Capital Asset Pricing Model (CAPM)
Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like Emerson Electric Co. common stock.
Rates of Return
Emerson Electric Co., monthly rates of return
| Emerson Electric Co. (EMR) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceEMR,t1 | DividendEMR,t1 | REMR,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Oct 31, 2013 | $66.97 | 1,756.54 | ||||
| 1. | Nov 30, 2013 | $66.99 | $0.43 | 0.67% | 1,805.81 | 2.80% |
| 2. | Dec 31, 2013 | $70.18 | 4.76% | 1,848.36 | 2.36% | |
| 3. | Jan 31, 2014 | $65.94 | -6.04% | 1,782.59 | -3.56% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | Aug 31, 2019 | $59.59 | $0.49 | -7.40% | 2,926.46 | -1.81% |
| 71. | Sep 30, 2019 | $66.86 | 12.20% | 2,976.74 | 1.72% | |
| Average (R): | 0.42% | 0.80% | ||||
| Standard deviation: | 5.69% | 3.29% | ||||
| Emerson Electric Co. (EMR) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceEMR,t1 | DividendEMR,t1 | REMR,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Oct 31, 2013 | $66.97 | 1,756.54 | ||||
| 1. | Nov 30, 2013 | $66.99 | $0.43 | 0.67% | 1,805.81 | 2.80% |
| 2. | Dec 31, 2013 | $70.18 | 4.76% | 1,848.36 | 2.36% | |
| 3. | Jan 31, 2014 | $65.94 | -6.04% | 1,782.59 | -3.56% | |
| 4. | Feb 28, 2014 | $65.26 | $0.43 | -0.38% | 1,859.45 | 4.31% |
| 5. | Mar 31, 2014 | $66.80 | 2.36% | 1,872.34 | 0.69% | |
| 6. | Apr 30, 2014 | $68.18 | 2.07% | 1,883.95 | 0.62% | |
| 7. | May 31, 2014 | $66.73 | $0.43 | -1.50% | 1,923.57 | 2.10% |
| 8. | Jun 30, 2014 | $66.36 | -0.55% | 1,960.23 | 1.91% | |
| 9. | Jul 31, 2014 | $63.65 | -4.08% | 1,930.67 | -1.51% | |
| 10. | Aug 31, 2014 | $64.02 | $0.43 | 1.26% | 2,003.37 | 3.77% |
| 11. | Sep 30, 2014 | $62.58 | -2.25% | 1,972.29 | -1.55% | |
| 12. | Oct 31, 2014 | $64.06 | 2.36% | 2,018.05 | 2.32% | |
| 13. | Nov 30, 2014 | $63.75 | $0.47 | 0.25% | 2,067.56 | 2.45% |
| 14. | Dec 31, 2014 | $61.73 | -3.17% | 2,058.90 | -0.42% | |
| 15. | Jan 31, 2015 | $56.94 | -7.76% | 1,994.99 | -3.10% | |
| 16. | Feb 28, 2015 | $57.92 | $0.47 | 2.55% | 2,104.50 | 5.49% |
| 17. | Mar 31, 2015 | $56.62 | -2.24% | 2,067.89 | -1.74% | |
| 18. | Apr 30, 2015 | $58.83 | 3.90% | 2,085.51 | 0.85% | |
| 19. | May 31, 2015 | $60.31 | $0.47 | 3.31% | 2,107.39 | 1.05% |
| 20. | Jun 30, 2015 | $55.43 | -8.09% | 2,063.11 | -2.10% | |
| 21. | Jul 31, 2015 | $51.75 | -6.64% | 2,103.84 | 1.97% | |
| 22. | Aug 31, 2015 | $47.72 | $0.47 | -6.88% | 1,972.18 | -6.26% |
