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 Procter & Gamble Co. common stock.
Rates of Return
Procter & Gamble Co., monthly rates of return
| Procter & Gamble Co. (PG) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PricePG,t1 | DividendPG,t1 | RPG,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Jul 31, 2017 | $90.82 | 2,470.30 | ||||
| 1. | Aug 31, 2017 | $92.27 | 1.60% | 2,471.65 | 0.05% | |
| 2. | Sep 30, 2017 | $90.98 | -1.40% | 2,519.36 | 1.93% | |
| 3. | Oct 31, 2017 | $86.34 | $0.6896 | -4.34% | 2,575.26 | 2.22% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | May 31, 2023 | $142.50 | -8.88% | 4,179.83 | 0.25% | |
| 71. | Jun 30, 2023 | $151.74 | 6.48% | 4,376.86 | 4.71% | |
| Average (R): | 1.08% | 0.94% | ||||
| Standard deviation: | 5.16% | 5.05% | ||||
| Procter & Gamble Co. (PG) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PricePG,t1 | DividendPG,t1 | RPG,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Jul 31, 2017 | $90.82 | 2,470.30 | ||||
| 1. | Aug 31, 2017 | $92.27 | 1.60% | 2,471.65 | 0.05% | |
| 2. | Sep 30, 2017 | $90.98 | -1.40% | 2,519.36 | 1.93% | |
| 3. | Oct 31, 2017 | $86.34 | $0.6896 | -4.34% | 2,575.26 | 2.22% |
| 4. | Nov 30, 2017 | $89.99 | 4.23% | 2,647.58 | 2.81% | |
| 5. | Dec 31, 2017 | $91.88 | 2.10% | 2,673.61 | 0.98% | |
| 6. | Jan 31, 2018 | $86.34 | $0.6896 | -5.28% | 2,823.81 | 5.62% |
| 7. | Feb 28, 2018 | $78.52 | -9.06% | 2,713.83 | -3.89% | |
| 8. | Mar 31, 2018 | $79.28 | 0.97% | 2,640.87 | -2.69% | |
| 9. | Apr 30, 2018 | $72.34 | $0.7172 | -7.85% | 2,648.05 | 0.27% |
| 10. | May 31, 2018 | $73.17 | 1.15% | 2,705.27 | 2.16% | |
| 11. | Jun 30, 2018 | $78.06 | 6.68% | 2,718.37 | 0.48% | |
| 12. | Jul 31, 2018 | $80.88 | $0.7172 | 4.53% | 2,816.29 | 3.60% |
| 13. | Aug 31, 2018 | $82.95 | 2.56% | 2,901.52 | 3.03% | |
| 14. | Sep 30, 2018 | $83.23 | 0.34% | 2,913.98 | 0.43% | |
| 15. | Oct 31, 2018 | $88.68 | $0.7172 | 7.41% | 2,711.74 | -6.94% |
| 16. | Nov 30, 2018 | $94.51 | 6.57% | 2,760.17 | 1.79% | |
| 17. | Dec 31, 2018 | $91.92 | -2.74% | 2,506.85 | -9.18% | |
| 18. | Jan 31, 2019 | $96.47 | $0.7172 | 5.73% | 2,704.10 | 7.87% |
| 19. | Feb 28, 2019 | $98.55 | 2.16% | 2,784.49 | 2.97% | |
| 20. | Mar 31, 2019 | $104.05 | 5.58% | 2,834.40 | 1.79% | |
| 21. | Apr 30, 2019 | $106.48 | $0.7459 | 3.05% | 2,945.83 | 3.93% |
| 22. | May 31, 2019 | $102.91 | -3.35% | 2,752.06 | -6.58% | |
| 23. | Jun 30, 2019 | $109.65 | 6.55% | 2,941.76 | 6.89% | |
