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rikkisong72 · 2024年01月24日

这道题为什么不用correlation计算

  1. CFA III
  2. Capital Market Expectations

* 问题详情，请 查看题干

NO.PZ202206070100000202

问题如下：

Using the data provided in Exhibit 1 and assuming perfect markets, the calculated beta for US real estate is closest to:

选项：

A.0.58. B.1.08. C.0.38.

解释：

Solution

A is correct.

βi = Cov(Ri,RM)/Var(RM)

Note that covariance is given as 0.0075.

Find Var(RM) by using the Sharpe ratio = RPM/σM and solve for σM

Expected return – Risk-free rate = RPM

7.2% – 3.1% = 4.1% (or 0.041)

σM = 0.041/0.36 = 0.1139

Var(RM) = (0.1139)2 = 0.0130

βi = 0.0075/0.0130 = 0.58

C is incorrect. It incorrectly uses the value for variance of 0.142 based upon the standard deviation of the global real estate asset class in the beta formula.

Var(RM) = (0.14)2 = 0.0196 βi

βi = 0.0075/0.0196 = 0.38

B is incorrect. It incorrectly uses the ratio of the correlations.

βi = 0.39 (given by Grey)/0.36= 1.08

βi = Cov(Ri,RM)/Var(RM) Note that covariance is given as 0.0075. Find Var(RM) by using the Sharpe ratio = RPM/σM and solve for σM Expected return – Risk-free rate = RPM 7.2% – 3.1% = 4.1% (or 0.041) σM = 0.041/0.36 = 0.1139 Var(RM) = (0.1139)^2 = 0.0130 βi = 0.0075/0.0130 = 0.58 C is incorrect. It incorrectly uses the value for variance of 0.142 based upon the standard deviation of the global real estate asset class in the beta formula. Var(RM) = (0.14)2 = 0.0196 βi βi = 0.0075/0.0196 = 0.38 B is incorrect. It incorrectly uses the ratio of the correlations. βi = 0.39 (given by Grey)/0.36= 1.08


βi = Cov(Ri,RM)/Var(RM)

注意协方差为0.0075。
用夏普比= RPM/σM求Var(RM)，求出σM
预期收益-无风险率= RPM
7.2% - 3.1% = 4.1%(或0.041)
σm = 0.041/0.36 = 0.1139
Var(RM) = (0.1139)^2 = 0.0130
βi = 0.0075/0.0130 = 0.58
C是不正确的。它错误地使用了基于贝塔公式中全球房地产资产类别的标准差的方差0.142的值。
Var(RM) = (0.14)^2 = 0.0196 βi
βi = 0.0075/0.0196 = 0.38
B是不正确的。它错误地使用了相关性的比率。
βi = 0.39(由Grey给出)/0.36= 1.08

βi = Cov(Ri,RM)/Var(RM)注意，协方差为0.0075。通过Sharpe ratio = RPM/σM求Var(RM)，求出σM。期望收益-无风险率= RPM 7.2% - 3.1% = 4.1%(或0.041)σM = 0.041/0.36 = 0.1139 Var(RM) = (0.1139)^2 = 0.0130 βi = 0.0075/0.0130 = 0.58 C是不正确的。它错误地使用0.142的值。Var(RM) = (0.14)^2 = 0.0196 βi βi = 0.0075/0.0196 = 0.38 B不正确。它错误地使用了相关性的比率。βi = 0.39(由Grey给出)/0.36= 1.08


上面给了covariance，确实可以直接除以方差得到beta。

但是下面也给了correlation，并且乘以行业和市场的标准差后不等于上面给的covariance。


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1 个答案

源_品职助教 · 2024年01月24日

嗨，努力学习的PZer你好：


题目是这样说的，

Cortez’s colleague Jason Grey notes that US real estate is a partially segmented market.

For this reason, Grey recommends using the Singer–Terhaar approach to the international extension of the CAPM and assumes a correlation of 0.39 between US real estate and the GIM.


也就是基于US real estate is a partially segmented market这个观察，然后Grey又重新做了假设，假设ρ=0.39.所以这里的相关性和上文已经没有什么关联了，它只是一个纯粹的假设而已。用上面的数据也得不到这个结果了。

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就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

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NO.PZ202206070100000202 问题如下 Using the ta proviin Exhibit 1 anassuming perfemarkets, the calculatebeta for US reestate is closest to: A.0.58. B.1.08. C.0.38. SolutionA is correct.βi = Cov(Ri,RM)/Var(RM)Note thcovarianis given 0.0075.FinVar(RM) using the Sharpe ratio = RPM/σM ansolve for σMExpectereturn – Risk-free rate = RPM7.2% – 3.1% = 4.1% (or 0.041)σM = 0.041/0.36 = 0.1139Var(RM) = (0.1139)2 = 0.0130βi = 0.0075/0.0130 = 0.58C is incorrect. It incorrectly uses the value for varianof 0.142 baseupon the stanrviation of the globreestate asset class in the beta formula.Var(RM) = (0.14)2 = 0.0196 βiβi = 0.0075/0.0196 = 0.38B is incorrect. It incorrectly uses the ratio of the correlations.βi = 0.39 (given Grey)/0.36= 1.08βi = Cov(Ri,RM)/Var(RM) Note thcovarianis given 0.0075. FinVar(RM) using the Sharpe ratio = RPM/σM ansolve for σM Expectereturn – Risk-free rate = RPM 7.2% – 3.1% = 4.1% (or 0.041) σM = 0.041/0.36 = 0.1139 Var(RM) = (0.1139)^2 = 0.0130 βi = 0.0075/0.0130 = 0.58 C is incorrect. It incorrectly uses the value for varianof 0.142 baseupon the stanrviation of the globreestate asset class in the beta formulVar(RM) = (0.14)2 = 0.0196 βi βi = 0.0075/0.0196 = 0.38 B is incorrect. It incorrectly uses the ratio of the correlations. βi = 0.39 (given Grey)/0.36= 1.08βi = Cov(Ri,RM)/Var(RM)注意协方差为0.0075。用夏普比= RPM/σM求Var(RM)，求出σM预期收益-无风险率= RPM7.2% - 3.1% = 4.1%(或0.041)σm = 0.041/0.36 = 0.1139Var(RM) = (0.1139)^2 = 0.0130βi = 0.0075/0.0130 = 0.58C是不正确的。它错误地使用了基于贝塔公式中全球房地产资产类别的标准差的方差0.142的值。Var(RM) = (0.14)^2 = 0.0196 βiβi = 0.0075/0.0196 = 0.38B是不正确的。它错误地使用了相关性的比率。βi = 0.39(由Grey给出)/0.36= 1.08βi = Cov(Ri,RM)/Var(RM)注意，协方差为0.0075。通过Sharpe ratio = RPM/σM求Var(RM)，求出σM。期望收益-无风险率= RPM 7.2% - 3.1% = 4.1%(或0.041)σM = 0.041/0.36 = 0.1139 Var(RM) = (0.1139)^2 = 0.0130 βi = 0.0075/0.0130 = 0.58 C是不正确的。它错误地使用0.142的值。Var(RM) = (0.14)^2 = 0.0196 βi βi = 0.0075/0.0196 = 0.38 B不正确。它错误地使用了相关性的比率。βi = 0.39(由Grey给出)/0.36= 1.08 这个题目考的是ST mol 吗？看了怎么感觉不是

2024-07-12 10:31 1 · 回答

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2024-01-13 08:01 1 · 回答

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