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 Johnson & Johnson common stock.
Rates of Return
Johnson & Johnson, monthly rates of return
| Johnson & Johnson (JNJ) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceJNJ,t1 | DividendJNJ,t1 | RJNJ,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Jan 31, 2020 | $148.87 | 3,225.52 | ||||
| 1. | Feb 29, 2020 | $134.48 | $0.95 | -9.03% | 2,954.22 | -8.41% |
| 2. | Mar 31, 2020 | $131.13 | -2.49% | 2,584.59 | -12.51% | |
| 3. | Apr 30, 2020 | $150.04 | 14.42% | 2,912.43 | 12.68% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2024 | $155.01 | $1.24 | -2.26% | 6,032.38 | 5.73% |
| 59. | Dec 31, 2024 | $144.62 | -6.70% | 5,881.63 | -2.50% | |
| Average (R): | 0.31% | 1.16% | ||||
| Standard deviation: | 5.05% | 5.28% | ||||
| Johnson & Johnson (JNJ) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceJNJ,t1 | DividendJNJ,t1 | RJNJ,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Jan 31, 2020 | $148.87 | 3,225.52 | ||||
| 1. | Feb 29, 2020 | $134.48 | $0.95 | -9.03% | 2,954.22 | -8.41% |
| 2. | Mar 31, 2020 | $131.13 | -2.49% | 2,584.59 | -12.51% | |
| 3. | Apr 30, 2020 | $150.04 | 14.42% | 2,912.43 | 12.68% | |
| 4. | May 31, 2020 | $148.75 | $1.01 | -0.19% | 3,044.31 | 4.53% |
| 5. | Jun 30, 2020 | $140.63 | -5.46% | 3,100.29 | 1.84% | |
| 6. | Jul 31, 2020 | $145.76 | 3.65% | 3,271.12 | 5.51% | |
| 7. | Aug 31, 2020 | $153.41 | $1.01 | 5.94% | 3,500.31 | 7.01% |
| 8. | Sep 30, 2020 | $148.88 | -2.95% | 3,363.00 | -3.92% | |
| 9. | Oct 31, 2020 | $137.11 | -7.91% | 3,269.96 | -2.77% | |
| 10. | Nov 30, 2020 | $144.68 | $1.01 | 6.26% | 3,621.63 | 10.75% |
| 11. | Dec 31, 2020 | $157.38 | 8.78% | 3,756.07 | 3.71% | |
| 12. | Jan 31, 2021 | $163.13 | 3.65% | 3,714.24 | -1.11% | |
| 13. | Feb 28, 2021 | $158.46 | $1.01 | -2.24% | 3,811.15 | 2.61% |
| 14. | Mar 31, 2021 | $164.35 | 3.72% | 3,972.89 | 4.24% | |
| 15. | Apr 30, 2021 | $162.73 | -0.99% | 4,181.17 | 5.24% | |
| 16. | May 31, 2021 | $169.25 | $1.06 | 4.66% | 4,204.11 | 0.55% |
| 17. | Jun 30, 2021 | $164.74 | -2.66% | 4,297.50 | 2.22% | |
| 18. | Jul 31, 2021 | $172.20 | 4.53% | 4,395.26 | 2.27% | |
| 19. | Aug 31, 2021 | $173.13 | $1.06 | 1.16% | 4,522.68 | 2.90% |
| 20. | Sep 30, 2021 | $161.50 | -6.72% | 4,307.54 | -4.76% | |
| 21. | Oct 31, 2021 | $162.88 | 0.85% | 4,605.38 | 6.91% | |
| 22. | Nov 30, 2021 | $155.93 | $1.06 | -3.62% | 4,567.00 | -0.83% |
| 23. | Dec 31, 2021 | $171.07 | 9.71% | 4,766.18 | 4.36% | |
| 24. | Jan 31, 2022 | $172.29 | 0.71% | 4,515.55 | -5.26% | |
| 25. | Feb 28, 2022 | $164.57 | $1.06 | -3.87% | 4,373.94 | -3.14% |
| 26. | Mar 31, 2022 | $177.23 | 7.69% | 4,530.41 | 3.58% | |
