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 |
| 2018. 7. 31. | $80.88 | 2,816.29 | ||||
| 1. | 2018. 8. 31. | $82.95 | 2.56% | 2,901.52 | 3.03% | |
| 2. | 2018. 9. 30. | $83.23 | 0.34% | 2,913.98 | 0.43% | |
| 3. | 2018. 10. 31. | $88.68 | $0.7172 | 7.41% | 2,711.74 | -6.94% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2024. 5. 31. | $164.54 | 0.82% | 5,277.51 | 4.80% | |
| 71. | 2024. 6. 30. | $164.92 | 0.23% | 5,460.48 | 3.47% | |
| 평균의 (R): | 1.33% | 1.07% | ||||
| 표준 편차: | 4.91% | 5.24% | ||||
| 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 |
| 2018. 7. 31. | $80.88 | 2,816.29 | ||||
| 1. | 2018. 8. 31. | $82.95 | 2.56% | 2,901.52 | 3.03% | |
| 2. | 2018. 9. 30. | $83.23 | 0.34% | 2,913.98 | 0.43% | |
| 3. | 2018. 10. 31. | $88.68 | $0.7172 | 7.41% | 2,711.74 | -6.94% |
| 4. | 2018. 11. 30. | $94.51 | 6.57% | 2,760.17 | 1.79% | |
| 5. | 2018. 12. 31. | $91.92 | -2.74% | 2,506.85 | -9.18% | |
| 6. | 2019. 1. 31. | $96.47 | $0.7172 | 5.73% | 2,704.10 | 7.87% |
| 7. | 2019. 2. 28. | $98.55 | 2.16% | 2,784.49 | 2.97% | |
| 8. | 2019. 3. 31. | $104.05 | 5.58% | 2,834.40 | 1.79% | |
| 9. | 2019. 4. 30. | $106.48 | $0.7459 | 3.05% | 2,945.83 | 3.93% |
| 10. | 2019. 5. 31. | $102.91 | -3.35% | 2,752.06 | -6.58% | |
| 11. | 2019. 6. 30. | $109.65 | 6.55% | 2,941.76 | 6.89% | |
| 12. | 2019. 7. 31. | $118.04 | $0.7459 | 8.33% | 2,980.38 | 1.31% |
| 13. | 2019. 8. 31. | $120.23 | 1.86% | 2,926.46 | -1.81% | |
| 14. | 2019. 9. 30. | $124.38 | 3.45% | 2,976.74 | 1.72% | |
| 15. | 2019. 10. 31. | $124.51 | $0.7459 | 0.70% | 3,037.56 | 2.04% |
| 16. | 2019. 11. 30. | $122.06 | -1.97% | 3,140.98 | 3.40% | |
| 17. | 2019. 12. 31. | $124.90 | 2.33% | 3,230.78 | 2.86% | |
| 18. | 2020. 1. 31. | $124.62 | $0.7459 | 0.37% | 3,225.52 | -0.16% |
| 19. | 2020. 2. 29. | $113.23 | -9.14% | 2,954.22 | -8.41% | |
| 20. | 2020. 3. 31. | $110.00 | -2.85% | 2,584.59 | -12.51% | |
| 21. | 2020. 4. 30. | $117.87 | $0.7907 | 7.87% | 2,912.43 | 12.68% |
| 22. | 2020. 5. 31. | $115.92 | -1.65% | 3,044.31 | 4.53% | |
| 23. | 2020. 6. 30. | $119.57 | 3.15% | 3,100.29 | 1.84% | |
| 24. | 2020. 7. 31. | $131.12 | $0.7907 | 10.32% | 3,271.12 | 5.51% |
| 25. | 2020. 8. 31. | $138.33 | 5.50% | 3,500.31 | 7.01% | |
