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 Becton, Dickinson & Co. common stock.
Rates of Return
Becton, Dickinson & Co., monthly rates of return
| Becton, Dickinson & Co. (BDX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceBDX,t1 | DividendBDX,t1 | RBDX,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Oct 31, 2015 | $142.52 | 2,079.36 | ||||
| 1. | Nov 30, 2015 | $150.25 | 5.42% | 2,080.41 | 0.05% | |
| 2. | Dec 31, 2015 | $154.09 | $0.66 | 3.00% | 2,043.94 | -1.75% |
| 3. | Jan 31, 2016 | $145.37 | -5.66% | 1,940.24 | -5.07% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | Aug 31, 2021 | $251.70 | -1.58% | 4,522.68 | 2.90% | |
| 71. | Sep 30, 2021 | $245.82 | $0.83 | -2.01% | 4,307.54 | -4.76% |
| Average (R): | 1.06% | 1.12% | ||||
| Standard deviation: | 5.86% | 4.19% | ||||
| Becton, Dickinson & Co. (BDX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceBDX,t1 | DividendBDX,t1 | RBDX,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Oct 31, 2015 | $142.52 | 2,079.36 | ||||
| 1. | Nov 30, 2015 | $150.25 | 5.42% | 2,080.41 | 0.05% | |
| 2. | Dec 31, 2015 | $154.09 | $0.66 | 3.00% | 2,043.94 | -1.75% |
| 3. | Jan 31, 2016 | $145.37 | -5.66% | 1,940.24 | -5.07% | |
| 4. | Feb 29, 2016 | $147.45 | 1.43% | 1,932.23 | -0.41% | |
| 5. | Mar 31, 2016 | $151.82 | $0.66 | 3.41% | 2,059.74 | 6.60% |
| 6. | Apr 30, 2016 | $161.26 | 6.22% | 2,065.30 | 0.27% | |
| 7. | May 31, 2016 | $166.45 | 3.22% | 2,096.95 | 1.53% | |
| 8. | Jun 30, 2016 | $169.59 | $0.66 | 2.28% | 2,098.86 | 0.09% |
| 9. | Jul 31, 2016 | $176.00 | 3.78% | 2,173.60 | 3.56% | |
| 10. | Aug 31, 2016 | $177.21 | 0.69% | 2,170.95 | -0.12% | |
| 11. | Sep 30, 2016 | $179.73 | $0.66 | 1.79% | 2,168.27 | -0.12% |
| 12. | Oct 31, 2016 | $167.91 | -6.58% | 2,126.15 | -1.94% | |
| 13. | Nov 30, 2016 | $169.10 | 0.71% | 2,198.81 | 3.42% | |
| 14. | Dec 31, 2016 | $165.55 | $0.73 | -1.67% | 2,238.83 | 1.82% |
| 15. | Jan 31, 2017 | $177.29 | 7.09% | 2,278.87 | 1.79% | |
| 16. | Feb 28, 2017 | $183.05 | 3.25% | 2,363.64 | 3.72% | |
| 17. | Mar 31, 2017 | $183.44 | $0.73 | 0.61% | 2,362.72 | -0.04% |
| 18. | Apr 30, 2017 | $186.97 | 1.92% | 2,384.20 | 0.91% | |
| 19. | May 31, 2017 | $189.23 | 1.21% | 2,411.80 | 1.16% | |
| 20. | Jun 30, 2017 | $195.11 | $0.73 | 3.49% | 2,423.41 | 0.48% |
| 21. | Jul 31, 2017 | $201.40 | 3.22% | 2,470.30 | 1.93% | |
| 22. | Aug 31, 2017 | $199.44 | -0.97% | 2,471.65 | 0.05% | |
