자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Colgate보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Colgate-Palmolive Co., 월별 수익률
| Colgate-Palmolive Co. (CL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값CL,t1 | 피제수CL,t1 | RCL,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2018. 1. 31. | $74.24 | 2,823.81 | ||||
| 1. | 2018. 2. 28. | $68.97 | -7.10% | 2,713.83 | -3.89% | |
| 2. | 2018. 3. 31. | $71.68 | 3.93% | 2,640.87 | -2.69% | |
| 3. | 2018. 4. 30. | $65.23 | $0.42 | -8.41% | 2,648.05 | 0.27% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2022. 11. 30. | $77.48 | 4.93% | 4,080.11 | 5.38% | |
| 59. | 2022. 12. 31. | $78.79 | 1.69% | 3,839.50 | -5.90% | |
| 평균의 (R): | 0.42% | 0.67% | ||||
| 표준 편차: | 5.07% | 5.40% | ||||
| Colgate-Palmolive Co. (CL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값CL,t1 | 피제수CL,t1 | RCL,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2018. 1. 31. | $74.24 | 2,823.81 | ||||
| 1. | 2018. 2. 28. | $68.97 | -7.10% | 2,713.83 | -3.89% | |
| 2. | 2018. 3. 31. | $71.68 | 3.93% | 2,640.87 | -2.69% | |
| 3. | 2018. 4. 30. | $65.23 | $0.42 | -8.41% | 2,648.05 | 0.27% |
| 4. | 2018. 5. 31. | $63.09 | -3.28% | 2,705.27 | 2.16% | |
| 5. | 2018. 6. 30. | $64.81 | 2.73% | 2,718.37 | 0.48% | |
| 6. | 2018. 7. 31. | $67.01 | $0.42 | 4.04% | 2,816.29 | 3.60% |
| 7. | 2018. 8. 31. | $66.41 | -0.90% | 2,901.52 | 3.03% | |
| 8. | 2018. 9. 30. | $66.95 | 0.81% | 2,913.98 | 0.43% | |
| 9. | 2018. 10. 31. | $59.55 | $0.42 | -10.43% | 2,711.74 | -6.94% |
| 10. | 2018. 11. 30. | $63.52 | 6.67% | 2,760.17 | 1.79% | |
| 11. | 2018. 12. 31. | $59.52 | -6.30% | 2,506.85 | -9.18% | |
| 12. | 2019. 1. 31. | $64.68 | $0.42 | 9.38% | 2,704.10 | 7.87% |
| 13. | 2019. 2. 28. | $65.87 | 1.84% | 2,784.49 | 2.97% | |
| 14. | 2019. 3. 31. | $68.54 | 4.05% | 2,834.40 | 1.79% | |
| 15. | 2019. 4. 30. | $72.79 | $0.43 | 6.83% | 2,945.83 | 3.93% |
| 16. | 2019. 5. 31. | $69.62 | -4.35% | 2,752.06 | -6.58% | |
| 17. | 2019. 6. 30. | $71.67 | 2.94% | 2,941.76 | 6.89% | |
| 18. | 2019. 7. 31. | $71.74 | $0.43 | 0.70% | 2,980.38 | 1.31% |
| 19. | 2019. 8. 31. | $74.15 | 3.36% | 2,926.46 | -1.81% | |
| 20. | 2019. 9. 30. | $73.51 | -0.86% | 2,976.74 | 1.72% | |
| 21. | 2019. 10. 31. | $68.60 | $0.43 | -6.09% | 3,037.56 | 2.04% |
| 22. | 2019. 11. 30. | $67.82 | -1.14% | 3,140.98 | 3.40% | |
| 23. | 2019. 12. 31. | $68.84 | 1.50% | 3,230.78 | 2.86% | |
| 24. | 2020. 1. 31. | $73.78 | $0.43 | 7.80% | 3,225.52 | -0.16% |
| 25. | 2020. 2. 29. | $67.57 | -8.42% | 2,954.22 | -8.41% | |
