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SHAO · 2025年02月12日

老师，帮看下下方笔记中我记的计算方式对吗，红色标记的这4个位置是不是都需要加一个ρ呀

  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%



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笛子_品职助教 · 2025年02月12日

嗨，从没放弃的小努力你好：


Hello，亲爱的同学~

同学的笔记这里。需要加上ρ。


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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.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% 现在只看得懂第一步 后面的计算步骤完全是晕的

2025-01-12 15:02 1 · 回答

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