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fresh · 2023年05月10日

相关系数计算

  1. CFA III
  2. Capital Market Expectations

* 问题详情，请 查看题干

NO.PZ202206070100000203

问题如下：

Using the data provided in Exhibit 1 and Grey’s recommended approach and assumed correlation, the expected return for US real estate is closest to:

选项：

A.6.9%.

B.4.3%.

C.6.3%.

解释：

C is correct. Grey recommends the Singer–Terhaar approach and a correlation of 0.39 between real estate and the market. Use these steps to solve for the expected return:

Fully integrated risk premium: R P i G = β i,GM R P GM = ρ i,GM σ i R P GM σ GM

  • Step 1 Fully integrated risk premium (14.0% × 0.39 × 0.36) = 1.97%
  • Fully segmented risk premium (14.0% × 0.36) = 5.04%
  • Step 2 Fully integrated and segmented risk premium, considering the degree of integration (1.97% × 0.6) + (5.04% × 0.4) = 3.20%
  • Step 3 Expected return estimate:
  • Fully integrated and segmented risk premium + Risk-free rate 3.20% + 3.1% = 6.3%

A is incorrect. The mistake is in reversing the weights for integrated and segmented.

B is incorrect. In step one, it uses the covariance 0.0075 instead of the Sharpe ratio

本题考查的ST模型：

C是正确的。格雷建议采用Singer-Terhaar方法，房地产和市场之间的相关性为0.39。使用以下步骤来求解预期收益:

完全整合风险溢价: R P i ,G = β i,GM R P GM = ρ i,GM σ i (R P GM/ σ GM)

完全分割风险溢价: R P i ,S =1×R P i, S =1× σ i( R P i S /σ i)


B是不正确的。在第一步中，它错误地使用0.0075的协方差代替夏普比率。A是不正确的。它错误在于颠倒了权重。

根据前一题的假设可以由协方差和标准差算出相关系数0.0075/（14%*11.39%）=0.47，和题目题目给的0.39不一样，请问这是为什么？有什么需要注意的点吗？谢谢

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1 个答案

源_品职助教 · 2023年05月10日

嗨，爱思考的PZer你好：



是这样的。同学的思路和公式本身是没有为的。

但是题目题干有这么句话，根据表一提供的信息计算。表一中是没有提供0.39数据的。

0.39是下一题中假设到的数据，那是一个新的假设，并不对本小题提供约束条件。

所以本题就无法用0.39计算。这种题目读题时候再仔细点就好了，不客气哦。

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