| 27. | Apr 30, 2022 | $180.46 | 1.82% | 4,131.93 | -8.80% | |
| 28. | May 31, 2022 | $179.53 | $1.13 | 0.11% | 4,132.15 | 0.01% |
| 29. | Jun 30, 2022 | $177.51 | -1.13% | 3,785.38 | -8.39% | |
| 30. | Jul 31, 2022 | $174.52 | -1.68% | 4,130.29 | 9.11% | |
| 31. | Aug 31, 2022 | $161.34 | $1.13 | -6.90% | 3,955.00 | -4.24% |
| 32. | Sep 30, 2022 | $163.36 | 1.25% | 3,585.62 | -9.34% | |
| 33. | Oct 31, 2022 | $173.97 | 6.49% | 3,871.98 | 7.99% | |
| 34. | Nov 30, 2022 | $178.00 | $1.13 | 2.97% | 4,080.11 | 5.38% |
| 35. | Dec 31, 2022 | $176.65 | -0.76% | 3,839.50 | -5.90% | |
| 36. | Jan 31, 2023 | $163.42 | -7.49% | 4,076.60 | 6.18% | |
| 37. | Feb 28, 2023 | $153.26 | $1.13 | -5.53% | 3,970.15 | -2.61% |
| 38. | Mar 31, 2023 | $155.00 | 1.14% | 4,109.31 | 3.51% | |
| 39. | Apr 30, 2023 | $163.70 | 5.61% | 4,169.48 | 1.46% | |
| 40. | May 31, 2023 | $155.06 | $1.19 | -4.55% | 4,179.83 | 0.25% |
| 41. | Jun 30, 2023 | $165.52 | 6.75% | 4,376.86 | 4.71% | |
| 42. | Jul 31, 2023 | $167.53 | 1.21% | 4,588.96 | 4.85% | |
| 43. | Aug 31, 2023 | $161.68 | $1.19 | -2.78% | 4,507.66 | -1.77% |
| 44. | Sep 30, 2023 | $155.75 | -3.67% | 4,288.05 | -4.87% | |
| 45. | Oct 31, 2023 | $148.34 | -4.76% | 4,193.80 | -2.20% | |
| 46. | Nov 30, 2023 | $154.66 | $1.19 | 5.06% | 4,567.80 | 8.92% |
| 47. | Dec 31, 2023 | $156.74 | 1.34% | 4,769.83 | 4.42% | |
| 48. | Jan 31, 2024 | $158.90 | 1.38% | 4,845.65 | 1.59% | |
| 49. | Feb 29, 2024 | $161.38 | $1.19 | 2.31% | 5,096.27 | 5.17% |
| 50. | Mar 31, 2024 | $158.19 | -1.98% | 5,254.35 | 3.10% | |
| 51. | Apr 30, 2024 | $144.59 | -8.60% | 5,035.69 | -4.16% | |
| 52. | May 31, 2024 | $146.67 | $1.24 | 2.30% | 5,277.51 | 4.80% |
| 53. | Jun 30, 2024 | $146.16 | -0.35% | 5,460.48 | 3.47% | |
| 54. | Jul 31, 2024 | $157.85 | 8.00% | 5,522.30 | 1.13% | |
| 55. | Aug 31, 2024 | $165.86 | $1.24 | 5.86% | 5,648.40 | 2.28% |
| 56. | Sep 30, 2024 | $162.06 | -2.29% | 5,762.48 | 2.02% | |
| 57. | Oct 31, 2024 | $159.86 | -1.36% | 5,705.45 | -0.99% | |
| 58. | Nov 30, 2024 | $155.01 | $1.24 | -2.26% | 6,032.38 | 5.73% |
| 59. | Dec 31, 2024 | $144.62 | -6.70% | 5,881.63 | -2.50% | |
| Average (R): | 0.31% | 1.16% | ||||
| Standard deviation: | 5.05% | 5.28% | ||||
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of JNJ during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
Johnson & Johnson, calculation of variance and covariance of returns
| t | Date | RJNJ,t | RS&P 500,t | (RJNJ,t–RJNJ)2 | (RS&P 500,t–RS&P 500)2 | (RJNJ,t–RJNJ)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Feb 29, 2020 | -9.03% | -8.41% | 87.25 | 91.63 | 89.41 |
| 2. | Mar 31, 2020 | -2.49% | -12.51% | 7.86 | 186.96 | 38.33 |
