자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 P&G보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Procter & Gamble Co., 월별 수익률
| Procter & Gamble Co. (PG) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값PG,t1 | 피제수PG,t1 | RPG,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 7. 31. | $118.04 | 2,980.38 | ||||
| 1. | 2019. 8. 31. | $120.23 | 1.86% | 2,926.46 | -1.81% | |
| 2. | 2019. 9. 30. | $124.38 | 3.45% | 2,976.74 | 1.72% | |
| 3. | 2019. 10. 31. | $124.51 | $0.7459 | 0.70% | 3,037.56 | 2.04% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2025. 5. 31. | $169.89 | 4.50% | 5,911.69 | 6.15% | |
| 71. | 2025. 6. 30. | $159.32 | -6.22% | 6,204.95 | 4.96% | |
| 평균의 (R): | 0.74% | 1.16% | ||||
| 표준 편차: | 4.99% | 4.98% | ||||
| Procter & Gamble Co. (PG) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값PG,t1 | 피제수PG,t1 | RPG,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 7. 31. | $118.04 | 2,980.38 | ||||
| 1. | 2019. 8. 31. | $120.23 | 1.86% | 2,926.46 | -1.81% | |
| 2. | 2019. 9. 30. | $124.38 | 3.45% | 2,976.74 | 1.72% | |
| 3. | 2019. 10. 31. | $124.51 | $0.7459 | 0.70% | 3,037.56 | 2.04% |
| 4. | 2019. 11. 30. | $122.06 | -1.97% | 3,140.98 | 3.40% | |
| 5. | 2019. 12. 31. | $124.90 | 2.33% | 3,230.78 | 2.86% | |
| 6. | 2020. 1. 31. | $124.62 | $0.7459 | 0.37% | 3,225.52 | -0.16% |
| 7. | 2020. 2. 29. | $113.23 | -9.14% | 2,954.22 | -8.41% | |
| 8. | 2020. 3. 31. | $110.00 | -2.85% | 2,584.59 | -12.51% | |
| 9. | 2020. 4. 30. | $117.87 | $0.7907 | 7.87% | 2,912.43 | 12.68% |
| 10. | 2020. 5. 31. | $115.92 | -1.65% | 3,044.31 | 4.53% | |
| 11. | 2020. 6. 30. | $119.57 | 3.15% | 3,100.29 | 1.84% | |
| 12. | 2020. 7. 31. | $131.12 | $0.7907 | 10.32% | 3,271.12 | 5.51% |
| 13. | 2020. 8. 31. | $138.33 | 5.50% | 3,500.31 | 7.01% | |
| 14. | 2020. 9. 30. | $138.99 | 0.48% | 3,363.00 | -3.92% | |
| 15. | 2020. 10. 31. | $137.10 | $0.7907 | -0.79% | 3,269.96 | -2.77% |
| 16. | 2020. 11. 30. | $138.87 | 1.29% | 3,621.63 | 10.75% | |
| 17. | 2020. 12. 31. | $139.14 | 0.19% | 3,756.07 | 3.71% | |
| 18. | 2021. 1. 31. | $128.21 | $0.7907 | -7.29% | 3,714.24 | -1.11% |
| 19. | 2021. 2. 28. | $123.53 | -3.65% | 3,811.15 | 2.61% | |
| 20. | 2021. 3. 31. | $135.43 | 9.63% | 3,972.89 | 4.24% | |
| 21. | 2021. 4. 30. | $133.42 | $0.8698 | -0.84% | 4,181.17 | 5.24% |
| 22. | 2021. 5. 31. | $134.85 | 1.07% | 4,204.11 | 0.55% | |
