자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 IBM보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
International Business Machines Corp., 월별 수익률
| International Business Machines Corp. (IBM) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값IBM,t1 | 피제수IBM,t1 | RIBM,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2020. 1. 31. | $143.73 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $130.15 | $1.62 | -8.32% | 2,954.22 | -8.41% |
| 2. | 2020. 3. 31. | $110.93 | -14.77% | 2,584.59 | -12.51% | |
| 3. | 2020. 4. 30. | $125.56 | 13.19% | 2,912.43 | 12.68% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | $227.41 | $1.67 | 10.82% | 6,032.38 | 5.73% |
| 59. | 2024. 12. 31. | $219.83 | -3.33% | 5,881.63 | -2.50% | |
| 평균의 (R): | 1.46% | 1.16% | ||||
| 표준 편차: | 6.87% | 5.28% | ||||
| International Business Machines Corp. (IBM) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값IBM,t1 | 피제수IBM,t1 | RIBM,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2020. 1. 31. | $143.73 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $130.15 | $1.62 | -8.32% | 2,954.22 | -8.41% |
| 2. | 2020. 3. 31. | $110.93 | -14.77% | 2,584.59 | -12.51% | |
| 3. | 2020. 4. 30. | $125.56 | 13.19% | 2,912.43 | 12.68% | |
| 4. | 2020. 5. 31. | $124.90 | $1.63 | 0.77% | 3,044.31 | 4.53% |
| 5. | 2020. 6. 30. | $120.77 | -3.31% | 3,100.29 | 1.84% | |
| 6. | 2020. 7. 31. | $122.94 | 1.80% | 3,271.12 | 5.51% | |
| 7. | 2020. 8. 31. | $123.31 | $1.63 | 1.63% | 3,500.31 | 7.01% |
| 8. | 2020. 9. 30. | $121.67 | -1.33% | 3,363.00 | -3.92% | |
| 9. | 2020. 10. 31. | $111.66 | -8.23% | 3,269.96 | -2.77% | |
| 10. | 2020. 11. 30. | $123.52 | $1.63 | 12.08% | 3,621.63 | 10.75% |
| 11. | 2020. 12. 31. | $125.88 | 1.91% | 3,756.07 | 3.71% | |
| 12. | 2021. 1. 31. | $119.11 | -5.38% | 3,714.24 | -1.11% | |
| 13. | 2021. 2. 28. | $118.93 | $1.63 | 1.22% | 3,811.15 | 2.61% |
| 14. | 2021. 3. 31. | $133.26 | 12.05% | 3,972.89 | 4.24% | |
| 15. | 2021. 4. 30. | $141.88 | 6.47% | 4,181.17 | 5.24% | |
| 16. | 2021. 5. 31. | $143.74 | $1.64 | 2.47% | 4,204.11 | 0.55% |
| 17. | 2021. 6. 30. | $146.59 | 1.98% | 4,297.50 | 2.22% | |
| 18. | 2021. 7. 31. | $140.96 | -3.84% | 4,395.26 | 2.27% | |
| 19. | 2021. 8. 31. | $140.34 | $1.64 | 0.72% | 4,522.68 | 2.90% |
| 20. | 2021. 9. 30. | $138.93 | -1.00% | 4,307.54 | -4.76% | |
| 21. | 2021. 10. 31. | $125.10 | $8.00 | -4.20% | 4,605.38 | 6.91% |
| 22. | 2021. 11. 30. | $117.10 | $1.64 | -5.08% | 4,567.00 | -0.83% |
| 23. | 2021. 12. 31. | $133.66 | 14.14% | 4,766.18 | 4.36% | |
| 24. | 2022. 1. 31. | $133.57 | -0.07% | 4,515.55 | -5.26% | |
