자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델 (CAPM)은 Visa의 보통주와 같은 위험 자산에 대한 예상 또는 요구 수익률을 나타냅니다.
수익률
Visa Inc., 월별 수익률
| Visa Inc. (V) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값V,t1 | 피제수V,t1 | RV,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2016. 10. 31. | $82.51 | 2,126.15 | ||||
| 1. | 2016. 11. 30. | $77.32 | $0.165 | -6.09% | 2,198.81 | 3.42% |
| 2. | 2016. 12. 31. | $78.02 | 0.91% | 2,238.83 | 1.82% | |
| 3. | 2017. 1. 31. | $82.71 | 6.01% | 2,278.87 | 1.79% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2022. 8. 31. | $198.71 | $0.375 | -6.14% | 3,955.00 | -4.24% |
| 71. | 2022. 9. 30. | $177.65 | -10.60% | 3,585.62 | -9.34% | |
| 평균의 (R): | 1.33% | 0.85% | ||||
| 표준 편차: | 6.20% | 4.82% | ||||
| Visa Inc. (V) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값V,t1 | 피제수V,t1 | RV,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2016. 10. 31. | $82.51 | 2,126.15 | ||||
| 1. | 2016. 11. 30. | $77.32 | $0.165 | -6.09% | 2,198.81 | 3.42% |
| 2. | 2016. 12. 31. | $78.02 | 0.91% | 2,238.83 | 1.82% | |
| 3. | 2017. 1. 31. | $82.71 | 6.01% | 2,278.87 | 1.79% | |
| 4. | 2017. 2. 28. | $87.94 | $0.165 | 6.52% | 2,363.64 | 3.72% |
| 5. | 2017. 3. 31. | $88.87 | 1.06% | 2,362.72 | -0.04% | |
| 6. | 2017. 4. 30. | $91.22 | 2.64% | 2,384.20 | 0.91% | |
| 7. | 2017. 5. 31. | $95.23 | $0.165 | 4.58% | 2,411.80 | 1.16% |
| 8. | 2017. 6. 30. | $93.78 | -1.52% | 2,423.41 | 0.48% | |
| 9. | 2017. 7. 31. | $99.56 | 6.16% | 2,470.30 | 1.93% | |
| 10. | 2017. 8. 31. | $103.52 | $0.165 | 4.14% | 2,471.65 | 0.05% |
| 11. | 2017. 9. 30. | $105.24 | 1.66% | 2,519.36 | 1.93% | |
| 12. | 2017. 10. 31. | $109.98 | 4.50% | 2,575.26 | 2.22% | |
| 13. | 2017. 11. 30. | $112.59 | $0.195 | 2.55% | 2,647.58 | 2.81% |
| 14. | 2017. 12. 31. | $114.02 | 1.27% | 2,673.61 | 0.98% | |
| 15. | 2018. 1. 31. | $124.23 | 8.95% | 2,823.81 | 5.62% | |
| 16. | 2018. 2. 28. | $122.94 | $0.21 | -0.87% | 2,713.83 | -3.89% |
| 17. | 2018. 3. 31. | $119.62 | -2.70% | 2,640.87 | -2.69% | |
| 18. | 2018. 4. 30. | $126.88 | 6.07% | 2,648.05 | 0.27% | |
| 19. | 2018. 5. 31. | $130.72 | $0.21 | 3.19% | 2,705.27 | 2.16% |
| 20. | 2018. 6. 30. | $132.45 | 1.32% | 2,718.37 | 0.48% | |
| 21. | 2018. 7. 31. | $136.74 | 3.24% | 2,816.29 | 3.60% | |
| 22. | 2018. 8. 31. | $146.89 | $0.21 | 7.58% | 2,901.52 | 3.03% |
| 23. | 2018. 9. 30. | $150.09 | 2.18% | 2,913.98 | 0.43% | |
| 24. | 2018. 10. 31. | $137.85 | -8.16% | 2,711.74 | -6.94% | |
| 25. | 2018. 11. 30. | $141.71 | $0.25 | 2.98% | 2,760.17 | 1.79% |
| 26. | 2018. 12. 31. | $131.94 | -6.89% | 2,506.85 | -9.18% | |
| 27. | 2019. 1. 31. | $135.01 | 2.33% | 2,704.10 | 7.87% | |
| 28. | 2019. 2. 28. | $148.12 | $0.25 | 9.90% | 2,784.49 | 2.97% |
| 29. | 2019. 3. 31. | $156.19 | 5.45% | 2,834.40 | 1.79% | |
| 30. | 2019. 4. 30. | $164.43 | 5.28% | 2,945.83 | 3.93% | |