| 23. | 2021. 6. 30. | $134.93 | 0.06% | 4,297.50 | 2.22% | |
| 24. | 2021. 7. 31. | $142.23 | $0.8698 | 6.05% | 4,395.26 | 2.27% |
| 25. | 2021. 8. 31. | $142.39 | 0.11% | 4,522.68 | 2.90% | |
| 26. | 2021. 9. 30. | $139.80 | -1.82% | 4,307.54 | -4.76% | |
| 27. | 2021. 10. 31. | $142.99 | $0.8698 | 2.90% | 4,605.38 | 6.91% |
| 28. | 2021. 11. 30. | $144.58 | 1.11% | 4,567.00 | -0.83% | |
| 29. | 2021. 12. 31. | $163.58 | 13.14% | 4,766.18 | 4.36% | |
| 30. | 2022. 1. 31. | $160.45 | $0.8698 | -1.38% | 4,515.55 | -5.26% |
| 31. | 2022. 2. 28. | $155.89 | -2.84% | 4,373.94 | -3.14% | |
| 32. | 2022. 3. 31. | $152.80 | -1.98% | 4,530.41 | 3.58% | |
| 33. | 2022. 4. 30. | $160.55 | $0.9133 | 5.67% | 4,131.93 | -8.80% |
| 34. | 2022. 5. 31. | $147.88 | -7.89% | 4,132.15 | 0.01% | |
| 35. | 2022. 6. 30. | $143.79 | -2.77% | 3,785.38 | -8.39% | |
| 36. | 2022. 7. 31. | $138.91 | $0.9133 | -2.76% | 4,130.29 | 9.11% |
| 37. | 2022. 8. 31. | $137.94 | -0.70% | 3,955.00 | -4.24% | |
| 38. | 2022. 9. 30. | $126.25 | -8.47% | 3,585.62 | -9.34% | |
| 39. | 2022. 10. 31. | $134.67 | $0.9133 | 7.39% | 3,871.98 | 7.99% |
| 40. | 2022. 11. 30. | $149.16 | 10.76% | 4,080.11 | 5.38% | |
| 41. | 2022. 12. 31. | $151.56 | 1.61% | 3,839.50 | -5.90% | |
| 42. | 2023. 1. 31. | $142.38 | $0.9133 | -5.45% | 4,076.60 | 6.18% |
| 43. | 2023. 2. 28. | $137.56 | -3.39% | 3,970.15 | -2.61% | |
| 44. | 2023. 3. 31. | $148.69 | 8.09% | 4,109.31 | 3.51% | |
| 45. | 2023. 4. 30. | $156.38 | $0.9407 | 5.80% | 4,169.48 | 1.46% |
| 46. | 2023. 5. 31. | $142.50 | -8.88% | 4,179.83 | 0.25% | |
| 47. | 2023. 6. 30. | $151.74 | 6.48% | 4,376.86 | 4.71% | |
| 48. | 2023. 7. 31. | $156.30 | $0.9407 | 3.63% | 4,588.96 | 4.85% |
| 49. | 2023. 8. 31. | $154.34 | -1.25% | 4,507.66 | -1.77% | |
| 50. | 2023. 9. 30. | $145.86 | -5.49% | 4,288.05 | -4.87% | |
| 51. | 2023. 10. 31. | $150.03 | $0.9407 | 3.50% | 4,193.80 | -2.20% |
| 52. | 2023. 11. 30. | $153.52 | 2.33% | 4,567.80 | 8.92% | |
| 53. | 2023. 12. 31. | $146.54 | -4.55% | 4,769.83 | 4.42% | |
| 54. | 2024. 1. 31. | $157.14 | $0.9407 | 7.88% | 4,845.65 | 1.59% |
| 55. | 2024. 2. 29. | $158.94 | 1.15% | 5,096.27 | 5.17% | |
| 56. | 2024. 3. 31. | $162.25 | 2.08% | 5,254.35 | 3.10% | |
| 57. | 2024. 4. 30. | $163.20 | $1.0065 | 1.21% | 5,035.69 | -4.16% |
| 58. | 2024. 5. 31. | $164.54 | 0.82% | 5,277.51 | 4.80% | |
