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 |
| 2019. 2. 28. | $150.42 | 2,784.49 | ||||
| 1. | 2019. 3. 31. | $163.87 | 8.94% | 2,834.40 | 1.79% | |
| 2. | 2019. 4. 30. | $176.35 | 7.62% | 2,945.83 | 3.93% | |
| 3. | 2019. 5. 31. | $165.59 | -6.10% | 2,752.06 | -6.58% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2024. 12. 31. | $382.41 | 19.26% | 5,881.63 | -2.50% | |
| 71. | 2025. 1. 31. | $414.20 | 8.31% | 6,040.53 | 2.70% | |
| 평균의 (R): | 1.98% | 1.22% | ||||
| 표준 편차: | 10.65% | 4.99% | ||||
| 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 |
| 2019. 2. 28. | $150.42 | 2,784.49 | ||||
| 1. | 2019. 3. 31. | $163.87 | 8.94% | 2,834.40 | 1.79% | |
| 2. | 2019. 4. 30. | $176.35 | 7.62% | 2,945.83 | 3.93% | |
| 3. | 2019. 5. 31. | $165.59 | -6.10% | 2,752.06 | -6.58% | |
| 4. | 2019. 6. 30. | $180.21 | 8.83% | 2,941.76 | 6.89% | |
| 5. | 2019. 7. 31. | $191.09 | 6.04% | 2,980.38 | 1.31% | |
| 6. | 2019. 8. 31. | $184.67 | -3.36% | 2,926.46 | -1.81% | |
| 7. | 2019. 9. 30. | $192.53 | 4.26% | 2,976.74 | 1.72% | |
| 8. | 2019. 10. 31. | $204.27 | 6.10% | 3,037.56 | 2.04% | |
| 9. | 2019. 11. 30. | $225.69 | 10.49% | 3,140.98 | 3.40% | |
| 10. | 2019. 12. 31. | $231.67 | 2.65% | 3,230.78 | 2.86% | |
| 11. | 2020. 1. 31. | $239.39 | 3.33% | 3,225.52 | -0.16% | |
| 12. | 2020. 2. 29. | $217.41 | -9.18% | 2,954.22 | -8.41% | |
| 13. | 2020. 3. 31. | $189.55 | -12.81% | 2,584.59 | -12.51% | |
| 14. | 2020. 4. 30. | $223.48 | 17.90% | 2,912.43 | 12.68% | |
| 15. | 2020. 5. 31. | $300.10 | 34.28% | 3,044.31 | 4.53% | |
| 16. | 2020. 6. 30. | $312.01 | 3.97% | 3,100.29 | 1.84% | |
| 17. | 2020. 7. 31. | $325.59 | 4.35% | 3,271.12 | 5.51% | |
| 18. | 2020. 8. 31. | $375.67 | 15.38% | 3,500.31 | 7.01% | |
| 19. | 2020. 9. 30. | $329.37 | -12.32% | 3,363.00 | -3.92% | |
| 20. | 2020. 10. 31. | $319.29 | -3.06% | 3,269.96 | -2.77% | |
| 21. | 2020. 11. 30. | $370.22 | 15.95% | 3,621.63 | 10.75% | |
| 22. | 2020. 12. 31. | $348.03 | -5.99% | 3,756.07 | 3.71% | |
| 23. | 2021. 1. 31. | $328.68 | -5.56% | 3,714.24 | -1.11% | |
| 24. | 2021. 2. 28. | $311.68 | -5.17% | 3,811.15 | 2.61% | |
| 25. | 2021. 3. 31. | $306.71 | -1.59% | 3,972.89 | 4.24% | |
| 26. | 2021. 4. 30. | $335.27 | 9.31% | 4,181.17 | 5.24% | |
