ANNUAL STOCK PRICE AND RETURN DATA FOR SIX STOCKSGeneral Electric (GE), Microsoft (MSFT), Johnson & Johnson (JNJ), Kellogg (K), Boeing (BA), IBMPrice dataDate GE MSFT JNJ K BA IBM4-一月-93 2.36 2.68 6.78 20.37 2.34 11.793-一月-94 4.15 2.64 7.20 18.47 4.21 14.623-一月-95 4.98 3.68 10.91 19.90 4.20 15.532-一月-96 8.80 5.73 19.43 29.03 8.09 20.412-一月-97 13.51 12.64 24.44 27.59 13.93 30.782-一月-98 21.64 18.49 29.15 38.01 20.19 31.604-一月-99 30.57 43.37 38.04 34.14 23.47 30.943-一月-00 40.51 48.51 39.36 20.93 36.27 39.242-一月-01 42.42 30.26 43.80 23.52 48.13 48.782-一月-02 34.82 31.58 55.19 28.70 41.39 51.052-一月-03 22.25 23.52 52.15 32.00 32.81 59.632-一月-04 31.86 28.16 51.49 37.36 48.86 81.95Shares outstanding 10.56 10.86 2.97 0.41 0.84 0.79Market value 336.44 305.82 152.93 15.44 41.01 65.13Percentage of portfolio 36.70% 33.36% 16.68% 1.68% 4.47% 7.10%Return dataDate GE MSFT JNJ K BA IBM3-一月-94 56.44% -1.50% 6.01% -9.79% 58.73% 21.51%3-一月-95 18.23% 33.21% 41.56% 7.46% -0.24% 6.04%2-一月-96 56.93% 44.28% 57.71% 37.76% 65.55% 27.33%2-一月-97 42.87% 79.12% 22.94% -5.09% 54.34% 41.08%2-一月-98 47.11% 38.04% 17.62% 32.04% 37.11% 2.63%4-一月-99 34.55% 85.25% 26.62% -10.74% 15.05% -2.11%3-一月-00 28.15% 11.20% 3.41% -48.93% 43.53% 23.76%2-一月-01 4.61% -47.19% 10.69% 11.67% 28.29% 21.76%2-一月-02 -19.74% 4.27% 23.11% 19.90% -15.09% 4.55%2-一月-03 -44.78% -29.47% -5.67% 10.88% -23.23% 15.54%2-一月-04 35.90% 18.01% -1.27% 15.49% 39.82% 31.80%Average 23.66% 21.38% 18.43% 5.51% 27.63% 17.63%Standard deviation 32.17% 40.71% 18.97% 23.86% 29.93% 13.56%Variance 0.1035 0.1657 0.0360 0.0570 0.0896 0.0184Excess returnsDate GE MSFT JNJ K BA IBM3-一月-94 32.78% -22.89% -12.42% -15.31% 31.11% 3.89%3-一月-95 -5.43% 11.83% 23.13% 1.94% -27.86% -11.59%2-一月-96 33.27% 22.90% 39.28% 32.25% 37.93% 9.70%2-一月-97 19.21% 57.73% 4.51% -10.60% 26.72% 23.46%2-一月-98 23.45% 16.65% -0.81% 26.53% 9.49% -15.00%4-一月-99 10.89% 63.87% 8.19% -16.25% -12.57% -19.74%3-一月-00 4.49% -10.18% -15.02% -54.44% 15.90% 6.14%A B C D E F G1234567891011121314151617181920212223242526272829303132333435363738394041424344454647482-一月-01 -19.05% -68.58% -7.74% 6.15% 0.67% 4.14%2-一月-02 -43.40% -17.11% 4.68% 14.39% -42.71% -13.08%2-一月-03 -68.45% -50.85% -24.10% 5.37% -50.86% -2.09%2-一月-04 12.24% -3.38% -19.70% 9.97% 12.20% 14.17%Uses the array formula 0.5)A B C D E F G H1234567891011121314151617181920212223242526272829303132相关系数矩阵方差-协方差矩阵GE MSFT JNJ K BA IBMGE 0.1035 0.0758 0.0222 -0.0043 0.0857 0.1414MSFT 0.0758 0.1657 0.0412 -0.0052 0.0379 0.1400JNJ 0.0222 0.0412 0.0360 0.0181 0.0101 0.0455K -0.0043 -0.0052 0.0181 0.0570 -0.0076 0.0122BA 0.0857 0.0379 0.0101 -0.0076 0.0896 0.0856IBM 0.1414 0.1400 0.0455 0.0122 0.0856 0.2993下面相关系数的基于公式0.5)A B C D E F G H1234567891011121314151617181920212223242526272829303132ESTIMATING THE VARIANCE-COVARIANCE MATRIX USINGTHE SINGLE-INDEX MODELReturn dataDate GE MSFT JNJ K BA IBM SP5003-一月-94 56.44% -1.50% 6.01% -9.79% 58.73% 21.51% -2.35%3-一月-95 18.23% 33.21% 41.56% 7.46% -0.24% 6.04% 30.16%2-一月-96 56.93% 44.28% 57.71% 37.76% 65.55% 27.33% 21.19%2-一月-97 42.87% 79.12% 22.94% -5.09% 54.34% 41.08% 22.07%2-一月-98 47.11% 38.04% 17.62% 32.04% 37.11% 2.63% 26.65%4-一月-99 34.55% 85.25% 26.62% -10.74% 15.05% -2.11% 8.59%3-一月-00 28.15% 11.20% 3.41% -48.93% 43.53% 23.76% -2.06%2-一月-01 4.61% -47.19% 10.69% 11.67% 28.29% 21.76% -18.95%2-一月-02 -19.74% 4.27% 23.11% 19.90% -15.09% 4.55% -27.82%2-一月-03 -44.78% -29.47% -5.67% 10.88% -23.23% 15.54% 27.91%2-一月-04 35.90% 18.01% -1.27% 15.49% 39.82% 31.80% 4.34%Average 23.66% 21.38% 18.43% 5.51% 27.63% 17.63% 8.16%Standard deviation 32.17% 40.71% 18.97% 23.86% 29.93% 13.56% 19.59%Variance 0.1035 0.1657 0.0360 0.0570 0.0896 0.0184 0.0384Beta 0.3411 0.9185 0.2598 0.2344 0.1046 0.0186The SIM var-cov matrix uses the array formula=IF(B24:G24=A25:A30,B18:G18,MMULT(TRANSPOSE(B20:G20),B20:G20)*H18) to compute thesample var-cov matrixGE MSFT JNJ K BA IBMGE 0.1035 0.0120 0.0034 0.0031 0.0014 0.0002MSFT 0.0120 0.1657 0.0092 0.0083 0.0037 0.0007JNJ 0.0034 0.0092 0.0360 0.0023 0.0010 0.0002K 0.0031 0.0083 0.0023 0.0570 0.0009 0.0002BA 0.0014 0.0037 0.0010 0.0009 0.0896 0.0001IBM 0.0002 0.0007 0.0002 0.0002 0.0001 0.0184Check-doing this another way: In the cells below we use the formula=IF($A36=B$35,B$18,B$20*$H36*$H$18)Row 34 and column H contain the firm betas0.3411 0.9185 0.2598 0.2344 0.1046 0.0186GE MSFT JNJ K BA IBMGE 0.1035 0.0120 0.0034 0.0031 0.0014 0.0002 0.3411MSFT 0.0120 0.1657 0.0092 0.0083 0.0037 0.0007 0.9185JNJ 0.0034 0.0092 0.0360 0.0023 0.0010 0.0002 0.2598K 0.0031 0.0083 0.0023 0.0570 0.0009 0.0002 0.2344BA 0.0014 0.0037 0.0010 0.0009 0.0896 0.0001 0.1046IBM 0.0002 0.0007 0.0002 0.0002 0.0001 0.0184 0.0186A B C D E F G H1234567891011121314151617181920212223242526272829303132333435363738394041- =AVERAGE(H4:H14)- =STDEV(H4:H14)- =VAR(H4:H14)- =SLOPE(G4:G14,$H$4:$H$14)ESTIMATING THE VARIANCE-COVARIANCE MATRIX USINGTHE SINGLE-INDEX MODELI1234567891011121314151617181920212223242526272829303132333435363738394041用单指数模型SIM估计方差-协方差矩阵收益数据日期 