Question

Please show all of your work and explain your answers!

You have $200,000 available to invest. The risk-free rate of return is 6% (you can borrow and lend at that rate of return). The return on the risky portfolio is 17%. If you wish to earn a 21% return, you should

__________ .

(a) invest $72,000 in the risk-free asset

(b) invest $70,000 in the risk-free asset

(c) borrow $70,000

(d) borrow $72,000

(e) no solution

Answer 1

Answer:

Expected Return / Portfolio Return = 21%
Risk Free Return = 6%
Risky Portfolio Return = 17%

Let the Weight of amount invested in Risk Free Return = x
Weight of amount invested in Risky Portfolio = 1 – x

Portfolio Return = (Risk Free Return Weight * Risk Free Return) + (Risky Portfolio Weight * Risky Portfolio Return)
21% = (x * 6%) + ((1 – x) * 17%)
21% = 6x% + 17% - 17x%
4% = -11x%
x = -0.36

Weight of Risk-free Asset = -0.36

Weight of Risky Portfolio = 1 - Weight of Risk-free Asset
Weight of Risky Portfolio = 1 - (-0.36)
Weight of Risky Portfolio = 1.36

Amount Invested in Risky Portfolio = 1.36 * Total Investment
Amount Invested in Risky Portfolio = 1.36 * $200,000
Amount Invested in Risky Portfolio = $272,000

So, you need to borrow $72,000 and invest $272,000 in risky portfolio.