Question

. You are given the following information: Stock Expected return (in %) σ (in %) A 10 10 B 5 5 The covariance between these returns is 16%2 . The risk-free rate is 6%) Which portfolio of A and B has: i. An expected return of 10% ii. An expected return of 7.5% iii. A standard deviation of 7.5% (Don’t be too rigorous, just try to find one portfolio with this SD. You might need Excel for this one).

Answer 1

Let w be the weight in A and 1-w in B

1.
w*10%+(1-w)*5%=10%
=>w=(10%-5%)/(10%-5%)=1

100% in A and 0% in B

2.
w*10%+(1-w)*5%=7.5%
=>w=(7.5%-5%)/(10%-5%)=0.5

50% in A and 50% in B

3.
sqrt((w*10%)^2+((1-w)*5%)^2+2*w*(1-w)*16%%)=7.5%
=>w=-0.492267814

IN EXCEL
Empty cell B1
Enter below formula in cell C2
=SQRT((B1*10%)^2+((1-B1)*5%)^2+2*B1*(1-B1)*16%%)-7.5%

Go to Data tab->What if Analysis->Goal Seek

Set cell C2
To value 0
By changing cell B1

B1=-0.492267814

Hence, -0.492267814% in A and 50.7732186% in B