GE MSFT JNJ K BA IBM SP5003-一月-94 56.44% -1.50% 6.01% -9.79% 58.73% 21.51% -2.35%3-一月-95 18.23% 33.21% 41.56% 7.46% -0.24% 6.04% 30.16%2-一月-96 56.93% 44.28% 57.71% 37.76% 65.55% 27.33% 21.19%2-一月-97 42.87% 79.12% 22.94% -5.09% 54.34% 41.08% 22.07%2-一月-98 47.11% 38.04% 17.62% 32.04% 37.11% 2.63% 26.65%4-一月-99 34.55% 85.25% 26.62% -10.74% 15.05% -2.11% 8.59%3-一月-00 28.15% 11.20% 3.41% -48.93% 43.53% 23.76% -2.06%2-一月-01 4.61% -47.19% 10.69% 11.67% 28.29% 21.76% -18.95%2-一月-02 -19.74% 4.27% 23.11% 19.90% -15.09% 4.55% -27.82%2-一月-03 -44.78% -29.47% -5.67% 10.88% -23.23% 15.54% 27.91%2-一月-04 35.90% 18.01% -1.27% 15.49% 39.82% 31.80% 4.34%均值 23.66% 21.38% 18.43% 5.51% 27.63% 17.63% 8.16%标准差 32.17% 40.71% 18.97% 23.86% 29.93% 13.56% 19.59%方差 0.1035 0.1657 0.0360 0.0570 0.0896 0.0184 0.0384Beta 0.3411 0.9185 0.2598 0.2344 0.1046 0.0186SIM的协差阵使用数组函数=IF(B24:G24=A25:A30,B18:G18,MMULT(TRANSPOSE(B20:G20),B20:G20)*H18) 计算样本方差-协方差矩阵GE MSFT JNJ K BA IBMGE 0.1035 0.0120 0.0034 0.0031 0.0014 0.0002MSFT 0.0120 0.1657 0.0092 0.0083 0.0037 0.0007JNJ 0.0034 0.0092 0.0360 0.0023 0.0010 0.0002K 0.0031 0.0083 0.0023 0.0570 0.0009 0.0002BA 0.0014 0.0037 0.0010 0.0009 0.0896 0.0001IBM 0.0002 0.0007 0.0002 0.0002 0.0001 0.0184检查-使用另一种方法计算: 在下面单元格我们使用公式 =IF($A36=B$35,B$18,B$20*$H36*$H$18)行 34 和列 H 包含了固定的beta0.3411 0.9185 0.2598 0.2344 0.1046 0.0186GE MSFT JNJ K BA IBMGE 0.1035 0.0120 0.0034 0.0031 0.0014 0.0002 0.3411MSFT 0.0120 0.1657 0.0092 0.0083 0.0037 0.0007 0.9185JNJ 0.0034 0.0092 0.0360 0.0023 0.0010 0.0002 0.2598K 0.0031 0.0083 0.0023 0.0570 0.0009 0.0002 0.2344BA 0.0014 0.0037 0.0010 0.0009 0.0896 0.0001 0.1046IBM 0.0002 0.0007 0.0002 0.0002 0.0001 0.0184 0.0186A B C D E F G H1234567891011121314151617181920212223242526272829303132333435363738394041- =AVERAGE(H4:H14)- =STDEV(H4:H14)- =VAR(H4:H14)- =SLOPE(G4:G14,$H$4:$H$14)用单指数模型SIM估计方差-协方差矩阵I1234567891011121314151617181920212223242526272829303132333435363738394041The SIM var-cov matrix uses the array formula=IF(B2:G2=A3:A8,1,0) to compute the sample var-cov matrixGE MSFT JNJ K BA IBMGE 1 0 0 0 0 0MSFT 0 1 0 0 0 0JNJ 0 0 1 0 0 0K 0 0 0 1 0 0BA 0 0 0 0 1 0IBM 0 0 0 0 0 1A B C D E F G12345678SIM 协差阵使用数组函数=IF(B2:G2=A3:A8,1,0) 计算样本方差-协方差矩阵GE MSFT JNJ K BA IBMGE 1 0 0 0 0 0MSFT 0 1 0 0 0 0JNJ 0 0 1 0 0 0K 0 0 0 1 0 0BA 0 0 0 0 1 0IBM 0 0 0 0 0 1A B C D E F G12345678ESTIMATING THE VARIANCE-COVARIANCE MATRIX USINGTHE CONSTANT-CORRELATION APPROACHReturn