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 Apple Inc. common stock.
Rates of Return
Apple Inc., monthly rates of return
| Apple Inc. (AAPL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceAAPL,t1 | DividendAAPL,t1 | RAAPL,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Oct 31, 2017 | $42.26 | 2,575.26 | ||||
| 1. | Nov 30, 2017 | $42.96 | $0.1575 | 2.03% | 2,647.58 | 2.81% |
| 2. | Dec 31, 2017 | $42.31 | -1.51% | 2,673.61 | 0.98% | |
| 3. | Jan 31, 2018 | $41.86 | -1.06% | 2,823.81 | 5.62% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | Aug 31, 2023 | $187.87 | $0.24 | -4.25% | 4,507.66 | -1.77% |
| 71. | Sep 30, 2023 | $171.21 | -8.87% | 4,288.05 | -4.87% | |
| Average (R): | 2.46% | 0.85% | ||||
| Standard deviation: | 8.90% | 5.13% | ||||
| Apple Inc. (AAPL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceAAPL,t1 | DividendAAPL,t1 | RAAPL,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Oct 31, 2017 | $42.26 | 2,575.26 | ||||
| 1. | Nov 30, 2017 | $42.96 | $0.1575 | 2.03% | 2,647.58 | 2.81% |
| 2. | Dec 31, 2017 | $42.31 | -1.51% | 2,673.61 | 0.98% | |
| 3. | Jan 31, 2018 | $41.86 | -1.06% | 2,823.81 | 5.62% | |
| 4. | Feb 28, 2018 | $44.53 | $0.1575 | 6.75% | 2,713.83 | -3.89% |
| 5. | Mar 31, 2018 | $41.95 | -5.79% | 2,640.87 | -2.69% | |
| 6. | Apr 30, 2018 | $41.32 | -1.50% | 2,648.05 | 0.27% | |
| 7. | May 31, 2018 | $46.72 | $0.1825 | 13.51% | 2,705.27 | 2.16% |
| 8. | Jun 30, 2018 | $46.28 | -0.94% | 2,718.37 | 0.48% | |
| 9. | Jul 31, 2018 | $47.57 | 2.79% | 2,816.29 | 3.60% | |
| 10. | Aug 31, 2018 | $56.91 | $0.1825 | 20.02% | 2,901.52 | 3.03% |
| 11. | Sep 30, 2018 | $56.44 | -0.83% | 2,913.98 | 0.43% | |
| 12. | Oct 31, 2018 | $54.72 | -3.05% | 2,711.74 | -6.94% | |
| 13. | Nov 30, 2018 | $44.65 | $0.1825 | -18.07% | 2,760.17 | 1.79% |
| 14. | Dec 31, 2018 | $39.44 | -11.67% | 2,506.85 | -9.18% | |
| 15. | Jan 31, 2019 | $41.61 | 5.50% | 2,704.10 | 7.87% | |
| 16. | Feb 28, 2019 | $43.29 | $0.1825 | 4.48% | 2,784.49 | 2.97% |
| 17. | Mar 31, 2019 | $47.49 | 9.70% | 2,834.40 | 1.79% | |
| 18. | Apr 30, 2019 | $50.17 | 5.64% | 2,945.83 | 3.93% | |
| 19. | May 31, 2019 | $43.77 | $0.1925 | -12.37% | 2,752.06 | -6.58% |
| 20. | Jun 30, 2019 | $49.48 | 13.05% | 2,941.76 | 6.89% | |
| 21. | Jul 31, 2019 | $53.26 | 7.64% | 2,980.38 | 1.31% | |
| 22. | Aug 31, 2019 | $52.19 | $0.1925 | -1.65% | 2,926.46 | -1.81% |
| 23. | Sep 30, 2019 | $55.99 | 7.28% | 2,976.74 | 1.72% | |
