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, 2019 | $133.08 | 2,704.10 | ||||
| 1. | Feb 28, 2019 | $136.64 | $0.90 | 3.35% | 2,784.49 | 2.97% |
| 2. | Mar 31, 2019 | $139.79 | 2.31% | 2,834.40 | 1.79% | |
| 3. | Apr 30, 2019 | $141.20 | 1.01% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2023 | $154.66 | $1.19 | 5.06% | 4,567.80 | 8.92% |
| 59. | Dec 31, 2023 | $156.74 | 1.34% | 4,769.83 | 4.42% | |
| Average (R): | 0.63% | 1.11% | ||||
| Standard deviation: | 4.96% | 5.31% | ||||
| 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, 2019 | $133.08 | 2,704.10 | ||||
| 1. | Feb 28, 2019 | $136.64 | $0.90 | 3.35% | 2,784.49 | 2.97% |
| 2. | Mar 31, 2019 | $139.79 | 2.31% | 2,834.40 | 1.79% | |
| 3. | Apr 30, 2019 | $141.20 | 1.01% | 2,945.83 | 3.93% | |
| 4. | May 31, 2019 | $131.15 | $0.95 | -6.44% | 2,752.06 | -6.58% |
| 5. | Jun 30, 2019 | $139.28 | 6.20% | 2,941.76 | 6.89% | |
| 6. | Jul 31, 2019 | $130.22 | -6.50% | 2,980.38 | 1.31% | |
| 7. | Aug 31, 2019 | $128.36 | $0.95 | -0.70% | 2,926.46 | -1.81% |
| 8. | Sep 30, 2019 | $129.38 | 0.79% | 2,976.74 | 1.72% | |
| 9. | Oct 31, 2019 | $132.04 | 2.06% | 3,037.56 | 2.04% | |
| 10. | Nov 30, 2019 | $137.49 | $0.95 | 4.85% | 3,140.98 | 3.40% |
| 11. | Dec 31, 2019 | $145.87 | 6.09% | 3,230.78 | 2.86% | |
| 12. | Jan 31, 2020 | $148.87 | 2.06% | 3,225.52 | -0.16% | |
| 13. | Feb 29, 2020 | $134.48 | $0.95 | -9.03% | 2,954.22 | -8.41% |
| 14. | Mar 31, 2020 | $131.13 | -2.49% | 2,584.59 | -12.51% | |
| 15. | Apr 30, 2020 | $150.04 | 14.42% | 2,912.43 | 12.68% | |
| 16. | May 31, 2020 | $148.75 | $1.01 | -0.19% | 3,044.31 | 4.53% |
| 17. | Jun 30, 2020 | $140.63 | -5.46% | 3,100.29 | 1.84% | |
| 18. | Jul 31, 2020 | $145.76 | 3.65% | 3,271.12 | 5.51% | |
| 19. | Aug 31, 2020 | $153.41 | $1.01 | 5.94% | 3,500.31 | 7.01% |
| 20. | Sep 30, 2020 | $148.88 | -2.95% | 3,363.00 | -3.92% | |
| 21. | Oct 31, 2020 | $137.11 | -7.91% | 3,269.96 | -2.77% | |
| 22. | Nov 30, 2020 | $144.68 | $1.01 | 6.26% | 3,621.63 | 10.75% |
| 23. | Dec 31, 2020 | $157.38 | 8.78% | 3,756.07 | 3.71% | |
| 24. | Jan 31, 2021 | $163.13 | 3.65% | 3,714.24 | -1.11% | |
| 25. | Feb 28, 2021 | $158.46 | $1.01 | -2.24% | 3,811.15 | 2.61% |
| 26. | Mar 31, 2021 | $164.35 | 3.72% | 3,972.89 | 4.24% | |
| 27. | Apr 30, 2021 | $162.73 | -0.99% | 4,181.17 | 5.24% | |
| 28. | May 31, 2021 | $169.25 | $1.06 | 4.66% | 4,204.11 | 0.55% |
| 29. | Jun 30, 2021 | $164.74 | -2.66% | 4,297.50 | 2.22% | |
