Question

You invest $100 in a risky asset with an expected rate of return of 9% and a standard deviation of 0.15 and a T­-bill with a rate of return of 4%. What percentages of your money must be invested in the risky asset to form a portfolio with an expected return of 9%?

Answer 1

Let the Weight of the risky asset be x

Hence the weight of T bill is (1-x)

Expected Return of Portfolio = (Weight of Risky Asset * Expected Return of Risky Asset) + ( Weight of T Bill * Expected Return of T Bill)

9 % = (x * 9%) + [ ( 1-x)* 4%]

9% = 0.09 x + [ 0.04 -0.04 x]

0.09 = 0.09 x + 0.04 - 0.04 x

0.09 - 0.04 = 0.09 x - 0.04 x

0.05= 0.05 x

or x = 0.05/0.05

= 100%

Hence the correct answer is 100%