자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 lululemon보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
lululemon athletica inc., 월별 수익률
| lululemon athletica inc. (LULU) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값LULU,t1 | 피제수LULU,t1 | RLULU,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2018. 2. 28. | $81.10 | 2,713.83 | ||||
| 1. | 2018. 3. 31. | $89.12 | 9.89% | 2,640.87 | -2.69% | |
| 2. | 2018. 4. 30. | $99.80 | 11.98% | 2,648.05 | 0.27% | |
| 3. | 2018. 5. 31. | $105.05 | 5.26% | 2,705.27 | 2.16% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2023. 12. 31. | $511.29 | 14.43% | 4,769.83 | 4.42% | |
| 71. | 2024. 1. 31. | $453.82 | -11.24% | 4,845.65 | 1.59% | |
| 평균의 (R): | 3.03% | 0.95% | ||||
| 표준 편차: | 11.02% | 5.18% | ||||
| lululemon athletica inc. (LULU) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값LULU,t1 | 피제수LULU,t1 | RLULU,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2018. 2. 28. | $81.10 | 2,713.83 | ||||
| 1. | 2018. 3. 31. | $89.12 | 9.89% | 2,640.87 | -2.69% | |
| 2. | 2018. 4. 30. | $99.80 | 11.98% | 2,648.05 | 0.27% | |
| 3. | 2018. 5. 31. | $105.05 | 5.26% | 2,705.27 | 2.16% | |
| 4. | 2018. 6. 30. | $124.85 | 18.85% | 2,718.37 | 0.48% | |
| 5. | 2018. 7. 31. | $119.95 | -3.92% | 2,816.29 | 3.60% | |
| 6. | 2018. 8. 31. | $154.93 | 29.16% | 2,901.52 | 3.03% | |
| 7. | 2018. 9. 30. | $162.49 | 4.88% | 2,913.98 | 0.43% | |
| 8. | 2018. 10. 31. | $140.73 | -13.39% | 2,711.74 | -6.94% | |
| 9. | 2018. 11. 30. | $132.55 | -5.81% | 2,760.17 | 1.79% | |
| 10. | 2018. 12. 31. | $121.61 | -8.25% | 2,506.85 | -9.18% | |
| 11. | 2019. 1. 31. | $147.81 | 21.54% | 2,704.10 | 7.87% | |
| 12. | 2019. 2. 28. | $150.42 | 1.77% | 2,784.49 | 2.97% | |
| 13. | 2019. 3. 31. | $163.87 | 8.94% | 2,834.40 | 1.79% | |
| 14. | 2019. 4. 30. | $176.35 | 7.62% | 2,945.83 | 3.93% | |
| 15. | 2019. 5. 31. | $165.59 | -6.10% | 2,752.06 | -6.58% | |
| 16. | 2019. 6. 30. | $180.21 | 8.83% | 2,941.76 | 6.89% | |
| 17. | 2019. 7. 31. | $191.09 | 6.04% | 2,980.38 | 1.31% | |
| 18. | 2019. 8. 31. | $184.67 | -3.36% | 2,926.46 | -1.81% | |
| 19. | 2019. 9. 30. | $192.53 | 4.26% | 2,976.74 | 1.72% | |
| 20. | 2019. 10. 31. | $204.27 | 6.10% | 3,037.56 | 2.04% | |
| 21. | 2019. 11. 30. | $225.69 | 10.49% | 3,140.98 | 3.40% | |
| 22. | 2019. 12. 31. | $231.67 | 2.65% | 3,230.78 | 2.86% | |
| 23. | 2020. 1. 31. | $239.39 | 3.33% | 3,225.52 | -0.16% | |