dataDate GE MSFT JNJ K BA IBM3-一月-94 56.44% -1.50% 6.01% -9.79% 58.73% 21.51%3-一月-95 18.23% 33.21% 41.56% 7.46% -0.24% 6.04%2-一月-96 56.93% 44.28% 57.71% 37.76% 65.55% 27.33%2-一月-97 42.87% 79.12% 22.94% -5.09% 54.34% 41.08%2-一月-98 47.11% 38.04% 17.62% 32.04% 37.11% 2.63%4-一月-99 34.55% 85.25% 26.62% -10.74% 15.05% -2.11%3-一月-00 28.15% 11.20% 3.41% -48.93% 43.53% 23.76%2-一月-01 4.61% -47.19% 10.69% 11.67% 28.29% 21.76%2-一月-02 -19.74% 4.27% 23.11% 19.90% -15.09% 4.55%2-一月-03 -44.78% -29.47% -5.67% 10.88% -23.23% 15.54%2-一月-04 35.90% 18.01% -1.27% 15.49% 39.82% 31.80%Average 23.66% 21.38% 18.43% 5.51% 27.63% 17.63%Standard deviation 32.17% 40.71% 18.97% 23.86% 29.93% 13.56%Variance 0.1035 0.1657 0.0360 0.0570 0.0896 0.0184Average correlation 0.1999 - =AVERAGE(B23:G28)-1/6Uses the array formula =MMULT(TRANSPOSE(B4:G14-B16:G16),B4:G14-B16:G16)/10/MMULT(TRANSPOSE(B17:G17),B17:G17) to compute the correlationsGE MSFT JNJ K BA IBMGE 1.0000 0.5791 0.3632 -0.0560 0.8905 0.2819MSFT 0.5791 1.0000 0.5340 -0.0532 0.3113 -0.0406JNJ 0.3632 0.5340 1.0000 0.4002 0.1780 -0.1529K -0.0560 -0.0532 0.4002 1.0000 -0.1067 -0.1427BA 0.8905 0.3113 0.1780 -0.1067 1.0000 0.6116IBM 0.2819 -0.0406 -0.1529 -0.1427 0.6116 1.0000Uses the array formula=IF(A33:A42=B32:H32,B18:G18,MMULT(TRANSPOSE(B17:G17),B17:G17)*B19) tocompute the constant correlation matrixGE MSFT JNJ K BA IBMGE 0.1035 0.0262 0.0122 0.0153 0.0192 0.0087MSFT 0.0262 0.1657 0.0154 0.0194 0.0244 0.0110JNJ 0.0122 0.0154 0.0360 0.0090 0.0113 0.0051K 0.0153 0.0194 0.0090 0.0570 0.0143 0.0065BA 0.0192 0.0244 0.0113 0.0143 0.0896 0.0081T 0.0087 0.0110 0.0051 0.0065 0.0081 0.0037A B C D E F G1234567891011121314151617181920212223242526272829303132333435363738- =AVERAGE(G4:G14)- =STDEV(G4:G14)- =VAR(G4:G14)ESTIMATING THE VARIANCE-COVARIANCE MATRIX USINGTHE CONSTANT-CORRELATION APPROACHUses the array formula =MMULT(TRANSPOSE(B4:G14-B16:G16),B4:G14-B16:G16)/10/MMULT(TRANSPOSE(B17:G17),B17:G17) to compute the correlationsH1234567891011121314151617181920212223242526272829303132333435363738使用常数-相关系数方法估计方差-协方差矩阵收益数据日期 GE MSFT JNJ K BA IBM3-一月-94 56.44% -1.50% 6.01% -9.79% 58.73% 21.51%3-一月-95 18.23% 33.21% 41.56% 7.46% -0.24% 6.04%2-一月-96 56.93% 44.28% 57.71% 37.76% 65.55% 27.33%2-一月-97 42.87% 79.12% 22.94% -5.09% 54.34% 41.08%2-一月-98 47.11% 38.04% 17.62% 32.04% 37.11% 2.63%4-一月-99 34.55% 85.25% 26.62% -10.74% 15.05% -2.11%3-一月-00 28.15% 11.20% 3.41% -48.93% 43.53% 23.76%2-一月-01 4.61% -47.19% 10.69% 11.67% 