자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Sherwin-Williams보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Sherwin-Williams Co., 월별 수익률
| Sherwin-Williams Co. (SHW) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값SHW,t1 | 피제수SHW,t1 | RSHW,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 1. 31. | $101.27 | 2,278.87 | ||||
| 1. | 2017. 2. 28. | $102.85 | $0.2833 | 1.84% | 2,363.64 | 3.72% |
| 2. | 2017. 3. 31. | $103.40 | 0.53% | 2,362.72 | -0.04% | |
| 3. | 2017. 4. 30. | $111.56 | 7.89% | 2,384.20 | 0.91% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2021. 11. 30. | $331.24 | $0.55 | 4.79% | 4,567.00 | -0.83% |
| 59. | 2021. 12. 31. | $352.16 | 6.32% | 4,766.18 | 4.36% | |
| 평균의 (R): | 2.41% | 1.36% | ||||
| 표준 편차: | 6.35% | 4.48% | ||||
| Sherwin-Williams Co. (SHW) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값SHW,t1 | 피제수SHW,t1 | RSHW,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 1. 31. | $101.27 | 2,278.87 | ||||
| 1. | 2017. 2. 28. | $102.85 | $0.2833 | 1.84% | 2,363.64 | 3.72% |
| 2. | 2017. 3. 31. | $103.40 | 0.53% | 2,362.72 | -0.04% | |
| 3. | 2017. 4. 30. | $111.56 | 7.89% | 2,384.20 | 0.91% | |
| 4. | 2017. 5. 31. | $110.59 | $0.2833 | -0.62% | 2,411.80 | 1.16% |
| 5. | 2017. 6. 30. | $116.99 | 5.79% | 2,423.41 | 0.48% | |
| 6. | 2017. 7. 31. | $112.42 | -3.91% | 2,470.30 | 1.93% | |
| 7. | 2017. 8. 31. | $113.09 | $0.2833 | 0.85% | 2,471.65 | 0.05% |
| 8. | 2017. 9. 30. | $119.35 | 5.54% | 2,519.36 | 1.93% | |
| 9. | 2017. 10. 31. | $131.72 | 10.36% | 2,575.26 | 2.22% | |
| 10. | 2017. 11. 30. | $133.14 | $0.2833 | 1.29% | 2,647.58 | 2.81% |
| 11. | 2017. 12. 31. | $136.68 | 2.66% | 2,673.61 | 0.98% | |
| 12. | 2018. 1. 31. | $139.04 | 1.73% | 2,823.81 | 5.62% | |
| 13. | 2018. 2. 28. | $133.86 | $0.2867 | -3.52% | 2,713.83 | -3.89% |
| 14. | 2018. 3. 31. | $130.71 | -2.35% | 2,640.87 | -2.69% | |
| 15. | 2018. 4. 30. | $122.55 | -6.24% | 2,648.05 | 0.27% | |
| 16. | 2018. 5. 31. | $126.42 | $0.2867 | 3.39% | 2,705.27 | 2.16% |
| 17. | 2018. 6. 30. | $135.86 | 7.47% | 2,718.37 | 0.48% | |
| 18. | 2018. 7. 31. | $146.91 | 8.13% | 2,816.29 | 3.60% | |
| 19. | 2018. 8. 31. | $151.86 | $0.2867 | 3.56% | 2,901.52 | 3.03% |
| 20. | 2018. 9. 30. | $151.74 | -0.08% | 2,913.98 | 0.43% | |
| 21. | 2018. 10. 31. | $131.16 | -13.56% | 2,711.74 | -6.94% | |
| 22. | 2018. 11. 30. | $141.36 | $0.2867 | 8.00% | 2,760.17 | 1.79% |
| 23. | 2018. 12. 31. | $131.15 | -7.22% | 2,506.85 | -9.18% | |
| 24. | 2019. 1. 31. | $140.51 | 7.14% | 2,704.10 | 7.87% | |