| 24. | 2020. 2. 29. | $217.41 | -9.18% | 2,954.22 | -8.41% | |
| 25. | 2020. 3. 31. | $189.55 | -12.81% | 2,584.59 | -12.51% | |
| 26. | 2020. 4. 30. | $223.48 | 17.90% | 2,912.43 | 12.68% | |
| 27. | 2020. 5. 31. | $300.10 | 34.28% | 3,044.31 | 4.53% | |
| 28. | 2020. 6. 30. | $312.01 | 3.97% | 3,100.29 | 1.84% | |
| 29. | 2020. 7. 31. | $325.59 | 4.35% | 3,271.12 | 5.51% | |
| 30. | 2020. 8. 31. | $375.67 | 15.38% | 3,500.31 | 7.01% | |
| 31. | 2020. 9. 30. | $329.37 | -12.32% | 3,363.00 | -3.92% | |
| 32. | 2020. 10. 31. | $319.29 | -3.06% | 3,269.96 | -2.77% | |
| 33. | 2020. 11. 30. | $370.22 | 15.95% | 3,621.63 | 10.75% | |
| 34. | 2020. 12. 31. | $348.03 | -5.99% | 3,756.07 | 3.71% | |
| 35. | 2021. 1. 31. | $328.68 | -5.56% | 3,714.24 | -1.11% | |
| 36. | 2021. 2. 28. | $311.68 | -5.17% | 3,811.15 | 2.61% | |
| 37. | 2021. 3. 31. | $306.71 | -1.59% | 3,972.89 | 4.24% | |
| 38. | 2021. 4. 30. | $335.27 | 9.31% | 4,181.17 | 5.24% | |
| 39. | 2021. 5. 31. | $323.13 | -3.62% | 4,204.11 | 0.55% | |
| 40. | 2021. 6. 30. | $364.97 | 12.95% | 4,297.50 | 2.22% | |
| 41. | 2021. 7. 31. | $400.17 | 9.64% | 4,395.26 | 2.27% | |
| 42. | 2021. 8. 31. | $400.17 | 0.00% | 4,522.68 | 2.90% | |
| 43. | 2021. 9. 30. | $404.70 | 1.13% | 4,307.54 | -4.76% | |
| 44. | 2021. 10. 31. | $466.01 | 15.15% | 4,605.38 | 6.91% | |
| 45. | 2021. 11. 30. | $454.41 | -2.49% | 4,567.00 | -0.83% | |
| 46. | 2021. 12. 31. | $391.45 | -13.86% | 4,766.18 | 4.36% | |
| 47. | 2022. 1. 31. | $333.76 | -14.74% | 4,515.55 | -5.26% | |
| 48. | 2022. 2. 28. | $319.94 | -4.14% | 4,373.94 | -3.14% | |
| 49. | 2022. 3. 31. | $365.23 | 14.16% | 4,530.41 | 3.58% | |
| 50. | 2022. 4. 30. | $354.63 | -2.90% | 4,131.93 | -8.80% | |
| 51. | 2022. 5. 31. | $292.69 | -17.47% | 4,132.15 | 0.01% | |
| 52. | 2022. 6. 30. | $272.61 | -6.86% | 3,785.38 | -8.39% | |
| 53. | 2022. 7. 31. | $310.51 | 13.90% | 4,130.29 | 9.11% | |
| 54. | 2022. 8. 31. | $299.96 | -3.40% | 3,955.00 | -4.24% | |
| 55. | 2022. 9. 30. | $279.56 | -6.80% | 3,585.62 | -9.34% | |
| 56. | 2022. 10. 31. | $329.04 | 17.70% | 3,871.98 | 7.99% | |
| 57. | 2022. 11. 30. | $380.31 | 15.58% | 4,080.11 | 5.38% | |
| 58. | 2022. 12. 31. | $320.38 | -15.76% | 3,839.50 | -5.90% | |
| 59. | 2023. 1. 31. | $306.88 | -4.21% | 4,076.60 | 6.18% | |
| 60. | 2023. 2. 28. | $309.20 | 0.76% | 3,970.15 | -2.61% | |