| 26. | 2020. 9. 30. | $138.99 | 0.48% | 3,363.00 | -3.92% | |
| 27. | 2020. 10. 31. | $137.10 | $0.7907 | -0.79% | 3,269.96 | -2.77% |
| 28. | 2020. 11. 30. | $138.87 | 1.29% | 3,621.63 | 10.75% | |
| 29. | 2020. 12. 31. | $139.14 | 0.19% | 3,756.07 | 3.71% | |
| 30. | 2021. 1. 31. | $128.21 | $0.7907 | -7.29% | 3,714.24 | -1.11% |
| 31. | 2021. 2. 28. | $123.53 | -3.65% | 3,811.15 | 2.61% | |
| 32. | 2021. 3. 31. | $135.43 | 9.63% | 3,972.89 | 4.24% | |
| 33. | 2021. 4. 30. | $133.42 | $0.8698 | -0.84% | 4,181.17 | 5.24% |
| 34. | 2021. 5. 31. | $134.85 | 1.07% | 4,204.11 | 0.55% | |
| 35. | 2021. 6. 30. | $134.93 | 0.06% | 4,297.50 | 2.22% | |
| 36. | 2021. 7. 31. | $142.23 | $0.8698 | 6.05% | 4,395.26 | 2.27% |
| 37. | 2021. 8. 31. | $142.39 | 0.11% | 4,522.68 | 2.90% | |
| 38. | 2021. 9. 30. | $139.80 | -1.82% | 4,307.54 | -4.76% | |
| 39. | 2021. 10. 31. | $142.99 | $0.8698 | 2.90% | 4,605.38 | 6.91% |
| 40. | 2021. 11. 30. | $144.58 | 1.11% | 4,567.00 | -0.83% | |
| 41. | 2021. 12. 31. | $163.58 | 13.14% | 4,766.18 | 4.36% | |
| 42. | 2022. 1. 31. | $160.45 | $0.8698 | -1.38% | 4,515.55 | -5.26% |
| 43. | 2022. 2. 28. | $155.89 | -2.84% | 4,373.94 | -3.14% | |
| 44. | 2022. 3. 31. | $152.80 | -1.98% | 4,530.41 | 3.58% | |
| 45. | 2022. 4. 30. | $160.55 | $0.9133 | 5.67% | 4,131.93 | -8.80% |
| 46. | 2022. 5. 31. | $147.88 | -7.89% | 4,132.15 | 0.01% | |
| 47. | 2022. 6. 30. | $143.79 | -2.77% | 3,785.38 | -8.39% | |
| 48. | 2022. 7. 31. | $138.91 | $0.9133 | -2.76% | 4,130.29 | 9.11% |
| 49. | 2022. 8. 31. | $137.94 | -0.70% | 3,955.00 | -4.24% | |
| 50. | 2022. 9. 30. | $126.25 | -8.47% | 3,585.62 | -9.34% | |
| 51. | 2022. 10. 31. | $134.67 | $0.9133 | 7.39% | 3,871.98 | 7.99% |
| 52. | 2022. 11. 30. | $149.16 | 10.76% | 4,080.11 | 5.38% | |
| 53. | 2022. 12. 31. | $151.56 | 1.61% | 3,839.50 | -5.90% | |
| 54. | 2023. 1. 31. | $142.38 | $0.9133 | -5.45% | 4,076.60 | 6.18% |
| 55. | 2023. 2. 28. | $137.56 | -3.39% | 3,970.15 | -2.61% | |
| 56. | 2023. 3. 31. | $148.69 | 8.09% | 4,109.31 | 3.51% | |
| 57. | 2023. 4. 30. | $156.38 | $0.9407 | 5.80% | 4,169.48 | 1.46% |
| 58. | 2023. 5. 31. | $142.50 | -8.88% | 4,179.83 | 0.25% | |
| 59. | 2023. 6. 30. | $151.74 | 6.48% | 4,376.86 | 4.71% | |