| 25. | 2019. 2. 28. | $144.40 | $0.3767 | 3.04% | 2,784.49 | 2.97% |
| 26. | 2019. 3. 31. | $143.57 | -0.57% | 2,834.40 | 1.79% | |
| 27. | 2019. 4. 30. | $151.61 | 5.60% | 2,945.83 | 3.93% | |
| 28. | 2019. 5. 31. | $139.82 | $0.3767 | -7.53% | 2,752.06 | -6.58% |
| 29. | 2019. 6. 30. | $152.76 | 9.25% | 2,941.76 | 6.89% | |
| 30. | 2019. 7. 31. | $171.01 | 11.95% | 2,980.38 | 1.31% | |
| 31. | 2019. 8. 31. | $175.58 | $0.3767 | 2.89% | 2,926.46 | -1.81% |
| 32. | 2019. 9. 30. | $183.29 | 4.39% | 2,976.74 | 1.72% | |
| 33. | 2019. 10. 31. | $190.77 | 4.08% | 3,037.56 | 2.04% | |
| 34. | 2019. 11. 30. | $194.38 | $0.3767 | 2.09% | 3,140.98 | 3.40% |
| 35. | 2019. 12. 31. | $194.51 | 0.07% | 3,230.78 | 2.86% | |
| 36. | 2020. 1. 31. | $185.66 | -4.55% | 3,225.52 | -0.16% | |
| 37. | 2020. 2. 29. | $172.25 | $0.4467 | -6.98% | 2,954.22 | -8.41% |
| 38. | 2020. 3. 31. | $153.17 | -11.08% | 2,584.59 | -12.51% | |
| 39. | 2020. 4. 30. | $178.79 | 16.73% | 2,912.43 | 12.68% | |
| 40. | 2020. 5. 31. | $197.95 | $0.4467 | 10.97% | 3,044.31 | 4.53% |
| 41. | 2020. 6. 30. | $192.62 | -2.69% | 3,100.29 | 1.84% | |
| 42. | 2020. 7. 31. | $215.97 | 12.12% | 3,271.12 | 5.51% | |
| 43. | 2020. 8. 31. | $223.68 | $0.4467 | 3.78% | 3,500.31 | 7.01% |
| 44. | 2020. 9. 30. | $232.25 | 3.83% | 3,363.00 | -3.92% | |
| 45. | 2020. 10. 31. | $229.33 | -1.26% | 3,269.96 | -2.77% | |
| 46. | 2020. 11. 30. | $249.21 | $0.4467 | 8.86% | 3,621.63 | 10.75% |
| 47. | 2020. 12. 31. | $244.97 | -1.70% | 3,756.07 | 3.71% | |
| 48. | 2021. 1. 31. | $230.60 | -5.87% | 3,714.24 | -1.11% | |
| 49. | 2021. 2. 28. | $226.78 | $0.55 | -1.42% | 3,811.15 | 2.61% |
| 50. | 2021. 3. 31. | $246.00 | 8.48% | 3,972.89 | 4.24% | |
| 51. | 2021. 4. 30. | $273.87 | 11.33% | 4,181.17 | 5.24% | |
| 52. | 2021. 5. 31. | $283.53 | $0.55 | 3.73% | 4,204.11 | 0.55% |
| 53. | 2021. 6. 30. | $272.45 | -3.91% | 4,297.50 | 2.22% | |
| 54. | 2021. 7. 31. | $291.03 | 6.82% | 4,395.26 | 2.27% | |
| 55. | 2021. 8. 31. | $303.67 | $0.55 | 4.53% | 4,522.68 | 2.90% |
| 56. | 2021. 9. 30. | $279.73 | -7.88% | 4,307.54 | -4.76% | |
| 57. | 2021. 10. 31. | $316.61 | 13.18% | 4,605.38 | 6.91% | |
| 58. | 2021. 11. 30. | $331.24 | $0.55 | 4.79% | 4,567.00 | -0.83% |
| 59. | 2021. 12. 31. | $352.16 | 6.32% | 4,766.18 | 4.36% | |
| 평균의 (R): | 2.41% | 1.36% | ||||
| 표준 편차: | 6.35% | 4.48% | ||||
모두 표시
1 보통주 주당 US$ 단위의 데이터로, 분할 및 주식 배당금에 맞게 조정됩니다.
2 기간 t 동안 SHW의 보통주에 대한 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)에 대한 수익률.