| 3. | Apr 30, 2020 | 14.42% | 12.68% | 199.04 | 132.78 | 162.57 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2024 | -2.26% | 5.73% | 6.61 | 20.87 | -11.75 |
| 59. | Dec 31, 2024 | -6.70% | -2.50% | 49.21 | 13.40 | 25.68 |
| Total (Σ): | 1,479.91 | 1,618.62 | 828.69 | |||
| t | Date | RJNJ,t | RS&P 500,t | (RJNJ,t–RJNJ)2 | (RS&P 500,t–RS&P 500)2 | (RJNJ,t–RJNJ)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Feb 29, 2020 | -9.03% | -8.41% | 87.25 | 91.63 | 89.41 |
| 2. | Mar 31, 2020 | -2.49% | -12.51% | 7.86 | 186.96 | 38.33 |
| 3. | Apr 30, 2020 | 14.42% | 12.68% | 199.04 | 132.78 | 162.57 |
| 4. | May 31, 2020 | -0.19% | 4.53% | 0.25 | 11.34 | -1.68 |
| 5. | Jun 30, 2020 | -5.46% | 1.84% | 33.31 | 0.46 | -3.91 |
| 6. | Jul 31, 2020 | 3.65% | 5.51% | 11.12 | 18.91 | 14.50 |
| 7. | Aug 31, 2020 | 5.94% | 7.01% | 31.68 | 34.17 | 32.90 |
| 8. | Sep 30, 2020 | -2.95% | -3.92% | 10.66 | 25.85 | 16.60 |
| 9. | Oct 31, 2020 | -7.91% | -2.77% | 67.54 | 15.43 | 32.28 |
| 10. | Nov 30, 2020 | 6.26% | 10.75% | 35.35 | 92.03 | 57.03 |
| 11. | Dec 31, 2020 | 8.78% | 3.71% | 71.66 | 6.51 | 21.59 |
| 12. | Jan 31, 2021 | 3.65% | -1.11% | 11.16 | 5.18 | -7.60 |
| 13. | Feb 28, 2021 | -2.24% | 2.61% | 6.53 | 2.10 | -3.70 |
| 14. | Mar 31, 2021 | 3.72% | 4.24% | 11.59 | 9.50 | 10.49 |
| 15. | Apr 30, 2021 | -0.99% | 5.24% | 1.69 | 16.66 | -5.30 |
| 16. | May 31, 2021 | 4.66% | 0.55% | 18.88 | 0.38 | -2.66 |
| 17. | Jun 30, 2021 | -2.66% | 2.22% | 8.86 | 1.12 | -3.16 |
| 18. | Jul 31, 2021 | 4.53% | 2.27% | 17.77 | 1.24 | 4.69 |
| 19. | Aug 31, 2021 | 1.16% | 2.90% | 0.71 | 3.02 | 1.47 |
| 20. | Sep 30, 2021 | -6.72% | -4.76% | 49.42 | 35.02 | 41.60 |
| 21. | Oct 31, 2021 | 0.85% | 6.91% | 0.29 | 33.10 | 3.12 |
| 22. | Nov 30, 2021 | -3.62% | -0.83% | 15.43 | 3.98 | 7.84 |
| 23. | Dec 31, 2021 | 9.71% | 4.36% | 88.30 | 10.24 | 30.07 |
| 24. | Jan 31, 2022 | 0.71% | -5.26% | 0.16 | 41.21 | -2.57 |
| 25. | Feb 28, 2022 | -3.87% | -3.14% | 17.46 | 18.47 | 17.95 |
| 26. | Mar 31, 2022 | 7.69% | 3.58% | 54.47 | 5.84 | 17.83 |
| 27. | Apr 30, 2022 | 1.82% | -8.80% | 2.28 | 99.14 | -15.03 |
| 28. | May 31, 2022 | 0.11% | 0.01% | 0.04 | 1.34 | 0.23 |
| 29. | Jun 30, 2022 | -1.13% | -8.39% | 2.07 | 91.26 | 13.73 |
| 30. | Jul 31, 2022 | -1.68% | 9.11% | 3.99 | 63.21 | -15.88 |
| 31. | Aug 31, 2022 | -6.90% | -4.24% | 52.09 | 29.22 | 39.01 |
| 32. | Sep 30, 2022 | 1.25% | -9.34% | 0.88 | 110.27 | -9.87 |
| 33. | Oct 31, 2022 | 6.49% | 7.99% | 38.22 | 46.58 | 42.19 |
| 34. | Nov 30, 2022 | 2.97% | 5.38% | 7.04 | 17.76 | 11.18 |
| 35. | Dec 31, 2022 | -0.76% | -5.90% | 1.15 | 49.82 | 7.56 |
| 36. | Jan 31, 2023 | -7.49% | 6.18% | 60.87 | 25.14 | -39.12 |
