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, 2020 | $131.12 | 3,271.12 | ||||
| 1. | Aug 31, 2020 | $138.33 | 5.50% | 3,500.31 | 7.01% | |
| 2. | Sep 30, 2020 | $138.99 | 0.48% | 3,363.00 | -3.92% | |
| 3. | Oct 31, 2020 | $137.10 | $0.7907 | -0.79% | 3,269.96 | -2.77% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | May 31, 2026 | $143.56 | -2.40% | 7,580.06 | 5.15% | |
| 71. | Jun 30, 2026 | $146.64 | 2.15% | 7,499.36 | -1.06% | |
| Average (R): | 0.49% | 1.28% | ||||
| Standard deviation: | 5.18% | 4.53% | ||||
| 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, 2020 | $131.12 | 3,271.12 | ||||
| 1. | Aug 31, 2020 | $138.33 | 5.50% | 3,500.31 | 7.01% | |
| 2. | Sep 30, 2020 | $138.99 | 0.48% | 3,363.00 | -3.92% | |
| 3. | Oct 31, 2020 | $137.10 | $0.7907 | -0.79% | 3,269.96 | -2.77% |
| 4. | Nov 30, 2020 | $138.87 | 1.29% | 3,621.63 | 10.75% | |
| 5. | Dec 31, 2020 | $139.14 | 0.19% | 3,756.07 | 3.71% | |
| 6. | Jan 31, 2021 | $128.21 | $0.7907 | -7.29% | 3,714.24 | -1.11% |
| 7. | Feb 28, 2021 | $123.53 | -3.65% | 3,811.15 | 2.61% | |
| 8. | Mar 31, 2021 | $135.43 | 9.63% | 3,972.89 | 4.24% | |
| 9. | Apr 30, 2021 | $133.42 | $0.8698 | -0.84% | 4,181.17 | 5.24% |
| 10. | May 31, 2021 | $134.85 | 1.07% | 4,204.11 | 0.55% | |
| 11. | Jun 30, 2021 | $134.93 | 0.06% | 4,297.50 | 2.22% | |
| 12. | Jul 31, 2021 | $142.23 | $0.8698 | 6.05% | 4,395.26 | 2.27% |
| 13. | Aug 31, 2021 | $142.39 | 0.11% | 4,522.68 | 2.90% | |
| 14. | Sep 30, 2021 | $139.80 | -1.82% | 4,307.54 | -4.76% | |
| 15. | Oct 31, 2021 | $142.99 | $0.8698 | 2.90% | 4,605.38 | 6.91% |
| 16. | Nov 30, 2021 | $144.58 | 1.11% | 4,567.00 | -0.83% | |
| 17. | Dec 31, 2021 | $163.58 | 13.14% | 4,766.18 | 4.36% | |
| 18. | Jan 31, 2022 | $160.45 | $0.8698 | -1.38% | 4,515.55 | -5.26% |
| 19. | Feb 28, 2022 | $155.89 | -2.84% | 4,373.94 | -3.14% | |
| 20. | Mar 31, 2022 | $152.80 | -1.98% | 4,530.41 | 3.58% | |
| 21. | Apr 30, 2022 | $160.55 | $0.9133 | 5.67% | 4,131.93 | -8.80% |
| 22. | May 31, 2022 | $147.88 | -7.89% | 4,132.15 | 0.01% | |
| 23. | Jun 30, 2022 | $143.79 | -2.77% | 3,785.38 | -8.39% | |
| 24. | Jul 31, 2022 | $138.91 | $0.9133 | -2.76% | 4,130.29 | 9.11% |
| 25. | Aug 31, 2022 | $137.94 | -0.70% | 3,955.00 | -4.24% | |
| 26. | Sep 30, 2022 | $126.25 | -8.47% | 3,585.62 | -9.34% | |
