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hyi725 · 2023年08月07日

probability ratio在基础班的哪里？

  1. CFA III
  2. Asset Allocation

* 问题详情，请 查看题干

NO.PZ202206210100000201

问题如下：

Which of the portfolios provided in Exhibit 1 has the highest probability of enabling Shipman to meet his goal for the vacation home?

选项：

A.Portfolio 1 B.Portfolio 2 C.Portfolio 3

解释：

Solution

B is correct. Portfolio 2 has the highest probability of enabling Shipman to meet his goal for the vacation home. All three of the portfolios’ expected returns over the next year exceed the 6.0% (see calculations below) required return threshold to avoid reducing the portfolio. However, on a risk-adjusted basis, Portfolio 2 (probability ratio of 0.231) has a higher probability of meeting and surpassing the threshold than either Portfolio 1 (probability ratio of 0.175) or Portfolio 3 (probability ratio of 0.225).


RP = The return for the portfolio

RL = The required return threshold

σP = The standard deviation of the portfolio

Portfolio 1: (10.50% – 6.0%) ÷ 20.0% = 4.50% ÷ 20.0% = 0.225.

Portfolio 2: (9.00% – 6.0%) ÷ 13.0% = 3.00% ÷ 13.0% = 0.231. (Highest)

Portfolio 3: (7.75% – 6.0%) ÷ 10.0% = 1.75% ÷ 10.0% = 0.175.

A is incorrect. Portfolio 1 was chosen because it has the highest projected return.

C is incorrect. Portfolio 3 was chosen because it has the lowest projected standard deviation.

如题

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1 个答案

lynn_品职助教 · 2023年08月08日

嗨，从没放弃的小努力你好：


本题考查资产配置的选择。 题目来源于官网的practice exam，这类题考的是教材中没有专门去讲的知识点，我们如果在考场中遇到了，要自己读题，慢慢分析来做。现在在练习中遇到了，就遇到一题会做一题即可。


Young 的目标：在没有承担更多风险的前提下，每年税后收益至少达到 6%（capital gains tax rate 25%）。


资产规模：$5.5 million； 


限制：a $500,000 minimum investment requirement for alternative assets。 


根据投资限制，如果配置 alternative assets（比如 Private Equity），至少投资$500,000，所以占到总资产的比重至少为$500,000/$5.5 million=9.09%。


三个组合中 Portfolio 1 对 Private Equity 的投资比重为 10%，满足要求；


Portfolio 2 对 Private Equity 的投资比重为 5%，不满足要求；


Portfolio 3 对 Private Equity 的投资比重为 0，不受该项限制影响。 


根据表 1 中各资产在 Portfolio 所占的权重，以及表 2 中各资产税前收益，分别计算各 Portfolio 的税收收益。


需要注意，Municipal Bonds 获得的 interest income 无需纳税，而 Small-Cap Equities、Large-Cap Equities 以及 Private Equity 获得的 capital gain 需要纳税（税率 25%）。 


因此: 


Portfolio 1: E(Rpt)=9.15%, σpt=28.2% 


Portfolio 2: E(Rpt)=6.64%, σpt=16.3% 


Portfolio 3: E(Rpt)=6.68%, σpt=15.5% 


三个组合都满足税后收益至少6%的要求。Portfolio 1虽然E(Rpt)最大，但σpt也远超其他组合， 


因此 Portfolio 1 不满足要求。Portfolio 2 与 Portfolio 3 比较接近，但 Portfolio 3 比 Portfolio 2 σpt小，E(Rpt)更大，所以 Portfolio 3 承担每单位风险获得的收益更大，Portfolio 2 不满足要求。 


应当选择 Portfolio 3。

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