| 24. | Oct 31, 2019 | $62.19 | 11.07% | 3,037.56 | 2.04% | |
| 25. | Nov 30, 2019 | $66.81 | $0.1925 | 7.74% | 3,140.98 | 3.40% |
| 26. | Dec 31, 2019 | $73.41 | 9.88% | 3,230.78 | 2.86% | |
| 27. | Jan 31, 2020 | $77.38 | 5.41% | 3,225.52 | -0.16% | |
| 28. | Feb 29, 2020 | $68.34 | $0.1925 | -11.43% | 2,954.22 | -8.41% |
| 29. | Mar 31, 2020 | $63.57 | -6.98% | 2,584.59 | -12.51% | |
| 30. | Apr 30, 2020 | $73.45 | 15.54% | 2,912.43 | 12.68% | |
| 31. | May 31, 2020 | $79.49 | $0.205 | 8.50% | 3,044.31 | 4.53% |
| 32. | Jun 30, 2020 | $91.20 | 14.73% | 3,100.29 | 1.84% | |
| 33. | Jul 31, 2020 | $106.26 | 16.51% | 3,271.12 | 5.51% | |
| 34. | Aug 31, 2020 | $129.04 | $0.205 | 21.63% | 3,500.31 | 7.01% |
| 35. | Sep 30, 2020 | $115.81 | -10.25% | 3,363.00 | -3.92% | |
| 36. | Oct 31, 2020 | $108.86 | -6.00% | 3,269.96 | -2.77% | |
| 37. | Nov 30, 2020 | $119.05 | $0.205 | 9.55% | 3,621.63 | 10.75% |
| 38. | Dec 31, 2020 | $132.69 | 11.46% | 3,756.07 | 3.71% | |
| 39. | Jan 31, 2021 | $131.96 | -0.55% | 3,714.24 | -1.11% | |
| 40. | Feb 28, 2021 | $121.26 | $0.205 | -7.95% | 3,811.15 | 2.61% |
| 41. | Mar 31, 2021 | $122.15 | 0.73% | 3,972.89 | 4.24% | |
| 42. | Apr 30, 2021 | $131.46 | 7.62% | 4,181.17 | 5.24% | |
| 43. | May 31, 2021 | $124.61 | $0.22 | -5.04% | 4,204.11 | 0.55% |
| 44. | Jun 30, 2021 | $136.96 | 9.91% | 4,297.50 | 2.22% | |
| 45. | Jul 31, 2021 | $145.86 | 6.50% | 4,395.26 | 2.27% | |
| 46. | Aug 31, 2021 | $151.83 | $0.22 | 4.24% | 4,522.68 | 2.90% |
| 47. | Sep 30, 2021 | $141.50 | -6.80% | 4,307.54 | -4.76% | |
| 48. | Oct 31, 2021 | $149.80 | 5.87% | 4,605.38 | 6.91% | |
| 49. | Nov 30, 2021 | $165.30 | $0.22 | 10.49% | 4,567.00 | -0.83% |
| 50. | Dec 31, 2021 | $177.57 | 7.42% | 4,766.18 | 4.36% | |
| 51. | Jan 31, 2022 | $174.78 | -1.57% | 4,515.55 | -5.26% | |
| 52. | Feb 28, 2022 | $165.12 | $0.22 | -5.40% | 4,373.94 | -3.14% |
| 53. | Mar 31, 2022 | $174.61 | 5.75% | 4,530.41 | 3.58% | |
| 54. | Apr 30, 2022 | $157.65 | -9.71% | 4,131.93 | -8.80% | |
| 55. | May 31, 2022 | $148.84 | $0.23 | -5.44% | 4,132.15 | 0.01% |
| 56. | Jun 30, 2022 | $136.72 | -8.14% | 3,785.38 | -8.39% | |
| 57. | Jul 31, 2022 | $162.51 | 18.86% | 4,130.29 | 9.11% | |
| 58. | Aug 31, 2022 | $157.22 | $0.23 | -3.11% | 3,955.00 | -4.24% |
| 59. | Sep 30, 2022 | $138.20 | -12.10% | 3,585.62 | -9.34% | |
| 60. | Oct 31, 2022 | $153.34 | 10.96% | 3,871.98 | 7.99% | |
| 61. | Nov 30, 2022 | $148.03 | $0.23 | -3.31% | 4,080.11 | 5.38% |
