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坏呼呼嘿嘿 · 2023年07月16日

麻烦给讲一下这个知识点

  1. 其他

NO.PZ2022122601000064

问题如下：

The SCI risk premium, equal to the SCI return minus the risk-free rate, denoted as SCIRP, is used as the dependent variable in a two-factor regression in which the independent variables are index returns minus the risk-free rate for the consumer credit industry (CCIRP) and the telecommunications industry (TELIRP). The regression results are in Exhibit 2.

Although volatility information is available from the SCI data and correspondingly for the SCIRP, Li’s team wants to determine the statistical relationship between the SCIRP and both the CCIRP and the TELIRP because forecasting the CCIRP and TELIRP is much less difficult than forecasting the SCIRP. After some discussion, the team believes that the volatility measure for the SCIRP data based on the volatility of CCIRP and TELIRP through the regression should be adjusted to incorporate a correlation coefficient of 0.25 between the CCIRP and TELIRP. Although the two index risk premiums were uncorrelated in the past and within the regression, Li’s team believes the two technologies will become more correlated in the future.

Based on the correlation that Li's team believes to exist between the CCIRP and TELIRP, the new volatility for the SCIRP is closest to:

选项：

A.

31.8%

B.56.4%

C.49.1%

解释：

Correct Answer: B

Begin with: Var (M) = Var (F1)× (b1)2 + Var (F2) × (b2)2 + 2 × b1 × b2 × Cov (F1, F2) +Var (ε).

Find the variance of the error term using values from Exhibit 2:

0.2704 = 0.0784 × (1.020)2+ 0.1024 × (1.045)2 + 2 × 1.020 × 1.045 × 0 +Var (ε),Var (ε) = 0.0770.

The adjustment is stated as being a correlation of 0.25.

Change the correlation into a covariance:

Cov(F1,F2) = Corr(F1,F2) × Std Dev (F1) × Std Dev (F2)= 0.25 × (0.0784)^0.5 × (0.1024)^0.5 = 0.0224

The volatility of SCI after adjusting for the correlation is0.3181^0.5=56.4%

中文解析：

Var (M) = Var (F1)× (b1)2 +Var (F2) × (b2)2 + 2 × b1 × b2 × Cov (F1, F2) +Var (ε)。

使用表2中的值找到误差项的方差:

0.2704 = 0.0784××0.1024(1.020)2 +(1.045)2 + 2×1.020×1.045×0 + Var(ε),Var(ε)= 0.0770。

调整的相关系数为0.25。

将相关性转化为协方差:

Cov(F1,F2) = Corr(F1,F2) × Std Dev (F1) × Std Dev (F2)= 0.25 × (0.0784)^0.5 × (0.1024)^0.5 = 0.0224