| 24. | Jul 31, 2019 | $118.04 | $0.7459 | 8.33% | 2,980.38 | 1.31% |
| 25. | Aug 31, 2019 | $120.23 | 1.86% | 2,926.46 | -1.81% | |
| 26. | Sep 30, 2019 | $124.38 | 3.45% | 2,976.74 | 1.72% | |
| 27. | Oct 31, 2019 | $124.51 | $0.7459 | 0.70% | 3,037.56 | 2.04% |
| 28. | Nov 30, 2019 | $122.06 | -1.97% | 3,140.98 | 3.40% | |
| 29. | Dec 31, 2019 | $124.90 | 2.33% | 3,230.78 | 2.86% | |
| 30. | Jan 31, 2020 | $124.62 | $0.7459 | 0.37% | 3,225.52 | -0.16% |
| 31. | Feb 29, 2020 | $113.23 | -9.14% | 2,954.22 | -8.41% | |
| 32. | Mar 31, 2020 | $110.00 | -2.85% | 2,584.59 | -12.51% | |
| 33. | Apr 30, 2020 | $117.87 | $0.7907 | 7.87% | 2,912.43 | 12.68% |
| 34. | May 31, 2020 | $115.92 | -1.65% | 3,044.31 | 4.53% | |
| 35. | Jun 30, 2020 | $119.57 | 3.15% | 3,100.29 | 1.84% | |
| 36. | Jul 31, 2020 | $131.12 | $0.7907 | 10.32% | 3,271.12 | 5.51% |
| 37. | Aug 31, 2020 | $138.33 | 5.50% | 3,500.31 | 7.01% | |
| 38. | Sep 30, 2020 | $138.99 | 0.48% | 3,363.00 | -3.92% | |
| 39. | Oct 31, 2020 | $137.10 | $0.7907 | -0.79% | 3,269.96 | -2.77% |
| 40. | Nov 30, 2020 | $138.87 | 1.29% | 3,621.63 | 10.75% | |
| 41. | Dec 31, 2020 | $139.14 | 0.19% | 3,756.07 | 3.71% | |
| 42. | Jan 31, 2021 | $128.21 | $0.7907 | -7.29% | 3,714.24 | -1.11% |
| 43. | Feb 28, 2021 | $123.53 | -3.65% | 3,811.15 | 2.61% | |
| 44. | Mar 31, 2021 | $135.43 | 9.63% | 3,972.89 | 4.24% | |
| 45. | Apr 30, 2021 | $133.42 | $0.8698 | -0.84% | 4,181.17 | 5.24% |
| 46. | May 31, 2021 | $134.85 | 1.07% | 4,204.11 | 0.55% | |
| 47. | Jun 30, 2021 | $134.93 | 0.06% | 4,297.50 | 2.22% | |
| 48. | Jul 31, 2021 | $142.23 | $0.8698 | 6.05% | 4,395.26 | 2.27% |
| 49. | Aug 31, 2021 | $142.39 | 0.11% | 4,522.68 | 2.90% | |
| 50. | Sep 30, 2021 | $139.80 | -1.82% | 4,307.54 | -4.76% | |
| 51. | Oct 31, 2021 | $142.99 | $0.8698 | 2.90% | 4,605.38 | 6.91% |
| 52. | Nov 30, 2021 | $144.58 | 1.11% | 4,567.00 | -0.83% | |
| 53. | Dec 31, 2021 | $163.58 | 13.14% | 4,766.18 | 4.36% | |
| 54. | Jan 31, 2022 | $160.45 | $0.8698 | -1.38% | 4,515.55 | -5.26% |
| 55. | Feb 28, 2022 | $155.89 | -2.84% | 4,373.94 | -3.14% | |
| 56. | Mar 31, 2022 | $152.80 | -1.98% | 4,530.41 | 3.58% | |
| 57. | Apr 30, 2022 | $160.55 | $0.9133 | 5.67% | 4,131.93 | -8.80% |
| 58. | May 31, 2022 | $147.88 | -7.89% | 4,132.15 | 0.01% | |
| 59. | Jun 30, 2022 | $143.79 | -2.77% | 3,785.38 | -8.39% | |
| 60. | Jul 31, 2022 | $138.91 | $0.9133 | -2.76% | 4,130.29 | 9.11% |