| 27. | 2021. 5. 31. | $323.13 | -3.62% | 4,204.11 | 0.55% | |
| 28. | 2021. 6. 30. | $364.97 | 12.95% | 4,297.50 | 2.22% | |
| 29. | 2021. 7. 31. | $400.17 | 9.64% | 4,395.26 | 2.27% | |
| 30. | 2021. 8. 31. | $400.17 | 0.00% | 4,522.68 | 2.90% | |
| 31. | 2021. 9. 30. | $404.70 | 1.13% | 4,307.54 | -4.76% | |
| 32. | 2021. 10. 31. | $466.01 | 15.15% | 4,605.38 | 6.91% | |
| 33. | 2021. 11. 30. | $454.41 | -2.49% | 4,567.00 | -0.83% | |
| 34. | 2021. 12. 31. | $391.45 | -13.86% | 4,766.18 | 4.36% | |
| 35. | 2022. 1. 31. | $333.76 | -14.74% | 4,515.55 | -5.26% | |
| 36. | 2022. 2. 28. | $319.94 | -4.14% | 4,373.94 | -3.14% | |
| 37. | 2022. 3. 31. | $365.23 | 14.16% | 4,530.41 | 3.58% | |
| 38. | 2022. 4. 30. | $354.63 | -2.90% | 4,131.93 | -8.80% | |
| 39. | 2022. 5. 31. | $292.69 | -17.47% | 4,132.15 | 0.01% | |
| 40. | 2022. 6. 30. | $272.61 | -6.86% | 3,785.38 | -8.39% | |
| 41. | 2022. 7. 31. | $310.51 | 13.90% | 4,130.29 | 9.11% | |
| 42. | 2022. 8. 31. | $299.96 | -3.40% | 3,955.00 | -4.24% | |
| 43. | 2022. 9. 30. | $279.56 | -6.80% | 3,585.62 | -9.34% | |
| 44. | 2022. 10. 31. | $329.04 | 17.70% | 3,871.98 | 7.99% | |
| 45. | 2022. 11. 30. | $380.31 | 15.58% | 4,080.11 | 5.38% | |
| 46. | 2022. 12. 31. | $320.38 | -15.76% | 3,839.50 | -5.90% | |
| 47. | 2023. 1. 31. | $306.88 | -4.21% | 4,076.60 | 6.18% | |
| 48. | 2023. 2. 28. | $309.20 | 0.76% | 3,970.15 | -2.61% | |
| 49. | 2023. 3. 31. | $364.19 | 17.78% | 4,109.31 | 3.51% | |
| 50. | 2023. 4. 30. | $379.93 | 4.32% | 4,169.48 | 1.46% | |
| 51. | 2023. 5. 31. | $331.93 | -12.63% | 4,179.83 | 0.25% | |
| 52. | 2023. 6. 30. | $378.50 | 14.03% | 4,376.86 | 4.71% | |
| 53. | 2023. 7. 31. | $378.53 | 0.01% | 4,588.96 | 4.85% | |
| 54. | 2023. 8. 31. | $381.26 | 0.72% | 4,507.66 | -1.77% | |
| 55. | 2023. 9. 30. | $385.61 | 1.14% | 4,288.05 | -4.87% | |
| 56. | 2023. 10. 31. | $393.48 | 2.04% | 4,193.80 | -2.20% | |
| 57. | 2023. 11. 30. | $446.80 | 13.55% | 4,567.80 | 8.92% | |
| 58. | 2023. 12. 31. | $511.29 | 14.43% | 4,769.83 | 4.42% | |
| 59. | 2024. 1. 31. | $453.82 | -11.24% | 4,845.65 | 1.59% | |
| 60. | 2024. 2. 29. | $467.09 | 2.92% | 5,096.27 | 5.17% | |
| 61. | 2024. 3. 31. | $390.65 | -16.37% | 5,254.35 | 3.10% | |