| 60. | 2023. 7. 31. | $156.30 | $0.9407 | 3.63% | 4,588.96 | 4.85% |
| 61. | 2023. 8. 31. | $154.34 | -1.25% | 4,507.66 | -1.77% | |
| 62. | 2023. 9. 30. | $145.86 | -5.49% | 4,288.05 | -4.87% | |
| 63. | 2023. 10. 31. | $150.03 | $0.9407 | 3.50% | 4,193.80 | -2.20% |
| 64. | 2023. 11. 30. | $153.52 | 2.33% | 4,567.80 | 8.92% | |
| 65. | 2023. 12. 31. | $146.54 | -4.55% | 4,769.83 | 4.42% | |
| 66. | 2024. 1. 31. | $157.14 | $0.9407 | 7.88% | 4,845.65 | 1.59% |
| 67. | 2024. 2. 29. | $158.94 | 1.15% | 5,096.27 | 5.17% | |
| 68. | 2024. 3. 31. | $162.25 | 2.08% | 5,254.35 | 3.10% | |
| 69. | 2024. 4. 30. | $163.20 | $1.0065 | 1.21% | 5,035.69 | -4.16% |
| 70. | 2024. 5. 31. | $164.54 | 0.82% | 5,277.51 | 4.80% | |
| 71. | 2024. 6. 30. | $164.92 | 0.23% | 5,460.48 | 3.47% | |
| 평균의 (R): | 1.33% | 1.07% | ||||
| 표준 편차: | 4.91% | 5.24% | ||||
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. | 2018. 8. 31. | 2.56% | 3.03% | 1.51 | 3.81 | 2.40 |
| 2. | 2018. 9. 30. | 0.34% | 0.43% | 0.99 | 0.41 | 0.64 |
| 3. | 2018. 10. 31. | 7.41% | -6.94% | 36.93 | 64.22 | -48.70 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2024. 5. 31. | 0.82% | 4.80% | 0.26 | 13.90 | -1.91 |
| 71. | 2024. 6. 30. | 0.23% | 3.47% | 1.21 | 5.73 | -2.64 |
| 합계 (Σ): | 1,685.30 | 1,922.79 | 754.65 | |||
| 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. | 2018. 8. 31. | 2.56% | 3.03% | 1.51 | 3.81 | 2.40 |
| 2. | 2018. 9. 30. | 0.34% | 0.43% | 0.99 | 0.41 | 0.64 |
| 3. | 2018. 10. 31. | 7.41% | -6.94% | 36.93 | 64.22 | -48.70 |
| 4. | 2018. 11. 30. | 6.57% | 1.79% | 27.47 | 0.51 | 3.74 |
| 5. | 2018. 12. 31. | -2.74% | -9.18% | 16.59 | 105.08 | 41.75 |
| 6. | 2019. 1. 31. | 5.73% | 7.87% | 19.34 | 46.17 | 29.88 |
| 7. | 2019. 2. 28. | 2.16% | 2.97% | 0.68 | 3.61 | 1.56 |
| 8. | 2019. 3. 31. | 5.58% | 1.79% | 18.05 | 0.52 | 3.05 |
| 9. | 2019. 4. 30. | 3.05% | 3.93% | 2.96 | 8.17 | 4.91 |
| 10. | 2019. 5. 31. | -3.35% | -6.58% | 21.95 | 58.54 | 35.85 |
| 11. | 2019. 6. 30. | 6.55% | 6.89% | 27.22 | 33.87 | 30.36 |
| 12. | 2019. 7. 31. | 8.33% | 1.31% | 48.99 | 0.06 | 1.68 |
| 13. | 2019. 8. 31. | 1.86% | -1.81% | 0.27 | 8.31 | -1.51 |
| 14. | 2019. 9. 30. | 3.45% | 1.72% | 4.49 | 0.42 | 1.37 |
| 15. | 2019. 10. 31. | 0.70% | 2.04% | 0.39 | 0.94 | -0.61 |