28.29% 21.76%2-一月-02 -19.74% 4.27% 23.11% 19.90% -15.09% 4.55%2-一月-03 -44.78% -29.47% -5.67% 10.88% -23.23% 15.54%2-一月-04 35.90% 18.01% -1.27% 15.49% 39.82% 31.80%均值 23.66% 21.38% 18.43% 5.51% 27.63% 17.63%标准差 32.17% 40.71% 18.97% 23.86% 29.93% 13.56%方差 0.1035 0.1657 0.0360 0.0570 0.0896 0.0184平均相关系数 0.1999 - =AVERAGE(B23:G28)-1/6使用数组函数 =MMULT(TRANSPOSE(B4:G14-B16:G16),B4:G14-B16:G16)/10/MMULT(TRANSPOSE(B17:G17),B17:G17) 计算相关系数GE MSFT JNJ K BA IBMGE 1.0000 0.5791 0.3632 -0.0560 0.8905 0.2819MSFT 0.5791 1.0000 0.5340 -0.0532 0.3113 -0.0406JNJ 0.3632 0.5340 1.0000 0.4002 0.1780 -0.1529K -0.0560 -0.0532 0.4002 1.0000 -0.1067 -0.1427BA 0.8905 0.3113 0.1780 -0.1067 1.0000 0.6116IBM 0.2819 -0.0406 -0.1529 -0.1427 0.6116 1.0000使用数组函数=IF(A33:A42=B32:H32,B18:G18,MMULT(TRANSPOSE(B17:G17),B17:G17)*B19) 计算常数相关系数矩阵GE MSFT JNJ K BA IBMGE 0.1035 0.0262 0.0122 0.0153 0.0192 0.0087MSFT 0.0262 0.1657 0.0154 0.0194 0.0244 0.0110JNJ 0.0122 0.0154 0.0360 0.0090 0.0113 0.0051K 0.0153 0.0194 0.0090 0.0570 0.0143 0.0065BA 0.0192 0.0244 0.0113 0.0143 0.0896 0.0081T 0.0087 0.0110 0.0051 0.0065 0.0081 0.0037A B C D E F G1234567891011121314151617181920212223242526272829303132333435363738- =AVERAGE(G4:G14)- =STDEV(G4:G14)- =VAR(G4:G14)使用常数-相关系数方法估计方差-协方差矩阵使用数组函数 =MMULT(TRANSPOSE(B4:G14-B16:G16),B4:G14-B16:G16)/10/MMULT(TRANSPOSE(B17:G17),B17:G17) 计算相关系数H1234567891011121314151617181920212223242526272829303132333435363738ESTIMATING THE VARIANCE-COVARIANCE MATRIX USINGTHE CONSTANT-CORRELATION APPROACHThe constant correlation is set as r = 0.3Return dataDate GE MSFT JNJ K BA IBM3-一月-94 56.44% -1.50% 6.01% -9.79% 58.73% 7.74%3-一月-95 18.23% 33.21% 41.56% 7.46% -0.24% -12.16%2-一月-96 56.93% 44.28% 57.71% 37.76% 65.55% 30.00%2-一月-97 42.87% 79.12% 22.94% -5.09% 54.34% -41.78%2-一月-98 47.11% 38.04% 17.62% 32.04% 37.11% 47.32%4-一月-99 34.55% 85.25% 26.62% -10.74% 15.05% 37.70%3-一月-00 28.15% 11.20% 3.41% -48.93% 43.53% -13.32%2-一月-01 4.61% -47.19% 10.69% 11.67% 28.29% -78.39%2-一月-02 -19.74% 4.27% 23.11% 19.90% -15.09% -25.16%2-一月-03 -44.78% -29.47% -5.67% 10.88% -23.23% -137.03%2-一月-04 35.90% 18.01% -1.27% 15.49% 39.82% 16.44%Average 23.66% 21.38% 18.43% 5.51% 27.63% -15.33%Standard deviation 32.17% 40.71% 18.97% 23.86% 29.93% 54.71%Variance 0.1035 0.1657 0.0360 0.0570 0.0896 0.2993Constant correlation 0.3000 - This is an educated guesstimateUses the array formula =IF(A23:A28=B22:G22,B18:G18,MMULT(TRANSPOSE(B17:G17),B17:G17)*B19) tocompute the constant correlation matrixGE