| 23. | Sep 30, 2015 | $44.17 | -7.44% | 1,920.03 | -2.64% | |
| 24. | Oct 31, 2015 | $47.23 | 6.93% | 2,079.36 | 8.30% | |
| 25. | Nov 30, 2015 | $50.00 | $0.475 | 6.87% | 2,080.41 | 0.05% |
| 26. | Dec 31, 2015 | $47.83 | -4.34% | 2,043.94 | -1.75% | |
| 27. | Jan 31, 2016 | $45.98 | -3.87% | 1,940.24 | -5.07% | |
| 28. | Feb 29, 2016 | $48.83 | $0.475 | 7.23% | 1,932.23 | -0.41% |
| 29. | Mar 31, 2016 | $54.38 | 11.37% | 2,059.74 | 6.60% | |
| 30. | Apr 30, 2016 | $54.63 | 0.46% | 2,065.30 | 0.27% | |
| 31. | May 31, 2016 | $52.02 | $0.475 | -3.91% | 2,096.95 | 1.53% |
| 32. | Jun 30, 2016 | $52.16 | 0.27% | 2,098.86 | 0.09% | |
| 33. | Jul 31, 2016 | $55.90 | 7.17% | 2,173.60 | 3.56% | |
| 34. | Aug 31, 2016 | $52.68 | $0.475 | -4.91% | 2,170.95 | -0.12% |
| 35. | Sep 30, 2016 | $54.51 | 3.47% | 2,168.27 | -0.12% | |
| 36. | Oct 31, 2016 | $50.68 | -7.03% | 2,126.15 | -1.94% | |
| 37. | Nov 30, 2016 | $56.44 | $0.48 | 12.31% | 2,198.81 | 3.42% |
| 38. | Dec 31, 2016 | $55.75 | -1.22% | 2,238.83 | 1.82% | |
| 39. | Jan 31, 2017 | $58.66 | 5.22% | 2,278.87 | 1.79% | |
| 40. | Feb 28, 2017 | $60.10 | $0.48 | 3.27% | 2,363.64 | 3.72% |
| 41. | Mar 31, 2017 | $59.86 | -0.40% | 2,362.72 | -0.04% | |
| 42. | Apr 30, 2017 | $60.28 | 0.70% | 2,384.20 | 0.91% | |
| 43. | May 31, 2017 | $59.12 | $0.48 | -1.13% | 2,411.80 | 1.16% |
| 44. | Jun 30, 2017 | $59.62 | 0.85% | 2,423.41 | 0.48% | |
| 45. | Jul 31, 2017 | $59.61 | -0.02% | 2,470.30 | 1.93% | |
| 46. | Aug 31, 2017 | $59.04 | $0.48 | -0.15% | 2,471.65 | 0.05% |
| 47. | Sep 30, 2017 | $62.84 | 6.44% | 2,519.36 | 1.93% | |
| 48. | Oct 31, 2017 | $64.46 | 2.58% | 2,575.26 | 2.22% | |
| 49. | Nov 30, 2017 | $64.82 | $0.485 | 1.31% | 2,647.58 | 2.81% |
| 50. | Dec 31, 2017 | $69.69 | 7.51% | 2,673.61 | 0.98% | |
| 51. | Jan 31, 2018 | $72.23 | 3.64% | 2,823.81 | 5.62% | |
| 52. | Feb 28, 2018 | $71.06 | $0.485 | -0.95% | 2,713.83 | -3.89% |
| 53. | Mar 31, 2018 | $68.30 | -3.88% | 2,640.87 | -2.69% | |
| 54. | Apr 30, 2018 | $66.41 | -2.77% | 2,648.05 | 0.27% | |
| 55. | May 31, 2018 | $70.84 | $0.485 | 7.40% | 2,705.27 | 2.16% |
| 56. | Jun 30, 2018 | $69.14 | -2.40% | 2,718.37 | 0.48% | |
| 57. | Jul 31, 2018 | $72.28 | 4.54% | 2,816.29 | 3.60% | |
| 58. | Aug 31, 2018 | $76.73 | $0.485 | 6.83% | 2,901.52 | 3.03% |
| 59. | Sep 30, 2018 | $76.58 | -0.20% | 2,913.98 | 0.43% | |
| 60. | Oct 31, 2018 | $67.88 | -11.36% | 2,711.74 | -6.94% | |
| 61. | Nov 30, 2018 | $67.52 | $0.49 | 0.19% | 2,760.17 | 1.79% |