经相关系数调整后的上证综指波动率为0.3181^0.5=56.4%

麻烦给讲一下这个知识点

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1 个答案

笛子_品职助教 · 2023年07月18日

嗨，爱思考的PZer你好：


麻烦给讲一下这个知识点


Hello，亲爱的同学！

老师一步一步拆解这道题，同学跟着学，一定可以理解的。


我们先看这道题的原始解析：


首先同学需要了解一个知识点：根据收益的回归式，得出方差的计算公式：


其次就是理解这道题的题意。


这道题有两个情景一。

情景一：相关系数为0，情景一的组合方差已知，要求根据方差公式计算出残差的方差。

情景二：相关系数为0.25，残差的方差就是用情景一计算出来的数字，要求计算情景二的组合方差。


情景一对残差方差的计算就是解析中：


情景二，把0.25相关系数和残差方差=0.0770代入：

1）我们首先计算出情景二的协方差：


2）我们代入数字：

计算出0.3181，这是方差，开根号得出标准差56.4%


如果还有其他问题，欢迎同学随时提问，祝学习顺利！



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

晶晶 · 2023年08月22日

老师为什么情景一的残差项方差我算出来是负的？是我算错了吗？

晶晶 · 2023年08月22日

是我算错了，不好意思

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NO.PZ2022122601000064问题如下 The Srisk premium, equto the Sreturn minus the risk-freerate, noteSCIRP, is usethe pennt variable in a two-factorregression in whithe inpennt variables are inx returns minus therisk-free rate for the consumer cret instry (CCIRP) anthetelecommunications instry (TELIRP). The regression results are in Exhibit 2. Althoughvolatility information is available from the Sta ancorresponngly forthe SCIRP, Li’s tewants to termine the statisticrelationship betweenthe SCIRP anboth the CCIRP anthe TELIRP because forecasting the CCIRP anELIRP is muless fficult thforecasting the SCIRP. After somescussion, the tebelieves ththe volatility measure for the SCIRP tabaseon the volatility of CCIRP anTELIRP through the regression shoulbeausteto incorporate a correlation coefficient of 0.25 between the CCIRP anELIRP. Although the two inx risk premiums were uncorrelatein the past anithin the regression, Li’s tebelieves the two technologies will become morecorrelatein the future.Baseon thecorrelation thLi's tebelieves to exist between the CCIRP anTELIRP, thenew volatility for the SCIRP is closest to: A.31.8%B.56.4%C.49.1% CorreAnswer: B Begin with: Var(M) = V(F1)× (b1)2 + V(F2) ×(b2)2 + 2 × × × Cov (F1,F2) +V(ε).Finthe varianceof the error term using values from Exhibit 2:0.2704 = 0.0784 ×(1.020)2+ 0.1024 × (1.045)2 + 2 × 1.020 × 1.045 × 0 +Var(ε),V(ε) = 0.0770.The austment isstatebeing a correlation of 0.25.Change thecorrelation into a covariance: Cov(F1,F2)= Corr(F1,F2) × Stv (F1) × Stv (F2)=0.25 × (0.0784)^0.5 × (0.1024)^0.5 = 0.0224The volatility ofSafter austing for the correlation is0.3181^0.5=56.4% 中文解析V(M) = V(F1)× (b1)2 +V(F2) × (b2)2 + 2 × × × Cov (F1, F2) +V(ε)。使用表2中的值找到误差项的方差:0.2704 = 0.0784××0.1024(1.020)2 +(1.045)2 + 2×1.020×1.045×0 + Var(ε),Var(ε)= 0.0770。调整的相关系数为0.25。将相关性转化为协方差:Cov(F1,F2) = Corr(F1,F2) × Stv (F1) × Stv (F2)= 0.25 × (0.0784)^0.5 × (0.1024)^0.5 = 0.0224经相关系数调整后的上证综指波动率为0.3181^0.5=56.4% Volatility分不清是指方差，还是标准差

2024-08-08 22:00 1 · 回答

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2024-08-07 01:50 2 · 回答

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2024-07-23 21:25 1 · 回答

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2024-02-13 11:46 1 · 回答

NO.PZ2022122601000064 问题如下 The Srisk premium, equto the Sreturn minus the risk-freerate, noteSCIRP, is usethe pennt variable in a two-factorregression in whithe inpennt variables are inx returns minus therisk-free rate for the consumer cret instry (CCIRP) anthetelecommunications instry (TELIRP). The regression results are in Exhibit 2. Althoughvolatility information is available from the Sta ancorresponngly forthe SCIRP, Li’s tewants to termine the statisticrelationship betweenthe SCIRP anboth the CCIRP anthe TELIRP because forecasting the CCIRP anELIRP is muless fficult thforecasting the SCIRP. After somescussion, the tebelieves ththe volatility measure for the SCIRP tabaseon the volatility of CCIRP anTELIRP through the regression shoulbeausteto incorporate a correlation coefficient of 0.25 between the CCIRP anELIRP. Although the two inx risk premiums were uncorrelatein the past anithin the regression, Li’s tebelieves the two technologies will become morecorrelatein the future.Baseon thecorrelation thLi's tebelieves to exist between the CCIRP anTELIRP, thenew volatility for the SCIRP is closest to: A.31.8% B.56.4% C.49.1% CorreAnswer: B Begin with: Var(M) = V(F1)× (b1)2 + V(F2) ×(b2)2 + 2 × × × Cov (F1,F2) +V(ε).Finthe varianceof the error term using values from Exhibit 2:0.2704 = 0.0784 ×(1.020)2+ 0.1024 × (1.045)2 + 2 × 1.020 × 1.045 × 0 +Var(ε),V(ε) = 0.0770.The austment isstatebeing a correlation of 0.25.Change thecorrelation into a covariance: Cov(F1,F2)= Corr(F1,F2) × Stv (F1) × Stv (F2)=0.25 × (0.0784)^0.5 × (0.1024)^0.5 = 0.0224The volatility ofSafter austing for the correlation is0.3181^0.5=56.4% 中文解析V(M) = V(F1)× (b1)2 +V(F2) × (b2)2 + 2 × × × Cov (F1, F2) +V(ε)。使用表2中的值找到误差项的方差:0.2704 = 0.0784××0.1024(1.020)2 +(1.045)2 + 2×1.020×1.045×0 + Var(ε),Var(ε)= 0.0770。调整的相关系数为0.25。将相关性转化为协方差:Cov(F1,F2) = Corr(F1,F2) × Stv (F1) × Stv (F2)= 0.25 × (0.0784)^0.5 × (0.1024)^0.5 = 0.0224经相关系数调整后的上证综指波动率为0.3181^0.5=56.4% 不需要计算残差项的方差，直接将题中给出的数据相乘计算出在ρ=0.25情况下，需要加到原有SCIRP方差上的新方差，具体计算如下2x1.02x1.045x0.25x(0.0784x0.1024)^0.5=0.047752新方差=0.2704+0.047752=0.3181标准差=0.3181^0.5=0.564请问老师这种思考路径是否可以？另外，题目中给出了三个inx的mean值，并且老师讲解过程中还提到了R=α+∑biFi+残差，能否用mean值或“R=α+∑biFi+残差”去计算该题，如果可以，应该如何计算？

2024-01-20 21:18 2 · 回答