| 62. | 2024. 4. 30. | $360.60 | -7.69% | 5,035.69 | -4.16% | |
| 63. | 2024. 5. 31. | $311.99 | -13.48% | 5,277.51 | 4.80% | |
| 64. | 2024. 6. 30. | $298.70 | -4.26% | 5,460.48 | 3.47% | |
| 65. | 2024. 7. 31. | $258.66 | -13.40% | 5,522.30 | 1.13% | |
| 66. | 2024. 8. 31. | $259.47 | 0.31% | 5,648.40 | 2.28% | |
| 67. | 2024. 9. 30. | $271.35 | 4.58% | 5,762.48 | 2.02% | |
| 68. | 2024. 10. 31. | $297.90 | 9.78% | 5,705.45 | -0.99% | |
| 69. | 2024. 11. 30. | $320.66 | 7.64% | 6,032.38 | 5.73% | |
| 70. | 2024. 12. 31. | $382.41 | 19.26% | 5,881.63 | -2.50% | |
| 71. | 2025. 1. 31. | $414.20 | 8.31% | 6,040.53 | 2.70% | |
| 평균의 (R): | 1.98% | 1.22% | ||||
| 표준 편차: | 10.65% | 4.99% | ||||
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. | 2019. 3. 31. | 8.94% | 1.79% | 48.44 | 0.33 | 3.98 |
| 2. | 2019. 4. 30. | 7.62% | 3.93% | 31.74 | 7.35 | 15.27 |
| 3. | 2019. 5. 31. | -6.10% | -6.58% | 65.34 | 60.81 | 63.03 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2024. 12. 31. | 19.26% | -2.50% | 298.43 | 13.83 | -64.25 |
| 71. | 2025. 1. 31. | 8.31% | 2.70% | 40.08 | 2.20 | 9.38 |
| 합계 (Σ): | 7,937.26 | 1,741.16 | 2,067.35 | |||
| 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. | 2019. 3. 31. | 8.94% | 1.79% | 48.44 | 0.33 | 3.98 |
| 2. | 2019. 4. 30. | 7.62% | 3.93% | 31.74 | 7.35 | 15.27 |
| 3. | 2019. 5. 31. | -6.10% | -6.58% | 65.34 | 60.81 | 63.03 |
| 4. | 2019. 6. 30. | 8.83% | 6.89% | 46.88 | 32.18 | 38.84 |
| 5. | 2019. 7. 31. | 6.04% | 1.31% | 16.45 | 0.01 | 0.38 |
| 6. | 2019. 8. 31. | -3.36% | -1.81% | 28.53 | 9.18 | 16.18 |
| 7. | 2019. 9. 30. | 4.26% | 1.72% | 5.17 | 0.25 | 1.13 |
| 8. | 2019. 10. 31. | 6.10% | 2.04% | 16.94 | 0.68 | 3.39 |
| 9. | 2019. 11. 30. | 10.49% | 3.40% | 72.32 | 4.77 | 18.58 |
| 10. | 2019. 12. 31. | 2.65% | 2.86% | 0.45 | 2.69 | 1.09 |
| 11. | 2020. 1. 31. | 3.33% | -0.16% | 1.82 | 1.91 | -1.87 |
| 12. | 2020. 2. 29. | -9.18% | -8.41% | 124.63 | 92.76 | 107.52 |
| 13. | 2020. 3. 31. | -12.81% | -12.51% | 218.94 | 188.57 | 203.19 |
| 14. | 2020. 4. 30. | 17.90% | 12.68% | 253.39 | 131.43 | 182.49 |
| 15. | 2020. 5. 31. | 34.28% | 4.53% | 1,043.48 | 10.94 | 106.86 |
| 16. | 2020. 6. 30. | 3.97% | 1.84% | 3.95 | 0.38 | 1.23 |
| 17. | 2020. 7. 31. | 4.35% | 5.51% | 5.62 | 18.41 | 10.17 |