| 61. | Aug 31, 2022 | $137.94 | -0.70% | 3,955.00 | -4.24% | |
| 62. | Sep 30, 2022 | $126.25 | -8.47% | 3,585.62 | -9.34% | |
| 63. | Oct 31, 2022 | $134.67 | $0.9133 | 7.39% | 3,871.98 | 7.99% |
| 64. | Nov 30, 2022 | $149.16 | 10.76% | 4,080.11 | 5.38% | |
| 65. | Dec 31, 2022 | $151.56 | 1.61% | 3,839.50 | -5.90% | |
| 66. | Jan 31, 2023 | $142.38 | $0.9133 | -5.45% | 4,076.60 | 6.18% |
| 67. | Feb 28, 2023 | $137.56 | -3.39% | 3,970.15 | -2.61% | |
| 68. | Mar 31, 2023 | $148.69 | 8.09% | 4,109.31 | 3.51% | |
| 69. | Apr 30, 2023 | $156.38 | $0.9407 | 5.80% | 4,169.48 | 1.46% |
| 70. | May 31, 2023 | $142.50 | -8.88% | 4,179.83 | 0.25% | |
| 71. | Jun 30, 2023 | $151.74 | 6.48% | 4,376.86 | 4.71% | |
| Average (R): | 1.08% | 0.94% | ||||
| Standard deviation: | 5.16% | 5.05% | ||||
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of PG during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
Procter & Gamble Co., calculation of variance and covariance of returns
| t | Date | RPG,t | RS&P 500,t | (RPG,t–RPG)2 | (RS&P 500,t–RS&P 500)2 | (RPG,t–RPG)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Aug 31, 2017 | 1.60% | 0.05% | 0.27 | 0.78 | -0.46 |
| 2. | Sep 30, 2017 | -1.40% | 1.93% | 6.12 | 0.99 | -2.46 |
| 3. | Oct 31, 2017 | -4.34% | 2.22% | 29.36 | 1.65 | -6.95 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | May 31, 2023 | -8.88% | 0.25% | 99.04 | 0.47 | 6.84 |
| 71. | Jun 30, 2023 | 6.48% | 4.71% | 29.25 | 14.27 | 20.43 |
| Total (Σ): | 1,860.61 | 1,786.26 | 745.18 | |||
| t | Date | RPG,t | RS&P 500,t | (RPG,t–RPG)2 | (RS&P 500,t–RS&P 500)2 | (RPG,t–RPG)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Aug 31, 2017 | 1.60% | 0.05% | 0.27 | 0.78 | -0.46 |
| 2. | Sep 30, 2017 | -1.40% | 1.93% | 6.12 | 0.99 | -2.46 |
| 3. | Oct 31, 2017 | -4.34% | 2.22% | 29.36 | 1.65 | -6.95 |
| 4. | Nov 30, 2017 | 4.23% | 2.81% | 9.93 | 3.51 | 5.90 |
| 5. | Dec 31, 2017 | 2.10% | 0.98% | 1.05 | 0.00 | 0.05 |
| 6. | Jan 31, 2018 | -5.28% | 5.62% | 40.39 | 21.92 | -29.76 |
| 7. | Feb 28, 2018 | -9.06% | -3.89% | 102.69 | 23.33 | 48.95 |
| 8. | Mar 31, 2018 | 0.97% | -2.69% | 0.01 | 13.14 | 0.39 |
| 9. | Apr 30, 2018 | -7.85% | 0.27% | 79.66 | 0.44 | 5.93 |
| 10. | May 31, 2018 | 1.15% | 2.16% | 0.01 | 1.50 | 0.09 |
| 11. | Jun 30, 2018 | 6.68% | 0.48% | 31.44 | 0.20 | -2.53 |
| 12. | Jul 31, 2018 | 4.53% | 3.60% | 11.94 | 7.11 | 9.21 |
| 13. | Aug 31, 2018 | 2.56% | 3.03% | 2.20 | 4.37 | 3.10 |