분산과 공분산
Sherwin-Williams Co., 수익률의 분산 및 공분산 계산
| t | 날짜 | RSHW,t | RS&P 500,t | (RSHW,t–RSHW)2 | (RS&P 500,t–RS&P 500)2 | (RSHW,t–RSHW)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 2. 28. | 1.84% | 3.72% | 0.32 | 5.58 | -1.34 |
| 2. | 2017. 3. 31. | 0.53% | -0.04% | 3.51 | 1.95 | 2.62 |
| 3. | 2017. 4. 30. | 7.89% | 0.91% | 30.07 | 0.20 | -2.46 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2021. 11. 30. | 4.79% | -0.83% | 5.70 | 4.80 | -5.23 |
| 59. | 2021. 12. 31. | 6.32% | 4.36% | 15.27 | 9.02 | 11.74 |
| 합계 (Σ): | 2,342.23 | 1,164.17 | 1,240.51 | |||
| t | 날짜 | RSHW,t | RS&P 500,t | (RSHW,t–RSHW)2 | (RS&P 500,t–RS&P 500)2 | (RSHW,t–RSHW)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 2. 28. | 1.84% | 3.72% | 0.32 | 5.58 | -1.34 |
| 2. | 2017. 3. 31. | 0.53% | -0.04% | 3.51 | 1.95 | 2.62 |
| 3. | 2017. 4. 30. | 7.89% | 0.91% | 30.07 | 0.20 | -2.46 |
| 4. | 2017. 5. 31. | -0.62% | 1.16% | 9.14 | 0.04 | 0.61 |
| 5. | 2017. 6. 30. | 5.79% | 0.48% | 11.42 | 0.77 | -2.96 |
| 6. | 2017. 7. 31. | -3.91% | 1.93% | 39.87 | 0.33 | -3.64 |
| 7. | 2017. 8. 31. | 0.85% | 0.05% | 2.43 | 1.70 | 2.03 |
| 8. | 2017. 9. 30. | 5.54% | 1.93% | 9.78 | 0.33 | 1.79 |
| 9. | 2017. 10. 31. | 10.36% | 2.22% | 63.31 | 0.74 | 6.85 |
| 10. | 2017. 11. 30. | 1.29% | 2.81% | 1.24 | 2.10 | -1.62 |
| 11. | 2017. 12. 31. | 2.66% | 0.98% | 0.06 | 0.14 | -0.09 |
| 12. | 2018. 1. 31. | 1.73% | 5.62% | 0.46 | 18.15 | -2.90 |
| 13. | 2018. 2. 28. | -3.52% | -3.89% | 35.13 | 27.59 | 31.13 |
| 14. | 2018. 3. 31. | -2.35% | -2.69% | 22.67 | 16.37 | 19.26 |
| 15. | 2018. 4. 30. | -6.24% | 0.27% | 74.83 | 1.18 | 9.39 |
| 16. | 2018. 5. 31. | 3.39% | 2.16% | 0.97 | 0.64 | 0.79 |
| 17. | 2018. 6. 30. | 7.47% | 0.48% | 25.60 | 0.76 | -4.42 |
| 18. | 2018. 7. 31. | 8.13% | 3.60% | 32.78 | 5.04 | 12.85 |
| 19. | 2018. 8. 31. | 3.56% | 3.03% | 1.34 | 2.78 | 1.93 |
| 20. | 2018. 9. 30. | -0.08% | 0.43% | 6.18 | 0.86 | 2.31 |
| 21. | 2018. 10. 31. | -13.56% | -6.94% | 255.05 | 68.86 | 132.53 |
| 22. | 2018. 11. 30. | 8.00% | 1.79% | 31.22 | 0.18 | 2.39 |
| 23. | 2018. 12. 31. | -7.22% | -9.18% | 92.74 | 111.00 | 101.46 |
| 24. | 2019. 1. 31. | 7.14% | 7.87% | 22.37 | 42.39 | 30.79 |
| 25. | 2019. 2. 28. | 3.04% | 2.97% | 0.40 | 2.61 | 1.02 |
| 26. | 2019. 3. 31. | -0.57% | 1.79% | 8.90 | 0.19 | -1.30 |
| 27. | 2019. 4. 30. | 5.60% | 3.93% | 10.19 | 6.62 | 8.22 |
| 28. | 2019. 5. 31. | -7.53% | -6.58% | 98.72 | 62.97 | 78.85 |
| 29. | 2019. 6. 30. | 9.25% | 6.89% | 46.88 | 30.64 | 37.90 |
| 30. | 2019. 7. 31. | 11.95% | 1.31% | 91.00 | 0.00 | -0.43 |
| 31. | 2019. 8. 31. | 2.89% | -1.81% | 0.24 | 10.03 | -1.54 |
| 32. | 2019. 9. 30. | 4.39% | 1.72% | 3.93 | 0.13 | 0.71 |
| 33. | 2019. 10. 31. | 4.08% | 2.04% | 2.80 | 0.47 | 1.15 |