| 18. | 2020. 8. 31. | 15.38% | 7.01% | 179.54 | 33.48 | 77.53 |
| 19. | 2020. 9. 30. | -12.32% | -3.92% | 204.68 | 26.45 | 73.58 |
| 20. | 2020. 10. 31. | -3.06% | -2.77% | 25.43 | 15.89 | 20.10 |
| 21. | 2020. 11. 30. | 15.95% | 10.75% | 195.13 | 90.91 | 133.19 |
| 22. | 2020. 12. 31. | -5.99% | 3.71% | 63.61 | 6.21 | -19.88 |
| 23. | 2021. 1. 31. | -5.56% | -1.11% | 56.88 | 5.45 | 17.60 |
| 24. | 2021. 2. 28. | -5.17% | 2.61% | 51.18 | 1.93 | -9.94 |
| 25. | 2021. 3. 31. | -1.59% | 4.24% | 12.79 | 9.14 | -10.82 |
| 26. | 2021. 4. 30. | 9.31% | 5.24% | 53.72 | 16.18 | 29.48 |
| 27. | 2021. 5. 31. | -3.62% | 0.55% | 31.39 | 0.45 | 3.76 |
| 28. | 2021. 6. 30. | 12.95% | 2.22% | 120.26 | 1.00 | 10.98 |
| 29. | 2021. 7. 31. | 9.64% | 2.27% | 58.71 | 1.11 | 8.08 |
| 30. | 2021. 8. 31. | 0.00% | 2.90% | 3.93 | 2.82 | -3.33 |
| 31. | 2021. 9. 30. | 1.13% | -4.76% | 0.72 | 35.72 | 5.08 |
| 32. | 2021. 10. 31. | 15.15% | 6.91% | 173.38 | 32.43 | 74.98 |
| 33. | 2021. 11. 30. | -2.49% | -0.83% | 19.99 | 4.22 | 9.18 |
| 34. | 2021. 12. 31. | -13.86% | 4.36% | 250.82 | 9.87 | -49.75 |
| 35. | 2022. 1. 31. | -14.74% | -5.26% | 279.54 | 41.97 | 108.32 |
| 36. | 2022. 2. 28. | -4.14% | -3.14% | 37.49 | 18.98 | 26.67 |
| 37. | 2022. 3. 31. | 14.16% | 3.58% | 148.20 | 5.56 | 28.70 |
| 38. | 2022. 4. 30. | -2.90% | -8.80% | 23.86 | 100.31 | 48.92 |
| 39. | 2022. 5. 31. | -17.47% | 0.01% | 378.23 | 1.48 | 23.62 |
| 40. | 2022. 6. 30. | -6.86% | -8.39% | 78.19 | 92.39 | 84.99 |
| 41. | 2022. 7. 31. | 13.90% | 9.11% | 142.10 | 62.28 | 94.07 |
| 42. | 2022. 8. 31. | -3.40% | -4.24% | 28.94 | 29.86 | 29.39 |
| 43. | 2022. 9. 30. | -6.80% | -9.34% | 77.14 | 111.50 | 92.74 |
| 44. | 2022. 10. 31. | 17.70% | 7.99% | 247.03 | 45.78 | 106.35 |
| 45. | 2022. 11. 30. | 15.58% | 5.38% | 184.95 | 17.27 | 56.51 |
| 46. | 2022. 12. 31. | -15.76% | -5.90% | 314.72 | 50.65 | 126.26 |
| 47. | 2023. 1. 31. | -4.21% | 6.18% | 38.39 | 24.55 | -30.70 |
| 48. | 2023. 2. 28. | 0.76% | -2.61% | 1.50 | 14.68 | 4.70 |
| 49. | 2023. 3. 31. | 17.78% | 3.51% | 249.72 | 5.22 | 36.11 |
| 50. | 2023. 4. 30. | 4.32% | 1.46% | 5.47 | 0.06 | 0.57 |
| 51. | 2023. 5. 31. | -12.63% | 0.25% | 213.63 | 0.94 | 14.20 |
| 52. | 2023. 6. 30. | 14.03% | 4.71% | 145.15 | 12.21 | 42.09 |