| 26. | 2020. 3. 31. | $66.36 | -1.79% | 2,584.59 | -12.51% | |
| 27. | 2020. 4. 30. | $70.27 | $0.44 | 6.56% | 2,912.43 | 12.68% |
| 28. | 2020. 5. 31. | $72.33 | 2.93% | 3,044.31 | 4.53% | |
| 29. | 2020. 6. 30. | $73.26 | 1.29% | 3,100.29 | 1.84% | |
| 30. | 2020. 7. 31. | $77.20 | $0.44 | 5.98% | 3,271.12 | 5.51% |
| 31. | 2020. 8. 31. | $79.26 | 2.67% | 3,500.31 | 7.01% | |
| 32. | 2020. 9. 30. | $77.15 | -2.66% | 3,363.00 | -3.92% | |
| 33. | 2020. 10. 31. | $78.89 | $0.44 | 2.83% | 3,269.96 | -2.77% |
| 34. | 2020. 11. 30. | $85.64 | 8.56% | 3,621.63 | 10.75% | |
| 35. | 2020. 12. 31. | $85.51 | -0.15% | 3,756.07 | 3.71% | |
| 36. | 2021. 1. 31. | $78.00 | $0.44 | -8.27% | 3,714.24 | -1.11% |
| 37. | 2021. 2. 28. | $75.20 | -3.59% | 3,811.15 | 2.61% | |
| 38. | 2021. 3. 31. | $78.83 | 4.83% | 3,972.89 | 4.24% | |
| 39. | 2021. 4. 30. | $80.70 | $0.45 | 2.94% | 4,181.17 | 5.24% |
| 40. | 2021. 5. 31. | $83.78 | 3.82% | 4,204.11 | 0.55% | |
| 41. | 2021. 6. 30. | $81.35 | -2.90% | 4,297.50 | 2.22% | |
| 42. | 2021. 7. 31. | $79.50 | $0.45 | -1.72% | 4,395.26 | 2.27% |
| 43. | 2021. 8. 31. | $77.95 | -1.95% | 4,522.68 | 2.90% | |
| 44. | 2021. 9. 30. | $75.58 | -3.04% | 4,307.54 | -4.76% | |
| 45. | 2021. 10. 31. | $76.19 | $0.45 | 1.40% | 4,605.38 | 6.91% |
| 46. | 2021. 11. 30. | $75.02 | -1.54% | 4,567.00 | -0.83% | |
| 47. | 2021. 12. 31. | $85.34 | 13.76% | 4,766.18 | 4.36% | |
| 48. | 2022. 1. 31. | $82.45 | $0.45 | -2.86% | 4,515.55 | -5.26% |
| 49. | 2022. 2. 28. | $76.95 | -6.67% | 4,373.94 | -3.14% | |
| 50. | 2022. 3. 31. | $75.83 | -1.46% | 4,530.41 | 3.58% | |
| 51. | 2022. 4. 30. | $77.05 | $0.47 | 2.23% | 4,131.93 | -8.80% |
| 52. | 2022. 5. 31. | $78.81 | 2.28% | 4,132.15 | 0.01% | |
| 53. | 2022. 6. 30. | $80.14 | 1.69% | 3,785.38 | -8.39% | |
| 54. | 2022. 7. 31. | $78.74 | $0.47 | -1.16% | 4,130.29 | 9.11% |
| 55. | 2022. 8. 31. | $78.21 | -0.67% | 3,955.00 | -4.24% | |
| 56. | 2022. 9. 30. | $70.25 | -10.18% | 3,585.62 | -9.34% | |
| 57. | 2022. 10. 31. | $73.84 | $0.47 | 5.78% | 3,871.98 | 7.99% |
| 58. | 2022. 11. 30. | $77.48 | 4.93% | 4,080.11 | 5.38% | |
| 59. | 2022. 12. 31. | $78.79 | 1.69% | 3,839.50 | -5.90% | |
| 평균의 (R): | 0.42% | 0.67% | ||||
| 표준 편차: | 5.07% | 5.40% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 CL의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Colgate-Palmolive Co., 수익률의 분산 및 공분산 계산
| t | 날짜 | RCL,t | RS&P 500,t | (RCL,t–RCL)2 | (RS&P 500,t–RS&P 500)2 | (RCL,t–RCL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018. 2. 28. | -7.10% | -3.89% | 56.55 | 20.81 | 34.30 |