| 31. | 2019. 5. 31. | $161.33 | $0.25 | -1.73% | 2,752.06 | -6.58% |
| 32. | 2019. 6. 30. | $173.55 | 7.57% | 2,941.76 | 6.89% | |
| 33. | 2019. 7. 31. | $178.00 | 2.56% | 2,980.38 | 1.31% | |
| 34. | 2019. 8. 31. | $180.82 | $0.25 | 1.72% | 2,926.46 | -1.81% |
| 35. | 2019. 9. 30. | $172.01 | -4.87% | 2,976.74 | 1.72% | |
| 36. | 2019. 10. 31. | $178.86 | 3.98% | 3,037.56 | 2.04% | |
| 37. | 2019. 11. 30. | $184.51 | $0.30 | 3.33% | 3,140.98 | 3.40% |
| 38. | 2019. 12. 31. | $187.90 | 1.84% | 3,230.78 | 2.86% | |
| 39. | 2020. 1. 31. | $198.97 | 5.89% | 3,225.52 | -0.16% | |
| 40. | 2020. 2. 29. | $181.76 | $0.30 | -8.50% | 2,954.22 | -8.41% |
| 41. | 2020. 3. 31. | $161.12 | -11.36% | 2,584.59 | -12.51% | |
| 42. | 2020. 4. 30. | $178.72 | 10.92% | 2,912.43 | 12.68% | |
| 43. | 2020. 5. 31. | $195.24 | $0.30 | 9.41% | 3,044.31 | 4.53% |
| 44. | 2020. 6. 30. | $193.17 | -1.06% | 3,100.29 | 1.84% | |
| 45. | 2020. 7. 31. | $190.40 | -1.43% | 3,271.12 | 5.51% | |
| 46. | 2020. 8. 31. | $211.99 | $0.30 | 11.50% | 3,500.31 | 7.01% |
| 47. | 2020. 9. 30. | $199.97 | -5.67% | 3,363.00 | -3.92% | |
| 48. | 2020. 10. 31. | $181.71 | -9.13% | 3,269.96 | -2.77% | |
| 49. | 2020. 11. 30. | $210.35 | $0.32 | 15.94% | 3,621.63 | 10.75% |
| 50. | 2020. 12. 31. | $218.73 | 3.98% | 3,756.07 | 3.71% | |
| 51. | 2021. 1. 31. | $193.25 | -11.65% | 3,714.24 | -1.11% | |
| 52. | 2021. 2. 28. | $212.39 | $0.32 | 10.07% | 3,811.15 | 2.61% |
| 53. | 2021. 3. 31. | $211.73 | -0.31% | 3,972.89 | 4.24% | |
| 54. | 2021. 4. 30. | $233.56 | 10.31% | 4,181.17 | 5.24% | |
| 55. | 2021. 5. 31. | $227.30 | $0.32 | -2.54% | 4,204.11 | 0.55% |
| 56. | 2021. 6. 30. | $233.82 | 2.87% | 4,297.50 | 2.22% | |
| 57. | 2021. 7. 31. | $246.39 | 5.38% | 4,395.26 | 2.27% | |
| 58. | 2021. 8. 31. | $229.10 | $0.32 | -6.89% | 4,522.68 | 2.90% |
| 59. | 2021. 9. 30. | $222.75 | -2.77% | 4,307.54 | -4.76% | |
| 60. | 2021. 10. 31. | $211.77 | -4.93% | 4,605.38 | 6.91% | |
| 61. | 2021. 11. 30. | $193.77 | $0.375 | -8.32% | 4,567.00 | -0.83% |
| 62. | 2021. 12. 31. | $216.71 | 11.84% | 4,766.18 | 4.36% | |
| 63. | 2022. 1. 31. | $226.17 | 4.37% | 4,515.55 | -5.26% | |
| 64. | 2022. 2. 28. | $216.12 | $0.375 | -4.28% | 4,373.94 | -3.14% |
| 65. | 2022. 3. 31. | $221.77 | 2.61% | 4,530.41 | 3.58% | |
| 66. | 2022. 4. 30. | $213.13 | -3.90% | 4,131.93 | -8.80% | |
| 67. | 2022. 5. 31. | $212.17 | $0.375 | -0.27% | 4,132.15 | 0.01% |
| 68. | 2022. 6. 30. | $196.89 | -7.20% | 3,785.38 | -8.39% | |
| 69. | 2022. 7. 31. | $212.11 | 7.73% | 4,130.29 | 9.11% | |
| 70. | 2022. 8. 31. | $198.71 | $0.375 | -6.14% | 3,955.00 | -4.24% |
| 71. | 2022. 9. 30. | $177.65 | -10.60% | 3,585.62 | -9.34% | |
| 평균의 (R): | 1.33% | 0.85% | ||||
| 표준 편차: | 6.20% | 4.82% | ||||
모두 보기
1 보통주의 주당 US $ 단위의 데이터, 분할 및 주식 배당을 위해 조정.
