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 |
| 2019. 1. 31. | $76.72 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $86.94 | 13.32% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $88.39 | $1.14 | 2.98% | 2,834.40 | 1.79% |
| 3. | 2019. 4. 30. | $86.56 | -2.07% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $93.36 | 4.71% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $94.08 | $1.30 | 2.16% | 4,769.83 | 4.42% |
| 평균의 (R): | 1.02% | 1.11% | ||||
| 표준 편차: | 6.39% | 5.31% | ||||
| 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 |
| 2019. 1. 31. | $76.72 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $86.94 | 13.32% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $88.39 | $1.14 | 2.98% | 2,834.40 | 1.79% |
| 3. | 2019. 4. 30. | $86.56 | -2.07% | 2,945.83 | 3.93% | |
| 4. | 2019. 5. 31. | $77.13 | -10.89% | 2,752.06 | -6.58% | |
| 5. | 2019. 6. 30. | $78.53 | $1.14 | 3.29% | 2,941.76 | 6.89% |
| 6. | 2019. 7. 31. | $83.61 | 6.47% | 2,980.38 | 1.31% | |
| 7. | 2019. 8. 31. | $72.09 | -13.78% | 2,926.46 | -1.81% | |
| 8. | 2019. 9. 30. | $75.93 | $1.17 | 6.95% | 2,976.74 | 1.72% |
| 9. | 2019. 10. 31. | $81.44 | 7.26% | 3,037.56 | 2.04% | |
| 10. | 2019. 11. 30. | $82.93 | 1.83% | 3,140.98 | 3.40% | |
| 11. | 2019. 12. 31. | $85.09 | $1.17 | 4.02% | 3,230.78 | 2.86% |
| 12. | 2020. 1. 31. | $82.70 | -2.81% | 3,225.52 | -0.16% | |
| 13. | 2020. 2. 29. | $81.87 | -1.00% | 2,954.22 | -8.41% | |
| 14. | 2020. 3. 31. | $72.96 | $1.17 | -9.45% | 2,584.59 | -12.51% |
| 15. | 2020. 4. 30. | $74.60 | 2.25% | 2,912.43 | 12.68% | |
| 16. | 2020. 5. 31. | $73.36 | -1.66% | 3,044.31 | 4.53% | |
| 17. | 2020. 6. 30. | $70.06 | $1.17 | -2.90% | 3,100.29 | 1.84% |
| 18. | 2020. 7. 31. | $76.81 | 9.63% | 3,271.12 | 5.51% | |
| 19. | 2020. 8. 31. | $79.79 | 3.88% | 3,500.31 | 7.01% | |
| 20. | 2020. 9. 30. | $74.99 | $1.20 | -4.51% | 3,363.00 | -3.92% |
| 21. | 2020. 10. 31. | $71.02 | -5.29% | 3,269.96 | -2.77% | |
| 22. | 2020. 11. 30. | $75.75 | 6.66% | 3,621.63 | 10.75% | |
| 23. | 2020. 12. 31. | $82.79 | $1.20 | 10.88% | 3,756.07 | 3.71% |
| 24. | 2021. 1. 31. | $79.65 | -3.79% | 3,714.24 | -1.11% | |
| 25. | 2021. 2. 28. | $84.02 | 5.49% | 3,811.15 | 2.61% | |
| 26. | 2021. 3. 31. | $88.74 | $1.20 | 7.05% | 3,972.89 | 4.24% |
| 27. | 2021. 4. 30. | $95.00 | 7.05% | 4,181.17 | 5.24% | |
| 28. | 2021. 5. 31. | $96.43 | 1.51% | 4,204.11 | 0.55% | |