| 14. | Sep 30, 2018 | 0.34% | 0.43% | 0.55 | 0.26 | 0.37 |
| 15. | Oct 31, 2018 | 7.41% | -6.94% | 40.11 | 62.03 | -49.88 |
| 16. | Nov 30, 2018 | 6.57% | 1.79% | 30.23 | 0.72 | 4.67 |
| 17. | Dec 31, 2018 | -2.74% | -9.18% | 14.57 | 102.28 | 38.60 |
| 18. | Jan 31, 2019 | 5.73% | 7.87% | 21.66 | 48.06 | 32.26 |
| 19. | Feb 28, 2019 | 2.16% | 2.97% | 1.17 | 4.15 | 2.20 |
| 20. | Mar 31, 2019 | 5.58% | 1.79% | 20.29 | 0.73 | 3.86 |
| 21. | Apr 30, 2019 | 3.05% | 3.93% | 3.90 | 8.97 | 5.92 |
| 22. | May 31, 2019 | -3.35% | -6.58% | 19.62 | 56.45 | 33.28 |
| 23. | Jun 30, 2019 | 6.55% | 6.89% | 29.95 | 35.49 | 32.60 |
| 24. | Jul 31, 2019 | 8.33% | 1.31% | 52.64 | 0.14 | 2.74 |
| 25. | Aug 31, 2019 | 1.86% | -1.81% | 0.61 | 7.53 | -2.14 |
| 26. | Sep 30, 2019 | 3.45% | 1.72% | 5.64 | 0.61 | 1.86 |
| 27. | Oct 31, 2019 | 0.70% | 2.04% | 0.14 | 1.23 | -0.41 |
| 28. | Nov 30, 2019 | -1.97% | 3.40% | 9.27 | 6.10 | -7.52 |
| 29. | Dec 31, 2019 | 2.33% | 2.86% | 1.56 | 3.70 | 2.40 |
| 30. | Jan 31, 2020 | 0.37% | -0.16% | 0.49 | 1.21 | 0.77 |
| 31. | Feb 29, 2020 | -9.14% | -8.41% | 104.37 | 87.36 | 95.49 |
| 32. | Mar 31, 2020 | -2.85% | -12.51% | 15.44 | 180.84 | 52.83 |
| 33. | Apr 30, 2020 | 7.87% | 12.68% | 46.20 | 138.03 | 79.86 |
| 34. | May 31, 2020 | -1.65% | 4.53% | 7.46 | 12.91 | -9.81 |
| 35. | Jun 30, 2020 | 3.15% | 1.84% | 4.29 | 0.82 | 1.87 |
| 36. | Jul 31, 2020 | 10.32% | 5.51% | 85.46 | 20.92 | 42.29 |
| 37. | Aug 31, 2020 | 5.50% | 7.01% | 19.56 | 36.85 | 26.85 |
| 38. | Sep 30, 2020 | 0.48% | -3.92% | 0.36 | 23.61 | 2.91 |
| 39. | Oct 31, 2020 | -0.79% | -2.77% | 3.49 | 13.71 | 6.91 |
| 40. | Nov 30, 2020 | 1.29% | 10.75% | 0.05 | 96.41 | 2.11 |
| 41. | Dec 31, 2020 | 0.19% | 3.71% | 0.78 | 7.71 | -2.45 |
| 42. | Jan 31, 2021 | -7.29% | -1.11% | 69.95 | 4.20 | 17.14 |
| 43. | Feb 28, 2021 | -3.65% | 2.61% | 22.34 | 2.80 | -7.91 |
| 44. | Mar 31, 2021 | 9.63% | 4.24% | 73.22 | 10.94 | 28.31 |
| 45. | Apr 30, 2021 | -0.84% | 5.24% | 3.68 | 18.55 | -8.26 |
| 46. | May 31, 2021 | 1.07% | 0.55% | 0.00 | 0.15 | 0.00 |
| 47. | Jun 30, 2021 | 0.06% | 2.22% | 1.03 | 1.65 | -1.31 |
| 48. | Jul 31, 2021 | 6.05% | 2.27% | 24.79 | 1.79 | 6.67 |
| 49. | Aug 31, 2021 | 0.11% | 2.90% | 0.93 | 3.85 | -1.89 |
| 50. | Sep 30, 2021 | -1.82% | -4.76% | 8.38 | 32.41 | 16.48 |
| 51. | Oct 31, 2021 | 2.90% | 6.91% | 3.34 | 35.74 | 10.93 |
| 52. | Nov 30, 2021 | 1.11% | -0.83% | 0.00 | 3.13 | -0.06 |