| 62. | Dec 31, 2018 | $59.75 | -11.51% | 2,506.85 | -9.18% | |
| 63. | Jan 31, 2019 | $65.47 | 9.57% | 2,704.10 | 7.87% | |
| 64. | Feb 28, 2019 | $68.15 | $0.49 | 4.84% | 2,784.49 | 2.97% |
| 65. | Mar 31, 2019 | $68.47 | 0.47% | 2,834.40 | 1.79% | |
| 66. | Apr 30, 2019 | $70.99 | 3.68% | 2,945.83 | 3.93% | |
| 67. | May 31, 2019 | $60.24 | $0.49 | -14.45% | 2,752.06 | -6.58% |
| 68. | Jun 30, 2019 | $66.72 | 10.76% | 2,941.76 | 6.89% | |
| 69. | Jul 31, 2019 | $64.88 | -2.76% | 2,980.38 | 1.31% | |
| 70. | Aug 31, 2019 | $59.59 | $0.49 | -7.40% | 2,926.46 | -1.81% |
| 71. | Sep 30, 2019 | $66.86 | 12.20% | 2,976.74 | 1.72% | |
| Average (R): | 0.42% | 0.80% | ||||
| Standard deviation: | 5.69% | 3.29% | ||||
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of EMR during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
Emerson Electric Co., calculation of variance and covariance of returns
| t | Date | REMR,t | RS&P 500,t | (REMR,t–REMR)2 | (RS&P 500,t–RS&P 500)2 | (REMR,t–REMR)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Nov 30, 2013 | 0.67% | 2.80% | 0.06 | 4.02 | 0.50 |
| 2. | Dec 31, 2013 | 4.76% | 2.36% | 18.84 | 2.42 | 6.76 |
| 3. | Jan 31, 2014 | -6.04% | -3.56% | 41.77 | 18.99 | 28.16 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | Aug 31, 2019 | -7.40% | -1.81% | 61.15 | 6.80 | 20.40 |
| 71. | Sep 30, 2019 | 12.20% | 1.72% | 138.74 | 0.84 | 10.82 |
| Total (Σ): | 2,262.58 | 758.73 | 1,001.26 | |||
| t | Date | REMR,t | RS&P 500,t | (REMR,t–REMR)2 | (RS&P 500,t–RS&P 500)2 | (REMR,t–REMR)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Nov 30, 2013 | 0.67% | 2.80% | 0.06 | 4.02 | 0.50 |
| 2. | Dec 31, 2013 | 4.76% | 2.36% | 18.84 | 2.42 | 6.76 |
| 3. | Jan 31, 2014 | -6.04% | -3.56% | 41.77 | 18.99 | 28.16 |
| 4. | Feb 28, 2014 | -0.38% | 4.31% | 0.64 | 12.34 | -2.81 |
| 5. | Mar 31, 2014 | 2.36% | 0.69% | 3.76 | 0.01 | -0.21 |
| 6. | Apr 30, 2014 | 2.07% | 0.62% | 2.70 | 0.03 | -0.29 |
| 7. | May 31, 2014 | -1.50% | 2.10% | 3.68 | 1.70 | -2.50 |
| 8. | Jun 30, 2014 | -0.55% | 1.91% | 0.95 | 1.22 | -1.08 |
| 9. | Jul 31, 2014 | -4.08% | -1.51% | 20.30 | 5.32 | 10.39 |
| 10. | Aug 31, 2014 | 1.26% | 3.77% | 0.70 | 8.80 | 2.48 |
| 11. | Sep 30, 2014 | -2.25% | -1.55% | 7.13 | 5.53 | 6.28 |
| 12. | Oct 31, 2014 | 2.36% | 2.32% | 3.78 | 2.31 | 2.96 |
| 13. | Nov 30, 2014 | 0.25% | 2.45% | 0.03 | 2.74 | -0.28 |
| 14. | Dec 31, 2014 | -3.17% | -0.42% | 12.89 | 1.48 | 4.37 |