| 37. | Feb 28, 2023 | -5.53% | -2.61% | 34.08 | 14.23 | 22.02 |
| 38. | Mar 31, 2023 | 1.14% | 3.51% | 0.68 | 5.49 | 1.93 |
| 39. | Apr 30, 2023 | 5.61% | 1.46% | 28.09 | 0.09 | 1.61 |
| 40. | May 31, 2023 | -4.55% | 0.25% | 23.65 | 0.83 | 4.44 |
| 41. | Jun 30, 2023 | 6.75% | 4.71% | 41.39 | 12.62 | 22.85 |
| 42. | Jul 31, 2023 | 1.21% | 4.85% | 0.81 | 13.58 | 3.32 |
| 43. | Aug 31, 2023 | -2.78% | -1.77% | 9.57 | 8.60 | 9.07 |
| 44. | Sep 30, 2023 | -3.67% | -4.87% | 15.84 | 36.40 | 24.01 |
| 45. | Oct 31, 2023 | -4.76% | -2.20% | 25.71 | 11.28 | 17.03 |
| 46. | Nov 30, 2023 | 5.06% | 8.92% | 22.56 | 60.17 | 36.85 |
| 47. | Dec 31, 2023 | 1.34% | 4.42% | 1.07 | 10.64 | 3.37 |
| 48. | Jan 31, 2024 | 1.38% | 1.59% | 1.14 | 0.18 | 0.46 |
| 49. | Feb 29, 2024 | 2.31% | 5.17% | 3.99 | 16.09 | 8.01 |
| 50. | Mar 31, 2024 | -1.98% | 3.10% | 5.24 | 3.77 | -4.44 |
| 51. | Apr 30, 2024 | -8.60% | -4.16% | 79.38 | 28.33 | 47.42 |
| 52. | May 31, 2024 | 2.30% | 4.80% | 3.93 | 13.26 | 7.22 |
| 53. | Jun 30, 2024 | -0.35% | 3.47% | 0.44 | 5.32 | -1.52 |
| 54. | Jul 31, 2024 | 8.00% | 1.13% | 59.07 | 0.00 | -0.22 |
| 55. | Aug 31, 2024 | 5.86% | 2.28% | 30.77 | 1.26 | 6.23 |
| 56. | Sep 30, 2024 | -2.29% | 2.02% | 6.78 | 0.74 | -2.23 |
| 57. | Oct 31, 2024 | -1.36% | -0.99% | 2.79 | 4.63 | 3.59 |
| 58. | Nov 30, 2024 | -2.26% | 5.73% | 6.61 | 20.87 | -11.75 |
| 59. | Dec 31, 2024 | -6.70% | -2.50% | 49.21 | 13.40 | 25.68 |
| Total (Σ): | 1,479.91 | 1,618.62 | 828.69 | |||
Show all
VarianceJNJ = Σ(RJNJ,t–RJNJ)2 ÷ (59 – 1)
= 1,479.91 ÷ (59 – 1)
= 25.52
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91
CovarianceJNJ, S&P 500 = Σ(RJNJ,t–RJNJ)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 828.69 ÷ (59 – 1)
= 14.29
Systematic Risk (β) Estimation
| VarianceJNJ | 25.52 |
| VarianceS&P 500 | 27.91 |
| CovarianceJNJ, S&P 500 | 14.29 |
| Correlation coefficientJNJ, S&P 5001 | 0.54 |
| βJNJ2 | 0.51 |
| αJNJ3 | -0.28% |
Calculations
1 Correlation coefficientJNJ, S&P 500
= CovarianceJNJ, S&P 500 ÷ (Standard deviationJNJ × Standard deviationS&P 500)
= 14.29 ÷ (5.05% × 5.28%)
= 0.54
2 βJNJ
= CovarianceJNJ, S&P 500 ÷ VarianceS&P 500
= 14.29 ÷ 27.91
= 0.51
3 αJNJ
= AverageJNJ – βJNJ × AverageS&P 500
= 0.31% – 0.51 × 1.16%
= -0.28%
Expected Rate of Return
| Assumptions | ||
| Rate of return on LT Treasury Composite1 | RF | 4.78% |
| Expected rate of return on market portfolio2 | E(RM) | 14.43% |
| Systematic risk (β) of Johnson & Johnson common stock | βJNJ | 0.51 |
| Expected rate of return on Johnson & Johnson common stock3 | E(RJNJ) | 9.72% |
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(RJNJ) = RF + βJNJ [E(RM) – RF]
= 4.78% + 0.51 [14.43% – 4.78%]
= 9.72%