| 27. | Oct 31, 2022 | $134.67 | $0.9133 | 7.39% | 3,871.98 | 7.99% |
| 28. | Nov 30, 2022 | $149.16 | 10.76% | 4,080.11 | 5.38% | |
| 29. | Dec 31, 2022 | $151.56 | 1.61% | 3,839.50 | -5.90% | |
| 30. | Jan 31, 2023 | $142.38 | $0.9133 | -5.45% | 4,076.60 | 6.18% |
| 31. | Feb 28, 2023 | $137.56 | -3.39% | 3,970.15 | -2.61% | |
| 32. | Mar 31, 2023 | $148.69 | 8.09% | 4,109.31 | 3.51% | |
| 33. | Apr 30, 2023 | $156.38 | $0.9407 | 5.80% | 4,169.48 | 1.46% |
| 34. | May 31, 2023 | $142.50 | -8.88% | 4,179.83 | 0.25% | |
| 35. | Jun 30, 2023 | $151.74 | 6.48% | 4,376.86 | 4.71% | |
| 36. | Jul 31, 2023 | $156.30 | $0.9407 | 3.63% | 4,588.96 | 4.85% |
| 37. | Aug 31, 2023 | $154.34 | -1.25% | 4,507.66 | -1.77% | |
| 38. | Sep 30, 2023 | $145.86 | -5.49% | 4,288.05 | -4.87% | |
| 39. | Oct 31, 2023 | $150.03 | $0.9407 | 3.50% | 4,193.80 | -2.20% |
| 40. | Nov 30, 2023 | $153.52 | 2.33% | 4,567.80 | 8.92% | |
| 41. | Dec 31, 2023 | $146.54 | -4.55% | 4,769.83 | 4.42% | |
| 42. | Jan 31, 2024 | $157.14 | $0.9407 | 7.88% | 4,845.65 | 1.59% |
| 43. | Feb 29, 2024 | $158.94 | 1.15% | 5,096.27 | 5.17% | |
| 44. | Mar 31, 2024 | $162.25 | 2.08% | 5,254.35 | 3.10% | |
| 45. | Apr 30, 2024 | $163.20 | $1.0065 | 1.21% | 5,035.69 | -4.16% |
| 46. | May 31, 2024 | $164.54 | 0.82% | 5,277.51 | 4.80% | |
| 47. | Jun 30, 2024 | $164.92 | 0.23% | 5,460.48 | 3.47% | |
| 48. | Jul 31, 2024 | $160.76 | $1.0065 | -1.91% | 5,522.30 | 1.13% |
| 49. | Aug 31, 2024 | $171.54 | 6.71% | 5,648.40 | 2.28% | |
| 50. | Sep 30, 2024 | $173.20 | 0.97% | 5,762.48 | 2.02% | |
| 51. | Oct 31, 2024 | $165.18 | $1.0065 | -4.05% | 5,705.45 | -0.99% |
| 52. | Nov 30, 2024 | $179.26 | 8.52% | 6,032.38 | 5.73% | |
| 53. | Dec 31, 2024 | $167.65 | -6.48% | 5,881.63 | -2.50% | |
| 54. | Jan 31, 2025 | $165.99 | $1.0065 | -0.39% | 6,040.53 | 2.70% |
| 55. | Feb 28, 2025 | $173.84 | 4.73% | 5,954.50 | -1.42% | |
| 56. | Mar 31, 2025 | $170.42 | -1.97% | 5,611.85 | -5.75% | |
| 57. | Apr 30, 2025 | $162.57 | $1.0568 | -3.99% | 5,569.06 | -0.76% |
| 58. | May 31, 2025 | $169.89 | 4.50% | 5,911.69 | 6.15% | |
| 59. | Jun 30, 2025 | $159.32 | -6.22% | 6,204.95 | 4.96% | |
| 60. | Jul 31, 2025 | $150.47 | $1.0568 | -4.89% | 6,339.39 | 2.17% |
| 61. | Aug 31, 2025 | $157.04 | 4.37% | 6,460.26 | 1.91% | |