| 15. | Jan 31, 2015 | -7.76% | -3.10% | 66.93 | 15.24 | 31.93 |
| 16. | Feb 28, 2015 | 2.55% | 5.49% | 4.52 | 22.00 | 9.97 |
| 17. | Mar 31, 2015 | -2.24% | -1.74% | 7.11 | 6.45 | 6.77 |
| 18. | Apr 30, 2015 | 3.90% | 0.85% | 12.12 | 0.00 | 0.18 |
| 19. | May 31, 2015 | 3.31% | 1.05% | 8.37 | 0.06 | 0.72 |
| 20. | Jun 30, 2015 | -8.09% | -2.10% | 72.47 | 8.41 | 24.69 |
| 21. | Jul 31, 2015 | -6.64% | 1.97% | 49.85 | 1.38 | -8.29 |
| 22. | Aug 31, 2015 | -6.88% | -6.26% | 53.30 | 49.81 | 51.52 |
| 23. | Sep 30, 2015 | -7.44% | -2.64% | 61.79 | 11.86 | 27.07 |
| 24. | Oct 31, 2015 | 6.93% | 8.30% | 42.33 | 56.23 | 48.79 |
| 25. | Nov 30, 2015 | 6.87% | 0.05% | 41.59 | 0.56 | -4.83 |
| 26. | Dec 31, 2015 | -4.34% | -1.75% | 22.67 | 6.51 | 12.15 |
| 27. | Jan 31, 2016 | -3.87% | -5.07% | 18.40 | 34.49 | 25.19 |
| 28. | Feb 29, 2016 | 7.23% | -0.41% | 46.38 | 1.47 | -8.26 |
| 29. | Mar 31, 2016 | 11.37% | 6.60% | 119.78 | 33.64 | 63.48 |
| 30. | Apr 30, 2016 | 0.46% | 0.27% | 0.00 | 0.28 | -0.02 |
| 31. | May 31, 2016 | -3.91% | 1.53% | 18.74 | 0.54 | -3.17 |
| 32. | Jun 30, 2016 | 0.27% | 0.09% | 0.02 | 0.50 | 0.11 |
| 33. | Jul 31, 2016 | 7.17% | 3.56% | 45.55 | 7.63 | 18.64 |
| 34. | Aug 31, 2016 | -4.91% | -0.12% | 28.43 | 0.85 | 4.91 |
| 35. | Sep 30, 2016 | 3.47% | -0.12% | 9.32 | 0.85 | -2.82 |
| 36. | Oct 31, 2016 | -7.03% | -1.94% | 55.47 | 7.52 | 20.42 |
| 37. | Nov 30, 2016 | 12.31% | 3.42% | 141.40 | 6.85 | 31.13 |
| 38. | Dec 31, 2016 | -1.22% | 1.82% | 2.70 | 1.04 | -1.68 |
| 39. | Jan 31, 2017 | 5.22% | 1.79% | 23.02 | 0.98 | 4.75 |
| 40. | Feb 28, 2017 | 3.27% | 3.72% | 8.13 | 8.53 | 8.33 |
| 41. | Mar 31, 2017 | -0.40% | -0.04% | 0.67 | 0.70 | 0.69 |
| 42. | Apr 30, 2017 | 0.70% | 0.91% | 0.08 | 0.01 | 0.03 |
| 43. | May 31, 2017 | -1.13% | 1.16% | 2.40 | 0.13 | -0.56 |
| 44. | Jun 30, 2017 | 0.85% | 0.48% | 0.18 | 0.10 | -0.13 |
| 45. | Jul 31, 2017 | -0.02% | 1.93% | 0.19 | 1.29 | -0.50 |
| 46. | Aug 31, 2017 | -0.15% | 0.05% | 0.33 | 0.55 | 0.43 |
| 47. | Sep 30, 2017 | 6.44% | 1.93% | 36.18 | 1.28 | 6.80 |
| 48. | Oct 31, 2017 | 2.58% | 2.22% | 4.65 | 2.01 | 3.06 |
| 49. | Nov 30, 2017 | 1.31% | 2.81% | 0.79 | 4.04 | 1.79 |
| 50. | Dec 31, 2017 | 7.51% | 0.98% | 50.29 | 0.03 | 1.30 |
| 51. | Jan 31, 2018 | 3.64% | 5.62% | 10.39 | 23.22 | 15.53 |
| 52. | Feb 28, 2018 | -0.95% | -3.89% | 1.88 | 22.03 | 6.43 |
| 53. | Mar 31, 2018 | -3.88% | -2.69% | 18.54 | 12.16 | 15.02 |
| 54. | Apr 30, 2018 | -2.77% | 0.27% | 10.17 | 0.28 | 1.68 |