| 30. | Jul 31, 2021 | $172.20 | 4.53% | 4,395.26 | 2.27% | |
| 31. | Aug 31, 2021 | $173.13 | $1.06 | 1.16% | 4,522.68 | 2.90% |
| 32. | Sep 30, 2021 | $161.50 | -6.72% | 4,307.54 | -4.76% | |
| 33. | Oct 31, 2021 | $162.88 | 0.85% | 4,605.38 | 6.91% | |
| 34. | Nov 30, 2021 | $155.93 | $1.06 | -3.62% | 4,567.00 | -0.83% |
| 35. | Dec 31, 2021 | $171.07 | 9.71% | 4,766.18 | 4.36% | |
| 36. | Jan 31, 2022 | $172.29 | 0.71% | 4,515.55 | -5.26% | |
| 37. | Feb 28, 2022 | $164.57 | $1.06 | -3.87% | 4,373.94 | -3.14% |
| 38. | Mar 31, 2022 | $177.23 | 7.69% | 4,530.41 | 3.58% | |
| 39. | Apr 30, 2022 | $180.46 | 1.82% | 4,131.93 | -8.80% | |
| 40. | May 31, 2022 | $179.53 | $1.13 | 0.11% | 4,132.15 | 0.01% |
| 41. | Jun 30, 2022 | $177.51 | -1.13% | 3,785.38 | -8.39% | |
| 42. | Jul 31, 2022 | $174.52 | -1.68% | 4,130.29 | 9.11% | |
| 43. | Aug 31, 2022 | $161.34 | $1.13 | -6.90% | 3,955.00 | -4.24% |
| 44. | Sep 30, 2022 | $163.36 | 1.25% | 3,585.62 | -9.34% | |
| 45. | Oct 31, 2022 | $173.97 | 6.49% | 3,871.98 | 7.99% | |
| 46. | Nov 30, 2022 | $178.00 | $1.13 | 2.97% | 4,080.11 | 5.38% |
| 47. | Dec 31, 2022 | $176.65 | -0.76% | 3,839.50 | -5.90% | |
| 48. | Jan 31, 2023 | $163.42 | -7.49% | 4,076.60 | 6.18% | |
| 49. | Feb 28, 2023 | $153.26 | $1.13 | -5.53% | 3,970.15 | -2.61% |
| 50. | Mar 31, 2023 | $155.00 | 1.14% | 4,109.31 | 3.51% | |
| 51. | Apr 30, 2023 | $163.70 | 5.61% | 4,169.48 | 1.46% | |
| 52. | May 31, 2023 | $155.06 | $1.19 | -4.55% | 4,179.83 | 0.25% |
| 53. | Jun 30, 2023 | $165.52 | 6.75% | 4,376.86 | 4.71% | |
| 54. | Jul 31, 2023 | $167.53 | 1.21% | 4,588.96 | 4.85% | |
| 55. | Aug 31, 2023 | $161.68 | $1.19 | -2.78% | 4,507.66 | -1.77% |
| 56. | Sep 30, 2023 | $155.75 | -3.67% | 4,288.05 | -4.87% | |
| 57. | Oct 31, 2023 | $148.34 | -4.76% | 4,193.80 | -2.20% | |
| 58. | Nov 30, 2023 | $154.66 | $1.19 | 5.06% | 4,567.80 | 8.92% |
| 59. | Dec 31, 2023 | $156.74 | 1.34% | 4,769.83 | 4.42% | |
| Average (R): | 0.63% | 1.11% | ||||
| Standard deviation: | 4.96% | 5.31% | ||||
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of 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 28, 2019 | 3.35% | 2.97% | 7.40 | 3.49 | 5.08 |
| 2. | Mar 31, 2019 | 2.31% | 1.79% | 2.81 | 0.47 | 1.15 |
| 3. | Apr 30, 2019 | 1.01% | 3.93% | 0.14 | 7.98 | 1.07 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2023 | 5.06% | 8.92% | 19.65 | 61.03 | 34.63 |
| 59. | Dec 31, 2023 | 1.34% | 4.42% | 0.51 | 11.00 | 2.37 |
| Total (Σ): | 1,426.41 | 1,634.30 | 867.47 | |||