| 59. | 2024. 6. 30. | $164.92 | 0.23% | 5,460.48 | 3.47% | |
| 60. | 2024. 7. 31. | $160.76 | $1.0065 | -1.91% | 5,522.30 | 1.13% |
| 61. | 2024. 8. 31. | $171.54 | 6.71% | 5,648.40 | 2.28% | |
| 62. | 2024. 9. 30. | $173.20 | 0.97% | 5,762.48 | 2.02% | |
| 63. | 2024. 10. 31. | $165.18 | $1.0065 | -4.05% | 5,705.45 | -0.99% |
| 64. | 2024. 11. 30. | $179.26 | 8.52% | 6,032.38 | 5.73% | |
| 65. | 2024. 12. 31. | $167.65 | -6.48% | 5,881.63 | -2.50% | |
| 66. | 2025. 1. 31. | $165.99 | $1.0065 | -0.39% | 6,040.53 | 2.70% |
| 67. | 2025. 2. 28. | $173.84 | 4.73% | 5,954.50 | -1.42% | |
| 68. | 2025. 3. 31. | $170.42 | -1.97% | 5,611.85 | -5.75% | |
| 69. | 2025. 4. 30. | $162.57 | $1.0568 | -3.99% | 5,569.06 | -0.76% |
| 70. | 2025. 5. 31. | $169.89 | 4.50% | 5,911.69 | 6.15% | |
| 71. | 2025. 6. 30. | $159.32 | -6.22% | 6,204.95 | 4.96% | |
| 평균의 (R): | 0.74% | 1.16% | ||||
| 표준 편차: | 4.99% | 4.98% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 PG의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Procter & Gamble Co., 수익률의 분산 및 공분산 계산
| t | 날짜 | 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. | 2019. 8. 31. | 1.86% | -1.81% | 1.23 | 8.82 | -3.30 |
| 2. | 2019. 9. 30. | 3.45% | 1.72% | 7.33 | 0.31 | 1.51 |
| 3. | 2019. 10. 31. | 0.70% | 2.04% | 0.00 | 0.78 | -0.04 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2025. 5. 31. | 4.50% | 6.15% | 14.13 | 24.91 | 18.76 |
| 71. | 2025. 6. 30. | -6.22% | 4.96% | 48.53 | 14.44 | -26.47 |
| 합계 (Σ): | 1,740.05 | 1,738.13 | 737.39 | |||
| t | 날짜 | 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. | 2019. 8. 31. | 1.86% | -1.81% | 1.23 | 8.82 | -3.30 |
| 2. | 2019. 9. 30. | 3.45% | 1.72% | 7.33 | 0.31 | 1.51 |
| 3. | 2019. 10. 31. | 0.70% | 2.04% | 0.00 | 0.78 | -0.04 |
| 4. | 2019. 11. 30. | -1.97% | 3.40% | 7.36 | 5.03 | -6.08 |
| 5. | 2019. 12. 31. | 2.33% | 2.86% | 2.50 | 2.88 | 2.69 |
| 6. | 2020. 1. 31. | 0.37% | -0.16% | 0.14 | 1.75 | 0.49 |
| 7. | 2020. 2. 29. | -9.14% | -8.41% | 97.70 | 91.63 | 94.61 |
| 8. | 2020. 3. 31. | -2.85% | -12.51% | 12.94 | 186.95 | 49.18 |
| 9. | 2020. 4. 30. | 7.87% | 12.68% | 50.82 | 132.79 | 82.15 |
| 10. | 2020. 5. 31. | -1.65% | 4.53% | 5.75 | 11.34 | -8.08 |
| 11. | 2020. 6. 30. | 3.15% | 1.84% | 5.78 | 0.46 | 1.63 |
| 12. | 2020. 7. 31. | 10.32% | 5.51% | 91.71 | 18.91 | 41.65 |
