자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Salesforce보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Salesforce Inc., 월별 수익률
| Salesforce Inc. (CRM) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값CRM,t1 | 피제수CRM,t1 | RCRM,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2018. 2. 28. | $116.25 | 2,713.83 | ||||
| 1. | 2018. 3. 31. | $116.30 | 0.04% | 2,640.87 | -2.69% | |
| 2. | 2018. 4. 30. | $120.99 | 4.03% | 2,648.05 | 0.27% | |
| 3. | 2018. 5. 31. | $129.33 | 6.89% | 2,705.27 | 2.16% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2023. 12. 31. | $263.14 | 4.46% | 4,769.83 | 4.42% | |
| 71. | 2024. 1. 31. | $281.09 | 6.82% | 4,845.65 | 1.59% | |
| 평균의 (R): | 1.74% | 0.95% | ||||
| 표준 편차: | 10.20% | 5.18% | ||||
| Salesforce Inc. (CRM) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값CRM,t1 | 피제수CRM,t1 | RCRM,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2018. 2. 28. | $116.25 | 2,713.83 | ||||
| 1. | 2018. 3. 31. | $116.30 | 0.04% | 2,640.87 | -2.69% | |
| 2. | 2018. 4. 30. | $120.99 | 4.03% | 2,648.05 | 0.27% | |
| 3. | 2018. 5. 31. | $129.33 | 6.89% | 2,705.27 | 2.16% | |
| 4. | 2018. 6. 30. | $136.40 | 5.47% | 2,718.37 | 0.48% | |
| 5. | 2018. 7. 31. | $137.15 | 0.55% | 2,816.29 | 3.60% | |
| 6. | 2018. 8. 31. | $152.68 | 11.32% | 2,901.52 | 3.03% | |
| 7. | 2018. 9. 30. | $159.03 | 4.16% | 2,913.98 | 0.43% | |
| 8. | 2018. 10. 31. | $137.24 | -13.70% | 2,711.74 | -6.94% | |
| 9. | 2018. 11. 30. | $142.76 | 4.02% | 2,760.17 | 1.79% | |
| 10. | 2018. 12. 31. | $136.97 | -4.06% | 2,506.85 | -9.18% | |
| 11. | 2019. 1. 31. | $151.97 | 10.95% | 2,704.10 | 7.87% | |
| 12. | 2019. 2. 28. | $163.65 | 7.69% | 2,784.49 | 2.97% | |
| 13. | 2019. 3. 31. | $158.37 | -3.23% | 2,834.40 | 1.79% | |
| 14. | 2019. 4. 30. | $165.35 | 4.41% | 2,945.83 | 3.93% | |
| 15. | 2019. 5. 31. | $151.41 | -8.43% | 2,752.06 | -6.58% | |
| 16. | 2019. 6. 30. | $151.73 | 0.21% | 2,941.76 | 6.89% | |
| 17. | 2019. 7. 31. | $154.50 | 1.83% | 2,980.38 | 1.31% | |
| 18. | 2019. 8. 31. | $156.07 | 1.02% | 2,926.46 | -1.81% | |
| 19. | 2019. 9. 30. | $148.44 | -4.89% | 2,976.74 | 1.72% | |
| 20. | 2019. 10. 31. | $156.49 | 5.42% | 3,037.56 | 2.04% | |
| 21. | 2019. 11. 30. | $162.89 | 4.09% | 3,140.98 | 3.40% | |
| 22. | 2019. 12. 31. | $162.64 | -0.15% | 3,230.78 | 2.86% | |
| 23. | 2020. 1. 31. | $182.31 | 12.09% | 3,225.52 | -0.16% | |
| 24. | 2020. 2. 29. | $170.40 | -6.53% | 2,954.22 | -8.41% | |
| 25. | 2020. 3. 31. | $143.98 | -15.50% | 2,584.59 | -12.51% | |
| 26. | 2020. 4. 30. | $161.95 | 12.48% | 2,912.43 | 12.68% | |
| 27. | 2020. 5. 31. | $174.79 | 7.93% | 3,044.31 | 4.53% | |
| 28. | 2020. 6. 30. | $187.33 | 7.17% | 3,100.29 | 1.84% | |
| 29. | 2020. 7. 31. | $194.85 | 4.01% | 3,271.12 | 5.51% | |