| 62. | Sep 30, 2025 | $153.65 | -2.16% | 6,688.46 | 3.53% | |
| 63. | Oct 31, 2025 | $150.37 | $1.0568 | -1.45% | 6,840.20 | 2.27% |
| 64. | Nov 30, 2025 | $148.16 | -1.47% | 6,849.09 | 0.13% | |
| 65. | Dec 31, 2025 | $143.31 | -3.27% | 6,845.50 | -0.05% | |
| 66. | Jan 31, 2026 | $151.77 | $1.0568 | 6.64% | 6,939.03 | 1.37% |
| 67. | Feb 28, 2026 | $167.20 | 10.17% | 6,878.88 | -0.87% | |
| 68. | Mar 31, 2026 | $144.44 | -13.61% | 6,528.52 | -5.09% | |
| 69. | Apr 30, 2026 | $147.09 | $1.0885 | 2.59% | 7,209.01 | 10.42% |
| 70. | May 31, 2026 | $143.56 | -2.40% | 7,580.06 | 5.15% | |
| 71. | Jun 30, 2026 | $146.64 | 2.15% | 7,499.36 | -1.06% | |
| Average (R): | 0.49% | 1.28% | ||||
| Standard deviation: | 5.18% | 4.53% | ||||
Show all
1 Data in US$ 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, 2020 | 5.50% | 7.01% | 25.05 | 32.84 | 28.68 |
| 2. | Sep 30, 2020 | 0.48% | -3.92% | 0.00 | 27.03 | 0.09 |
| 3. | Oct 31, 2020 | -0.79% | -2.77% | 1.65 | 16.34 | 5.19 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | May 31, 2026 | -2.40% | 5.15% | 8.37 | 14.98 | -11.20 |
| 71. | Jun 30, 2026 | 2.15% | -1.06% | 2.73 | 5.48 | -3.87 |
| Total (Σ): | 1,876.41 | 1,436.39 | 551.23 | |||
| 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, 2020 | 5.50% | 7.01% | 25.05 | 32.84 | 28.68 |
| 2. | Sep 30, 2020 | 0.48% | -3.92% | 0.00 | 27.03 | 0.09 |
| 3. | Oct 31, 2020 | -0.79% | -2.77% | 1.65 | 16.34 | 5.19 |
| 4. | Nov 30, 2020 | 1.29% | 10.75% | 0.64 | 89.84 | 7.56 |
| 5. | Dec 31, 2020 | 0.19% | 3.71% | 0.09 | 5.93 | -0.73 |
| 6. | Jan 31, 2021 | -7.29% | -1.11% | 60.54 | 5.71 | 18.60 |
| 7. | Feb 28, 2021 | -3.65% | 2.61% | 17.17 | 1.78 | -5.52 |
| 8. | Mar 31, 2021 | 9.63% | 4.24% | 83.53 | 8.81 | 27.12 |
| 9. | Apr 30, 2021 | -0.84% | 5.24% | 1.78 | 15.73 | -5.30 |
| 10. | May 31, 2021 | 1.07% | 0.55% | 0.33 | 0.53 | -0.42 |
| 11. | Jun 30, 2021 | 0.06% | 2.22% | 0.19 | 0.89 | -0.41 |
| 12. | Jul 31, 2021 | 6.05% | 2.27% | 30.92 | 1.00 | 5.55 |
| 13. | Aug 31, 2021 | 0.11% | 2.90% | 0.15 | 2.63 | -0.62 |
| 14. | Sep 30, 2021 | -1.82% | -4.76% | 5.35 | 36.40 | 13.95 |
| 15. | Oct 31, 2021 | 2.90% | 6.91% | 5.81 | 31.79 | 13.59 |
| 16. | Nov 30, 2021 | 1.11% | -0.83% | 0.38 | 4.45 | -1.30 |
| 17. | Dec 31, 2021 | 13.14% | 4.36% | 159.96 | 9.52 | 39.02 |
