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You have R829000 available to invest
You have R829000 available to invest. The risk-free rate, as well as your borrowing rate, is 7%. The return on the risky portfolio is 15%. If you wish to earn a 16.04% return, you should _________. A) Invest R134173.65 in the risk-free asset B) Borrow R107770 C) None of the answers are correct D) Invest R134173.65 in the risk-free asset E) Borrow R107770
Expert Solution
First we calculate Weights of Risk-free Security and Debt as follows:
Expected Return on Portfolio = Weight of Risk-free Security * Risk-free Rate + Weight of Risky Security * Return on Risky Portfolio
Let us assume,
Weight of Risk-free Security = x
Weight of Risky Security = 1-x
Expected Return on Portfolio = Weight of Risk-free Security * Risk-free Rate + Weight of Risky Security * Return on Risky Portfolio
16.04% = x * 7% + (1-x)*15%
16.04% = 7%x + 15% - 15%x
16.04% - 15% = -8% x
1.04%/-8% = x
x = -13%
So, Weight of Risk-free Security is -13%.
Amount to be Invested = R829000*-13% = -R107,770
So, the correct option is E "Borrow R107770".
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