2 기간 t동안 V의 보통주에 대한 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)에 대한 수익률.
분산과 공분산
Visa Inc., 수익의 분산 및 공분산 계산
| t | 날짜 | RV,t | RS&P 500,t | (RV,t–RV)2 | (RS&P 500,t–RS&P 500)2 | (RV,t–RV)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2016. 11. 30. | -6.09% | 3.42% | 55.08 | 6.57 | -19.02 |
| 2. | 2016. 12. 31. | 0.91% | 1.82% | 0.18 | 0.93 | -0.41 |
| 3. | 2017. 1. 31. | 6.01% | 1.79% | 21.90 | 0.87 | 4.37 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2022. 8. 31. | -6.14% | -4.24% | 55.83 | 25.99 | 38.10 |
| 71. | 2022. 9. 30. | -10.60% | -9.34% | 142.31 | 103.92 | 121.61 |
| 합계 (Σ): | 2,687.47 | 1,625.64 | 1,480.15 | |||
| t | 날짜 | RV,t | RS&P 500,t | (RV,t–RV)2 | (RS&P 500,t–RS&P 500)2 | (RV,t–RV)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2016. 11. 30. | -6.09% | 3.42% | 55.08 | 6.57 | -19.02 |
| 2. | 2016. 12. 31. | 0.91% | 1.82% | 0.18 | 0.93 | -0.41 |
| 3. | 2017. 1. 31. | 6.01% | 1.79% | 21.90 | 0.87 | 4.37 |
| 4. | 2017. 2. 28. | 6.52% | 3.72% | 26.95 | 8.21 | 14.88 |
| 5. | 2017. 3. 31. | 1.06% | -0.04% | 0.07 | 0.80 | 0.24 |
| 6. | 2017. 4. 30. | 2.64% | 0.91% | 1.72 | 0.00 | 0.07 |
| 7. | 2017. 5. 31. | 4.58% | 1.16% | 10.53 | 0.09 | 0.98 |
| 8. | 2017. 6. 30. | -1.52% | 0.48% | 8.14 | 0.14 | 1.06 |
| 9. | 2017. 7. 31. | 6.16% | 1.93% | 23.35 | 1.17 | 5.22 |
| 10. | 2017. 8. 31. | 4.14% | 0.05% | 7.91 | 0.64 | -2.25 |
| 11. | 2017. 9. 30. | 1.66% | 1.93% | 0.11 | 1.16 | 0.36 |
| 12. | 2017. 10. 31. | 4.50% | 2.22% | 10.07 | 1.86 | 4.33 |
| 13. | 2017. 11. 30. | 2.55% | 2.81% | 1.49 | 3.82 | 2.38 |
| 14. | 2017. 12. 31. | 1.27% | 0.98% | 0.00 | 0.02 | -0.01 |
| 15. | 2018. 1. 31. | 8.95% | 5.62% | 58.12 | 22.69 | 36.31 |
| 16. | 2018. 2. 28. | -0.87% | -3.89% | 4.84 | 22.56 | 10.45 |
| 17. | 2018. 3. 31. | -2.70% | -2.69% | 16.25 | 12.55 | 14.28 |
| 18. | 2018. 4. 30. | 6.07% | 0.27% | 22.45 | 0.34 | -2.76 |
| 19. | 2018. 5. 31. | 3.19% | 2.16% | 3.46 | 1.71 | 2.43 |
| 20. | 2018. 6. 30. | 1.32% | 0.48% | 0.00 | 0.14 | 0.00 |
| 21. | 2018. 7. 31. | 3.24% | 3.60% | 3.64 | 7.55 | 5.24 |