| 25. | 2022. 2. 28. | $122.51 | $1.64 | -7.05% | 4,373.94 | -3.14% |
| 26. | 2022. 3. 31. | $130.02 | 6.13% | 4,530.41 | 3.58% | |
| 27. | 2022. 4. 30. | $132.21 | 1.68% | 4,131.93 | -8.80% | |
| 28. | 2022. 5. 31. | $138.84 | $1.65 | 6.26% | 4,132.15 | 0.01% |
| 29. | 2022. 6. 30. | $141.19 | 1.69% | 3,785.38 | -8.39% | |
| 30. | 2022. 7. 31. | $130.79 | -7.37% | 4,130.29 | 9.11% | |
| 31. | 2022. 8. 31. | $128.45 | $1.65 | -0.53% | 3,955.00 | -4.24% |
| 32. | 2022. 9. 30. | $118.81 | -7.50% | 3,585.62 | -9.34% | |
| 33. | 2022. 10. 31. | $138.29 | 16.40% | 3,871.98 | 7.99% | |
| 34. | 2022. 11. 30. | $148.90 | $1.65 | 8.87% | 4,080.11 | 5.38% |
| 35. | 2022. 12. 31. | $140.89 | -5.38% | 3,839.50 | -5.90% | |
| 36. | 2023. 1. 31. | $134.73 | -4.37% | 4,076.60 | 6.18% | |
| 37. | 2023. 2. 28. | $129.30 | $1.65 | -2.81% | 3,970.15 | -2.61% |
| 38. | 2023. 3. 31. | $131.09 | 1.38% | 4,109.31 | 3.51% | |
| 39. | 2023. 4. 30. | $126.41 | -3.57% | 4,169.48 | 1.46% | |
| 40. | 2023. 5. 31. | $128.59 | $1.66 | 3.04% | 4,179.83 | 0.25% |
| 41. | 2023. 6. 30. | $133.81 | 4.06% | 4,376.86 | 4.71% | |
| 42. | 2023. 7. 31. | $144.18 | 7.75% | 4,588.96 | 4.85% | |
| 43. | 2023. 8. 31. | $146.83 | $1.66 | 2.99% | 4,507.66 | -1.77% |
| 44. | 2023. 9. 30. | $140.30 | -4.45% | 4,288.05 | -4.87% | |
| 45. | 2023. 10. 31. | $144.64 | 3.09% | 4,193.80 | -2.20% | |
| 46. | 2023. 11. 30. | $158.56 | $1.66 | 10.77% | 4,567.80 | 8.92% |
| 47. | 2023. 12. 31. | $163.55 | 3.15% | 4,769.83 | 4.42% | |
| 48. | 2024. 1. 31. | $183.66 | 12.30% | 4,845.65 | 1.59% | |
| 49. | 2024. 2. 29. | $185.03 | $1.66 | 1.65% | 5,096.27 | 5.17% |
| 50. | 2024. 3. 31. | $190.96 | 3.20% | 5,254.35 | 3.10% | |
| 51. | 2024. 4. 30. | $166.20 | -12.97% | 5,035.69 | -4.16% | |
| 52. | 2024. 5. 31. | $166.85 | $1.67 | 1.40% | 5,277.51 | 4.80% |
| 53. | 2024. 6. 30. | $172.95 | 3.66% | 5,460.48 | 3.47% | |
| 54. | 2024. 7. 31. | $192.14 | 11.10% | 5,522.30 | 1.13% | |
| 55. | 2024. 8. 31. | $202.13 | $1.67 | 6.07% | 5,648.40 | 2.28% |
| 56. | 2024. 9. 30. | $221.08 | 9.38% | 5,762.48 | 2.02% | |
| 57. | 2024. 10. 31. | $206.72 | -6.50% | 5,705.45 | -0.99% | |
| 58. | 2024. 11. 30. | $227.41 | $1.67 | 10.82% | 6,032.38 | 5.73% |
| 59. | 2024. 12. 31. | $219.83 | -3.33% | 5,881.63 | -2.50% | |
| 평균의 (R): | 1.46% | 1.16% | ||||
| 표준 편차: | 6.87% | 5.28% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 t 기간 동안 IBM의 보통주 수익률
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
International Business Machines Corp., 수익률의 분산 및 공분산 계산
| t | 날짜 | RIBM,t | RS&P 500,t | (RIBM,t–RIBM)2 | (RS&P 500,t–RS&P 500)2 | (RIBM,t–RIBM)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2020. 2. 29. | -8.32% | -8.41% | 95.59 | 91.63 | 93.59 |