| 23. | Sep 30, 2017 | $195.95 | $0.73 | -1.38% | 2,519.36 | 1.93% |
| 24. | Oct 31, 2017 | $208.67 | 6.49% | 2,575.26 | 2.22% | |
| 25. | Nov 30, 2017 | $228.21 | 9.36% | 2,647.58 | 2.81% | |
| 26. | Dec 31, 2017 | $214.06 | $0.75 | -5.87% | 2,673.61 | 0.98% |
| 27. | Jan 31, 2018 | $242.94 | 13.49% | 2,823.81 | 5.62% | |
| 28. | Feb 28, 2018 | $222.02 | -8.61% | 2,713.83 | -3.89% | |
| 29. | Mar 31, 2018 | $216.70 | $0.75 | -2.06% | 2,640.87 | -2.69% |
| 30. | Apr 30, 2018 | $231.87 | 7.00% | 2,648.05 | 0.27% | |
| 31. | May 31, 2018 | $221.59 | -4.43% | 2,705.27 | 2.16% | |
| 32. | Jun 30, 2018 | $239.56 | $0.75 | 8.45% | 2,718.37 | 0.48% |
| 33. | Jul 31, 2018 | $250.37 | 4.51% | 2,816.29 | 3.60% | |
| 34. | Aug 31, 2018 | $261.87 | 4.59% | 2,901.52 | 3.03% | |
| 35. | Sep 30, 2018 | $261.00 | $0.75 | -0.05% | 2,913.98 | 0.43% |
| 36. | Oct 31, 2018 | $230.50 | -11.69% | 2,711.74 | -6.94% | |
| 37. | Nov 30, 2018 | $252.75 | 9.65% | 2,760.17 | 1.79% | |
| 38. | Dec 31, 2018 | $225.32 | $0.77 | -10.55% | 2,506.85 | -9.18% |
| 39. | Jan 31, 2019 | $249.46 | 10.71% | 2,704.10 | 7.87% | |
| 40. | Feb 28, 2019 | $248.79 | -0.27% | 2,784.49 | 2.97% | |
| 41. | Mar 31, 2019 | $249.73 | $0.77 | 0.69% | 2,834.40 | 1.79% |
| 42. | Apr 30, 2019 | $240.74 | -3.60% | 2,945.83 | 3.93% | |
| 43. | May 31, 2019 | $233.44 | -3.03% | 2,752.06 | -6.58% | |
| 44. | Jun 30, 2019 | $252.01 | $0.77 | 8.28% | 2,941.76 | 6.89% |
| 45. | Jul 31, 2019 | $252.80 | 0.31% | 2,980.38 | 1.31% | |
| 46. | Aug 31, 2019 | $253.92 | 0.44% | 2,926.46 | -1.81% | |
| 47. | Sep 30, 2019 | $252.96 | $0.77 | -0.07% | 2,976.74 | 1.72% |
| 48. | Oct 31, 2019 | $256.00 | 1.20% | 3,037.56 | 2.04% | |
| 49. | Nov 30, 2019 | $258.50 | 0.98% | 3,140.98 | 3.40% | |
| 50. | Dec 31, 2019 | $271.97 | $0.79 | 5.52% | 3,230.78 | 2.86% |
| 51. | Jan 31, 2020 | $275.18 | 1.18% | 3,225.52 | -0.16% | |
| 52. | Feb 29, 2020 | $237.82 | -13.58% | 2,954.22 | -8.41% | |
| 53. | Mar 31, 2020 | $229.77 | $0.79 | -3.05% | 2,584.59 | -12.51% |
| 54. | Apr 30, 2020 | $252.53 | 9.91% | 2,912.43 | 12.68% | |
| 55. | May 31, 2020 | $246.93 | -2.22% | 3,044.31 | 4.53% | |
| 56. | Jun 30, 2020 | $239.27 | $0.79 | -2.78% | 3,100.29 | 1.84% |
| 57. | Jul 31, 2020 | $281.34 | 17.58% | 3,271.12 | 5.51% | |
| 58. | Aug 31, 2020 | $242.77 | -13.71% | 3,500.31 | 7.01% | |
| 59. | Sep 30, 2020 | $232.68 | $0.79 | -3.83% | 3,363.00 | -3.92% |
| 60. | Oct 31, 2020 | $231.13 | -0.67% | 3,269.96 | -2.77% | |