| 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 28, 2019 | 3.35% | 2.97% | 7.40 | 3.49 | 5.08 |
| 2. | Mar 31, 2019 | 2.31% | 1.79% | 2.81 | 0.47 | 1.15 |
| 3. | Apr 30, 2019 | 1.01% | 3.93% | 0.14 | 7.98 | 1.07 |
| 4. | May 31, 2019 | -6.44% | -6.58% | 50.06 | 59.04 | 54.36 |
| 5. | Jun 30, 2019 | 6.20% | 6.89% | 31.01 | 33.49 | 32.23 |
| 6. | Jul 31, 2019 | -6.50% | 1.31% | 50.91 | 0.04 | -1.48 |
| 7. | Aug 31, 2019 | -0.70% | -1.81% | 1.77 | 8.50 | 3.87 |
| 8. | Sep 30, 2019 | 0.79% | 1.72% | 0.03 | 0.37 | 0.10 |
| 9. | Oct 31, 2019 | 2.06% | 2.04% | 2.03 | 0.88 | 1.34 |
| 10. | Nov 30, 2019 | 4.85% | 3.40% | 17.78 | 5.28 | 9.69 |
| 11. | Dec 31, 2019 | 6.09% | 2.86% | 29.86 | 3.07 | 9.58 |
| 12. | Jan 31, 2020 | 2.06% | -0.16% | 2.03 | 1.61 | -1.81 |
| 13. | Feb 29, 2020 | -9.03% | -8.41% | 93.28 | 90.57 | 91.92 |
| 14. | Mar 31, 2020 | -2.49% | -12.51% | 9.74 | 185.44 | 42.51 |
| 15. | Apr 30, 2020 | 14.42% | 12.68% | 190.18 | 134.06 | 159.67 |
| 16. | May 31, 2020 | -0.19% | 4.53% | 0.67 | 11.71 | -2.80 |
| 17. | Jun 30, 2020 | -5.46% | 1.84% | 37.08 | 0.54 | -4.46 |
| 18. | Jul 31, 2020 | 3.65% | 5.51% | 9.11 | 19.40 | 13.29 |
| 19. | Aug 31, 2020 | 5.94% | 7.01% | 28.21 | 34.82 | 31.34 |
| 20. | Sep 30, 2020 | -2.95% | -3.92% | 12.84 | 25.29 | 18.02 |
| 21. | Oct 31, 2020 | -7.91% | -2.77% | 72.86 | 15.00 | 33.06 |
| 22. | Nov 30, 2020 | 6.26% | 10.75% | 31.67 | 93.10 | 54.30 |
| 23. | Dec 31, 2020 | 8.78% | 3.71% | 66.38 | 6.79 | 21.24 |
| 24. | Jan 31, 2021 | 3.65% | -1.11% | 9.14 | 4.93 | -6.71 |
| 25. | Feb 28, 2021 | -2.24% | 2.61% | 8.26 | 2.26 | -4.32 |
| 26. | Mar 31, 2021 | 3.72% | 4.24% | 9.53 | 9.85 | 9.69 |
| 27. | Apr 30, 2021 | -0.99% | 5.24% | 2.61 | 17.11 | -6.69 |
| 28. | May 31, 2021 | 4.66% | 0.55% | 16.22 | 0.31 | -2.24 |
| 29. | Jun 30, 2021 | -2.66% | 2.22% | 10.86 | 1.24 | -3.68 |
| 30. | Jul 31, 2021 | 4.53% | 2.27% | 15.19 | 1.37 | 4.56 |
| 31. | Aug 31, 2021 | 1.16% | 2.90% | 0.28 | 3.22 | 0.94 |
| 32. | Sep 30, 2021 | -6.72% | -4.76% | 53.99 | 34.37 | 43.08 |
| 33. | Oct 31, 2021 | 0.85% | 6.91% | 0.05 | 33.74 | 1.30 |
| 34. | Nov 30, 2021 | -3.62% | -0.83% | 18.03 | 3.76 | 8.24 |
| 35. | Dec 31, 2021 | 9.71% | 4.36% | 82.43 | 10.60 | 29.56 |
| 36. | Jan 31, 2022 | 0.71% | -5.26% | 0.01 | 40.51 | -0.53 |
| 37. | Feb 28, 2022 | -3.87% | -3.14% | 20.21 | 17.99 | 19.07 |
| 38. | Mar 31, 2022 | 7.69% | 3.58% | 49.88 | 6.11 | 17.45 |
| 39. | Apr 30, 2022 | 1.82% | -8.80% | 1.42 | 98.04 | -11.80 |
