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Spencer · 2023年04月17日

β=ρ x σi / σGM

  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


老师请问，为何根据下面这两个公式 β=ρ x σi / σGM是无法计算出正确答案？


其中σGM从SR=(Rp - Rf) / σGM可以推导，SR=0.36，Rp=7.2%, Rf=3.1%, σGM=(7.2%-3.1%)/0.36=0.1139


ρ=0.39, σi=0.14, σGM=0.1139, 得出β=ρ x σi / σGM = (0.39 x 0.14) / 0.1139 = 0.4794

添加评论
awen · 2023年08月20日

这题反推covariance 也不对，cov=0.39 x 0.14x0.1139=0.0062,题目给的cov= 0.0075，说明这个题目给的参数有问题。也就是相关系数=0.39没法用

5 个答案

源_品职助教 · 2023年08月21日

嗨，爱思考的PZer你好：



同学自己算的步骤里，有一个0.39的数据，表格一并未提供，

0.39是表格一后面一段给出的数据。本题说的是根据表一数据求解。

这个数据应该是针对下一小题的一个新的假设数据，本题就没法使用了@awen


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加油吧，让我们一起遇见更好的自己！

源_品职助教 · 2023年05月30日

嗨，努力学习的PZer你好：


如果同学有好的观点，欢迎补充

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

源_品职助教 · 2023年04月19日

嗨，爱思考的PZer你好：


ρ代表的是相关关系，是全球市场和投资资产的相关关系。

本题并没给出ρ的数据哦。如果要求，可以利用ρ和β两者关系求得（就是同学截图最后一个等式两边的关系）

不过就本题而言，是没有必要求ρ的。


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努力的时光都是限量版，加油！

Carina9999 · 2023年05月30日

感觉解释了3条都没有回答到点子上

源_品职助教 · 2023年04月18日

嗨，爱思考的PZer你好：


同学提问里的公式本身是可以用来计算β的。

本题之所以不用，是因为本题的题干没有对应的ρ的数据，也就是表一里没有这个数据。

如果表一中提供了类似的数据，就可以用这个公式来计算。


----------------------------------------------
虽然现在很辛苦，但努力过的感觉真的很好，加油！

源_品职助教 · 2023年04月17日

嗨，爱思考的PZer你好：


是这样的。本题是依据表格1的数据求解，

同学自己算的步骤里，有一个0.39的数据，表格一并未提供，

0.39是表格一后面一段给出的数据。

这个数据应该是针对下一小题的一个新的假设数据，本题就没法使用了。

----------------------------------------------
努力的时光都是限量版，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

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 这个公式是怎么推导出来的呢？谢谢老师

2024-04-20 16:16 1 · 回答

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 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。

2024-01-24 17:04 1 · 回答

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 如题，求相关知识点的视频讲解

2024-01-13 08:01 1 · 回答

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 如题

2023-12-19 14:45 1 · 回答