| 34. | 2019. 11. 30. | 2.09% | 3.40% | 0.10 | 4.19 | -0.65 |
| 35. | 2019. 12. 31. | 0.07% | 2.86% | 5.48 | 2.25 | -3.51 |
| 36. | 2020. 1. 31. | -4.55% | -0.16% | 48.41 | 2.31 | 10.58 |
| 37. | 2020. 2. 29. | -6.98% | -8.41% | 88.17 | 95.43 | 91.73 |
| 38. | 2020. 3. 31. | -11.08% | -12.51% | 181.83 | 192.37 | 187.03 |
| 39. | 2020. 4. 30. | 16.73% | 12.68% | 205.03 | 128.29 | 162.18 |
| 40. | 2020. 5. 31. | 10.97% | 4.53% | 73.25 | 10.05 | 27.13 |
| 41. | 2020. 6. 30. | -2.69% | 1.84% | 26.01 | 0.23 | -2.45 |
| 42. | 2020. 7. 31. | 12.12% | 5.51% | 94.37 | 17.24 | 40.34 |
| 43. | 2020. 8. 31. | 3.78% | 7.01% | 1.87 | 31.91 | 7.73 |
| 44. | 2020. 9. 30. | 3.83% | -3.92% | 2.03 | 27.89 | -7.52 |
| 45. | 2020. 10. 31. | -1.26% | -2.77% | 13.43 | 17.01 | 15.12 |
| 46. | 2020. 11. 30. | 8.86% | 10.75% | 41.68 | 88.30 | 60.66 |
| 47. | 2020. 12. 31. | -1.70% | 3.71% | 16.88 | 5.54 | -9.67 |
| 48. | 2021. 1. 31. | -5.87% | -1.11% | 68.45 | 6.11 | 20.45 |
| 49. | 2021. 2. 28. | -1.42% | 2.61% | 14.64 | 1.57 | -4.79 |
| 50. | 2021. 3. 31. | 8.48% | 4.24% | 36.81 | 8.33 | 17.51 |
| 51. | 2021. 4. 30. | 11.33% | 5.24% | 79.59 | 15.09 | 34.66 |
| 52. | 2021. 5. 31. | 3.73% | 0.55% | 1.74 | 0.65 | -1.07 |
| 53. | 2021. 6. 30. | -3.91% | 2.22% | 39.89 | 0.75 | -5.45 |
| 54. | 2021. 7. 31. | 6.82% | 2.27% | 19.46 | 0.84 | 4.05 |
| 55. | 2021. 8. 31. | 4.53% | 2.90% | 4.51 | 2.38 | 3.27 |
| 56. | 2021. 9. 30. | -7.88% | -4.76% | 105.91 | 37.39 | 62.93 |
| 57. | 2021. 10. 31. | 13.18% | 6.91% | 116.13 | 30.87 | 59.88 |
| 58. | 2021. 11. 30. | 4.79% | -0.83% | 5.70 | 4.80 | -5.23 |
| 59. | 2021. 12. 31. | 6.32% | 4.36% | 15.27 | 9.02 | 11.74 |
| 합계 (Σ): | 2,342.23 | 1,164.17 | 1,240.51 | |||
모두 표시
분산SHW = Σ(RSHW,t–RSHW)2 ÷ (59 – 1)
= 2,342.23 ÷ (59 – 1)
= 40.38
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,164.17 ÷ (59 – 1)
= 20.07
공분산SHW, S&P 500 = Σ(RSHW,t–RSHW)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,240.51 ÷ (59 – 1)
= 21.39
체계적인 위험 추정 (β)
| 분산SHW | 40.38 |
| 분산S&P 500 | 20.07 |
| 공분산SHW, S&P 500 | 21.39 |
| 상관 계수SHW, S&P 5001 | 0.75 |
| βSHW2 | 1.07 |
| αSHW3 | 0.96% |
계산
1 상관 계수SHW, S&P 500
= 공분산SHW, S&P 500 ÷ (표준 편차SHW × 표준 편차S&P 500)
= 21.39 ÷ (6.35% × 4.48%)
= 0.75
2 βSHW
= 공분산SHW, S&P 500 ÷ 분산S&P 500
= 21.39 ÷ 20.07
= 1.07
3 αSHW
= 평균의SHW – βSHW × 평균의S&P 500
= 2.41% – 1.07 × 1.36%
= 0.96%
예상 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.83% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.48% |
| 보통주의 체계적 위험Sherwin-Williams | βSHW | 1.07 |
| Sherwin-Williams 보통주의 예상 수익률3 | E(RSHW) | 14.05% |
1 10년 이내에 만기가 되지 않거나 콜 가능하지 않은 모든 미결제 고정 쿠폰 미국 재무부 채권에 대한 입찰 수익률의 가중 평균(무위험 수익률 프록시).
2 자세히 보기 »
3 E(RSHW) = RF + βSHW [E(RM) – RF]
= 4.83% + 1.07 [13.48% – 4.83%]
= 14.05%