| 2. | 2020. 3. 31. | -14.77% | -12.51% | 263.20 | 186.96 | 221.83 |
| 3. | 2020. 4. 30. | 13.19% | 12.68% | 137.65 | 132.78 | 135.19 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | 10.82% | 5.73% | 87.62 | 20.87 | 42.77 |
| 59. | 2024. 12. 31. | -3.33% | -2.50% | 22.94 | 13.40 | 17.53 |
| 합계 (Σ): | 2,736.67 | 1,618.62 | 1,262.36 | |||
| t | 날짜 | RIBM,t | RS&P 500,t | (RIBM,t–RIBM)2 | (RS&P 500,t–RS&P 500)2 | (RIBM,t–RIBM)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2020. 2. 29. | -8.32% | -8.41% | 95.59 | 91.63 | 93.59 |
| 2. | 2020. 3. 31. | -14.77% | -12.51% | 263.20 | 186.96 | 221.83 |
| 3. | 2020. 4. 30. | 13.19% | 12.68% | 137.65 | 132.78 | 135.19 |
| 4. | 2020. 5. 31. | 0.77% | 4.53% | 0.47 | 11.34 | -2.30 |
| 5. | 2020. 6. 30. | -3.31% | 1.84% | 22.68 | 0.46 | -3.23 |
| 6. | 2020. 7. 31. | 1.80% | 5.51% | 0.12 | 18.91 | 1.48 |
| 7. | 2020. 8. 31. | 1.63% | 7.01% | 0.03 | 34.17 | 1.00 |
| 8. | 2020. 9. 30. | -1.33% | -3.92% | 7.76 | 25.85 | 14.16 |
| 9. | 2020. 10. 31. | -8.23% | -2.77% | 93.76 | 15.43 | 38.03 |
| 10. | 2020. 11. 30. | 12.08% | 10.75% | 112.90 | 92.03 | 101.93 |
| 11. | 2020. 12. 31. | 1.91% | 3.71% | 0.21 | 6.51 | 1.16 |
| 12. | 2021. 1. 31. | -5.38% | -1.11% | 46.71 | 5.18 | 15.55 |
| 13. | 2021. 2. 28. | 1.22% | 2.61% | 0.06 | 2.10 | -0.35 |
| 14. | 2021. 3. 31. | 12.05% | 4.24% | 112.21 | 9.50 | 32.65 |
| 15. | 2021. 4. 30. | 6.47% | 5.24% | 25.13 | 16.66 | 20.46 |
| 16. | 2021. 5. 31. | 2.47% | 0.55% | 1.02 | 0.38 | -0.62 |
| 17. | 2021. 6. 30. | 1.98% | 2.22% | 0.28 | 1.12 | 0.56 |
| 18. | 2021. 7. 31. | -3.84% | 2.27% | 28.05 | 1.24 | -5.90 |
| 19. | 2021. 8. 31. | 0.72% | 2.90% | 0.54 | 3.02 | -1.27 |
| 20. | 2021. 9. 30. | -1.00% | -4.76% | 6.06 | 35.02 | 14.56 |
| 21. | 2021. 10. 31. | -4.20% | 6.91% | 31.95 | 33.10 | -32.52 |
| 22. | 2021. 11. 30. | -5.08% | -0.83% | 42.77 | 3.98 | 13.04 |
| 23. | 2021. 12. 31. | 14.14% | 4.36% | 160.93 | 10.24 | 40.59 |
| 24. | 2022. 1. 31. | -0.07% | -5.26% | 2.32 | 41.21 | 9.78 |
| 25. | 2022. 2. 28. | -7.05% | -3.14% | 72.39 | 18.47 | 36.56 |
| 26. | 2022. 3. 31. | 6.13% | 3.58% | 21.85 | 5.84 | 11.29 |
| 27. | 2022. 4. 30. | 1.68% | -8.80% | 0.05 | 99.14 | -2.27 |
| 28. | 2022. 5. 31. | 6.26% | 0.01% | 23.10 | 1.34 | -5.56 |
| 29. | 2022. 6. 30. | 1.69% | -8.39% | 0.06 | 91.26 | -2.26 |
| 30. | 2022. 7. 31. | -7.37% | 9.11% | 77.83 | 63.21 | -70.14 |
| 31. | 2022. 8. 31. | -0.53% | -4.24% | 3.93 | 29.22 | 10.72 |
| 32. | 2022. 9. 30. | -7.50% | -9.34% | 80.30 | 110.27 | 94.10 |
| 33. | 2022. 10. 31. | 16.40% | 7.99% | 223.20 | 46.58 | 101.97 |