| 18. | Jan 31, 2022 | -1.38% | -5.26% | 3.52 | 42.70 | 12.26 |
| 19. | Feb 28, 2022 | -2.84% | -3.14% | 11.13 | 19.47 | 14.72 |
| 20. | Mar 31, 2022 | -1.98% | 3.58% | 6.13 | 5.29 | -5.70 |
| 21. | Apr 30, 2022 | 5.67% | -8.80% | 26.79 | 101.44 | -52.13 |
| 22. | May 31, 2022 | -7.89% | 0.01% | 70.32 | 1.62 | 10.66 |
| 23. | Jun 30, 2022 | -2.77% | -8.39% | 10.63 | 93.48 | 31.51 |
| 24. | Jul 31, 2022 | -2.76% | 9.11% | 10.58 | 61.39 | -25.48 |
| 25. | Aug 31, 2022 | -0.70% | -4.24% | 1.42 | 30.47 | 6.58 |
| 26. | Sep 30, 2022 | -8.47% | -9.34% | 80.44 | 112.70 | 95.21 |
| 27. | Oct 31, 2022 | 7.39% | 7.99% | 47.59 | 45.03 | 46.29 |
| 28. | Nov 30, 2022 | 10.76% | 5.38% | 105.39 | 16.80 | 42.08 |
| 29. | Dec 31, 2022 | 1.61% | -5.90% | 1.24 | 51.46 | -8.00 |
| 30. | Jan 31, 2023 | -5.45% | 6.18% | 35.38 | 24.00 | -29.14 |
| 31. | Feb 28, 2023 | -3.39% | -2.61% | 15.05 | 15.11 | 15.08 |
| 32. | Mar 31, 2023 | 8.09% | 3.51% | 57.72 | 4.97 | 16.93 |
| 33. | Apr 30, 2023 | 5.80% | 1.46% | 28.20 | 0.04 | 1.00 |
| 34. | May 31, 2023 | -8.88% | 0.25% | 87.79 | 1.06 | 9.63 |
| 35. | Jun 30, 2023 | 6.48% | 4.71% | 35.88 | 11.82 | 20.59 |
| 36. | Jul 31, 2023 | 3.63% | 4.85% | 9.80 | 12.74 | 11.18 |
| 37. | Aug 31, 2023 | -1.25% | -1.77% | 3.06 | 9.29 | 5.33 |
| 38. | Sep 30, 2023 | -5.49% | -4.87% | 35.86 | 37.80 | 36.82 |
| 39. | Oct 31, 2023 | 3.50% | -2.20% | 9.06 | 12.07 | -10.46 |
| 40. | Nov 30, 2023 | 2.33% | 8.92% | 3.36 | 58.40 | 14.00 |
| 41. | Dec 31, 2023 | -4.55% | 4.42% | 25.41 | 9.90 | -15.86 |
| 42. | Jan 31, 2024 | 7.88% | 1.59% | 54.49 | 0.10 | 2.31 |
| 43. | Feb 29, 2024 | 1.15% | 5.17% | 0.42 | 15.18 | 2.54 |
| 44. | Mar 31, 2024 | 2.08% | 3.10% | 2.52 | 3.33 | 2.90 |
| 45. | Apr 30, 2024 | 1.21% | -4.16% | 0.51 | 29.57 | -3.87 |
| 46. | May 31, 2024 | 0.82% | 4.80% | 0.11 | 12.43 | 1.15 |
| 47. | Jun 30, 2024 | 0.23% | 3.47% | 0.07 | 4.80 | -0.58 |
| 48. | Jul 31, 2024 | -1.91% | 1.13% | 5.79 | 0.02 | 0.35 |
| 49. | Aug 31, 2024 | 6.71% | 2.28% | 38.59 | 1.01 | 6.26 |
| 50. | Sep 30, 2024 | 0.97% | 2.02% | 0.22 | 0.55 | 0.35 |
| 51. | Oct 31, 2024 | -4.05% | -0.99% | 20.64 | 5.13 | 10.29 |
| 52. | Nov 30, 2024 | 8.52% | 5.73% | 64.48 | 19.84 | 35.77 |
| 53. | Dec 31, 2024 | -6.48% | -2.50% | 48.59 | 14.25 | 26.32 |
| 54. | Jan 31, 2025 | -0.39% | 2.70% | 0.78 | 2.03 | -1.26 |
