Question

The risk-free rate is 5% and the tangency portfolio has 20% expected return and 40% return standard deviation. A risk-loving investor has $1000 of wealth and she seeks to attain 27.5% expected return. How much money does she need to borrow from the bank? A. 250 B. 500 C. 1500 D. 1000

Answer 1

B. 500

Step-by-step explanation:

Portfolio return = Weighted average return

Let the amount invested in portfolio is x and amount invested in risk free = 1000 - x

27.5% = 20%*x + 5%*(1000-x)

27.5% * 1,000 = 20%x + 50 – 5%x

0.275 * 1,000 = 15%x + 50

275 - 50 = 15%x

225 = 15%x

x = 225 / 0.15

x = $1,500

Hence, the amount of money borrowed = $1,500 - $1000

= $500