| 34. | 2022. 11. 30. | 8.87% | 5.38% | 54.90 | 17.76 | 31.22 |
| 35. | 2022. 12. 31. | -5.38% | -5.90% | 46.72 | 49.82 | 48.25 |
| 36. | 2023. 1. 31. | -4.37% | 6.18% | 33.97 | 25.14 | -29.22 |
| 37. | 2023. 2. 28. | -2.81% | -2.61% | 18.16 | 14.23 | 16.08 |
| 38. | 2023. 3. 31. | 1.38% | 3.51% | 0.01 | 5.49 | -0.17 |
| 39. | 2023. 4. 30. | -3.57% | 1.46% | 25.26 | 0.09 | -1.52 |
| 40. | 2023. 5. 31. | 3.04% | 0.25% | 2.50 | 0.83 | -1.44 |
| 41. | 2023. 6. 30. | 4.06% | 4.71% | 6.78 | 12.62 | 9.25 |
| 42. | 2023. 7. 31. | 7.75% | 4.85% | 39.61 | 13.58 | 23.19 |
| 43. | 2023. 8. 31. | 2.99% | -1.77% | 2.35 | 8.60 | -4.50 |
| 44. | 2023. 9. 30. | -4.45% | -4.87% | 34.85 | 36.40 | 35.62 |
| 45. | 2023. 10. 31. | 3.09% | -2.20% | 2.68 | 11.28 | -5.50 |
| 46. | 2023. 11. 30. | 10.77% | 8.92% | 86.78 | 60.17 | 72.26 |
| 47. | 2023. 12. 31. | 3.15% | 4.42% | 2.86 | 10.64 | 5.52 |
| 48. | 2024. 1. 31. | 12.30% | 1.59% | 117.50 | 0.18 | 4.64 |
| 49. | 2024. 2. 29. | 1.65% | 5.17% | 0.04 | 16.09 | 0.78 |
| 50. | 2024. 3. 31. | 3.20% | 3.10% | 3.06 | 3.77 | 3.39 |
| 51. | 2024. 4. 30. | -12.97% | -4.16% | 208.00 | 28.33 | 76.77 |
| 52. | 2024. 5. 31. | 1.40% | 4.80% | 0.00 | 13.26 | -0.22 |
| 53. | 2024. 6. 30. | 3.66% | 3.47% | 4.84 | 5.32 | 5.07 |
| 54. | 2024. 7. 31. | 11.10% | 1.13% | 92.92 | 0.00 | -0.28 |
| 55. | 2024. 8. 31. | 6.07% | 2.28% | 21.27 | 1.26 | 5.18 |
| 56. | 2024. 9. 30. | 9.38% | 2.02% | 62.71 | 0.74 | 6.80 |
| 57. | 2024. 10. 31. | -6.50% | -0.99% | 63.22 | 4.63 | 17.10 |
| 58. | 2024. 11. 30. | 10.82% | 5.73% | 87.62 | 20.87 | 42.77 |
| 59. | 2024. 12. 31. | -3.33% | -2.50% | 22.94 | 13.40 | 17.53 |
| 합계 (Σ): | 2,736.67 | 1,618.62 | 1,262.36 | |||
모두 보기
분산IBM = Σ(RIBM,t–RIBM)2 ÷ (59 – 1)
= 2,736.67 ÷ (59 – 1)
= 47.18
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91
공분산IBM, S&P 500 = Σ(RIBM,t–RIBM)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,262.36 ÷ (59 – 1)
= 21.76
체계적인 위험 추정 (β)
| 분산IBM | 47.18 |
| 분산S&P 500 | 27.91 |
| 공분산IBM, S&P 500 | 21.76 |
| 상관 계수IBM, S&P 5001 | 0.60 |
| βIBM2 | 0.78 |
| αIBM3 | 0.55% |
계산
1 상관 계수IBM, S&P 500
= 공분산IBM, S&P 500 ÷ (표준 편차IBM × 표준 편차S&P 500)
= 21.76 ÷ (6.87% × 5.28%)
= 0.60
2 βIBM
= 공분산IBM, S&P 500 ÷ 분산S&P 500
= 21.76 ÷ 27.91
= 0.78
3 αIBM
= 평균의IBM – βIBM × 평균의S&P 500
= 1.46% – 0.78 × 1.16%
= 0.55%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.78% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.88% |
| 보통주의 체계적 위험IBM | βIBM | 0.78 |
| IBM 보통주에 대한 기대 수익률3 | E(RIBM) | 12.66% |
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(RIBM) = RF + βIBM [E(RM) – RF]
= 4.78% + 0.78 [14.88% – 4.78%]
= 12.66%