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 Bristol-Myers Squibb Co. common stock.
Rates of Return
Bristol-Myers Squibb Co., monthly rates of return
| Bristol-Myers Squibb Co. (BMY) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceBMY,t1 | DividendBMY,t1 | RBMY,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Jan 31, 2019 | $49.37 | 2,704.10 | ||||
| 1. | Feb 28, 2019 | $51.66 | 4.64% | 2,784.49 | 2.97% | |
| 2. | Mar 31, 2019 | $47.71 | -7.65% | 2,834.40 | 1.79% | |
| 3. | Apr 30, 2019 | $46.43 | $0.41 | -1.82% | 2,945.83 | 3.93% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2023 | $49.38 | -4.17% | 4,567.80 | 8.92% | |
| 59. | Dec 31, 2023 | $51.31 | 3.91% | 4,769.83 | 4.42% | |
| Average (R): | 0.49% | 1.11% | ||||
| Standard deviation: | 5.87% | 5.31% | ||||
| Bristol-Myers Squibb Co. (BMY) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceBMY,t1 | DividendBMY,t1 | RBMY,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Jan 31, 2019 | $49.37 | 2,704.10 | ||||
| 1. | Feb 28, 2019 | $51.66 | 4.64% | 2,784.49 | 2.97% | |
| 2. | Mar 31, 2019 | $47.71 | -7.65% | 2,834.40 | 1.79% | |
| 3. | Apr 30, 2019 | $46.43 | $0.41 | -1.82% | 2,945.83 | 3.93% |
| 4. | May 31, 2019 | $45.37 | -2.28% | 2,752.06 | -6.58% | |
| 5. | Jun 30, 2019 | $45.35 | -0.04% | 2,941.76 | 6.89% | |
| 6. | Jul 31, 2019 | $44.41 | $0.41 | -1.17% | 2,980.38 | 1.31% |
| 7. | Aug 31, 2019 | $48.07 | 8.24% | 2,926.46 | -1.81% | |
| 8. | Sep 30, 2019 | $50.71 | 5.49% | 2,976.74 | 1.72% | |
| 9. | Oct 31, 2019 | $57.37 | $0.41 | 13.94% | 3,037.56 | 2.04% |
| 10. | Nov 30, 2019 | $56.94 | -0.75% | 3,140.98 | 3.40% | |
| 11. | Dec 31, 2019 | $64.19 | 12.73% | 3,230.78 | 2.86% | |
| 12. | Jan 31, 2020 | $62.95 | $0.45 | -1.23% | 3,225.52 | -0.16% |
| 13. | Feb 29, 2020 | $59.06 | -6.18% | 2,954.22 | -8.41% | |
| 14. | Mar 31, 2020 | $55.74 | -5.62% | 2,584.59 | -12.51% | |
| 15. | Apr 30, 2020 | $60.81 | $0.45 | 9.90% | 2,912.43 | 12.68% |
| 16. | May 31, 2020 | $59.72 | -1.79% | 3,044.31 | 4.53% | |
| 17. | Jun 30, 2020 | $58.80 | -1.54% | 3,100.29 | 1.84% | |
| 18. | Jul 31, 2020 | $58.66 | $0.45 | 0.53% | 3,271.12 | 5.51% |
| 19. | Aug 31, 2020 | $62.20 | 6.03% | 3,500.31 | 7.01% | |
| 20. | Sep 30, 2020 | $60.29 | -3.07% | 3,363.00 | -3.92% | |
| 21. | Oct 31, 2020 | $58.45 | $0.45 | -2.31% | 3,269.96 | -2.77% |
| 22. | Nov 30, 2020 | $62.40 | 6.76% | 3,621.63 | 10.75% | |
| 23. | Dec 31, 2020 | $62.03 | $0.49 | 0.19% | 3,756.07 | 3.71% |
| 24. | Jan 31, 2021 | $61.43 | -0.97% | 3,714.24 | -1.11% | |
| 25. | Feb 28, 2021 | $61.33 | -0.16% | 3,811.15 | 2.61% | |
| 26. | Mar 31, 2021 | $63.13 | $0.49 | 3.73% | 3,972.89 | 4.24% |
