자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 PMI보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Philip Morris International Inc., 월별 수익률
| Philip Morris International Inc. (PM) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값PM,t1 | 피제수PM,t1 | RPM,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2021. 1. 31. | $79.65 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $84.02 | 5.49% | 3,811.15 | 2.61% | |
| 2. | 2021. 3. 31. | $88.74 | $1.20 | 7.05% | 3,972.89 | 4.24% |
| 3. | 2021. 4. 30. | $95.00 | 7.05% | 4,181.17 | 5.24% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | $157.48 | 9.11% | 6,849.09 | 0.13% | |
| 59. | 2025. 12. 31. | $160.40 | $1.47 | 2.79% | 6,845.50 | -0.05% |
| 평균의 (R): | 1.82% | 1.14% | ||||
| 표준 편차: | 6.49% | 4.37% | ||||
| Philip Morris International Inc. (PM) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값PM,t1 | 피제수PM,t1 | RPM,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2021. 1. 31. | $79.65 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $84.02 | 5.49% | 3,811.15 | 2.61% | |
| 2. | 2021. 3. 31. | $88.74 | $1.20 | 7.05% | 3,972.89 | 4.24% |
| 3. | 2021. 4. 30. | $95.00 | 7.05% | 4,181.17 | 5.24% | |
| 4. | 2021. 5. 31. | $96.43 | 1.51% | 4,204.11 | 0.55% | |
| 5. | 2021. 6. 30. | $99.11 | $1.20 | 4.02% | 4,297.50 | 2.22% |
| 6. | 2021. 7. 31. | $100.09 | 0.99% | 4,395.26 | 2.27% | |
| 7. | 2021. 8. 31. | $103.00 | 2.91% | 4,522.68 | 2.90% | |
| 8. | 2021. 9. 30. | $94.79 | $1.25 | -6.76% | 4,307.54 | -4.76% |
| 9. | 2021. 10. 31. | $94.54 | -0.26% | 4,605.38 | 6.91% | |
| 10. | 2021. 11. 30. | $85.94 | -9.10% | 4,567.00 | -0.83% | |
| 11. | 2021. 12. 31. | $95.00 | $1.25 | 12.00% | 4,766.18 | 4.36% |
| 12. | 2022. 1. 31. | $102.85 | 8.26% | 4,515.55 | -5.26% | |
| 13. | 2022. 2. 28. | $101.07 | -1.73% | 4,373.94 | -3.14% | |
| 14. | 2022. 3. 31. | $93.94 | $1.25 | -5.82% | 4,530.41 | 3.58% |
| 15. | 2022. 4. 30. | $100.00 | 6.45% | 4,131.93 | -8.80% | |
| 16. | 2022. 5. 31. | $106.25 | 6.25% | 4,132.15 | 0.01% | |
| 17. | 2022. 6. 30. | $98.74 | $1.25 | -5.89% | 3,785.38 | -8.39% |
| 18. | 2022. 7. 31. | $97.15 | -1.61% | 4,130.29 | 9.11% | |
| 19. | 2022. 8. 31. | $95.49 | -1.71% | 3,955.00 | -4.24% | |
| 20. | 2022. 9. 30. | $83.01 | $1.27 | -11.74% | 3,585.62 | -9.34% |
| 21. | 2022. 10. 31. | $91.85 | 10.65% | 3,871.98 | 7.99% | |
| 22. | 2022. 11. 30. | $99.67 | 8.51% | 4,080.11 | 5.38% | |
| 23. | 2022. 12. 31. | $101.21 | $1.27 | 2.82% | 3,839.50 | -5.90% |
| 24. | 2023. 1. 31. | $104.24 | 2.99% | 4,076.60 | 6.18% | |
| 25. | 2023. 2. 28. | $97.30 | -6.66% | 3,970.15 | -2.61% | |