| 61. | Nov 30, 2020 | $234.84 | 1.61% | 3,621.63 | 10.75% | |
| 62. | Dec 31, 2020 | $250.22 | $0.83 | 6.90% | 3,756.07 | 3.71% |
| 63. | Jan 31, 2021 | $261.79 | 4.62% | 3,714.24 | -1.11% | |
| 64. | Feb 28, 2021 | $241.15 | -7.88% | 3,811.15 | 2.61% | |
| 65. | Mar 31, 2021 | $243.15 | $0.83 | 1.17% | 3,972.89 | 4.24% |
| 66. | Apr 30, 2021 | $248.81 | 2.33% | 4,181.17 | 5.24% | |
| 67. | May 31, 2021 | $241.89 | -2.78% | 4,204.11 | 0.55% | |
| 68. | Jun 30, 2021 | $243.19 | $0.83 | 0.88% | 4,297.50 | 2.22% |
| 69. | Jul 31, 2021 | $255.75 | 5.16% | 4,395.26 | 2.27% | |
| 70. | Aug 31, 2021 | $251.70 | -1.58% | 4,522.68 | 2.90% | |
| 71. | Sep 30, 2021 | $245.82 | $0.83 | -2.01% | 4,307.54 | -4.76% |
| Average (R): | 1.06% | 1.12% | ||||
| Standard deviation: | 5.86% | 4.19% | ||||
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of BDX during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
Becton, Dickinson & Co., calculation of variance and covariance of returns
| t | Date | RBDX,t | RS&P 500,t | (RBDX,t–RBDX)2 | (RS&P 500,t–RS&P 500)2 | (RBDX,t–RBDX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Nov 30, 2015 | 5.42% | 0.05% | 19.05 | 1.14 | -4.66 |
| 2. | Dec 31, 2015 | 3.00% | -1.75% | 3.75 | 8.24 | -5.56 |
| 3. | Jan 31, 2016 | -5.66% | -5.07% | 45.14 | 38.33 | 41.60 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | Aug 31, 2021 | -1.58% | 2.90% | 6.98 | 3.17 | -4.71 |
| 71. | Sep 30, 2021 | -2.01% | -4.76% | 9.40 | 34.51 | 18.01 |
| Total (Σ): | 2,401.77 | 1,226.33 | 898.82 | |||
| t | Date | RBDX,t | RS&P 500,t | (RBDX,t–RBDX)2 | (RS&P 500,t–RS&P 500)2 | (RBDX,t–RBDX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Nov 30, 2015 | 5.42% | 0.05% | 19.05 | 1.14 | -4.66 |
| 2. | Dec 31, 2015 | 3.00% | -1.75% | 3.75 | 8.24 | -5.56 |
| 3. | Jan 31, 2016 | -5.66% | -5.07% | 45.14 | 38.33 | 41.60 |
| 4. | Feb 29, 2016 | 1.43% | -0.41% | 0.14 | 2.34 | -0.57 |
| 5. | Mar 31, 2016 | 3.41% | 6.60% | 5.53 | 30.04 | 12.89 |
| 6. | Apr 30, 2016 | 6.22% | 0.27% | 26.61 | 0.72 | -4.37 |
| 7. | May 31, 2016 | 3.22% | 1.53% | 4.66 | 0.17 | 0.89 |
| 8. | Jun 30, 2016 | 2.28% | 0.09% | 1.50 | 1.05 | -1.26 |
| 9. | Jul 31, 2016 | 3.78% | 3.56% | 7.40 | 5.97 | 6.65 |
| 10. | Aug 31, 2016 | 0.69% | -0.12% | 0.14 | 1.54 | 0.46 |
| 11. | Sep 30, 2016 | 1.79% | -0.12% | 0.54 | 1.54 | -0.91 |
| 12. | Oct 31, 2016 | -6.58% | -1.94% | 58.31 | 9.37 | 23.37 |
| 13. | Nov 30, 2016 | 0.71% | 3.42% | 0.12 | 5.29 | -0.81 |