| 61. | 2023. 3. 31. | $364.19 | 17.78% | 4,109.31 | 3.51% | |
| 62. | 2023. 4. 30. | $379.93 | 4.32% | 4,169.48 | 1.46% | |
| 63. | 2023. 5. 31. | $331.93 | -12.63% | 4,179.83 | 0.25% | |
| 64. | 2023. 6. 30. | $378.50 | 14.03% | 4,376.86 | 4.71% | |
| 65. | 2023. 7. 31. | $378.53 | 0.01% | 4,588.96 | 4.85% | |
| 66. | 2023. 8. 31. | $381.26 | 0.72% | 4,507.66 | -1.77% | |
| 67. | 2023. 9. 30. | $385.61 | 1.14% | 4,288.05 | -4.87% | |
| 68. | 2023. 10. 31. | $393.48 | 2.04% | 4,193.80 | -2.20% | |
| 69. | 2023. 11. 30. | $446.80 | 13.55% | 4,567.80 | 8.92% | |
| 70. | 2023. 12. 31. | $511.29 | 14.43% | 4,769.83 | 4.42% | |
| 71. | 2024. 1. 31. | $453.82 | -11.24% | 4,845.65 | 1.59% | |
| 평균의 (R): | 3.03% | 0.95% | ||||
| 표준 편차: | 11.02% | 5.18% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 LULU의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
lululemon athletica inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RLULU,t | RS&P 500,t | (RLULU,t–RLULU)2 | (RS&P 500,t–RS&P 500)2 | (RLULU,t–RLULU)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018. 3. 31. | 9.89% | -2.69% | 47.06 | 13.26 | -24.98 |
| 2. | 2018. 4. 30. | 11.98% | 0.27% | 80.19 | 0.46 | -6.10 |
| 3. | 2018. 5. 31. | 5.26% | 2.16% | 4.98 | 1.46 | 2.70 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2023. 12. 31. | 14.43% | 4.42% | 130.06 | 12.04 | 39.57 |
| 71. | 2024. 1. 31. | -11.24% | 1.59% | 203.61 | 0.41 | -9.08 |
| 합계 (Σ): | 8,497.00 | 1,876.53 | 2,520.47 | |||
| t | 날짜 | RLULU,t | RS&P 500,t | (RLULU,t–RLULU)2 | (RS&P 500,t–RS&P 500)2 | (RLULU,t–RLULU)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018. 3. 31. | 9.89% | -2.69% | 47.06 | 13.26 | -24.98 |
| 2. | 2018. 4. 30. | 11.98% | 0.27% | 80.19 | 0.46 | -6.10 |
| 3. | 2018. 5. 31. | 5.26% | 2.16% | 4.98 | 1.46 | 2.70 |
| 4. | 2018. 6. 30. | 18.85% | 0.48% | 250.24 | 0.22 | -7.41 |
| 5. | 2018. 7. 31. | -3.92% | 3.60% | 48.36 | 7.02 | -18.42 |
| 6. | 2018. 8. 31. | 29.16% | 3.03% | 682.93 | 4.30 | 54.18 |
| 7. | 2018. 9. 30. | 4.88% | 0.43% | 3.42 | 0.27 | -0.97 |
| 8. | 2018. 10. 31. | -13.39% | -6.94% | 269.64 | 62.30 | 129.61 |
| 9. | 2018. 11. 30. | -5.81% | 1.79% | 78.18 | 0.69 | -7.37 |
| 10. | 2018. 12. 31. | -8.25% | -9.18% | 127.30 | 102.63 | 114.30 |
| 11. | 2019. 1. 31. | 21.54% | 7.87% | 342.81 | 47.82 | 128.04 |
| 12. | 2019. 2. 28. | 1.77% | 2.97% | 1.60 | 4.08 | -2.55 |
| 13. | 2019. 3. 31. | 8.94% | 1.79% | 34.96 | 0.70 | 4.96 |