| 29. | 2021. 6. 30. | $99.11 | $1.20 | 4.02% | 4,297.50 | 2.22% |
| 30. | 2021. 7. 31. | $100.09 | 0.99% | 4,395.26 | 2.27% | |
| 31. | 2021. 8. 31. | $103.00 | 2.91% | 4,522.68 | 2.90% | |
| 32. | 2021. 9. 30. | $94.79 | $1.25 | -6.76% | 4,307.54 | -4.76% |
| 33. | 2021. 10. 31. | $94.54 | -0.26% | 4,605.38 | 6.91% | |
| 34. | 2021. 11. 30. | $85.94 | -9.10% | 4,567.00 | -0.83% | |
| 35. | 2021. 12. 31. | $95.00 | $1.25 | 12.00% | 4,766.18 | 4.36% |
| 36. | 2022. 1. 31. | $102.85 | 8.26% | 4,515.55 | -5.26% | |
| 37. | 2022. 2. 28. | $101.07 | -1.73% | 4,373.94 | -3.14% | |
| 38. | 2022. 3. 31. | $93.94 | $1.25 | -5.82% | 4,530.41 | 3.58% |
| 39. | 2022. 4. 30. | $100.00 | 6.45% | 4,131.93 | -8.80% | |
| 40. | 2022. 5. 31. | $106.25 | 6.25% | 4,132.15 | 0.01% | |
| 41. | 2022. 6. 30. | $98.74 | $1.25 | -5.89% | 3,785.38 | -8.39% |
| 42. | 2022. 7. 31. | $97.15 | -1.61% | 4,130.29 | 9.11% | |
| 43. | 2022. 8. 31. | $95.49 | -1.71% | 3,955.00 | -4.24% | |
| 44. | 2022. 9. 30. | $83.01 | $1.27 | -11.74% | 3,585.62 | -9.34% |
| 45. | 2022. 10. 31. | $91.85 | 10.65% | 3,871.98 | 7.99% | |
| 46. | 2022. 11. 30. | $99.67 | 8.51% | 4,080.11 | 5.38% | |
| 47. | 2022. 12. 31. | $101.21 | $1.27 | 2.82% | 3,839.50 | -5.90% |
| 48. | 2023. 1. 31. | $104.24 | 2.99% | 4,076.60 | 6.18% | |
| 49. | 2023. 2. 28. | $97.30 | -6.66% | 3,970.15 | -2.61% | |
| 50. | 2023. 3. 31. | $97.25 | $1.27 | 1.25% | 4,109.31 | 3.51% |
| 51. | 2023. 4. 30. | $99.97 | 2.80% | 4,169.48 | 1.46% | |
| 52. | 2023. 5. 31. | $90.01 | -9.96% | 4,179.83 | 0.25% | |
| 53. | 2023. 6. 30. | $97.62 | $1.27 | 9.87% | 4,376.86 | 4.71% |
| 54. | 2023. 7. 31. | $99.72 | 2.15% | 4,588.96 | 4.85% | |
| 55. | 2023. 8. 31. | $96.06 | -3.67% | 4,507.66 | -1.77% | |
| 56. | 2023. 9. 30. | $92.58 | $1.30 | -2.27% | 4,288.05 | -4.87% |
| 57. | 2023. 10. 31. | $89.16 | -3.69% | 4,193.80 | -2.20% | |
| 58. | 2023. 11. 30. | $93.36 | 4.71% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $94.08 | $1.30 | 2.16% | 4,769.83 | 4.42% |
| 평균의 (R): | 1.02% | 1.11% | ||||
| 표준 편차: | 6.39% | 5.31% | ||||
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. | 2019. 2. 28. | 13.32% | 2.97% | 151.29 | 3.49 | 22.96 |
| 2. | 2019. 3. 31. | 2.98% | 1.79% | 3.83 | 0.47 | 1.34 |
| 3. | 2019. 4. 30. | -2.07% | 3.93% | 9.56 | 7.98 | -8.74 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | 4.71% | 8.92% | 13.61 | 61.03 | 28.82 |