| 62. | Dec 31, 2022 | $129.93 | -12.23% | 3,839.50 | -5.90% | |
| 63. | Jan 31, 2023 | $144.29 | 11.05% | 4,076.60 | 6.18% | |
| 64. | Feb 28, 2023 | $147.41 | $0.23 | 2.32% | 3,970.15 | -2.61% |
| 65. | Mar 31, 2023 | $164.90 | 11.86% | 4,109.31 | 3.51% | |
| 66. | Apr 30, 2023 | $169.68 | 2.90% | 4,169.48 | 1.46% | |
| 67. | May 31, 2023 | $177.25 | $0.24 | 4.60% | 4,179.83 | 0.25% |
| 68. | Jun 30, 2023 | $193.97 | 9.43% | 4,376.86 | 4.71% | |
| 69. | Jul 31, 2023 | $196.45 | 1.28% | 4,588.96 | 4.85% | |
| 70. | Aug 31, 2023 | $187.87 | $0.24 | -4.25% | 4,507.66 | -1.77% |
| 71. | Sep 30, 2023 | $171.21 | -8.87% | 4,288.05 | -4.87% | |
| Average (R): | 2.46% | 0.85% | ||||
| Standard deviation: | 8.90% | 5.13% | ||||
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of AAPL during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
Apple Inc., calculation of variance and covariance of returns
| t | Date | RAAPL,t | RS&P 500,t | (RAAPL,t–RAAPL)2 | (RS&P 500,t–RS&P 500)2 | (RAAPL,t–RAAPL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Nov 30, 2017 | 2.03% | 2.81% | 0.19 | 3.83 | -0.84 |
| 2. | Dec 31, 2017 | -1.51% | 0.98% | 15.78 | 0.02 | -0.52 |
| 3. | Jan 31, 2018 | -1.06% | 5.62% | 12.41 | 22.72 | -16.79 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | Aug 31, 2023 | -4.25% | -1.77% | 44.95 | 6.88 | 17.59 |
| 71. | Sep 30, 2023 | -8.87% | -4.87% | 128.31 | 32.75 | 64.83 |
| Total (Σ): | 5,545.99 | 1,838.69 | 2,309.32 | |||
| t | Date | RAAPL,t | RS&P 500,t | (RAAPL,t–RAAPL)2 | (RS&P 500,t–RS&P 500)2 | (RAAPL,t–RAAPL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Nov 30, 2017 | 2.03% | 2.81% | 0.19 | 3.83 | -0.84 |
| 2. | Dec 31, 2017 | -1.51% | 0.98% | 15.78 | 0.02 | -0.52 |
| 3. | Jan 31, 2018 | -1.06% | 5.62% | 12.41 | 22.72 | -16.79 |
| 4. | Feb 28, 2018 | 6.75% | -3.89% | 18.45 | 22.52 | -20.38 |
| 5. | Mar 31, 2018 | -5.79% | -2.69% | 68.12 | 12.53 | 29.21 |
| 6. | Apr 30, 2018 | -1.50% | 0.27% | 15.69 | 0.34 | 2.30 |
| 7. | May 31, 2018 | 13.51% | 2.16% | 122.12 | 1.71 | 14.47 |
| 8. | Jun 30, 2018 | -0.94% | 0.48% | 11.57 | 0.13 | 1.25 |
| 9. | Jul 31, 2018 | 2.79% | 3.60% | 0.11 | 7.57 | 0.90 |
| 10. | Aug 31, 2018 | 20.02% | 3.03% | 308.30 | 4.73 | 38.19 |
| 11. | Sep 30, 2018 | -0.83% | 0.43% | 10.79 | 0.18 | 1.39 |
| 12. | Oct 31, 2018 | -3.05% | -6.94% | 30.33 | 60.71 | 42.91 |
| 13. | Nov 30, 2018 | -18.07% | 1.79% | 421.43 | 0.87 | -19.19 |
| 14. | Dec 31, 2018 | -11.67% | -9.18% | 199.60 | 100.58 | 141.69 |