| 14. | Dec 31, 2016 | -1.67% | 1.82% | 7.44 | 0.49 | -1.91 |
| 15. | Jan 31, 2017 | 7.09% | 1.79% | 36.39 | 0.45 | 4.04 |
| 16. | Feb 28, 2017 | 3.25% | 3.72% | 4.79 | 6.77 | 5.70 |
| 17. | Mar 31, 2017 | 0.61% | -0.04% | 0.20 | 1.34 | 0.52 |
| 18. | Apr 30, 2017 | 1.92% | 0.91% | 0.75 | 0.04 | -0.18 |
| 19. | May 31, 2017 | 1.21% | 1.16% | 0.02 | 0.00 | 0.01 |
| 20. | Jun 30, 2017 | 3.49% | 0.48% | 5.92 | 0.41 | -1.55 |
| 21. | Jul 31, 2017 | 3.22% | 1.93% | 4.69 | 0.67 | 1.77 |
| 22. | Aug 31, 2017 | -0.97% | 0.05% | 4.13 | 1.13 | 2.16 |
| 23. | Sep 30, 2017 | -1.38% | 1.93% | 5.97 | 0.66 | -1.98 |
| 24. | Oct 31, 2017 | 6.49% | 2.22% | 29.51 | 1.21 | 5.98 |
| 25. | Nov 30, 2017 | 9.36% | 2.81% | 68.97 | 2.86 | 14.04 |
| 26. | Dec 31, 2017 | -5.87% | 0.98% | 48.04 | 0.02 | 0.93 |
| 27. | Jan 31, 2018 | 13.49% | 5.62% | 154.56 | 20.25 | 55.94 |
| 28. | Feb 28, 2018 | -8.61% | -3.89% | 93.52 | 25.13 | 48.48 |
| 29. | Mar 31, 2018 | -2.06% | -2.69% | 9.72 | 14.49 | 11.87 |
| 30. | Apr 30, 2018 | 7.00% | 0.27% | 35.30 | 0.72 | -5.03 |
| 31. | May 31, 2018 | -4.43% | 2.16% | 30.17 | 1.09 | -5.73 |
| 32. | Jun 30, 2018 | 8.45% | 0.48% | 54.59 | 0.40 | -4.68 |
| 33. | Jul 31, 2018 | 4.51% | 3.60% | 11.92 | 6.17 | 8.58 |
| 34. | Aug 31, 2018 | 4.59% | 3.03% | 12.49 | 3.64 | 6.74 |
| 35. | Sep 30, 2018 | -0.05% | 0.43% | 1.22 | 0.47 | 0.76 |
| 36. | Oct 31, 2018 | -11.69% | -6.94% | 162.44 | 64.94 | 102.70 |
| 37. | Nov 30, 2018 | 9.65% | 1.79% | 73.85 | 0.45 | 5.74 |
| 38. | Dec 31, 2018 | -10.55% | -9.18% | 134.73 | 106.00 | 119.50 |
| 39. | Jan 31, 2019 | 10.71% | 7.87% | 93.21 | 45.57 | 65.17 |
| 40. | Feb 28, 2019 | -0.27% | 2.97% | 1.76 | 3.44 | -2.46 |
| 41. | Mar 31, 2019 | 0.69% | 1.79% | 0.14 | 0.45 | -0.25 |
| 42. | Apr 30, 2019 | -3.60% | 3.93% | 21.71 | 7.92 | -13.11 |
| 43. | May 31, 2019 | -3.03% | -6.58% | 16.74 | 59.22 | 31.49 |
| 44. | Jun 30, 2019 | 8.28% | 6.89% | 52.21 | 33.35 | 41.73 |
| 45. | Jul 31, 2019 | 0.31% | 1.31% | 0.56 | 0.04 | -0.15 |
| 46. | Aug 31, 2019 | 0.44% | -1.81% | 0.38 | 8.57 | 1.80 |
| 47. | Sep 30, 2019 | -0.07% | 1.72% | 1.29 | 0.36 | -0.68 |
| 48. | Oct 31, 2019 | 1.20% | 2.04% | 0.02 | 0.86 | 0.13 |
| 49. | Nov 30, 2019 | 0.98% | 3.40% | 0.01 | 5.23 | -0.19 |
| 50. | Dec 31, 2019 | 5.52% | 2.86% | 19.87 | 3.03 | 7.76 |
| 51. | Jan 31, 2020 | 1.18% | -0.16% | 0.01 | 1.64 | -0.15 |
| 52. | Feb 29, 2020 | -13.58% | -8.41% | 214.21 | 90.80 | 139.47 |
| 53. | Mar 31, 2020 | -3.05% | -12.51% | 16.91 | 185.77 | 56.05 |
