Answer-first summary for fast verification
Answer: Portfolio 3, because it maximizes the safety-first ratio.
The safety-first optimal portfolio is determined by maximizing the safety-first ratio (SFRatio), which is calculated as: \[ \text{SFRatio} = \frac{E(R_p) - R_L}{\sigma_p} \] where: - \(E(R_p)\) is the expected portfolio return, - \(R_L\) is the investor's minimum acceptable return (5% in this case, derived from the $5,000 withdrawal requirement), - \(\sigma_p\) is the standard deviation of portfolio returns. Calculations: - **Portfolio 1**: \(\frac{23\% - 5\%}{15\%} = 1.20\) - **Portfolio 2**: \(\frac{12\% - 5\%}{6\%} = 1.17\) - **Portfolio 3**: \(\frac{15\% - 5\%}{8\%} = 1.25\) Portfolio 3 has the highest SFRatio (1.25), making it the safety-first optimal choice. This minimizes the probability of the portfolio's return falling below the minimum acceptable return (shortfall risk).
Author: LeetQuiz Editorial Team
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A portfolio manager is considering investing $100,000 and has the following information about three portfolios with normally distributed returns:
Expected Annual Return | Standard Deviation of Returns Portfolio 1: 23% | 15% Portfolio 2: 12% | 6% Portfolio 3: 15% | 8%
If the manager aims to withdraw $5,000 in one year without depleting the initial capital, which portfolio is the safety-first optimal choice?
A
Portfolio 1, due to its high expected return and standard deviation.
B
Portfolio 2, as it has the lowest standard deviation and a high return-to-standard-deviation ratio.
C
Portfolio 3, because it maximizes the safety-first ratio.
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