| 27. | Apr 30, 2021 | $62.42 | -1.12% | 4,181.17 | 5.24% | |
| 28. | May 31, 2021 | $65.72 | 5.29% | 4,204.11 | 0.55% | |
| 29. | Jun 30, 2021 | $66.82 | 1.67% | 4,297.50 | 2.22% | |
| 30. | Jul 31, 2021 | $67.87 | $0.49 | 2.30% | 4,395.26 | 2.27% |
| 31. | Aug 31, 2021 | $66.86 | -1.49% | 4,522.68 | 2.90% | |
| 32. | Sep 30, 2021 | $59.17 | $0.49 | -10.77% | 4,307.54 | -4.76% |
| 33. | Oct 31, 2021 | $58.40 | -1.30% | 4,605.38 | 6.91% | |
| 34. | Nov 30, 2021 | $53.63 | -8.17% | 4,567.00 | -0.83% | |
| 35. | Dec 31, 2021 | $62.35 | 16.26% | 4,766.18 | 4.36% | |
| 36. | Jan 31, 2022 | $64.89 | $0.54 | 4.94% | 4,515.55 | -5.26% |
| 37. | Feb 28, 2022 | $68.67 | 5.83% | 4,373.94 | -3.14% | |
| 38. | Mar 31, 2022 | $73.03 | $0.54 | 7.14% | 4,530.41 | 3.58% |
| 39. | Apr 30, 2022 | $75.27 | 3.07% | 4,131.93 | -8.80% | |
| 40. | May 31, 2022 | $75.45 | 0.24% | 4,132.15 | 0.01% | |
| 41. | Jun 30, 2022 | $77.00 | $0.54 | 2.77% | 3,785.38 | -8.39% |
| 42. | Jul 31, 2022 | $73.78 | -4.18% | 4,130.29 | 9.11% | |
| 43. | Aug 31, 2022 | $67.41 | -8.63% | 3,955.00 | -4.24% | |
| 44. | Sep 30, 2022 | $71.09 | 5.46% | 3,585.62 | -9.34% | |
| 45. | Oct 31, 2022 | $77.47 | $0.54 | 9.73% | 3,871.98 | 7.99% |
| 46. | Nov 30, 2022 | $80.28 | 3.63% | 4,080.11 | 5.38% | |
| 47. | Dec 31, 2022 | $71.95 | -10.38% | 3,839.50 | -5.90% | |
| 48. | Jan 31, 2023 | $72.65 | $0.57 | 1.77% | 4,076.60 | 6.18% |
| 49. | Feb 28, 2023 | $68.96 | -5.08% | 3,970.15 | -2.61% | |
| 50. | Mar 31, 2023 | $69.31 | 0.51% | 4,109.31 | 3.51% | |
| 51. | Apr 30, 2023 | $66.77 | $0.57 | -2.84% | 4,169.48 | 1.46% |
| 52. | May 31, 2023 | $64.44 | -3.49% | 4,179.83 | 0.25% | |
| 53. | Jun 30, 2023 | $63.95 | -0.76% | 4,376.86 | 4.71% | |
| 54. | Jul 31, 2023 | $62.19 | $0.57 | -1.86% | 4,588.96 | 4.85% |
| 55. | Aug 31, 2023 | $61.65 | -0.87% | 4,507.66 | -1.77% | |
| 56. | Sep 30, 2023 | $58.04 | -5.86% | 4,288.05 | -4.87% | |
| 57. | Oct 31, 2023 | $51.53 | $0.57 | -10.23% | 4,193.80 | -2.20% |
| 58. | Nov 30, 2023 | $49.38 | -4.17% | 4,567.80 | 8.92% | |
| 59. | Dec 31, 2023 | $51.31 | 3.91% | 4,769.83 | 4.42% | |
| Average (R): | 0.49% | 1.11% | ||||
| Standard deviation: | 5.87% | 5.31% | ||||
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of BMY during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
Bristol-Myers Squibb Co., calculation of variance and covariance of returns
| t | Date | RBMY,t | RS&P 500,t | (RBMY,t–RBMY)2 | (RS&P 500,t–RS&P 500)2 | (RBMY,t–RBMY)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Feb 28, 2019 | 4.64% | 2.97% | 17.21 | 3.49 | 7.75 |
| 2. | Mar 31, 2019 | -7.65% | 1.79% | 66.20 | 0.47 | -5.59 |