| 14. | 2019. 4. 30. | 7.62% | 3.93% | 21.04 | 8.87 | 13.66 |
| 15. | 2019. 5. 31. | -6.10% | -6.58% | 83.37 | 56.71 | 68.76 |
| 16. | 2019. 6. 30. | 8.83% | 6.89% | 33.64 | 35.28 | 34.45 |
| 17. | 2019. 7. 31. | 6.04% | 1.31% | 9.05 | 0.13 | 1.08 |
| 18. | 2019. 8. 31. | -3.36% | -1.81% | 40.82 | 7.63 | 17.65 |
| 19. | 2019. 9. 30. | 4.26% | 1.72% | 1.51 | 0.59 | 0.94 |
| 20. | 2019. 10. 31. | 6.10% | 2.04% | 9.42 | 1.19 | 3.35 |
| 21. | 2019. 11. 30. | 10.49% | 3.40% | 55.61 | 6.01 | 18.28 |
| 22. | 2019. 12. 31. | 2.65% | 2.86% | 0.14 | 3.63 | -0.72 |
| 23. | 2020. 1. 31. | 3.33% | -0.16% | 0.09 | 1.24 | -0.34 |
| 24. | 2020. 2. 29. | -9.18% | -8.41% | 149.10 | 87.68 | 114.34 |
| 25. | 2020. 3. 31. | -12.81% | -12.51% | 251.02 | 181.30 | 213.33 |
| 26. | 2020. 4. 30. | 17.90% | 12.68% | 221.15 | 137.63 | 174.46 |
| 27. | 2020. 5. 31. | 34.28% | 4.53% | 976.92 | 12.78 | 111.75 |
| 28. | 2020. 6. 30. | 3.97% | 1.84% | 0.88 | 0.78 | 0.83 |
| 29. | 2020. 7. 31. | 4.35% | 5.51% | 1.75 | 20.77 | 6.03 |
| 30. | 2020. 8. 31. | 15.38% | 7.01% | 152.58 | 36.65 | 74.77 |
| 31. | 2020. 9. 30. | -12.32% | -3.92% | 235.74 | 23.77 | 74.86 |
| 32. | 2020. 10. 31. | -3.06% | -2.77% | 37.08 | 13.83 | 22.65 |
| 33. | 2020. 11. 30. | 15.95% | 10.75% | 166.97 | 96.07 | 126.66 |
| 34. | 2020. 12. 31. | -5.99% | 3.71% | 81.41 | 7.61 | -24.90 |
| 35. | 2021. 1. 31. | -5.56% | -1.11% | 73.77 | 4.27 | 17.75 |
| 36. | 2021. 2. 28. | -5.17% | 2.61% | 67.26 | 2.74 | -13.58 |
| 37. | 2021. 3. 31. | -1.59% | 4.24% | 21.38 | 10.83 | -15.22 |
| 38. | 2021. 4. 30. | 9.31% | 5.24% | 39.47 | 18.40 | 26.95 |
| 39. | 2021. 5. 31. | -3.62% | 0.55% | 44.22 | 0.16 | 2.69 |
| 40. | 2021. 6. 30. | 12.95% | 2.22% | 98.39 | 1.61 | 12.58 |
| 41. | 2021. 7. 31. | 9.64% | 2.27% | 43.76 | 1.75 | 8.74 |
| 42. | 2021. 8. 31. | 0.00% | 2.90% | 9.18 | 3.79 | -5.90 |
| 43. | 2021. 9. 30. | 1.13% | -4.76% | 3.60 | 32.60 | 10.83 |
| 44. | 2021. 10. 31. | 15.15% | 6.91% | 146.90 | 35.54 | 72.26 |
| 45. | 2021. 11. 30. | -2.49% | -0.83% | 30.45 | 3.19 | 9.86 |
| 46. | 2021. 12. 31. | -13.86% | 4.36% | 285.09 | 11.62 | -57.55 |
| 47. | 2022. 1. 31. | -14.74% | -5.26% | 315.65 | 38.58 | 110.36 |
| 48. | 2022. 2. 28. | -4.14% | -3.14% | 51.41 | 16.72 | 29.32 |
| 49. | 2022. 3. 31. | 14.16% | 3.58% | 123.80 | 6.89 | 29.20 |
| 50. | 2022. 4. 30. | -2.90% | -8.80% | 35.18 | 95.04 | 57.82 |