| 40. | May 31, 2022 | 0.11% | 0.01% | 0.27 | 1.21 | 0.57 |
| 41. | Jun 30, 2022 | -1.13% | -8.39% | 3.08 | 90.21 | 16.67 |
| 42. | Jul 31, 2022 | -1.68% | 9.11% | 5.36 | 64.09 | -18.53 |
| 43. | Aug 31, 2022 | -6.90% | -4.24% | 56.78 | 28.62 | 40.31 |
| 44. | Sep 30, 2022 | 1.25% | -9.34% | 0.39 | 109.11 | -6.49 |
| 45. | Oct 31, 2022 | 6.49% | 7.99% | 34.39 | 47.34 | 40.35 |
| 46. | Nov 30, 2022 | 2.97% | 5.38% | 5.46 | 18.23 | 9.97 |
| 47. | Dec 31, 2022 | -0.76% | -5.90% | 1.93 | 49.04 | 9.73 |
| 48. | Jan 31, 2023 | -7.49% | 6.18% | 65.93 | 25.70 | -41.16 |
| 49. | Feb 28, 2023 | -5.53% | -2.61% | 37.90 | 13.82 | 22.88 |
| 50. | Mar 31, 2023 | 1.14% | 3.51% | 0.25 | 5.76 | 1.21 |
| 51. | Apr 30, 2023 | 5.61% | 1.46% | 24.83 | 0.13 | 1.79 |
| 52. | May 31, 2023 | -4.55% | 0.25% | 26.85 | 0.74 | 4.44 |
| 53. | Jun 30, 2023 | 6.75% | 4.71% | 37.40 | 13.02 | 22.06 |
| 54. | Jul 31, 2023 | 1.21% | 4.85% | 0.34 | 13.99 | 2.18 |
| 55. | Aug 31, 2023 | -2.78% | -1.77% | 11.64 | 8.28 | 9.82 |
| 56. | Sep 30, 2023 | -3.67% | -4.87% | 18.47 | 35.73 | 25.69 |
| 57. | Oct 31, 2023 | -4.76% | -2.20% | 29.03 | 10.92 | 17.80 |
| 58. | Nov 30, 2023 | 5.06% | 8.92% | 19.65 | 61.03 | 34.63 |
| 59. | Dec 31, 2023 | 1.34% | 4.42% | 0.51 | 11.00 | 2.37 |
| Total (Σ): | 1,426.41 | 1,634.30 | 867.47 | |||
Show all
VarianceJNJ = Σ(RJNJ,t–RJNJ)2 ÷ (59 – 1)
= 1,426.41 ÷ (59 – 1)
= 24.59
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
CovarianceJNJ, S&P 500 = Σ(RJNJ,t–RJNJ)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 867.47 ÷ (59 – 1)
= 14.96
Systematic Risk (β) Estimation
| VarianceJNJ | 24.59 |
| VarianceS&P 500 | 28.18 |
| CovarianceJNJ, S&P 500 | 14.96 |
| Correlation coefficientJNJ, S&P 5001 | 0.57 |
| βJNJ2 | 0.53 |
| αJNJ3 | 0.04% |
Calculations
1 Correlation coefficientJNJ, S&P 500
= CovarianceJNJ, S&P 500 ÷ (Standard deviationJNJ × Standard deviationS&P 500)
= 14.96 ÷ (4.96% × 5.31%)
= 0.57
2 βJNJ
= CovarianceJNJ, S&P 500 ÷ VarianceS&P 500
= 14.96 ÷ 28.18
= 0.53
3 αJNJ
= AverageJNJ – βJNJ × AverageS&P 500
= 0.63% – 0.53 × 1.11%
= 0.04%
Expected Rate of Return
| Assumptions | ||
| Rate of return on LT Treasury Composite1 | RF | 4.90% |
| Expected rate of return on market portfolio2 | E(RM) | 13.86% |
| Systematic risk (β) of Johnson & Johnson common stock | βJNJ | 0.53 |
| Expected rate of return on Johnson & Johnson common stock3 | E(RJNJ) | 9.66% |
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]
= 4.90% + 0.53 [13.86% – 4.90%]
= 9.66%