| 13. | 2020. 8. 31. | 5.50% | 7.01% | 22.60 | 34.17 | 27.79 |
| 14. | 2020. 9. 30. | 0.48% | -3.92% | 0.07 | 25.85 | 1.36 |
| 15. | 2020. 10. 31. | -0.79% | -2.77% | 2.36 | 15.43 | 6.03 |
| 16. | 2020. 11. 30. | 1.29% | 10.75% | 0.30 | 92.03 | 5.24 |
| 17. | 2020. 12. 31. | 0.19% | 3.71% | 0.30 | 6.51 | -1.40 |
| 18. | 2021. 1. 31. | -7.29% | -1.11% | 64.50 | 5.17 | 18.27 |
| 19. | 2021. 2. 28. | -3.65% | 2.61% | 19.31 | 2.10 | -6.36 |
| 20. | 2021. 3. 31. | 9.63% | 4.24% | 79.01 | 9.50 | 27.40 |
| 21. | 2021. 4. 30. | -0.84% | 5.24% | 2.52 | 16.66 | -6.47 |
| 22. | 2021. 5. 31. | 1.07% | 0.55% | 0.11 | 0.38 | -0.20 |
| 23. | 2021. 6. 30. | 0.06% | 2.22% | 0.47 | 1.12 | -0.73 |
| 24. | 2021. 7. 31. | 6.05% | 2.27% | 28.20 | 1.24 | 5.91 |
| 25. | 2021. 8. 31. | 0.11% | 2.90% | 0.40 | 3.02 | -1.10 |
| 26. | 2021. 9. 30. | -1.82% | -4.76% | 6.57 | 35.02 | 15.17 |
| 27. | 2021. 10. 31. | 2.90% | 6.91% | 4.66 | 33.10 | 12.43 |
| 28. | 2021. 11. 30. | 1.11% | -0.83% | 0.14 | 3.98 | -0.73 |
| 29. | 2021. 12. 31. | 13.14% | 4.36% | 153.69 | 10.24 | 39.67 |
| 30. | 2022. 1. 31. | -1.38% | -5.26% | 4.52 | 41.21 | 13.65 |
| 31. | 2022. 2. 28. | -2.84% | -3.14% | 12.86 | 18.47 | 15.41 |
| 32. | 2022. 3. 31. | -1.98% | 3.58% | 7.43 | 5.84 | -6.59 |
| 33. | 2022. 4. 30. | 5.67% | -8.80% | 24.26 | 99.14 | -49.04 |
| 34. | 2022. 5. 31. | -7.89% | 0.01% | 74.58 | 1.34 | 9.98 |
| 35. | 2022. 6. 30. | -2.77% | -8.39% | 12.32 | 91.26 | 33.53 |
| 36. | 2022. 7. 31. | -2.76% | 9.11% | 12.27 | 63.21 | -27.85 |
| 37. | 2022. 8. 31. | -0.70% | -4.24% | 2.08 | 29.22 | 7.80 |
| 38. | 2022. 9. 30. | -8.47% | -9.34% | 84.99 | 110.27 | 96.81 |
| 39. | 2022. 10. 31. | 7.39% | 7.99% | 44.20 | 46.58 | 45.38 |
| 40. | 2022. 11. 30. | 10.76% | 5.38% | 100.31 | 17.76 | 42.21 |
| 41. | 2022. 12. 31. | 1.61% | -5.90% | 0.75 | 49.82 | -6.10 |
| 42. | 2023. 1. 31. | -5.45% | 6.18% | 38.42 | 25.14 | -31.08 |
| 43. | 2023. 2. 28. | -3.39% | -2.61% | 17.05 | 14.23 | 15.58 |
| 44. | 2023. 3. 31. | 8.09% | 3.51% | 53.97 | 5.49 | 17.22 |
| 45. | 2023. 4. 30. | 5.80% | 1.46% | 25.61 | 0.09 | 1.53 |
| 46. | 2023. 5. 31. | -8.88% | 0.25% | 92.55 | 0.83 | 8.78 |
| 47. | 2023. 6. 30. | 6.48% | 4.71% | 32.95 | 12.62 | 20.39 |
| 48. | 2023. 7. 31. | 3.63% | 4.85% | 8.30 | 13.58 | 10.61 |
| 49. | 2023. 8. 31. | -1.25% | -1.77% | 3.99 | 8.60 | 5.86 |
| 50. | 2023. 9. 30. | -5.49% | -4.87% | 38.92 | 36.40 | 37.64 |