| 55. | Feb 28, 2025 | 4.73% | -1.42% | 17.94 | 7.29 | -11.44 |
| 56. | Mar 31, 2025 | -1.97% | -5.75% | 6.06 | 49.43 | 17.30 |
| 57. | Apr 30, 2025 | -3.99% | -0.76% | 20.07 | 4.16 | 9.13 |
| 58. | May 31, 2025 | 4.50% | 6.15% | 16.07 | 23.78 | 19.55 |
| 59. | Jun 30, 2025 | -6.22% | 4.96% | 45.10 | 13.58 | -24.74 |
| 60. | Jul 31, 2025 | -4.89% | 2.17% | 29.00 | 0.79 | -4.80 |
| 61. | Aug 31, 2025 | 4.37% | 1.91% | 15.00 | 0.40 | 2.44 |
| 62. | Sep 30, 2025 | -2.16% | 3.53% | 7.04 | 5.09 | -5.98 |
| 63. | Oct 31, 2025 | -1.45% | 2.27% | 3.77 | 0.98 | -1.93 |
| 64. | Nov 30, 2025 | -1.47% | 0.13% | 3.86 | 1.31 | 2.25 |
| 65. | Dec 31, 2025 | -3.27% | -0.05% | 14.19 | 1.77 | 5.01 |
| 66. | Jan 31, 2026 | 6.64% | 1.37% | 37.78 | 0.01 | 0.55 |
| 67. | Feb 28, 2026 | 10.17% | -0.87% | 93.56 | 4.59 | -20.73 |
| 68. | Mar 31, 2026 | -13.61% | -5.09% | 198.99 | 40.57 | 89.85 |
| 69. | Apr 30, 2026 | 2.59% | 10.42% | 4.39 | 83.67 | 19.16 |
| 70. | May 31, 2026 | -2.40% | 5.15% | 8.37 | 14.98 | -11.20 |
| 71. | Jun 30, 2026 | 2.15% | -1.06% | 2.73 | 5.48 | -3.87 |
| Total (Σ): | 1,876.41 | 1,436.39 | 551.23 | |||
Show all
VariancePG = Σ(RPG,t–RPG)2 ÷ (71 – 1)
= 1,876.41 ÷ (71 – 1)
= 26.81
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,436.39 ÷ (71 – 1)
= 20.52
CovariancePG, S&P 500 = Σ(RPG,t–RPG)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 551.23 ÷ (71 – 1)
= 7.87
Systematic Risk (β) Estimation
| VariancePG | 26.81 |
| VarianceS&P 500 | 20.52 |
| CovariancePG, S&P 500 | 7.87 |
| Correlation coefficientPG, S&P 5001 | 0.34 |
| βPG2 | 0.38 |
| αPG3 | 0.00% |
Calculations
1 Correlation coefficientPG, S&P 500
= CovariancePG, S&P 500 ÷ (Standard deviationPG × Standard deviationS&P 500)
= 7.87 ÷ (5.18% × 4.53%)
= 0.34
2 βPG
= CovariancePG, S&P 500 ÷ VarianceS&P 500
= 7.87 ÷ 20.52
= 0.38
3 αPG
= AveragePG – βPG × AverageS&P 500
= 0.49% – 0.38 × 1.28%
= 0.00%
Expected Rate of Return
| Assumptions | ||
| Rate of return on LT Treasury Composite1 | RF | 5.64% |
| Expected rate of return on market portfolio2 | E(RM) | 17.45% |
| Systematic risk (β) of Procter & Gamble Co. common stock | βPG | 0.38 |
| Expected rate of return on Procter & Gamble Co. common stock3 | E(RPG) | 10.17% |
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]
= 5.64% + 0.38 [17.45% – 5.64%]
= 10.17%