| 30. | 2020. 8. 31. | $272.65 | 39.93% | 3,500.31 | 7.01% | |
| 31. | 2020. 9. 30. | $251.32 | -7.82% | 3,363.00 | -3.92% | |
| 32. | 2020. 10. 31. | $232.27 | -7.58% | 3,269.96 | -2.77% | |
| 33. | 2020. 11. 30. | $245.80 | 5.83% | 3,621.63 | 10.75% | |
| 34. | 2020. 12. 31. | $222.53 | -9.47% | 3,756.07 | 3.71% | |
| 35. | 2021. 1. 31. | $225.56 | 1.36% | 3,714.24 | -1.11% | |
| 36. | 2021. 2. 28. | $216.50 | -4.02% | 3,811.15 | 2.61% | |
| 37. | 2021. 3. 31. | $211.87 | -2.14% | 3,972.89 | 4.24% | |
| 38. | 2021. 4. 30. | $230.32 | 8.71% | 4,181.17 | 5.24% | |
| 39. | 2021. 5. 31. | $238.10 | 3.38% | 4,204.11 | 0.55% | |
| 40. | 2021. 6. 30. | $244.27 | 2.59% | 4,297.50 | 2.22% | |
| 41. | 2021. 7. 31. | $241.93 | -0.96% | 4,395.26 | 2.27% | |
| 42. | 2021. 8. 31. | $265.27 | 9.65% | 4,522.68 | 2.90% | |
| 43. | 2021. 9. 30. | $271.22 | 2.24% | 4,307.54 | -4.76% | |
| 44. | 2021. 10. 31. | $299.69 | 10.50% | 4,605.38 | 6.91% | |
| 45. | 2021. 11. 30. | $284.96 | -4.92% | 4,567.00 | -0.83% | |
| 46. | 2021. 12. 31. | $254.13 | -10.82% | 4,766.18 | 4.36% | |
| 47. | 2022. 1. 31. | $232.63 | -8.46% | 4,515.55 | -5.26% | |
| 48. | 2022. 2. 28. | $210.53 | -9.50% | 4,373.94 | -3.14% | |
| 49. | 2022. 3. 31. | $212.32 | 0.85% | 4,530.41 | 3.58% | |
| 50. | 2022. 4. 30. | $175.94 | -17.13% | 4,131.93 | -8.80% | |
| 51. | 2022. 5. 31. | $160.24 | -8.92% | 4,132.15 | 0.01% | |
| 52. | 2022. 6. 30. | $165.04 | 3.00% | 3,785.38 | -8.39% | |
| 53. | 2022. 7. 31. | $184.02 | 11.50% | 4,130.29 | 9.11% | |
| 54. | 2022. 8. 31. | $156.12 | -15.16% | 3,955.00 | -4.24% | |
| 55. | 2022. 9. 30. | $143.84 | -7.87% | 3,585.62 | -9.34% | |
| 56. | 2022. 10. 31. | $162.59 | 13.04% | 3,871.98 | 7.99% | |
| 57. | 2022. 11. 30. | $160.25 | -1.44% | 4,080.11 | 5.38% | |
| 58. | 2022. 12. 31. | $132.59 | -17.26% | 3,839.50 | -5.90% | |
| 59. | 2023. 1. 31. | $167.97 | 26.68% | 4,076.60 | 6.18% | |
| 60. | 2023. 2. 28. | $163.61 | -2.60% | 3,970.15 | -2.61% | |
| 61. | 2023. 3. 31. | $199.78 | 22.11% | 4,109.31 | 3.51% | |
| 62. | 2023. 4. 30. | $198.37 | -0.71% | 4,169.48 | 1.46% | |
| 63. | 2023. 5. 31. | $223.38 | 12.61% | 4,179.83 | 0.25% | |
| 64. | 2023. 6. 30. | $211.26 | -5.43% | 4,376.86 | 4.71% | |
| 65. | 2023. 7. 31. | $225.01 | 6.51% | 4,588.96 | 4.85% | |
| 66. | 2023. 8. 31. | $221.46 | -1.58% | 4,507.66 | -1.77% | |
| 67. | 2023. 9. 30. | $202.78 | -8.43% | 4,288.05 | -4.87% | |
| 68. | 2023. 10. 31. | $200.83 | -0.96% | 4,193.80 | -2.20% | |
| 69. | 2023. 11. 30. | $251.90 | 25.43% | 4,567.80 | 8.92% | |
| 70. | 2023. 12. 31. | $263.14 | 4.46% | 4,769.83 | 4.42% | |
| 71. | 2024. 1. 31. | $281.09 | 6.82% | 4,845.65 | 1.59% | |
| 평균의 (R): | 1.74% | 0.95% | ||||
| 표준 편차: | 10.20% | 5.18% | ||||
모두 표시
1 보통주 주당 US$ 단위의 데이터로, 분할 및 주식 배당금에 맞게 조정됩니다.