| 55. | May 31, 2018 | 7.40% | 2.16% | 48.72 | 1.85 | 9.50 |
| 56. | Jun 30, 2018 | -2.40% | 0.48% | 7.96 | 0.10 | 0.89 |
| 57. | Jul 31, 2018 | 4.54% | 3.60% | 16.98 | 7.86 | 11.55 |
| 58. | Aug 31, 2018 | 6.83% | 3.03% | 41.04 | 4.96 | 14.27 |
| 59. | Sep 30, 2018 | -0.20% | 0.43% | 0.38 | 0.14 | 0.23 |
| 60. | Oct 31, 2018 | -11.36% | -6.94% | 138.82 | 59.90 | 91.19 |
| 61. | Nov 30, 2018 | 0.19% | 1.79% | 0.05 | 0.97 | -0.23 |
| 62. | Dec 31, 2018 | -11.51% | -9.18% | 142.30 | 99.54 | 119.02 |
| 63. | Jan 31, 2019 | 9.57% | 7.87% | 83.76 | 49.97 | 64.70 |
| 64. | Feb 28, 2019 | 4.84% | 2.97% | 19.54 | 4.72 | 9.61 |
| 65. | Mar 31, 2019 | 0.47% | 1.79% | 0.00 | 0.99 | 0.05 |
| 66. | Apr 30, 2019 | 3.68% | 3.93% | 10.62 | 9.81 | 10.21 |
| 67. | May 31, 2019 | -14.45% | -6.58% | 221.24 | 54.42 | 109.73 |
| 68. | Jun 30, 2019 | 10.76% | 6.89% | 106.83 | 37.13 | 62.98 |
| 69. | Jul 31, 2019 | -2.76% | 1.31% | 10.11 | 0.26 | -1.63 |
| 70. | Aug 31, 2019 | -7.40% | -1.81% | 61.15 | 6.80 | 20.40 |
| 71. | Sep 30, 2019 | 12.20% | 1.72% | 138.74 | 0.84 | 10.82 |
| Total (Σ): | 2,262.58 | 758.73 | 1,001.26 | |||
Show all
VarianceEMR = Σ(REMR,t–REMR)2 ÷ (71 – 1)
= 2,262.58 ÷ (71 – 1)
= 32.32
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 758.73 ÷ (71 – 1)
= 10.84
CovarianceEMR, S&P 500 = Σ(REMR,t–REMR)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 1,001.26 ÷ (71 – 1)
= 14.30
Systematic Risk (β) Estimation
| VarianceEMR | 32.32 |
| VarianceS&P 500 | 10.84 |
| CovarianceEMR, S&P 500 | 14.30 |
| Correlation coefficientEMR, S&P 5001 | 0.76 |
| βEMR2 | 1.32 |
| αEMR3 | -0.63% |
Calculations
1 Correlation coefficientEMR, S&P 500
= CovarianceEMR, S&P 500 ÷ (Standard deviationEMR × Standard deviationS&P 500)
= 14.30 ÷ (5.69% × 3.29%)
= 0.76
2 βEMR
= CovarianceEMR, S&P 500 ÷ VarianceS&P 500
= 14.30 ÷ 10.84
= 1.32
3 αEMR
= AverageEMR – βEMR × AverageS&P 500
= 0.42% – 1.32 × 0.80%
= -0.63%
Expected Rate of Return
| Assumptions | ||
| Rate of return on LT Treasury Composite1 | RF | 4.89% |
| Expected rate of return on market portfolio2 | E(RM) | 13.87% |
| Systematic risk (β) of Emerson Electric Co. common stock | βEMR | 1.32 |
| Expected rate of return on Emerson Electric Co. common stock3 | E(REMR) | 16.74% |
1 Unweighted average of bid yields on all outstanding fixed-coupon U.S. Treasury bonds neither due or callable in less than 10 years (risk-free rate of return proxy).
3 E(REMR) = RF + βEMR [E(RM) – RF]
= 4.89% + 1.32 [13.87% – 4.89%]
= 16.74%