| 22. | 2018. 8. 31. | 7.58% | 3.03% | 39.00 | 4.72 | 13.56 |
| 23. | 2018. 9. 30. | 2.18% | 0.43% | 0.72 | 0.18 | -0.36 |
| 24. | 2018. 10. 31. | -8.16% | -6.94% | 89.99 | 60.76 | 73.94 |
| 25. | 2018. 11. 30. | 2.98% | 1.79% | 2.72 | 0.87 | 1.54 |
| 26. | 2018. 12. 31. | -6.89% | -9.18% | 67.66 | 100.65 | 82.52 |
| 27. | 2019. 1. 31. | 2.33% | 7.87% | 0.99 | 49.20 | 6.98 |
| 28. | 2019. 2. 28. | 9.90% | 2.97% | 73.35 | 4.49 | 18.14 |
| 29. | 2019. 3. 31. | 5.45% | 1.79% | 16.95 | 0.88 | 3.86 |
| 30. | 2019. 4. 30. | 5.28% | 3.93% | 15.56 | 9.47 | 12.14 |
| 31. | 2019. 5. 31. | -1.73% | -6.58% | 9.39 | 55.24 | 22.78 |
| 32. | 2019. 6. 30. | 7.57% | 6.89% | 38.98 | 36.46 | 37.70 |
| 33. | 2019. 7. 31. | 2.56% | 1.31% | 1.52 | 0.21 | 0.57 |
| 34. | 2019. 8. 31. | 1.72% | -1.81% | 0.15 | 7.10 | -1.05 |
| 35. | 2019. 9. 30. | -4.87% | 1.72% | 38.48 | 0.75 | -5.36 |
| 36. | 2019. 10. 31. | 3.98% | 2.04% | 7.03 | 1.41 | 3.15 |
| 37. | 2019. 11. 30. | 3.33% | 3.40% | 3.98 | 6.50 | 5.09 |
| 38. | 2019. 12. 31. | 1.84% | 2.86% | 0.26 | 4.02 | 1.01 |
| 39. | 2020. 1. 31. | 5.89% | -0.16% | 20.80 | 1.03 | -4.64 |
| 40. | 2020. 2. 29. | -8.50% | -8.41% | 96.63 | 85.85 | 91.08 |
| 41. | 2020. 3. 31. | -11.36% | -12.51% | 160.95 | 178.66 | 169.58 |
| 42. | 2020. 4. 30. | 10.92% | 12.68% | 92.01 | 139.95 | 113.48 |
| 43. | 2020. 5. 31. | 9.41% | 4.53% | 65.29 | 13.50 | 29.68 |
| 44. | 2020. 6. 30. | -1.06% | 1.84% | 5.72 | 0.97 | -2.35 |
| 45. | 2020. 7. 31. | -1.43% | 5.51% | 7.65 | 21.67 | -12.87 |
| 46. | 2020. 8. 31. | 11.50% | 7.01% | 103.34 | 37.85 | 62.54 |
| 47. | 2020. 9. 30. | -5.67% | -3.92% | 49.02 | 22.82 | 33.45 |
| 48. | 2020. 10. 31. | -9.13% | -2.77% | 109.46 | 13.11 | 37.89 |
| 49. | 2020. 11. 30. | 15.94% | 10.75% | 213.35 | 98.01 | 144.60 |
| 50. | 2020. 12. 31. | 3.98% | 3.71% | 7.04 | 8.17 | 7.58 |
| 51. | 2021. 1. 31. | -11.65% | -1.11% | 168.48 | 3.87 | 25.55 |
| 52. | 2021. 2. 28. | 10.07% | 2.61% | 76.37 | 3.08 | 15.33 |
| 53. | 2021. 3. 31. | -0.31% | 4.24% | 2.70 | 11.49 | -5.56 |
| 54. | 2021. 4. 30. | 10.31% | 5.24% | 80.63 | 19.25 | 39.40 |