| 15. | Jan 31, 2019 | 5.50% | 7.87% | 9.26 | 49.24 | 21.35 |
| 16. | Feb 28, 2019 | 4.48% | 2.97% | 4.07 | 4.50 | 4.28 |
| 17. | Mar 31, 2019 | 9.70% | 1.79% | 52.45 | 0.89 | 6.82 |
| 18. | Apr 30, 2019 | 5.64% | 3.93% | 10.14 | 9.49 | 9.81 |
| 19. | May 31, 2019 | -12.37% | -6.58% | 220.00 | 55.19 | 110.19 |
| 20. | Jun 30, 2019 | 13.05% | 6.89% | 112.06 | 36.50 | 63.96 |
| 21. | Jul 31, 2019 | 7.64% | 1.31% | 26.83 | 0.21 | 2.39 |
| 22. | Aug 31, 2019 | -1.65% | -1.81% | 16.87 | 7.08 | 10.93 |
| 23. | Sep 30, 2019 | 7.28% | 1.72% | 23.25 | 0.75 | 4.18 |
| 24. | Oct 31, 2019 | 11.07% | 2.04% | 74.20 | 1.42 | 10.27 |
| 25. | Nov 30, 2019 | 7.74% | 3.40% | 27.87 | 6.52 | 13.48 |
| 26. | Dec 31, 2019 | 9.88% | 2.86% | 55.05 | 4.03 | 14.90 |
| 27. | Jan 31, 2020 | 5.41% | -0.16% | 8.69 | 1.03 | -2.99 |
| 28. | Feb 29, 2020 | -11.43% | -8.41% | 193.02 | 85.79 | 128.68 |
| 29. | Mar 31, 2020 | -6.98% | -12.51% | 89.10 | 178.57 | 126.14 |
| 30. | Apr 30, 2020 | 15.54% | 12.68% | 171.15 | 140.02 | 154.81 |
| 31. | May 31, 2020 | 8.50% | 4.53% | 36.52 | 13.52 | 22.22 |
| 32. | Jun 30, 2020 | 14.73% | 1.84% | 150.60 | 0.98 | 12.12 |
| 33. | Jul 31, 2020 | 16.51% | 5.51% | 197.51 | 21.71 | 65.47 |
| 34. | Aug 31, 2020 | 21.63% | 7.01% | 367.54 | 37.89 | 118.00 |
| 35. | Sep 30, 2020 | -10.25% | -3.92% | 161.60 | 22.79 | 60.69 |
| 36. | Oct 31, 2020 | -6.00% | -2.77% | 71.58 | 13.09 | 30.61 |
| 37. | Nov 30, 2020 | 9.55% | 10.75% | 50.26 | 98.08 | 70.21 |
| 38. | Dec 31, 2020 | 11.46% | 3.71% | 80.96 | 8.18 | 25.74 |
| 39. | Jan 31, 2021 | -0.55% | -1.11% | 9.06 | 3.86 | 5.91 |
| 40. | Feb 28, 2021 | -7.95% | 2.61% | 108.42 | 3.09 | -18.30 |
| 41. | Mar 31, 2021 | 0.73% | 4.24% | 2.98 | 11.51 | -5.85 |
| 42. | Apr 30, 2021 | 7.62% | 5.24% | 26.65 | 19.28 | 22.67 |
| 43. | May 31, 2021 | -5.04% | 0.55% | 56.29 | 0.09 | 2.27 |
| 44. | Jun 30, 2021 | 9.91% | 2.22% | 55.52 | 1.88 | 10.21 |
| 45. | Jul 31, 2021 | 6.50% | 2.27% | 16.31 | 2.03 | 5.75 |
| 46. | Aug 31, 2021 | 4.24% | 2.90% | 3.18 | 4.19 | 3.65 |
| 47. | Sep 30, 2021 | -6.80% | -4.76% | 85.81 | 31.45 | 51.95 |
| 48. | Oct 31, 2021 | 5.87% | 6.91% | 11.60 | 36.76 | 20.65 |
| 49. | Nov 30, 2021 | 10.49% | -0.83% | 64.55 | 2.84 | -13.54 |
| 50. | Dec 31, 2021 | 7.42% | 4.36% | 24.64 | 12.32 | 17.42 |
| 51. | Jan 31, 2022 | -1.57% | -5.26% | 16.25 | 37.33 | 24.63 |
| 52. | Feb 28, 2022 | -5.40% | -3.14% | 61.79 | 15.90 | 31.34 |
| 53. | Mar 31, 2022 | 5.75% | 3.58% | 10.81 | 7.43 | 8.96 |