| 3. | Apr 30, 2019 | -1.82% | 3.93% | 5.35 | 7.98 | -6.54 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2023 | -4.17% | 8.92% | 21.74 | 61.03 | -36.42 |
| 59. | Dec 31, 2023 | 3.91% | 4.42% | 11.69 | 11.00 | 11.34 |
| Total (Σ): | 1,995.90 | 1,634.30 | 621.26 | |||
| t | Date | RBMY,t | RS&P 500,t | (RBMY,t–RBMY)2 | (RS&P 500,t–RS&P 500)2 | (RBMY,t–RBMY)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Feb 28, 2019 | 4.64% | 2.97% | 17.21 | 3.49 | 7.75 |
| 2. | Mar 31, 2019 | -7.65% | 1.79% | 66.20 | 0.47 | -5.59 |
| 3. | Apr 30, 2019 | -1.82% | 3.93% | 5.35 | 7.98 | -6.54 |
| 4. | May 31, 2019 | -2.28% | -6.58% | 7.69 | 59.04 | 21.31 |
| 5. | Jun 30, 2019 | -0.04% | 6.89% | 0.29 | 33.49 | -3.09 |
| 6. | Jul 31, 2019 | -1.17% | 1.31% | 2.75 | 0.04 | -0.34 |
| 7. | Aug 31, 2019 | 8.24% | -1.81% | 60.08 | 8.50 | -22.60 |
| 8. | Sep 30, 2019 | 5.49% | 1.72% | 25.02 | 0.37 | 3.06 |
| 9. | Oct 31, 2019 | 13.94% | 2.04% | 180.96 | 0.88 | 12.61 |
| 10. | Nov 30, 2019 | -0.75% | 3.40% | 1.54 | 5.28 | -2.85 |
| 11. | Dec 31, 2019 | 12.73% | 2.86% | 149.88 | 3.07 | 21.46 |
| 12. | Jan 31, 2020 | -1.23% | -0.16% | 2.96 | 1.61 | 2.18 |
| 13. | Feb 29, 2020 | -6.18% | -8.41% | 44.48 | 90.57 | 63.47 |
| 14. | Mar 31, 2020 | -5.62% | -12.51% | 37.35 | 185.44 | 83.22 |
| 15. | Apr 30, 2020 | 9.90% | 12.68% | 88.61 | 134.06 | 108.99 |
| 16. | May 31, 2020 | -1.79% | 4.53% | 5.21 | 11.71 | -7.81 |
| 17. | Jun 30, 2020 | -1.54% | 1.84% | 4.12 | 0.54 | -1.49 |
| 18. | Jul 31, 2020 | 0.53% | 5.51% | 0.00 | 19.40 | 0.16 |
| 19. | Aug 31, 2020 | 6.03% | 7.01% | 30.74 | 34.82 | 32.72 |
| 20. | Sep 30, 2020 | -3.07% | -3.92% | 12.68 | 25.29 | 17.91 |
| 21. | Oct 31, 2020 | -2.31% | -2.77% | 7.81 | 15.00 | 10.83 |
| 22. | Nov 30, 2020 | 6.76% | 10.75% | 39.29 | 93.10 | 60.48 |
| 23. | Dec 31, 2020 | 0.19% | 3.71% | 0.09 | 6.79 | -0.78 |
| 24. | Jan 31, 2021 | -0.97% | -1.11% | 2.12 | 4.93 | 3.23 |
| 25. | Feb 28, 2021 | -0.16% | 2.61% | 0.43 | 2.26 | -0.98 |
| 26. | Mar 31, 2021 | 3.73% | 4.24% | 10.52 | 9.85 | 10.18 |
| 27. | Apr 30, 2021 | -1.12% | 5.24% | 2.61 | 17.11 | -6.68 |
| 28. | May 31, 2021 | 5.29% | 0.55% | 23.01 | 0.31 | -2.67 |
| 29. | Jun 30, 2021 | 1.67% | 2.22% | 1.40 | 1.24 | 1.32 |
| 30. | Jul 31, 2021 | 2.30% | 2.27% | 3.29 | 1.37 | 2.12 |
| 31. | Aug 31, 2021 | -1.49% | 2.90% | 3.91 | 3.22 | -3.55 |
| 32. | Sep 30, 2021 | -10.77% | -4.76% | 126.76 | 34.37 | 66.01 |
| 33. | Oct 31, 2021 | -1.30% | 6.91% | 3.21 | 33.74 | -10.40 |
| 34. | Nov 30, 2021 | -8.17% | -0.83% | 74.96 | 3.76 | 16.79 |
| 35. | Dec 31, 2021 | 16.26% | 4.36% | 248.68 | 10.60 | 51.34 |
| 36. | Jan 31, 2022 | 4.94% | -5.26% | 19.80 | 40.51 | -28.32 |
| 37. | Feb 28, 2022 | 5.83% | -3.14% | 28.47 | 17.99 | -22.63 |