2 기간 t 동안 CRM의 보통주에 대한 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)에 대한 수익률.
분산과 공분산
Salesforce Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RCRM,t | RS&P 500,t | (RCRM,t–RCRM)2 | (RS&P 500,t–RS&P 500)2 | (RCRM,t–RCRM)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018. 3. 31. | 0.04% | -2.69% | 2.87 | 13.26 | 6.17 |
| 2. | 2018. 4. 30. | 4.03% | 0.27% | 5.27 | 0.46 | -1.56 |
| 3. | 2018. 5. 31. | 6.89% | 2.16% | 26.59 | 1.46 | 6.23 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2023. 12. 31. | 4.46% | 4.42% | 7.43 | 12.04 | 9.46 |
| 71. | 2024. 1. 31. | 6.82% | 1.59% | 25.85 | 0.41 | 3.24 |
| 합계 (Σ): | 7,284.09 | 1,876.53 | 2,389.03 | |||
| t | 날짜 | RCRM,t | RS&P 500,t | (RCRM,t–RCRM)2 | (RS&P 500,t–RS&P 500)2 | (RCRM,t–RCRM)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018. 3. 31. | 0.04% | -2.69% | 2.87 | 13.26 | 6.17 |
| 2. | 2018. 4. 30. | 4.03% | 0.27% | 5.27 | 0.46 | -1.56 |
| 3. | 2018. 5. 31. | 6.89% | 2.16% | 26.59 | 1.46 | 6.23 |
| 4. | 2018. 6. 30. | 5.47% | 0.48% | 13.91 | 0.22 | -1.75 |
| 5. | 2018. 7. 31. | 0.55% | 3.60% | 1.41 | 7.02 | -3.14 |
| 6. | 2018. 8. 31. | 11.32% | 3.03% | 91.90 | 4.30 | 19.88 |
| 7. | 2018. 9. 30. | 4.16% | 0.43% | 5.87 | 0.27 | -1.27 |
| 8. | 2018. 10. 31. | -13.70% | -6.94% | 238.35 | 62.30 | 121.86 |
| 9. | 2018. 11. 30. | 4.02% | 1.79% | 5.22 | 0.69 | 1.90 |
| 10. | 2018. 12. 31. | -4.06% | -9.18% | 33.55 | 102.63 | 58.68 |
| 11. | 2019. 1. 31. | 10.95% | 7.87% | 84.91 | 47.82 | 63.72 |
| 12. | 2019. 2. 28. | 7.69% | 2.97% | 35.39 | 4.08 | 12.02 |
| 13. | 2019. 3. 31. | -3.23% | 1.79% | 24.63 | 0.70 | -4.17 |
| 14. | 2019. 4. 30. | 4.41% | 3.93% | 7.13 | 8.87 | 7.95 |
| 15. | 2019. 5. 31. | -8.43% | -6.58% | 103.38 | 56.71 | 76.57 |
| 16. | 2019. 6. 30. | 0.21% | 6.89% | 2.33 | 35.28 | -9.06 |
| 17. | 2019. 7. 31. | 1.83% | 1.31% | 0.01 | 0.13 | 0.03 |
| 18. | 2019. 8. 31. | 1.02% | -1.81% | 0.52 | 7.63 | 1.99 |
| 19. | 2019. 9. 30. | -4.89% | 1.72% | 43.90 | 0.59 | -5.07 |
| 20. | 2019. 10. 31. | 5.42% | 2.04% | 13.59 | 1.19 | 4.02 |
| 21. | 2019. 11. 30. | 4.09% | 3.40% | 5.54 | 6.01 | 5.77 |