| 54. | Apr 30, 2022 | -9.71% | -8.80% | 148.17 | 93.06 | 117.43 |
| 55. | May 31, 2022 | -5.44% | 0.01% | 62.44 | 0.72 | 6.68 |
| 56. | Jun 30, 2022 | -8.14% | -8.39% | 112.41 | 85.44 | 98.00 |
| 57. | Jul 31, 2022 | 18.86% | 9.11% | 269.09 | 68.23 | 135.50 |
| 58. | Aug 31, 2022 | -3.11% | -4.24% | 31.06 | 25.96 | 28.40 |
| 59. | Sep 30, 2022 | -12.10% | -9.34% | 211.91 | 103.85 | 148.35 |
| 60. | Oct 31, 2022 | 10.96% | 7.99% | 72.18 | 50.91 | 60.62 |
| 61. | Nov 30, 2022 | -3.31% | 5.38% | 33.32 | 20.47 | -26.11 |
| 62. | Dec 31, 2022 | -12.23% | -5.90% | 215.70 | 45.54 | 99.11 |
| 63. | Jan 31, 2023 | 11.05% | 6.18% | 73.83 | 28.35 | 45.75 |
| 64. | Feb 28, 2023 | 2.32% | -2.61% | 0.02 | 11.99 | 0.48 |
| 65. | Mar 31, 2023 | 11.86% | 3.51% | 88.46 | 7.04 | 24.96 |
| 66. | Apr 30, 2023 | 2.90% | 1.46% | 0.19 | 0.38 | 0.27 |
| 67. | May 31, 2023 | 4.60% | 0.25% | 4.59 | 0.36 | -1.29 |
| 68. | Jun 30, 2023 | 9.43% | 4.71% | 48.63 | 14.92 | 26.94 |
| 69. | Jul 31, 2023 | 1.28% | 4.85% | 1.39 | 15.96 | -4.72 |
| 70. | Aug 31, 2023 | -4.25% | -1.77% | 44.95 | 6.88 | 17.59 |
| 71. | Sep 30, 2023 | -8.87% | -4.87% | 128.31 | 32.75 | 64.83 |
| Total (Σ): | 5,545.99 | 1,838.69 | 2,309.32 | |||
Show all
VarianceAAPL = Σ(RAAPL,t–RAAPL)2 ÷ (71 – 1)
= 5,545.99 ÷ (71 – 1)
= 79.23
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,838.69 ÷ (71 – 1)
= 26.27
CovarianceAAPL, S&P 500 = Σ(RAAPL,t–RAAPL)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 2,309.32 ÷ (71 – 1)
= 32.99
Systematic Risk (β) Estimation
| VarianceAAPL | 79.23 |
| VarianceS&P 500 | 26.27 |
| CovarianceAAPL, S&P 500 | 32.99 |
| Correlation coefficientAAPL, S&P 5001 | 0.72 |
| βAAPL2 | 1.26 |
| αAAPL3 | 1.39% |
Calculations
1 Correlation coefficientAAPL, S&P 500
= CovarianceAAPL, S&P 500 ÷ (Standard deviationAAPL × Standard deviationS&P 500)
= 32.99 ÷ (8.90% × 5.13%)
= 0.72
2 βAAPL
= CovarianceAAPL, S&P 500 ÷ VarianceS&P 500
= 32.99 ÷ 26.27
= 1.26
3 αAAPL
= AverageAAPL – βAAPL × AverageS&P 500
= 2.46% – 1.26 × 0.85%
= 1.39%
Expected Rate of Return
| Assumptions | ||
| Rate of return on LT Treasury Composite1 | RF | 4.86% |
| Expected rate of return on market portfolio2 | E(RM) | 13.52% |
| Systematic risk (β) of Apple Inc. common stock | βAAPL | 1.26 |
| Expected rate of return on Apple Inc. common stock3 | E(RAAPL) | 15.74% |
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(RAAPL) = RF + βAAPL [E(RM) – RF]
= 4.86% + 1.26 [13.52% – 4.86%]
= 15.74%