Question

You invest $100 in a risky asset with an expected rate of return of 0.11 and a standard deviation of 0.21 and a T-bill with a rate of return of 0.045. What percentages of your money must be invested in the risky asset and the risk-free asset, respectively, to form a portfolio with an expected return of 0.13?

Group of answer choices

a)57.75% and 42.25%

b)Cannot be determined.

c)67.67% and 33.33%

D)130.77% and –30.77%

e)–30.77% and 130.77%

Answer 1

Let weight be

Risky Asset = W1

T Bill = W2

Expected Return = W1*R1 + W2*R2

0.13 = W1*0.11+W2*0.045

and we also know that

W1+W2 = 1

as there is only two things in portfolio

Putting W2 = 1-W1

0.13 = W1*0.11+(1-W1)*0.045

W1 = 0.085/0.065 = 130.77% 0r 1.3077

W2 = 1-1.3077 = -30.77%

answer is D