Question

Suppose that the risk-free rate is 6 percent and the expected return on the market portfolio...

Suppose that the risk-free rate is 6 percent and the expected return on the market portfolio is 15
percent. An investor with \$1.5 million to invest wants to achieve a 25 percent return on a
portfolio combining the risk-free asset and the market portfolio. Calculate how much this
investor would need to borrow at the risk-free rate in order to establish this target expected
return. Provide your final answers up to two decimal points.

Homework Answers

Answer #1
 Let weight of the risk asset be x Then weight of risk free asset = 1-x Now, 25 = 15*x+6*(1-x) 25 = 15*x+6-6*x 19 = 9*x x = 19/9 = 2.11 Weight of the risk free asset = 1-19/9 = -1.11 Borrowings at risk free rate = 1.5*10/9 = \$1.67 million VERIFICATION: Return from the risky asset = 3.17*15% = \$0.4755 Less: Borrowing cost = 1.67*6% = \$0.1002 Net dollar return \$0.3753 % return on investment = 0.3755/1.5 = 25.02% ANSWER: Amount to be borrowed at risk free rate = \$1.67 million
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