| 26. | 2023. 3. 31. | $97.25 | $1.27 | 1.25% | 4,109.31 | 3.51% |
| 27. | 2023. 4. 30. | $99.97 | 2.80% | 4,169.48 | 1.46% | |
| 28. | 2023. 5. 31. | $90.01 | -9.96% | 4,179.83 | 0.25% | |
| 29. | 2023. 6. 30. | $97.62 | $1.27 | 9.87% | 4,376.86 | 4.71% |
| 30. | 2023. 7. 31. | $99.72 | 2.15% | 4,588.96 | 4.85% | |
| 31. | 2023. 8. 31. | $96.06 | -3.67% | 4,507.66 | -1.77% | |
| 32. | 2023. 9. 30. | $92.58 | $1.30 | -2.27% | 4,288.05 | -4.87% |
| 33. | 2023. 10. 31. | $89.16 | -3.69% | 4,193.80 | -2.20% | |
| 34. | 2023. 11. 30. | $93.36 | 4.71% | 4,567.80 | 8.92% | |
| 35. | 2023. 12. 31. | $94.08 | $1.30 | 2.16% | 4,769.83 | 4.42% |
| 36. | 2024. 1. 31. | $90.85 | -3.43% | 4,845.65 | 1.59% | |
| 37. | 2024. 2. 29. | $89.96 | -0.98% | 5,096.27 | 5.17% | |
| 38. | 2024. 3. 31. | $91.62 | $1.30 | 3.29% | 5,254.35 | 3.10% |
| 39. | 2024. 4. 30. | $94.94 | 3.62% | 5,035.69 | -4.16% | |
| 40. | 2024. 5. 31. | $101.38 | 6.78% | 5,277.51 | 4.80% | |
| 41. | 2024. 6. 30. | $101.33 | $1.30 | 1.23% | 5,460.48 | 3.47% |
| 42. | 2024. 7. 31. | $115.16 | 13.65% | 5,522.30 | 1.13% | |
| 43. | 2024. 8. 31. | $123.29 | 7.06% | 5,648.40 | 2.28% | |
| 44. | 2024. 9. 30. | $121.40 | $1.35 | -0.44% | 5,762.48 | 2.02% |
| 45. | 2024. 10. 31. | $132.70 | 9.31% | 5,705.45 | -0.99% | |
| 46. | 2024. 11. 30. | $133.06 | 0.27% | 6,032.38 | 5.73% | |
| 47. | 2024. 12. 31. | $120.35 | $1.35 | -8.54% | 5,881.63 | -2.50% |
| 48. | 2025. 1. 31. | $130.20 | 8.18% | 6,040.53 | 2.70% | |
| 49. | 2025. 2. 28. | $155.28 | 19.26% | 5,954.50 | -1.42% | |
| 50. | 2025. 3. 31. | $158.73 | $1.35 | 3.09% | 5,611.85 | -5.75% |
| 51. | 2025. 4. 30. | $171.36 | 7.96% | 5,569.06 | -0.76% | |
| 52. | 2025. 5. 31. | $180.59 | 5.39% | 5,911.69 | 6.15% | |
| 53. | 2025. 6. 30. | $182.13 | $1.35 | 1.60% | 6,204.95 | 4.96% |
| 54. | 2025. 7. 31. | $164.05 | -9.93% | 6,339.39 | 2.17% | |
| 55. | 2025. 8. 31. | $167.13 | 1.88% | 6,460.26 | 1.91% | |
| 56. | 2025. 9. 30. | $162.20 | -2.95% | 6,688.46 | 3.53% | |
| 57. | 2025. 10. 31. | $144.33 | $1.47 | -10.11% | 6,840.20 | 2.27% |
| 58. | 2025. 11. 30. | $157.48 | 9.11% | 6,849.09 | 0.13% | |
| 59. | 2025. 12. 31. | $160.40 | $1.47 | 2.79% | 6,845.50 | -0.05% |
| 평균의 (R): | 1.82% | 1.14% | ||||
| 표준 편차: | 6.49% | 4.37% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 PM의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Philip Morris International Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RPM,t | RS&P 500,t | (RPM,t–RPM)2 | (RS&P 500,t–RS&P 500)2 | (RPM,t–RPM)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021. 2. 28. | 5.49% | 2.61% | 13.48 | 2.17 | 5.41 |