| 2. | 2018. 3. 31. | 3.93% | -2.69% | 12.31 | 11.26 | -11.77 |
| 3. | 2018. 4. 30. | -8.41% | 0.27% | 78.03 | 0.16 | 3.49 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2022. 11. 30. | 4.93% | 5.38% | 20.33 | 22.17 | 21.23 |
| 59. | 2022. 12. 31. | 1.69% | -5.90% | 1.61 | 43.08 | -8.33 |
| 합계 (Σ): | 1,488.93 | 1,691.48 | 881.07 | |||
| t | 날짜 | RCL,t | RS&P 500,t | (RCL,t–RCL)2 | (RS&P 500,t–RS&P 500)2 | (RCL,t–RCL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018. 2. 28. | -7.10% | -3.89% | 56.55 | 20.81 | 34.30 |
| 2. | 2018. 3. 31. | 3.93% | -2.69% | 12.31 | 11.26 | -11.77 |
| 3. | 2018. 4. 30. | -8.41% | 0.27% | 78.03 | 0.16 | 3.49 |
| 4. | 2018. 5. 31. | -3.28% | 2.16% | 13.70 | 2.23 | -5.53 |
| 5. | 2018. 6. 30. | 2.73% | 0.48% | 5.31 | 0.03 | -0.42 |
| 6. | 2018. 7. 31. | 4.04% | 3.60% | 13.12 | 8.62 | 10.63 |
| 7. | 2018. 8. 31. | -0.90% | 3.03% | 1.73 | 5.57 | -3.11 |
| 8. | 2018. 9. 30. | 0.81% | 0.43% | 0.15 | 0.06 | -0.09 |
| 9. | 2018. 10. 31. | -10.43% | -6.94% | 117.65 | 57.87 | 82.51 |
| 10. | 2018. 11. 30. | 6.67% | 1.79% | 39.01 | 1.25 | 6.99 |
| 11. | 2018. 12. 31. | -6.30% | -9.18% | 45.14 | 96.91 | 66.14 |
| 12. | 2019. 1. 31. | 9.38% | 7.87% | 80.17 | 51.87 | 64.48 |
| 13. | 2019. 2. 28. | 1.84% | 2.97% | 2.01 | 5.32 | 3.27 |
| 14. | 2019. 3. 31. | 4.05% | 1.79% | 13.19 | 1.27 | 4.09 |
| 15. | 2019. 4. 30. | 6.83% | 3.93% | 41.05 | 10.66 | 20.92 |
| 16. | 2019. 5. 31. | -4.35% | -6.58% | 22.81 | 52.48 | 34.60 |
| 17. | 2019. 6. 30. | 2.94% | 6.89% | 6.37 | 38.77 | 15.71 |
| 18. | 2019. 7. 31. | 0.70% | 1.31% | 0.08 | 0.42 | 0.18 |
| 19. | 2019. 8. 31. | 3.36% | -1.81% | 8.63 | 6.13 | -7.27 |
| 20. | 2019. 9. 30. | -0.86% | 1.72% | 1.65 | 1.11 | -1.35 |
| 21. | 2019. 10. 31. | -6.09% | 2.04% | 42.45 | 1.89 | -8.97 |
| 22. | 2019. 11. 30. | -1.14% | 3.40% | 2.43 | 7.50 | -4.27 |
| 23. | 2019. 12. 31. | 1.50% | 2.86% | 1.17 | 4.81 | 2.37 |
| 24. | 2020. 1. 31. | 7.80% | -0.16% | 54.46 | 0.69 | -6.12 |
| 25. | 2020. 2. 29. | -8.42% | -8.41% | 78.11 | 82.40 | 80.23 |
| 26. | 2020. 3. 31. | -1.79% | -12.51% | 4.89 | 173.67 | 29.15 |
| 27. | 2020. 4. 30. | 6.56% | 12.68% | 37.63 | 144.43 | 73.72 |
| 28. | 2020. 5. 31. | 2.93% | 4.53% | 6.30 | 14.91 | 9.69 |
| 29. | 2020. 6. 30. | 1.29% | 1.84% | 0.75 | 1.37 | 1.01 |
| 30. | 2020. 7. 31. | 5.98% | 5.51% | 30.89 | 23.46 | 26.92 |
| 31. | 2020. 8. 31. | 2.67% | 7.01% | 5.05 | 40.19 | 14.25 |
| 32. | 2020. 9. 30. | -2.66% | -3.92% | 9.51 | 21.06 | 14.15 |
| 33. | 2020. 10. 31. | 2.83% | -2.77% | 5.78 | 11.79 | -8.26 |
| 34. | 2020. 11. 30. | 8.56% | 10.75% | 66.18 | 101.77 | 82.07 |