| 53. | Dec 31, 2021 | 13.14% | 4.36% | 145.57 | 11.73 | 41.33 |
| 54. | Jan 31, 2022 | -1.38% | -5.26% | 6.04 | 38.37 | 15.23 |
| 55. | Feb 28, 2022 | -2.84% | -3.14% | 15.35 | 16.58 | 15.95 |
| 56. | Mar 31, 2022 | -1.98% | 3.58% | 9.35 | 6.98 | -8.08 |
| 57. | Apr 30, 2022 | 5.67% | -8.80% | 21.10 | 94.70 | -44.70 |
| 58. | May 31, 2022 | -7.89% | 0.01% | 80.42 | 0.87 | 8.34 |
| 59. | Jun 30, 2022 | -2.77% | -8.39% | 14.76 | 87.01 | 35.84 |
| 60. | Jul 31, 2022 | -2.76% | 9.11% | 14.71 | 66.84 | -31.35 |
| 61. | Aug 31, 2022 | -0.70% | -4.24% | 3.15 | 26.83 | 9.19 |
| 62. | Sep 30, 2022 | -8.47% | -9.34% | 91.22 | 105.58 | 98.14 |
| 63. | Oct 31, 2022 | 7.39% | 7.99% | 39.90 | 49.71 | 44.53 |
| 64. | Nov 30, 2022 | 10.76% | 5.38% | 93.77 | 19.71 | 42.99 |
| 65. | Dec 31, 2022 | 1.61% | -5.90% | 0.28 | 46.69 | -3.64 |
| 66. | Jan 31, 2023 | -5.45% | 6.18% | 42.65 | 27.45 | -34.22 |
| 67. | Feb 28, 2023 | -3.39% | -2.61% | 19.91 | 12.58 | 15.83 |
| 68. | Mar 31, 2023 | 8.09% | 3.51% | 49.21 | 6.60 | 18.02 |
| 69. | Apr 30, 2023 | 5.80% | 1.46% | 22.36 | 0.28 | 2.50 |
| 70. | May 31, 2023 | -8.88% | 0.25% | 99.04 | 0.47 | 6.84 |
| 71. | Jun 30, 2023 | 6.48% | 4.71% | 29.25 | 14.27 | 20.43 |
| Total (Σ): | 1,860.61 | 1,786.26 | 745.18 | |||
Show all
VariancePG = Σ(RPG,t–RPG)2 ÷ (71 – 1)
= 1,860.61 ÷ (71 – 1)
= 26.58
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,786.26 ÷ (71 – 1)
= 25.52
CovariancePG, S&P 500 = Σ(RPG,t–RPG)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 745.18 ÷ (71 – 1)
= 10.65
Systematic Risk (β) Estimation
| VariancePG | 26.58 |
| VarianceS&P 500 | 25.52 |
| CovariancePG, S&P 500 | 10.65 |
| Correlation coefficientPG, S&P 5001 | 0.41 |
| βPG2 | 0.42 |
| αPG3 | 0.69% |
Calculations
1 Correlation coefficientPG, S&P 500
= CovariancePG, S&P 500 ÷ (Standard deviationPG × Standard deviationS&P 500)
= 10.65 ÷ (5.16% × 5.05%)
= 0.41
2 βPG
= CovariancePG, S&P 500 ÷ VarianceS&P 500
= 10.65 ÷ 25.52
= 0.42
3 αPG
= AveragePG – βPG × AverageS&P 500
= 1.08% – 0.42 × 0.94%
= 0.69%
Expected Rate of Return
| Assumptions | ||
| Rate of return on LT Treasury Composite1 | RF | 4.81% |
| Expected rate of return on market portfolio2 | E(RM) | 13.54% |
| Systematic risk (β) of Procter & Gamble Co. common stock | βPG | 0.42 |
| Expected rate of return on Procter & Gamble Co. common stock3 | E(RPG) | 8.45% |
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(RPG) = RF + βPG [E(RM) – RF]
= 4.81% + 0.42 [13.54% – 4.81%]
= 8.45%