| 2. | 2021. 3. 31. | 7.05% | 4.24% | 27.36 | 9.66 | 16.25 |
| 3. | 2021. 4. 30. | 7.05% | 5.24% | 27.44 | 16.86 | 21.51 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | 9.11% | 0.13% | 53.22 | 1.01 | -7.34 |
| 59. | 2025. 12. 31. | 2.79% | -0.05% | 0.94 | 1.41 | -1.16 |
| 합계 (Σ): | 2,442.45 | 1,108.23 | 424.01 | |||
| t | 날짜 | RPM,t | RS&P 500,t | (RPM,t–RPM)2 | (RS&P 500,t–RS&P 500)2 | (RPM,t–RPM)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021. 2. 28. | 5.49% | 2.61% | 13.48 | 2.17 | 5.41 |
| 2. | 2021. 3. 31. | 7.05% | 4.24% | 27.36 | 9.66 | 16.25 |
| 3. | 2021. 4. 30. | 7.05% | 5.24% | 27.44 | 16.86 | 21.51 |
| 4. | 2021. 5. 31. | 1.51% | 0.55% | 0.10 | 0.35 | 0.18 |
| 5. | 2021. 6. 30. | 4.02% | 2.22% | 4.88 | 1.18 | 2.40 |
| 6. | 2021. 7. 31. | 0.99% | 2.27% | 0.68 | 1.30 | -0.94 |
| 7. | 2021. 8. 31. | 2.91% | 2.90% | 1.19 | 3.11 | 1.92 |
| 8. | 2021. 9. 30. | -6.76% | -4.76% | 73.49 | 34.73 | 50.52 |
| 9. | 2021. 10. 31. | -0.26% | 6.91% | 4.32 | 33.39 | -12.01 |
| 10. | 2021. 11. 30. | -9.10% | -0.83% | 119.08 | 3.88 | 21.49 |
| 11. | 2021. 12. 31. | 12.00% | 4.36% | 103.66 | 10.40 | 32.84 |
| 12. | 2022. 1. 31. | 8.26% | -5.26% | 41.57 | 40.89 | -41.23 |
| 13. | 2022. 2. 28. | -1.73% | -3.14% | 12.58 | 18.25 | 15.15 |
| 14. | 2022. 3. 31. | -5.82% | 3.58% | 58.27 | 5.96 | -18.63 |
| 15. | 2022. 4. 30. | 6.45% | -8.80% | 21.49 | 98.64 | -46.04 |
| 16. | 2022. 5. 31. | 6.25% | 0.01% | 19.66 | 1.28 | -5.01 |
| 17. | 2022. 6. 30. | -5.89% | -8.39% | 59.40 | 90.79 | 73.44 |
| 18. | 2022. 7. 31. | -1.61% | 9.11% | 11.74 | 63.61 | -27.32 |
| 19. | 2022. 8. 31. | -1.71% | -4.24% | 12.42 | 28.95 | 18.96 |
| 20. | 2022. 9. 30. | -11.74% | -9.34% | 183.74 | 109.74 | 142.00 |
| 21. | 2022. 10. 31. | 10.65% | 7.99% | 78.03 | 46.93 | 60.51 |
| 22. | 2022. 11. 30. | 8.51% | 5.38% | 44.87 | 17.97 | 28.40 |
| 23. | 2022. 12. 31. | 2.82% | -5.90% | 1.01 | 49.47 | -7.06 |
| 24. | 2023. 1. 31. | 2.99% | 6.18% | 1.39 | 25.39 | 5.94 |
| 25. | 2023. 2. 28. | -6.66% | -2.61% | 71.80 | 14.04 | 31.75 |
| 26. | 2023. 3. 31. | 1.25% | 3.51% | 0.32 | 5.61 | -1.33 |
| 27. | 2023. 4. 30. | 2.80% | 1.46% | 0.96 | 0.11 | 0.32 |
| 28. | 2023. 5. 31. | -9.96% | 0.25% | 138.73 | 0.79 | 10.46 |
| 29. | 2023. 6. 30. | 9.87% | 4.71% | 64.80 | 12.80 | 28.80 |
| 30. | 2023. 7. 31. | 2.15% | 4.85% | 0.11 | 13.76 | 1.25 |
| 31. | 2023. 8. 31. | -3.67% | -1.77% | 30.09 | 8.46 | 15.95 |
| 32. | 2023. 9. 30. | -2.27% | -4.87% | 16.69 | 36.10 | 24.54 |
| 33. | 2023. 10. 31. | -3.69% | -2.20% | 30.36 | 11.12 | 18.37 |
