Question

You invest $100 in a risky asset with an expected rate of return of 0.21 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 risk-free asset to form a portfolio with an expected return of 0.28?

Answer 1

-0.4242

Step-by-step explanation:

Ra = 0.21 or 21%

Rf = 0.045 or 4.5%

Rp = 0.28 or 28%

Expected return on a portfolio is weighted average return of its assets :

Rp = Rf*(1-w) + Ra*w

28 = 4.5*(1-w) + 21*w

28 = 4.5 - 4.5w + 21w

28 - 4.5 = 21w - 4.5w

21w - 4.5w = 28 - 4.5

16.5w = 23.5

w = 23.5/16.5

w = 1.4242

Hence, weight of risky asset = 1.4242

So, Weight of risk free asset = 1 - 1.4242

Weight of risk free asset = -0.4242