| 22. | 2019. 12. 31. | -0.15% | 2.86% | 3.57 | 3.63 | -3.60 |
| 23. | 2020. 1. 31. | 12.09% | -0.16% | 107.27 | 1.24 | -11.56 |
| 24. | 2020. 2. 29. | -6.53% | -8.41% | 68.39 | 87.68 | 77.44 |
| 25. | 2020. 3. 31. | -15.50% | -12.51% | 297.27 | 181.30 | 232.15 |
| 26. | 2020. 4. 30. | 12.48% | 12.68% | 115.43 | 137.63 | 126.04 |
| 27. | 2020. 5. 31. | 7.93% | 4.53% | 38.34 | 12.78 | 22.14 |
| 28. | 2020. 6. 30. | 7.17% | 1.84% | 29.57 | 0.78 | 4.82 |
| 29. | 2020. 7. 31. | 4.01% | 5.51% | 5.19 | 20.77 | 10.38 |
| 30. | 2020. 8. 31. | 39.93% | 7.01% | 1,458.58 | 36.65 | 231.19 |
| 31. | 2020. 9. 30. | -7.82% | -3.92% | 91.39 | 23.77 | 46.61 |
| 32. | 2020. 10. 31. | -7.58% | -2.77% | 86.80 | 13.83 | 34.65 |
| 33. | 2020. 11. 30. | 5.83% | 10.75% | 16.71 | 96.07 | 40.07 |
| 34. | 2020. 12. 31. | -9.47% | 3.71% | 125.53 | 7.61 | -30.91 |
| 35. | 2021. 1. 31. | 1.36% | -1.11% | 0.14 | 4.27 | 0.78 |
| 36. | 2021. 2. 28. | -4.02% | 2.61% | 33.10 | 2.74 | -9.53 |
| 37. | 2021. 3. 31. | -2.14% | 4.24% | 15.02 | 10.83 | -12.75 |
| 38. | 2021. 4. 30. | 8.71% | 5.24% | 48.60 | 18.40 | 29.90 |
| 39. | 2021. 5. 31. | 3.38% | 0.55% | 2.69 | 0.16 | -0.66 |
| 40. | 2021. 6. 30. | 2.59% | 2.22% | 0.73 | 1.61 | 1.08 |
| 41. | 2021. 7. 31. | -0.96% | 2.27% | 7.26 | 1.75 | -3.56 |
| 42. | 2021. 8. 31. | 9.65% | 2.90% | 62.58 | 3.79 | 15.39 |
| 43. | 2021. 9. 30. | 2.24% | -4.76% | 0.26 | 32.60 | -2.89 |
| 44. | 2021. 10. 31. | 10.50% | 6.91% | 76.74 | 35.54 | 52.22 |
| 45. | 2021. 11. 30. | -4.92% | -0.83% | 44.25 | 3.19 | 11.88 |
| 46. | 2021. 12. 31. | -10.82% | 4.36% | 157.65 | 11.62 | -42.80 |
| 47. | 2022. 1. 31. | -8.46% | -5.26% | 103.98 | 38.58 | 63.34 |
| 48. | 2022. 2. 28. | -9.50% | -3.14% | 126.27 | 16.72 | 45.95 |
| 49. | 2022. 3. 31. | 0.85% | 3.58% | 0.79 | 6.89 | -2.33 |
| 50. | 2022. 4. 30. | -17.13% | -8.80% | 356.13 | 95.04 | 183.97 |
| 51. | 2022. 5. 31. | -8.92% | 0.01% | 113.64 | 0.90 | 10.10 |
| 52. | 2022. 6. 30. | 3.00% | -8.39% | 1.58 | 87.33 | -11.76 |
| 53. | 2022. 7. 31. | 11.50% | 9.11% | 95.32 | 66.56 | 79.66 |
| 54. | 2022. 8. 31. | -15.16% | -4.24% | 285.55 | 27.01 | 87.82 |
| 55. | 2022. 9. 30. | -7.87% | -9.34% | 92.21 | 105.94 | 98.83 |
