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You have R829000 available to invest

Finance

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 

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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".