Question

You have $100,000 available to invest. The risk-free rate, as well as your borrowing rate, is 4%. The risky portfolio has an expected return of 10% and a return standard deviation of 20%. If you want the standard deviation of your investment to be 30%, you must _________.

Answer 1

c. borrow $50,000 at the risk-free rate

Step-by-step explanation:

Options are: "invest $100,000 in the risk-free asset, borrow $25,000 at the risk-free rate, borrow $50,000 at the risk-free rate, invest $125,000 in the risk-free asset"

Standard Deviation of the portfolio = Weight of Risky assets * Standard Deviation of risky assets

30% = Weight of Risky assets * 20%

Weight of Risky assets = 30% / 20%

Weight of Risky assets = 1.50

Weight of Risk Free Assets = 1 - 1.50

Weight of Risk Free Assets = -0.50

Borrow from risk assets = 0.50 * $100,000

Borrow from risk assets = $50,000

Hence, If we want the standard deviation of our investment to be 30%, we must borrow $50,000