| 38. | Mar 31, 2022 | 7.14% | 3.58% | 44.16 | 6.11 | 16.42 |
| 39. | Apr 30, 2022 | 3.07% | -8.80% | 6.64 | 98.04 | -25.52 |
| 40. | May 31, 2022 | 0.24% | 0.01% | 0.06 | 1.21 | 0.28 |
| 41. | Jun 30, 2022 | 2.77% | -8.39% | 5.20 | 90.21 | -21.66 |
| 42. | Jul 31, 2022 | -4.18% | 9.11% | 21.83 | 64.09 | -37.40 |
| 43. | Aug 31, 2022 | -8.63% | -4.24% | 83.24 | 28.62 | 48.81 |
| 44. | Sep 30, 2022 | 5.46% | -9.34% | 24.69 | 109.11 | -51.90 |
| 45. | Oct 31, 2022 | 9.73% | 7.99% | 85.45 | 47.34 | 63.60 |
| 46. | Nov 30, 2022 | 3.63% | 5.38% | 9.84 | 18.23 | 13.39 |
| 47. | Dec 31, 2022 | -10.38% | -5.90% | 118.07 | 49.04 | 76.10 |
| 48. | Jan 31, 2023 | 1.77% | 6.18% | 1.63 | 25.70 | 6.46 |
| 49. | Feb 28, 2023 | -5.08% | -2.61% | 31.02 | 13.82 | 20.70 |
| 50. | Mar 31, 2023 | 0.51% | 3.51% | 0.00 | 5.76 | 0.04 |
| 51. | Apr 30, 2023 | -2.84% | 1.46% | 11.10 | 0.13 | -1.19 |
| 52. | May 31, 2023 | -3.49% | 0.25% | 15.84 | 0.74 | 3.41 |
| 53. | Jun 30, 2023 | -0.76% | 4.71% | 1.56 | 13.02 | -4.51 |
| 54. | Jul 31, 2023 | -1.86% | 4.85% | 5.53 | 13.99 | -8.79 |
| 55. | Aug 31, 2023 | -0.87% | -1.77% | 1.84 | 8.28 | 3.91 |
| 56. | Sep 30, 2023 | -5.86% | -4.87% | 40.27 | 35.73 | 37.93 |
| 57. | Oct 31, 2023 | -10.23% | -2.20% | 115.01 | 10.92 | 35.43 |
| 58. | Nov 30, 2023 | -4.17% | 8.92% | 21.74 | 61.03 | -36.42 |
| 59. | Dec 31, 2023 | 3.91% | 4.42% | 11.69 | 11.00 | 11.34 |
| Total (Σ): | 1,995.90 | 1,634.30 | 621.26 | |||
Show all
VarianceBMY = Σ(RBMY,t–RBMY)2 ÷ (59 – 1)
= 1,995.90 ÷ (59 – 1)
= 34.41
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
CovarianceBMY, S&P 500 = Σ(RBMY,t–RBMY)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 621.26 ÷ (59 – 1)
= 10.71
Systematic Risk (β) Estimation
| VarianceBMY | 34.41 |
| VarianceS&P 500 | 28.18 |
| CovarianceBMY, S&P 500 | 10.71 |
| Correlation coefficientBMY, S&P 5001 | 0.34 |
| βBMY2 | 0.38 |
| αBMY3 | 0.07% |
Calculations
1 Correlation coefficientBMY, S&P 500
= CovarianceBMY, S&P 500 ÷ (Standard deviationBMY × Standard deviationS&P 500)
= 10.71 ÷ (5.87% × 5.31%)
= 0.34
2 βBMY
= CovarianceBMY, S&P 500 ÷ VarianceS&P 500
= 10.71 ÷ 28.18
= 0.38
3 αBMY
= AverageBMY – βBMY × AverageS&P 500
= 0.49% – 0.38 × 1.11%
= 0.07%
Expected Rate of Return
| Assumptions | ||
| Rate of return on LT Treasury Composite1 | RF | 4.65% |
| Expected rate of return on market portfolio2 | E(RM) | 13.79% |
| Systematic risk (β) of Bristol-Myers Squibb Co. common stock | βBMY | 0.38 |
| Expected rate of return on Bristol-Myers Squibb Co. common stock3 | E(RBMY) | 8.12% |
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(RBMY) = RF + βBMY [E(RM) – RF]
= 4.65% + 0.38 [13.79% – 4.65%]
= 8.12%