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Mia Li · 2025年02月11日

老师请问

  1. CFA III
  2. Asset Allocation

* 问题详情，请 查看题干

NO.PZ201805280100000302

问题如下：

A broker proposes to Young three portfolios, shown in Exhibit 1. The broker also provides Young with asset class estimated returns and portfolio standard deviations in Exhibit 2 and Exhibit 3, respectively. The broker notes that there is a $500,000 minimum investment requirement for alternative assets. Finally, because the funds in the money market account are readily investible, the broker suggests using that account only for this initial investment round.


Young wants to earn at least 6.0% after tax per year, without taking on additional incremental risk. Young’s capital gains and overall tax rate is 25%.

Determine which proposed portfolio most closely meets Young’s desired objectives. (Circle one.) Justify your response.


选项：

解释：



题目中给出了投资者要求最低收益率6%，我的第一反应是用safety-first ratio解题的。看了之前的提问了解到“它说希望满足最低6%的收益率，然后without taking on additional incremental risk，即既要考虑收益，也不希望产生增量风险。这里其实是将收益和风险单独考虑，在满足收益要求的情况下，风险要足够低，所以是两条独立标准。”是不是以后题目中出现without taking on additional incremental risk的表达，都不能使用Sharpe ratio或者SFR来作为选择标准？具体怎么辨析呢

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1 个答案

Lucky_品职助教 · 2025年02月11日

嗨，爱思考的PZer你好：


同学你好：


你的结论太绝对了，需要具体情况具体分析。

如果题目的核心要求是在满足特定收益目标（如本题中至少 6% 的税后年收益）的基础上，让风险尽可能低，并且将收益和风险作为相互独立的考量因素，此时SR和SFR都不太适用。这是因为SR衡量的是单位风险下的超额收益，它并没有直接针对满足最低收益要求这一目标；SFR虽然考虑了最低可接受收益，但它是通过比较投资组合收益率超过最低可接受收益率的概率或距离来评估，不是单纯在满足收益前提下找最低风险 。在本题中，Young 希望先满足 6% 的税后收益，再在此基础上使风险最低，所以这两个比率都无法直接解决问题，需要分别计算各投资组合的收益和风险来判断。

但是如果题目要求在一定风险承受范围内，追求收益的最大化，或者在收益和风险之间进行综合权衡时，夏普比率就有其用武之地。比如，当投资者给定了一个可接受的风险水平（标准差）范围，希望在这个范围内找到收益最高的投资组合，夏普比率可以帮助投资者衡量在承担单位风险时能够获得的额外收益，从而选择最优组合。SFR适用于当投资者极度厌恶收益低于某一特定水平的情况，此时可以通过计算该比率来评估投资组合低于最低可接受收益的风险程度，进而做出决策。


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