| 34. | 2023. 11. 30. | 4.71% | 8.92% | 8.38 | 60.56 | 22.53 |
| 35. | 2023. 12. 31. | 2.16% | 4.42% | 0.12 | 10.80 | 1.14 |
| 36. | 2024. 1. 31. | -3.43% | 1.59% | 27.55 | 0.21 | -2.38 |
| 37. | 2024. 2. 29. | -0.98% | 5.17% | 7.81 | 16.29 | -11.28 |
| 38. | 2024. 3. 31. | 3.29% | 3.10% | 2.17 | 3.86 | 2.90 |
| 39. | 2024. 4. 30. | 3.62% | -4.16% | 3.27 | 28.06 | -9.58 |
| 40. | 2024. 5. 31. | 6.78% | 4.80% | 24.68 | 13.44 | 18.21 |
| 41. | 2024. 6. 30. | 1.23% | 3.47% | 0.34 | 5.43 | -1.36 |
| 42. | 2024. 7. 31. | 13.65% | 1.13% | 140.02 | 0.00 | -0.05 |
| 43. | 2024. 8. 31. | 7.06% | 2.28% | 27.50 | 1.32 | 6.02 |
| 44. | 2024. 9. 30. | -0.44% | 2.02% | 5.08 | 0.78 | -1.99 |
| 45. | 2024. 10. 31. | 9.31% | -0.99% | 56.14 | 4.52 | -15.93 |
| 46. | 2024. 11. 30. | 0.27% | 5.73% | 2.38 | 21.10 | -7.09 |
| 47. | 2024. 12. 31. | -8.54% | -2.50% | 107.19 | 13.21 | 37.63 |
| 48. | 2025. 1. 31. | 8.18% | 2.70% | 40.56 | 2.45 | 9.97 |
| 49. | 2025. 2. 28. | 19.26% | -1.42% | 304.40 | 6.56 | -44.67 |
| 50. | 2025. 3. 31. | 3.09% | -5.75% | 1.63 | 47.48 | -8.79 |
| 51. | 2025. 4. 30. | 7.96% | -0.76% | 37.72 | 3.60 | -11.66 |
| 52. | 2025. 5. 31. | 5.39% | 6.15% | 12.75 | 25.16 | 17.91 |
| 53. | 2025. 6. 30. | 1.60% | 4.96% | 0.05 | 14.63 | -0.82 |
| 54. | 2025. 7. 31. | -9.93% | 2.17% | 137.89 | 1.06 | -12.10 |
| 55. | 2025. 8. 31. | 1.88% | 1.91% | 0.00 | 0.59 | 0.05 |
| 56. | 2025. 9. 30. | -2.95% | 3.53% | 22.71 | 5.74 | -11.42 |
| 57. | 2025. 10. 31. | -10.11% | 2.27% | 142.24 | 1.28 | -13.51 |
| 58. | 2025. 11. 30. | 9.11% | 0.13% | 53.22 | 1.01 | -7.34 |
| 59. | 2025. 12. 31. | 2.79% | -0.05% | 0.94 | 1.41 | -1.16 |
| 합계 (Σ): | 2,442.45 | 1,108.23 | 424.01 | |||
모두 보기
분산PM = Σ(RPM,t–RPM)2 ÷ (59 – 1)
= 2,442.45 ÷ (59 – 1)
= 42.11
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,108.23 ÷ (59 – 1)
= 19.11
공분산PM, S&P 500 = Σ(RPM,t–RPM)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 424.01 ÷ (59 – 1)
= 7.31
체계적인 위험 추정 (β)
| 분산PM | 42.11 |
| 분산S&P 500 | 19.11 |
| 공분산PM, S&P 500 | 7.31 |
| 상관 계수PM, S&P 5001 | 0.26 |
| βPM2 | 0.38 |
| αPM3 | 1.38% |
계산
1 상관 계수PM, S&P 500
= 공분산PM, S&P 500 ÷ (표준 편차PM × 표준 편차S&P 500)
= 7.31 ÷ (6.49% × 4.37%)
= 0.26
2 βPM
= 공분산PM, S&P 500 ÷ 분산S&P 500
= 7.31 ÷ 19.11
= 0.38
3 αPM
= 평균의PM – βPM × 평균의S&P 500
= 1.82% – 0.38 × 1.14%
= 1.38%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.88% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 17.51% |
| 보통주의 체계적 위험PMI | βPM | 0.38 |
| PMI 보통주 기대수익률3 | E(RPM) | 9.71% |
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(RPM) = RF + βPM [E(RM) – RF]
= 4.88% + 0.38 [17.51% – 4.88%]
= 9.71%