond & Equity respectively
WA & WB = Weight of Bond & Equity respectively

0.15 = 0.061*X +0.159*(1 - X)
0.15 = 0.061*X +0.159 - 0.159X
0.098X = 0.009
X = 0.091837 or 9.18%

Weight of Bonds = 9.18%
Weight of Equity = 1- 0.0918 = 0.9082 or 90.82%  

(ii) Calculation of Beta of combined bond and equity​ portfolio

0.8* 9.18% + 1.2* 90.82%  
1.1633

b) Calculation of Weights of 2 assets which gives Lisa desired expected return 13​%  

Let the Weight of Bonds be X  
Weight of Equity = 1- X

where, ER(A) & ER(B) = Expected Return of Bond & Equity respectively
WA & WB = Weight of Bond & Equity respectively

0.13 = 0.061*X +0.159*(1 - X)
0.13 = 0.061*X +0.159 - 0.159X
0.098X = 0.029
X = 0.2959 or 29.59%

Weight of Bonds = 29.59%
Weight of Equity = 1-  0.2959 = 0.7041 or 70.41%  

(ii) Calculation of Beta of combined bond and equity​ portfolio

0.8* 29.59% + 1.2* 70.41%   
1.0816

c) Calculation of Weights of 2 assets which gives Maggie desired expected return 11​%  

Let the Weight of Bonds be X
Weight of Equity = 1- X

where, ER(A) & ER(B) = Expected Return of Bond & Equity respectively
WA & WB = Weight of Bond & Equity respectively

0.11 = 0.061*X +0.159*(1 - X)
0.11 = 0.061*X +0.159 - 0.159X
0.098X = 0.049
X = 0.5 or 50%

Weight of Bonds = 50%
Weight of Equity = 1-  0.5 = 0.5 or 50%  

(ii) Calculation of Beta of combined bond and equity​ portfolio

0.8* 50% + 1.2*  50%   
1