| 56. | 2022. 10. 31. | 13.04% | 7.99% | 127.66 | 49.47 | 79.47 |
| 57. | 2022. 11. 30. | -1.44% | 5.38% | 10.09 | 19.56 | -14.05 |
| 58. | 2022. 12. 31. | -17.26% | -5.90% | 360.90 | 46.92 | 130.13 |
| 59. | 2023. 1. 31. | 26.68% | 6.18% | 622.35 | 27.27 | 130.28 |
| 60. | 2023. 2. 28. | -2.60% | -2.61% | 18.77 | 12.70 | 15.44 |
| 61. | 2023. 3. 31. | 22.11% | 3.51% | 414.96 | 6.51 | 51.99 |
| 62. | 2023. 4. 30. | -0.71% | 1.46% | 5.97 | 0.26 | -1.25 |
| 63. | 2023. 5. 31. | 12.61% | 0.25% | 118.18 | 0.50 | -7.66 |
| 64. | 2023. 6. 30. | -5.43% | 4.71% | 51.30 | 14.14 | -26.94 |
| 65. | 2023. 7. 31. | 6.51% | 4.85% | 22.77 | 15.16 | 18.58 |
| 66. | 2023. 8. 31. | -1.58% | -1.77% | 10.99 | 7.42 | 9.03 |
| 67. | 2023. 9. 30. | -8.43% | -4.87% | 103.46 | 33.93 | 59.25 |
| 68. | 2023. 10. 31. | -0.96% | -2.20% | 7.28 | 9.93 | 8.50 |
| 69. | 2023. 11. 30. | 25.43% | 8.92% | 561.34 | 63.44 | 188.71 |
| 70. | 2023. 12. 31. | 4.46% | 4.42% | 7.43 | 12.04 | 9.46 |
| 71. | 2024. 1. 31. | 6.82% | 1.59% | 25.85 | 0.41 | 3.24 |
| 합계 (Σ): | 7,284.09 | 1,876.53 | 2,389.03 | |||
모두 표시
분산CRM = Σ(RCRM,t–RCRM)2 ÷ (71 – 1)
= 7,284.09 ÷ (71 – 1)
= 104.06
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,876.53 ÷ (71 – 1)
= 26.81
공분산CRM, S&P 500 = Σ(RCRM,t–RCRM)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 2,389.03 ÷ (71 – 1)
= 34.13
체계적인 위험 추정 (β)
| 분산CRM | 104.06 |
| 분산S&P 500 | 26.81 |
| 공분산CRM, S&P 500 | 34.13 |
| 상관 계수CRM, S&P 5001 | 0.65 |
| βCRM2 | 1.27 |
| αCRM3 | 0.52% |
계산
1 상관 계수CRM, S&P 500
= 공분산CRM, S&P 500 ÷ (표준 편차CRM × 표준 편차S&P 500)
= 34.13 ÷ (10.20% × 5.18%)
= 0.65
2 βCRM
= 공분산CRM, S&P 500 ÷ 분산S&P 500
= 34.13 ÷ 26.81
= 1.27
3 αCRM
= 평균의CRM – βCRM × 평균의S&P 500
= 1.74% – 1.27 × 0.95%
= 0.52%
예상 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.90% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.54% |
| 보통주의 체계적 위험Salesforce | βCRM | 1.27 |
| Salesforce 보통주에 대한 예상 수익률3 | E(RCRM) | 15.90% |
1 10년 이내에 만기가 되지 않거나 콜 가능하지 않은 모든 미결제 고정 쿠폰 미국 재무부 채권에 대한 입찰 수익률의 가중 평균(무위험 수익률 프록시).
2 자세히 보기 »
3 E(RCRM) = RF + βCRM [E(RM) – RF]
= 4.90% + 1.27 [13.54% – 4.90%]
= 15.90%