| 16. | 2019. 11. 30. | -1.97% | 3.40% | 10.89 | 5.44 | -7.69 |
| 17. | 2019. 12. 31. | 2.33% | 2.86% | 0.99 | 3.19 | 1.78 |
| 18. | 2020. 1. 31. | 0.37% | -0.16% | 0.92 | 1.53 | 1.19 |
| 19. | 2020. 2. 29. | -9.14% | -8.41% | 109.67 | 89.95 | 99.32 |
| 20. | 2020. 3. 31. | -2.85% | -12.51% | 17.52 | 184.56 | 56.86 |
| 21. | 2020. 4. 30. | 7.87% | 12.68% | 42.78 | 134.82 | 75.95 |
| 22. | 2020. 5. 31. | -1.65% | 4.53% | 8.92 | 11.94 | -10.32 |
| 23. | 2020. 6. 30. | 3.15% | 1.84% | 3.30 | 0.59 | 1.39 |
| 24. | 2020. 7. 31. | 10.32% | 5.51% | 80.79 | 19.68 | 39.88 |
| 25. | 2020. 8. 31. | 5.50% | 7.01% | 17.36 | 35.20 | 24.72 |
| 26. | 2020. 9. 30. | 0.48% | -3.92% | 0.73 | 24.96 | 4.27 |
| 27. | 2020. 10. 31. | -0.79% | -2.77% | 4.51 | 14.75 | 8.15 |
| 28. | 2020. 11. 30. | 1.29% | 10.75% | 0.00 | 93.73 | -0.40 |
| 29. | 2020. 12. 31. | 0.19% | 3.71% | 1.30 | 6.96 | -3.00 |
| 30. | 2021. 1. 31. | -7.29% | -1.11% | 74.30 | 4.78 | 18.85 |
| 31. | 2021. 2. 28. | -3.65% | 2.61% | 24.83 | 2.36 | -7.65 |
| 32. | 2021. 3. 31. | 9.63% | 4.24% | 68.90 | 10.05 | 26.32 |
| 33. | 2021. 4. 30. | -0.84% | 5.24% | 4.73 | 17.38 | -9.07 |
| 34. | 2021. 5. 31. | 1.07% | 0.55% | 0.07 | 0.28 | 0.14 |
| 35. | 2021. 6. 30. | 0.06% | 2.22% | 1.62 | 1.32 | -1.46 |
| 36. | 2021. 7. 31. | 6.05% | 2.27% | 22.30 | 1.44 | 5.67 |
| 37. | 2021. 8. 31. | 0.11% | 2.90% | 1.49 | 3.33 | -2.23 |
| 38. | 2021. 9. 30. | -1.82% | -4.76% | 9.93 | 33.99 | 18.37 |
| 39. | 2021. 10. 31. | 2.90% | 6.91% | 2.47 | 34.12 | 9.18 |
| 40. | 2021. 11. 30. | 1.11% | -0.83% | 0.05 | 3.64 | 0.42 |
| 41. | 2021. 12. 31. | 13.14% | 4.36% | 139.45 | 10.81 | 38.83 |
| 42. | 2022. 1. 31. | -1.38% | -5.26% | 7.37 | 40.09 | 17.19 |
| 43. | 2022. 2. 28. | -2.84% | -3.14% | 17.43 | 17.72 | 17.57 |
| 44. | 2022. 3. 31. | -1.98% | 3.58% | 10.99 | 6.27 | -8.30 |
| 45. | 2022. 4. 30. | 5.67% | -8.80% | 18.81 | 97.40 | -42.80 |
| 46. | 2022. 5. 31. | -7.89% | 0.01% | 85.09 | 1.14 | 9.85 |
| 47. | 2022. 6. 30. | -2.77% | -8.39% | 16.80 | 89.59 | 38.79 |
| 48. | 2022. 7. 31. | -2.76% | 9.11% | 16.74 | 64.61 | -32.89 |
| 49. | 2022. 8. 31. | -0.70% | -4.24% | 4.12 | 28.27 | 10.80 |
| 50. | 2022. 9. 30. | -8.47% | -9.34% | 96.18 | 108.43 | 102.12 |