| 35. | 2020. 12. 31. | -0.15% | 3.71% | 0.33 | 9.28 | -1.74 |
| 36. | 2021. 1. 31. | -8.27% | -1.11% | 75.50 | 3.17 | 15.47 |
| 37. | 2021. 2. 28. | -3.59% | 2.61% | 16.09 | 3.77 | -7.79 |
| 38. | 2021. 3. 31. | 4.83% | 4.24% | 19.41 | 12.80 | 15.76 |
| 39. | 2021. 4. 30. | 2.94% | 5.24% | 6.36 | 20.94 | 11.54 |
| 40. | 2021. 5. 31. | 3.82% | 0.55% | 11.53 | 0.01 | -0.40 |
| 41. | 2021. 6. 30. | -2.90% | 2.22% | 11.03 | 2.42 | -5.16 |
| 42. | 2021. 7. 31. | -1.72% | 2.27% | 4.59 | 2.59 | -3.44 |
| 43. | 2021. 8. 31. | -1.95% | 2.90% | 5.62 | 4.98 | -5.29 |
| 44. | 2021. 9. 30. | -3.04% | -4.76% | 11.98 | 29.42 | 18.77 |
| 45. | 2021. 10. 31. | 1.40% | 6.91% | 0.96 | 39.03 | 6.13 |
| 46. | 2021. 11. 30. | -1.54% | -0.83% | 3.83 | 2.25 | 2.94 |
| 47. | 2021. 12. 31. | 13.76% | 4.36% | 177.83 | 13.65 | 49.27 |
| 48. | 2022. 1. 31. | -2.86% | -5.26% | 10.76 | 35.11 | 19.44 |
| 49. | 2022. 2. 28. | -6.67% | -3.14% | 50.29 | 14.46 | 26.97 |
| 50. | 2022. 3. 31. | -1.46% | 3.58% | 3.52 | 8.47 | -5.46 |
| 51. | 2022. 4. 30. | 2.23% | -8.80% | 3.27 | 89.54 | -17.10 |
| 52. | 2022. 5. 31. | 2.28% | 0.01% | 3.47 | 0.44 | -1.23 |
| 53. | 2022. 6. 30. | 1.69% | -8.39% | 1.60 | 82.06 | -11.47 |
| 54. | 2022. 7. 31. | -1.16% | 9.11% | 2.50 | 71.32 | -13.36 |
| 55. | 2022. 8. 31. | -0.67% | -4.24% | 1.20 | 24.11 | 5.37 |
| 56. | 2022. 9. 30. | -10.18% | -9.34% | 112.34 | 100.12 | 106.05 |
| 57. | 2022. 10. 31. | 5.78% | 7.99% | 28.71 | 53.58 | 39.22 |
| 58. | 2022. 11. 30. | 4.93% | 5.38% | 20.33 | 22.17 | 21.23 |
| 59. | 2022. 12. 31. | 1.69% | -5.90% | 1.61 | 43.08 | -8.33 |
| 합계 (Σ): | 1,488.93 | 1,691.48 | 881.07 | |||
모두 보기
분산CL = Σ(RCL,t–RCL)2 ÷ (59 – 1)
= 1,488.93 ÷ (59 – 1)
= 25.67
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,691.48 ÷ (59 – 1)
= 29.16
공분산CL, S&P 500 = Σ(RCL,t–RCL)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 881.07 ÷ (59 – 1)
= 15.19
체계적인 위험 추정 (β)
| 분산CL | 25.67 |
| 분산S&P 500 | 29.16 |
| 공분산CL, S&P 500 | 15.19 |
| 상관 계수CL, S&P 5001 | 0.56 |
| βCL2 | 0.52 |
| αCL3 | 0.07% |
계산
1 상관 계수CL, S&P 500
= 공분산CL, S&P 500 ÷ (표준 편차CL × 표준 편차S&P 500)
= 15.19 ÷ (5.07% × 5.40%)
= 0.56
2 βCL
= 공분산CL, S&P 500 ÷ 분산S&P 500
= 15.19 ÷ 29.16
= 0.52
3 αCL
= 평균의CL – βCL × 평균의S&P 500
= 0.42% – 0.52 × 0.67%
= 0.07%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.91% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.84% |
| 보통주의 체계적 위험Colgate | βCL | 0.52 |
| Colgate 보통주의 예상 수익률3 | E(RCL) | 10.08% |
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(RCL) = RF + βCL [E(RM) – RF]
= 4.91% + 0.52 [14.84% – 4.91%]
= 10.08%