MSFT JNJ K BA IBMGE 0.1035 0.0393 0.0183 0.0230 0.0289 0.0528MSFT 0.0393 0.1657 0.0232 0.0291 0.0366 0.0668JNJ 0.0183 0.0232 0.0360 0.0136 0.0170 0.0311K 0.0230 0.0291 0.0136 0.0570 0.0214 0.0392BA 0.0289 0.0366 0.0170 0.0214 0.0896 0.0491IBM 0.0528 0.0668 0.0311 0.0392 0.0491 0.2993A B C D E F G12345678910111213141516171819202122232425262728- =AVERAGE(G4:G14)- =STDEV(G4:G14)- =VAR(G4:G14)ESTIMATING THE VARIANCE-COVARIANCE MATRIX USINGTHE CONSTANT-CORRELATION APPROACHThe constant correlation is set as r = 0.3Uses the array formula =IF(A23:A28=B22:G22,B18:G18,MMULT(TRANSPOSE(B17:G17),B17:G17)*B19) tocompute the constant correlation matrixH12345678910111213141516171819202122232425262728使用常数-相关系数方法估计方差-协方差矩阵常数相关系数被设定为 r = 0.3收益数据日期 GE MSFT JNJ K BA IBM3-一月-94 56.44% -1.50% 6.01% -9.79% 58.73% 7.74%3-一月-95 18.23% 33.21% 41.56% 7.46% -0.24% -12.16%2-一月-96 56.93% 44.28% 57.71% 37.76% 65.55% 30.00%2-一月-97 42.87% 79.12% 22.94% -5.09% 54.34% -41.78%2-一月-98 47.11% 38.04% 17.62% 32.04% 37.11% 47.32%4-一月-99 34.55% 85.25% 26.62% -10.74% 15.05% 37.70%3-一月-00 28.15% 11.20% 3.41% -48.93% 43.53% -13.32%2-一月-01 4.61% -47.19% 10.69% 11.67% 28.29% -78.39%2-一月-02 -19.74% 4.27% 23.11% 19.90% -15.09% -25.16%2-一月-03 -44.78% -29.47% -5.67% 10.88% -23.23% -137.03%2-一月-04 35.90% 18.01% -1.27% 15.49% 39.82% 16.44%均值 23.66% 21.38% 18.43% 5.51% 27.63% -15.33%标准差 32.17% 40.71% 18.97% 23.86% 29.93% 54.71%方差 0.1035 0.1657 0.0360 0.0570 0.0896 0.2993常数相关系数 0.3000 - 这是一个有把握的猜测使用数组函数 =IF(A23:A28=B22:G22,B18:G18,MMULT(TRANSPOSE(B17:G17),B17:G17)*B19) 计算常数相关系数矩阵GE MSFT JNJ K BA IBMGE 0.1035 0.0393 0.0183 0.0230 0.0289 0.0528MSFT 0.0393 0.1657 0.0232 0.0291 0.0366 0.0668JNJ 0.0183 0.0232 0.0360 0.0136 0.0170 0.0311K 0.0230 0.0291 0.0136 0.0570 0.0214 0.0392BA 0.0289 0.0366 0.0170 0.0214 0.0896 0.0491IBM 0.0528 0.0668 0.0311 0.0392 0.0491 0.2993A B C D E F G12345678910111213141516171819202122232425262728- =AVERAGE(G4:G14)- =STDEV(G4:G14)- =VAR(G4:G14)使用常数-相关系数方法估计方差-协方差矩阵常数相关系数被设定为 r = 0.3使用数组函数 =IF(A23:A28=B22:G22,B18:G18,MMULT(TRANSPOSE(B17:G17),B17:G17)*B19) 计算常数相关系数矩阵H12345678910111213141516171819202122232425262728ESTIMATING THE VARIANCE-COVARIANCE MATRIX USINGTHE SHRINKAGE APPROACHGives weight 0.30 (the shrinkage factor) to sample var-cov andweight 0.70 to a diagonal matrix of only variancesReturn dataDate GE MSFT JNJ K BA IBM3-一月-94 56.44% -1.50% 6.01% -9.79% 58.73% 7.74%3-一月-95 18.23% 33.21% 41.56% 7.46% -0.24% -12.16%2-一月-96 56.93% 44.28% 57.71% 37.76