| 54. | Apr 30, 2020 | 9.91% | 12.68% | 78.26 | 133.78 | 102.32 |
| 55. | May 31, 2020 | -2.22% | 4.53% | 10.74 | 11.63 | -11.17 |
| 56. | Jun 30, 2020 | -2.78% | 1.84% | 14.76 | 0.52 | -2.77 |
| 57. | Jul 31, 2020 | 17.58% | 5.51% | 273.02 | 19.29 | 72.57 |
| 58. | Aug 31, 2020 | -13.71% | 7.01% | 218.11 | 34.67 | -86.97 |
| 59. | Sep 30, 2020 | -3.83% | -3.92% | 23.91 | 25.41 | 24.65 |
| 60. | Oct 31, 2020 | -0.67% | -2.77% | 2.98 | 15.09 | 6.70 |
| 61. | Nov 30, 2020 | 1.61% | 10.75% | 0.30 | 92.86 | 5.26 |
| 62. | Dec 31, 2020 | 6.90% | 3.71% | 34.14 | 6.73 | 15.16 |
| 63. | Jan 31, 2021 | 4.62% | -1.11% | 12.71 | 4.98 | -7.96 |
| 64. | Feb 28, 2021 | -7.88% | 2.61% | 79.99 | 2.22 | -13.34 |
| 65. | Mar 31, 2021 | 1.17% | 4.24% | 0.01 | 9.77 | 0.36 |
| 66. | Apr 30, 2021 | 2.33% | 5.24% | 1.61 | 17.01 | 5.23 |
| 67. | May 31, 2021 | -2.78% | 0.55% | 14.75 | 0.32 | 2.19 |
| 68. | Jun 30, 2021 | 0.88% | 2.22% | 0.03 | 1.22 | -0.20 |
| 69. | Jul 31, 2021 | 5.16% | 2.27% | 16.85 | 1.34 | 4.75 |
| 70. | Aug 31, 2021 | -1.58% | 2.90% | 6.98 | 3.17 | -4.71 |
| 71. | Sep 30, 2021 | -2.01% | -4.76% | 9.40 | 34.51 | 18.01 |
| Total (Σ): | 2,401.77 | 1,226.33 | 898.82 | |||
Show all
VarianceBDX = Σ(RBDX,t–RBDX)2 ÷ (71 – 1)
= 2,401.77 ÷ (71 – 1)
= 34.31
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,226.33 ÷ (71 – 1)
= 17.52
CovarianceBDX, S&P 500 = Σ(RBDX,t–RBDX)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 898.82 ÷ (71 – 1)
= 12.84
Systematic Risk (β) Estimation
| VarianceBDX | 34.31 |
| VarianceS&P 500 | 17.52 |
| CovarianceBDX, S&P 500 | 12.84 |
| Correlation coefficientBDX, S&P 5001 | 0.52 |
| βBDX2 | 0.73 |
| αBDX3 | 0.24% |
Calculations
1 Correlation coefficientBDX, S&P 500
= CovarianceBDX, S&P 500 ÷ (Standard deviationBDX × Standard deviationS&P 500)
= 12.84 ÷ (5.86% × 4.19%)
= 0.52
2 βBDX
= CovarianceBDX, S&P 500 ÷ VarianceS&P 500
= 12.84 ÷ 17.52
= 0.73
3 αBDX
= AverageBDX – βBDX × AverageS&P 500
= 1.06% – 0.73 × 1.12%
= 0.24%
Expected Rate of Return
| Assumptions | ||
| Rate of return on LT Treasury Composite1 | RF | 4.79% |
| Expected rate of return on market portfolio2 | E(RM) | 13.79% |
| Systematic risk (β) of Becton, Dickinson & Co. common stock | βBDX | 0.73 |
| Expected rate of return on Becton, Dickinson & Co. common stock3 | E(RBDX) | 11.39% |
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(RBDX) = RF + βBDX [E(RM) – RF]
= 4.79% + 0.73 [13.79% – 4.79%]
= 11.39%