| 51. | 2023. 10. 31. | 3.50% | -2.20% | 7.61 | 11.28 | -9.27 |
| 52. | 2023. 11. 30. | 2.33% | 8.92% | 2.50 | 60.17 | 12.27 |
| 53. | 2023. 12. 31. | -4.55% | 4.42% | 27.99 | 10.64 | -17.26 |
| 54. | 2024. 1. 31. | 7.88% | 1.59% | 50.85 | 0.18 | 3.06 |
| 55. | 2024. 2. 29. | 1.15% | 5.17% | 0.16 | 16.09 | 1.61 |
| 56. | 2024. 3. 31. | 2.08% | 3.10% | 1.79 | 3.77 | 2.60 |
| 57. | 2024. 4. 30. | 1.21% | -4.16% | 0.21 | 28.33 | -2.46 |
| 58. | 2024. 5. 31. | 0.82% | 4.80% | 0.01 | 13.26 | 0.28 |
| 59. | 2024. 6. 30. | 0.23% | 3.47% | 0.26 | 5.32 | -1.18 |
| 60. | 2024. 7. 31. | -1.91% | 1.13% | 7.06 | 0.00 | 0.08 |
| 61. | 2024. 8. 31. | 6.71% | 2.28% | 35.54 | 1.26 | 6.69 |
| 62. | 2024. 9. 30. | 0.97% | 2.02% | 0.05 | 0.74 | 0.19 |
| 63. | 2024. 10. 31. | -4.05% | -0.99% | 22.98 | 4.63 | 10.31 |
| 64. | 2024. 11. 30. | 8.52% | 5.73% | 60.52 | 20.88 | 35.55 |
| 65. | 2024. 12. 31. | -6.48% | -2.50% | 52.14 | 13.40 | 26.43 |
| 66. | 2025. 1. 31. | -0.39% | 2.70% | 1.29 | 2.37 | -1.75 |
| 67. | 2025. 2. 28. | 4.73% | -1.42% | 15.88 | 6.68 | -10.30 |
| 68. | 2025. 3. 31. | -1.97% | -5.75% | 7.35 | 47.83 | 18.75 |
| 69. | 2025. 4. 30. | -3.99% | -0.76% | 22.38 | 3.70 | 9.10 |
| 70. | 2025. 5. 31. | 4.50% | 6.15% | 14.13 | 24.91 | 18.76 |
| 71. | 2025. 6. 30. | -6.22% | 4.96% | 48.53 | 14.44 | -26.47 |
| 합계 (Σ): | 1,740.05 | 1,738.13 | 737.39 | |||
모두 보기
분산PG = Σ(RPG,t–RPG)2 ÷ (71 – 1)
= 1,740.05 ÷ (71 – 1)
= 24.86
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,738.13 ÷ (71 – 1)
= 24.83
공분산PG, S&P 500 = Σ(RPG,t–RPG)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 737.39 ÷ (71 – 1)
= 10.53
체계적인 위험 추정 (β)
| 분산PG | 24.86 |
| 분산S&P 500 | 24.83 |
| 공분산PG, S&P 500 | 10.53 |
| 상관 계수PG, S&P 5001 | 0.42 |
| βPG2 | 0.42 |
| αPG3 | 0.25% |
계산
1 상관 계수PG, S&P 500
= 공분산PG, S&P 500 ÷ (표준 편차PG × 표준 편차S&P 500)
= 10.53 ÷ (4.99% × 4.98%)
= 0.42
2 βPG
= 공분산PG, S&P 500 ÷ 분산S&P 500
= 10.53 ÷ 24.83
= 0.42
3 αPG
= 평균의PG – βPG × 평균의S&P 500
= 0.74% – 0.42 × 1.16%
= 0.25%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.61% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.88% |
| 보통주의 체계적 위험P&G | βPG | 0.42 |
| P&G 보통주 기대수익률3 | E(RPG) | 8.97% |
1 10년 이내에 만기가 도래하거나 콜링할 수 없는 모든 미결제 고정 쿠폰 미국 국채에 대한 입찰 수익률의 비가중 평균(무위험 수익률 대리).
2 자세히 보기 »
3 E(RPG) = RF + βPG [E(RM) – RF]
= 4.61% + 0.42 [14.88% – 4.61%]
= 8.97%