Question

A. Suppose you have an asset with an expected return of 0.12 and a standard deviation of 0.18. If the riskless rate is 0.04, what combination of the risky asset and a riskless asset would give you an expected return of 0.09? What would be the standard deviation of this combination? (5 pts.)

B.Find the proportion of risky and riskless assets contained in a combined portfolio whose expected return is 0.12 per year, where the riskless rate is 0.05 and the expected return on the all-stock portfolio is 0.08. (3 pts.)

Answer 1

Asset 1 with expected return=0.12

standard deviation=0.18

If thhe riskless rate is 0.04

standard deviation =0

1) Total expected return=0.09

0.09=w1*0.12+w2*.04

0.09=W1*0.12+(1-W1)*0.04

0.09-0.04=W1(0.12-0.04)

W1=0.05/0.08==0.625

W2=1-0.625=0.375

2) Standard Deviation:

Cov(1,2)=correlation(1/2)*sd1*sd2=0

SD=(0.625^2*0.18^2+0.375^2*0+2*0.375*0.625*)^0.5

SD=(0.625^2*0.18^2)^0.5

SD=0.1125 of the portflolio

3) Portfolio expected return=0.12

Expected return of riskfree asset=0.05

Expected return of stock(considering this stock portfoilo as one) =0.08

Let's consider x no of riskfree asset. y no of stock assets

1=x1+x2--Xx+y1+y2+    yy( these are individul weights of the assets whose sum is equal to 1

We also know:

Expected return of stock portfolio:

E(Rs)=y1*r1+y2r2+.......yy*ry=0.08

We can consider all the stock is giving return of 0.08

E(rp)=(x1*.05+x2*.05+++++Xx*.05)+0.08

E(R0)=0.05*W1+0.08

0.12=0.05*W1+0.08

W1=(0.12-0.08)/0.05=0.80

W2=(1-0.80)=0.20