| 55. | 2021. 5. 31. | -2.54% | 0.55% | 15.01 | 0.09 | 1.19 |
| 56. | 2021. 6. 30. | 2.87% | 2.22% | 2.36 | 1.87 | 2.10 |
| 57. | 2021. 7. 31. | 5.38% | 2.27% | 16.36 | 2.02 | 5.74 |
| 58. | 2021. 8. 31. | -6.89% | 2.90% | 67.54 | 4.18 | -16.80 |
| 59. | 2021. 9. 30. | -2.77% | -4.76% | 16.83 | 31.49 | 23.02 |
| 60. | 2021. 10. 31. | -4.93% | 6.91% | 39.19 | 36.72 | -37.94 |
| 61. | 2021. 11. 30. | -8.32% | -0.83% | 93.20 | 2.85 | 16.29 |
| 62. | 2021. 12. 31. | 11.84% | 4.36% | 110.41 | 12.30 | 36.85 |
| 63. | 2022. 1. 31. | 4.37% | -5.26% | 9.21 | 37.37 | -18.55 |
| 64. | 2022. 2. 28. | -4.28% | -3.14% | 31.46 | 15.92 | 22.38 |
| 65. | 2022. 3. 31. | 2.61% | 3.58% | 1.65 | 7.41 | 3.49 |
| 66. | 2022. 4. 30. | -3.90% | -8.80% | 27.32 | 93.13 | 50.44 |
| 67. | 2022. 5. 31. | -0.27% | 0.01% | 2.58 | 0.72 | 1.36 |
| 68. | 2022. 6. 30. | -7.20% | -8.39% | 72.81 | 85.50 | 78.90 |
| 69. | 2022. 7. 31. | 7.73% | 9.11% | 40.95 | 68.18 | 52.84 |
| 70. | 2022. 8. 31. | -6.14% | -4.24% | 55.83 | 25.99 | 38.10 |
| 71. | 2022. 9. 30. | -10.60% | -9.34% | 142.31 | 103.92 | 121.61 |
| 합계 (Σ): | 2,687.47 | 1,625.64 | 1,480.15 | |||
모두 보기
분산V = Σ(RV,t–RV)2 ÷ (71 – 1)
= 2,687.47 ÷ (71 – 1)
= 38.39
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,625.64 ÷ (71 – 1)
= 23.22
공분산V, S&P 500 = Σ(RV,t–RV)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 1,480.15 ÷ (71 – 1)
= 21.14
체계적인 위험 추정 (β)
| 분산V | 38.39 |
| 분산S&P 500 | 23.22 |
| 공분산V, S&P 500 | 21.14 |
| 상관 계수V, S&P 5001 | 0.71 |
| βV2 | 0.91 |
| αV3 | 0.55% |
계산
1 상관 계수V, S&P 500
= 공분산V, S&P 500 ÷ (표준 편차V × 표준 편차S&P 500)
= 21.14 ÷ (6.20% × 4.82%)
= 0.71
2 βV
= 공분산V, S&P 500 ÷ 분산S&P 500
= 21.14 ÷ 23.22
= 0.91
3 αV
= 평균의V – βV × 평균의S&P 500
= 1.33% – 0.91 × 0.85%
= 0.55%
예상 수익률
| 가정 | ||
| LT 재무부 복합재의 수익률1 | RF | 3.85% |
| 시장 포트폴리오의 예상 수익률2 | E(RM) | 13.71% |
| 보통주 Visa 의 체계적인 위험 | βV | 0.91 |
| Visa 보통주의 예상 수익률3 | E(RV) | 12.83% |
1 모든 미결 고정 쿠폰 미국 국채 채권에 대한 입찰 수익률의 무중 평균은 10 년 이내에 만기가되거나 호출 할 수 없습니다 (위험이없는 수익률 프록시).
3 E(RV) = RF + βV [E(RM) – RF]
= 3.85% + 0.91 [13.71% – 3.85%]
= 12.83%