| 51. | 2022. 5. 31. | -17.47% | 0.01% | 420.05 | 0.90 | 19.42 |
| 52. | 2022. 6. 30. | -6.86% | -8.39% | 97.81 | 87.33 | 92.42 |
| 53. | 2022. 7. 31. | 13.90% | 9.11% | 118.23 | 66.56 | 88.71 |
| 54. | 2022. 8. 31. | -3.40% | -4.24% | 41.30 | 27.01 | 33.40 |
| 55. | 2022. 9. 30. | -6.80% | -9.34% | 96.63 | 105.94 | 101.18 |
| 56. | 2022. 10. 31. | 17.70% | 7.99% | 215.21 | 49.47 | 103.18 |
| 57. | 2022. 11. 30. | 15.58% | 5.38% | 157.57 | 19.56 | 55.51 |
| 58. | 2022. 12. 31. | -15.76% | -5.90% | 352.96 | 46.92 | 128.69 |
| 59. | 2023. 1. 31. | -4.21% | 6.18% | 52.46 | 27.27 | -37.83 |
| 60. | 2023. 2. 28. | 0.76% | -2.61% | 5.17 | 12.70 | 8.10 |
| 61. | 2023. 3. 31. | 17.78% | 3.51% | 217.72 | 6.51 | 37.66 |
| 62. | 2023. 4. 30. | 4.32% | 1.46% | 1.67 | 0.26 | 0.66 |
| 63. | 2023. 5. 31. | -12.63% | 0.25% | 245.33 | 0.50 | 11.04 |
| 64. | 2023. 6. 30. | 14.03% | 4.71% | 121.02 | 14.14 | 41.37 |
| 65. | 2023. 7. 31. | 0.01% | 4.85% | 9.13 | 15.16 | -11.76 |
| 66. | 2023. 8. 31. | 0.72% | -1.77% | 5.33 | 7.42 | 6.29 |
| 67. | 2023. 9. 30. | 1.14% | -4.87% | 3.57 | 33.93 | 11.00 |
| 68. | 2023. 10. 31. | 2.04% | -2.20% | 0.98 | 9.93 | 3.11 |
| 69. | 2023. 11. 30. | 13.55% | 8.92% | 110.71 | 63.44 | 83.81 |
| 70. | 2023. 12. 31. | 14.43% | 4.42% | 130.06 | 12.04 | 39.57 |
| 71. | 2024. 1. 31. | -11.24% | 1.59% | 203.61 | 0.41 | -9.08 |
| 합계 (Σ): | 8,497.00 | 1,876.53 | 2,520.47 | |||
모두 보기
분산LULU = Σ(RLULU,t–RLULU)2 ÷ (71 – 1)
= 8,497.00 ÷ (71 – 1)
= 121.39
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,876.53 ÷ (71 – 1)
= 26.81
공분산LULU, S&P 500 = Σ(RLULU,t–RLULU)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 2,520.47 ÷ (71 – 1)
= 36.01
체계적인 위험 추정 (β)
| 분산LULU | 121.39 |
| 분산S&P 500 | 26.81 |
| 공분산LULU, S&P 500 | 36.01 |
| 상관 계수LULU, S&P 5001 | 0.63 |
| βLULU2 | 1.34 |
| αLULU3 | 1.75% |
계산
1 상관 계수LULU, S&P 500
= 공분산LULU, S&P 500 ÷ (표준 편차LULU × 표준 편차S&P 500)
= 36.01 ÷ (11.02% × 5.18%)
= 0.63
2 βLULU
= 공분산LULU, S&P 500 ÷ 분산S&P 500
= 36.01 ÷ 26.81
= 1.34
3 αLULU
= 평균의LULU – βLULU × 평균의S&P 500
= 3.03% – 1.34 × 0.95%
= 1.75%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.67% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.79% |
| 보통주의 체계적 위험lululemon | βLULU | 1.34 |
| 룰루레몬 보통주 예상 수익률3 | E(RLULU) | 16.91% |
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(RLULU) = RF + βLULU [E(RM) – RF]
= 4.67% + 1.34 [13.79% – 4.67%]
= 16.91%