| 59. | 2023. 12. 31. | 2.16% | 4.42% | 1.30 | 11.00 | 3.79 |
| 합계 (Σ): | 2,369.08 | 1,634.30 | 1,032.35 | |||
| 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. | 2019. 2. 28. | 13.32% | 2.97% | 151.29 | 3.49 | 22.96 |
| 2. | 2019. 3. 31. | 2.98% | 1.79% | 3.83 | 0.47 | 1.34 |
| 3. | 2019. 4. 30. | -2.07% | 3.93% | 9.56 | 7.98 | -8.74 |
| 4. | 2019. 5. 31. | -10.89% | -6.58% | 141.98 | 59.04 | 91.55 |
| 5. | 2019. 6. 30. | 3.29% | 6.89% | 5.16 | 33.49 | 13.15 |
| 6. | 2019. 7. 31. | 6.47% | 1.31% | 29.68 | 0.04 | 1.13 |
| 7. | 2019. 8. 31. | -13.78% | -1.81% | 219.03 | 8.50 | 43.14 |
| 8. | 2019. 9. 30. | 6.95% | 1.72% | 35.14 | 0.37 | 3.63 |
| 9. | 2019. 10. 31. | 7.26% | 2.04% | 38.88 | 0.88 | 5.84 |
| 10. | 2019. 11. 30. | 1.83% | 3.40% | 0.65 | 5.28 | 1.86 |
| 11. | 2019. 12. 31. | 4.02% | 2.86% | 8.96 | 3.07 | 5.25 |
| 12. | 2020. 1. 31. | -2.81% | -0.16% | 14.67 | 1.61 | 4.86 |
| 13. | 2020. 2. 29. | -1.00% | -8.41% | 4.10 | 90.57 | 19.27 |
| 14. | 2020. 3. 31. | -9.45% | -12.51% | 109.73 | 185.44 | 142.65 |
| 15. | 2020. 4. 30. | 2.25% | 12.68% | 1.50 | 134.06 | 14.20 |
| 16. | 2020. 5. 31. | -1.66% | 4.53% | 7.20 | 11.71 | -9.18 |
| 17. | 2020. 6. 30. | -2.90% | 1.84% | 15.40 | 0.54 | -2.88 |
| 18. | 2020. 7. 31. | 9.63% | 5.51% | 74.19 | 19.40 | 37.94 |
| 19. | 2020. 8. 31. | 3.88% | 7.01% | 8.17 | 34.82 | 16.87 |
| 20. | 2020. 9. 30. | -4.51% | -3.92% | 30.62 | 25.29 | 27.82 |
| 21. | 2020. 10. 31. | -5.29% | -2.77% | 39.88 | 15.00 | 24.46 |
| 22. | 2020. 11. 30. | 6.66% | 10.75% | 31.80 | 93.10 | 54.41 |
| 23. | 2020. 12. 31. | 10.88% | 3.71% | 97.15 | 6.79 | 25.69 |
| 24. | 2021. 1. 31. | -3.79% | -1.11% | 23.18 | 4.93 | 10.68 |
| 25. | 2021. 2. 28. | 5.49% | 2.61% | 19.94 | 2.26 | 6.71 |
| 26. | 2021. 3. 31. | 7.05% | 4.24% | 36.30 | 9.85 | 18.91 |
| 27. | 2021. 4. 30. | 7.05% | 5.24% | 36.40 | 17.11 | 24.96 |
| 28. | 2021. 5. 31. | 1.51% | 0.55% | 0.23 | 0.31 | -0.27 |
| 29. | 2021. 6. 30. | 4.02% | 2.22% | 9.01 | 1.24 | 3.35 |
| 30. | 2021. 7. 31. | 0.99% | 2.27% | 0.00 | 1.37 | -0.04 |
| 31. | 2021. 8. 31. | 2.91% | 2.90% | 3.56 | 3.22 | 3.38 |
| 32. | 2021. 9. 30. | -6.76% | -4.76% | 60.51 | 34.37 | 45.60 |
| 33. | 2021. 10. 31. | -0.26% | 6.91% | 1.65 | 33.74 | -7.46 |
| 34. | 2021. 11. 30. | -9.10% | -0.83% | 102.37 | 3.76 | 19.62 |
| 35. | 2021. 12. 31. | 12.00% | 4.36% | 120.46 | 10.60 | 35.73 |
| 36. | 2022. 1. 31. | 8.26% | -5.26% | 52.44 | 40.51 | -46.09 |