| 53. | 2023. 7. 31. | 0.01% | 4.85% | 3.90 | 13.15 | -7.16 |
| 54. | 2023. 8. 31. | 0.72% | -1.77% | 1.59 | 8.95 | 3.77 |
| 55. | 2023. 9. 30. | 1.14% | -4.87% | 0.71 | 37.11 | 5.12 |
| 56. | 2023. 10. 31. | 2.04% | -2.20% | 0.00 | 11.68 | -0.20 |
| 57. | 2023. 11. 30. | 13.55% | 8.92% | 133.84 | 59.26 | 89.06 |
| 58. | 2023. 12. 31. | 14.43% | 4.42% | 155.04 | 10.26 | 39.88 |
| 59. | 2024. 1. 31. | -11.24% | 1.59% | 174.83 | 0.14 | -4.89 |
| 60. | 2024. 2. 29. | 2.92% | 5.17% | 0.89 | 15.62 | 3.72 |
| 61. | 2024. 3. 31. | -16.37% | 3.10% | 336.62 | 3.54 | -34.53 |
| 62. | 2024. 4. 30. | -7.69% | -4.16% | 93.59 | 28.96 | 52.06 |
| 63. | 2024. 5. 31. | -13.48% | 4.80% | 239.09 | 12.83 | -55.39 |
| 64. | 2024. 6. 30. | -4.26% | 3.47% | 38.96 | 5.05 | -14.03 |
| 65. | 2024. 7. 31. | -13.40% | 1.13% | 236.75 | 0.01 | 1.35 |
| 66. | 2024. 8. 31. | 0.31% | 2.28% | 2.79 | 1.13 | -1.77 |
| 67. | 2024. 9. 30. | 4.58% | 2.02% | 6.74 | 0.64 | 2.08 |
| 68. | 2024. 10. 31. | 9.78% | -0.99% | 60.88 | 4.88 | -17.24 |
| 69. | 2024. 11. 30. | 7.64% | 5.73% | 32.01 | 20.34 | 25.52 |
| 70. | 2024. 12. 31. | 19.26% | -2.50% | 298.43 | 13.83 | -64.25 |
| 71. | 2025. 1. 31. | 8.31% | 2.70% | 40.08 | 2.20 | 9.38 |
| 합계 (Σ): | 7,937.26 | 1,741.16 | 2,067.35 | |||
모두 보기
분산LULU = Σ(RLULU,t–RLULU)2 ÷ (71 – 1)
= 7,937.26 ÷ (71 – 1)
= 113.39
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,741.16 ÷ (71 – 1)
= 24.87
공분산LULU, S&P 500 = Σ(RLULU,t–RLULU)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 2,067.35 ÷ (71 – 1)
= 29.53
체계적인 위험 추정 (β)
| 분산LULU | 113.39 |
| 분산S&P 500 | 24.87 |
| 공분산LULU, S&P 500 | 29.53 |
| 상관 계수LULU, S&P 5001 | 0.56 |
| βLULU2 | 1.19 |
| αLULU3 | 0.53% |
계산
1 상관 계수LULU, S&P 500
= 공분산LULU, S&P 500 ÷ (표준 편차LULU × 표준 편차S&P 500)
= 29.53 ÷ (10.65% × 4.99%)
= 0.56
2 βLULU
= 공분산LULU, S&P 500 ÷ 분산S&P 500
= 29.53 ÷ 24.87
= 1.19
3 αLULU
= 평균의LULU – βLULU × 평균의S&P 500
= 1.98% – 1.19 × 1.22%
= 0.53%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.91% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.84% |
| 보통주의 체계적 위험lululemon | βLULU | 1.19 |
| 룰루레몬 보통주 예상 수익률3 | E(RLULU) | 16.70% |
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]
= 4.91% + 1.19 [14.84% – 4.91%]
= 16.70%