Answer-first summary for fast verification
Answer: a portfolio with a negative investment in the risk-free asset.
The expected return of the portfolio, \(E(R_p)\), is calculated as: \[E(R_p) = W \times R_f + (1 - W) \times E(R_m)\] where: - \(W\) is the proportion invested in the risk-free asset (\(R_f = 3%\)), - \(E(R_m)\) is the expected return on the market portfolio (\(15%\)). Given \(E(R_p) = 18%\), solving for \(W\): \[0.18 = W \times 0.03 + (1 - W) \times 0.15\] Simplifying: \[0.18 - 0.15 = W \times (0.03 - 0.15)\] \[0.03 = W \times (-0.12)\] \[W = \frac{0.03}{-0.12} = -0.25\] A negative \(W\) indicates borrowing (a leveraged position) rather than lending. Thus, the portfolio is leveraged, not a lending portfolio (Option A) or the market portfolio (Option C).
Author: LeetQuiz Editorial Team
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An investor constructs a portfolio by combining the risk-free asset and the market portfolio, with the ability to lend and borrow at the risk-free rate. Given a risk-free rate of 3% and an expected market return of 15%, if the investor's portfolio has an expected return of 18%, the portfolio is best described as:
A
a portfolio with a positive investment in the risk-free asset.
B
a portfolio with a negative investment in the risk-free asset.
C
the market portfolio.
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