开发者:上海品职教育科技有限公司 隐私政策详情

应用版本:4.2.11(IOS)｜3.2.5(安卓)APP下载

返回

WINWIN8 · 2024年08月07日

老师可以麻烦翻译一下题目吗？

  1. CFA III
  2. Capital Market Expectations

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%

主要是开头这段：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). 

添加评论
2 个答案

笛子_品职助教 · 2024年08月08日

嗨，从没放弃的小努力你好：


好的，明白了。还有请问Var (ε)如果=0的话，题目一般会标注出来的吧？

是的。同学理解正确。

----------------------------------------------
加油吧，让我们一起遇见更好的自己！

笛子_品职助教 · 2024年08月07日

嗨，爱思考的PZer你好：


Hello，亲爱的同学~

翻译为：

SCI风险溢价等于SCI回报减去无风险利率，记为SCIRP，用作双因素回归中的因变量。

其中自变量是消费信贷行业（CCIRP）和电信行业（TELIRP）的指数回报减去无危机利率。


同学这里需理解数学里因变量和自变量的含义。

例如对于方程：Y = 2*X+1来说。

X是自变量，X自己变。

Y是因变量，Y的变化量 = 2*X+1，Y变动是因为X变动，因此Y是因变量。


结合题目信息：这是用文字的形式，描述了一个回归方程。

SCIRP return = 1.02* CCIRP return + 1.045*TELIRP return + 0.011


根据return的回归方程，可以写出varinace的回归方程，即：

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

解上述方程：Var (ε) = 0.0770.

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

  • 2

    回答

  • 0

    关注

  • 137

    浏览
相关问题

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

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% Var的公式倒是会，但是求出Var(ε)是为了什么？求Cov(F1,F2) 又是为什么？最后的0.3181是怎么来的呢

2024-07-23 21:25 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% 计算如下0.0784x1.02^2+1.045^2x0.1.24+1.02x1.045x(0.0784x0.1024)^(0.5)x0.25+0.077=0.294和答案的0.3181对不上，但是计算步骤没有问题呀？

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