| 51. | 2022. 10. 31. | 7.39% | 7.99% | 36.73 | 47.79 | 41.89 |
| 52. | 2022. 11. 30. | 10.76% | 5.38% | 88.87 | 18.51 | 40.55 |
| 53. | 2022. 12. 31. | 1.61% | -5.90% | 0.08 | 48.59 | -1.93 |
| 54. | 2023. 1. 31. | -5.45% | 6.18% | 46.06 | 26.03 | -34.63 |
| 55. | 2023. 2. 28. | -3.39% | -2.61% | 22.26 | 13.58 | 17.38 |
| 56. | 2023. 3. 31. | 8.09% | 3.51% | 45.68 | 5.91 | 16.44 |
| 57. | 2023. 4. 30. | 5.80% | 1.46% | 20.00 | 0.15 | 1.75 |
| 58. | 2023. 5. 31. | -8.88% | 0.25% | 104.21 | 0.68 | 8.42 |
| 59. | 2023. 6. 30. | 6.48% | 4.71% | 26.54 | 13.25 | 18.75 |
| 60. | 2023. 7. 31. | 3.63% | 4.85% | 5.26 | 14.23 | 8.65 |
| 61. | 2023. 8. 31. | -1.25% | -1.77% | 6.69 | 8.09 | 7.36 |
| 62. | 2023. 9. 30. | -5.49% | -4.87% | 46.61 | 35.35 | 40.59 |
| 63. | 2023. 10. 31. | 3.50% | -2.20% | 4.71 | 10.70 | -7.10 |
| 64. | 2023. 11. 30. | 2.33% | 8.92% | 0.99 | 61.54 | 7.79 |
| 65. | 2023. 12. 31. | -4.55% | 4.42% | 34.56 | 11.22 | -19.69 |
| 66. | 2024. 1. 31. | 7.88% | 1.59% | 42.81 | 0.27 | 3.38 |
| 67. | 2024. 2. 29. | 1.15% | 5.17% | 0.03 | 16.80 | -0.77 |
| 68. | 2024. 3. 31. | 2.08% | 3.10% | 0.56 | 4.11 | 1.52 |
| 69. | 2024. 4. 30. | 1.21% | -4.16% | 0.02 | 27.40 | 0.66 |
| 70. | 2024. 5. 31. | 0.82% | 4.80% | 0.26 | 13.90 | -1.91 |
| 71. | 2024. 6. 30. | 0.23% | 3.47% | 1.21 | 5.73 | -2.64 |
| 합계 (Σ): | 1,685.30 | 1,922.79 | 754.65 | |||
모두 보기
분산PG = Σ(RPG,t–RPG)2 ÷ (71 – 1)
= 1,685.30 ÷ (71 – 1)
= 24.08
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,922.79 ÷ (71 – 1)
= 27.47
공분산PG, S&P 500 = Σ(RPG,t–RPG)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 754.65 ÷ (71 – 1)
= 10.78
체계적인 위험 추정 (β)
| 분산PG | 24.08 |
| 분산S&P 500 | 27.47 |
| 공분산PG, S&P 500 | 10.78 |
| 상관 계수PG, S&P 5001 | 0.42 |
| βPG2 | 0.39 |
| αPG3 | 0.91% |
계산
1 상관 계수PG, S&P 500
= 공분산PG, S&P 500 ÷ (표준 편차PG × 표준 편차S&P 500)
= 10.78 ÷ (4.91% × 5.24%)
= 0.42
2 βPG
= 공분산PG, S&P 500 ÷ 분산S&P 500
= 10.78 ÷ 27.47
= 0.39
3 αPG
= 평균의PG – βPG × 평균의S&P 500
= 1.33% – 0.39 × 1.07%
= 0.91%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.91% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.84% |
| 보통주의 체계적 위험P&G | βPG | 0.39 |
| P&G 보통주 기대수익률3 | E(RPG) | 8.81% |
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]
= 4.91% + 0.39 [14.84% – 4.91%]
= 8.81%