关于残差项的计算

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

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% 主要是开头这段The Srisk premium, equto the Sreturn minus the risk-free rate, noteSCIRP, is usethe pennt variable in a two-factor regression in whithe inpennt variables are inx returns minus the risk-free rate for the consumer cret instry (CCIRP) anthe telecommunications instry (TELIRP).

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

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？

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？