| 37. | 2022. 2. 28. | -1.73% | -3.14% | 7.57 | 17.99 | 11.67 |
| 38. | 2022. 3. 31. | -5.82% | 3.58% | 46.77 | 6.11 | -16.90 |
| 39. | 2022. 4. 30. | 6.45% | -8.80% | 29.48 | 98.04 | -53.76 |
| 40. | 2022. 5. 31. | 6.25% | 0.01% | 27.34 | 1.21 | -5.75 |
| 41. | 2022. 6. 30. | -5.89% | -8.39% | 47.79 | 90.21 | 65.66 |
| 42. | 2022. 7. 31. | -1.61% | 9.11% | 6.93 | 64.09 | -21.07 |
| 43. | 2022. 8. 31. | -1.71% | -4.24% | 7.45 | 28.62 | 14.61 |
| 44. | 2022. 9. 30. | -11.74% | -9.34% | 162.84 | 109.11 | 133.29 |
| 45. | 2022. 10. 31. | 10.65% | 7.99% | 92.70 | 47.34 | 66.25 |
| 46. | 2022. 11. 30. | 8.51% | 5.38% | 56.14 | 18.23 | 31.99 |
| 47. | 2022. 12. 31. | 2.82% | -5.90% | 3.23 | 49.04 | -12.59 |
| 48. | 2023. 1. 31. | 2.99% | 6.18% | 3.89 | 25.70 | 10.00 |
| 49. | 2023. 2. 28. | -6.66% | -2.61% | 58.97 | 13.82 | 28.54 |
| 50. | 2023. 3. 31. | 1.25% | 3.51% | 0.05 | 5.76 | 0.56 |
| 51. | 2023. 4. 30. | 2.80% | 1.46% | 3.15 | 0.13 | 0.64 |
| 52. | 2023. 5. 31. | -9.96% | 0.25% | 120.66 | 0.74 | 9.42 |
| 53. | 2023. 6. 30. | 9.87% | 4.71% | 78.22 | 13.02 | 31.91 |
| 54. | 2023. 7. 31. | 2.15% | 4.85% | 1.28 | 13.99 | 4.23 |
| 55. | 2023. 8. 31. | -3.67% | -1.77% | 22.01 | 8.28 | 13.50 |
| 56. | 2023. 9. 30. | -2.27% | -4.87% | 10.83 | 35.73 | 19.67 |
| 57. | 2023. 10. 31. | -3.69% | -2.20% | 22.24 | 10.92 | 15.58 |
| 58. | 2023. 11. 30. | 4.71% | 8.92% | 13.61 | 61.03 | 28.82 |
| 59. | 2023. 12. 31. | 2.16% | 4.42% | 1.30 | 11.00 | 3.79 |
| 합계 (Σ): | 2,369.08 | 1,634.30 | 1,032.35 | |||
모두 보기
분산PM = Σ(RPM,t–RPM)2 ÷ (59 – 1)
= 2,369.08 ÷ (59 – 1)
= 40.85
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산PM, S&P 500 = Σ(RPM,t–RPM)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,032.35 ÷ (59 – 1)
= 17.80
체계적인 위험 추정 (β)
| 분산PM | 40.85 |
| 분산S&P 500 | 28.18 |
| 공분산PM, S&P 500 | 17.80 |
| 상관 계수PM, S&P 5001 | 0.52 |
| βPM2 | 0.63 |
| αPM3 | 0.32% |
계산
1 상관 계수PM, S&P 500
= 공분산PM, S&P 500 ÷ (표준 편차PM × 표준 편차S&P 500)
= 17.80 ÷ (6.39% × 5.31%)
= 0.52
2 βPM
= 공분산PM, S&P 500 ÷ 분산S&P 500
= 17.80 ÷ 28.18
= 0.63
3 αPM
= 평균의PM – βPM × 평균의S&P 500
= 1.02% – 0.63 × 1.11%
= 0.32%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.55% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.83% |
| 보통주의 체계적 위험PMI | βPM | 0.63 |
| PMI 보통주 기대수익률3 | E(RPM) | 10.41% |
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]
= 4.55% + 0.63 [13.83% – 4.55%]
= 10.41%