자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Lilly보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Eli Lilly & Co., 월별 수익률
| Eli Lilly & Co. (LLY) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값LLY,t1 | 피제수LLY,t1 | RLLY,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $119.86 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $126.29 | $0.645 | 5.90% | 2,784.49 | 2.97% |
| 2. | 2019. 3. 31. | $129.76 | 2.75% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $117.04 | -9.80% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $591.04 | $1.13 | 6.90% | 4,567.80 | 8.92% |
| 59. | 2023. 12. 31. | $582.92 | -1.37% | 4,769.83 | 4.42% | |
| 평균의 (R): | 3.19% | 1.11% | ||||
| 표준 편차: | 8.33% | 5.31% | ||||
| Eli Lilly & Co. (LLY) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값LLY,t1 | 피제수LLY,t1 | RLLY,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $119.86 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $126.29 | $0.645 | 5.90% | 2,784.49 | 2.97% |
| 2. | 2019. 3. 31. | $129.76 | 2.75% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $117.04 | -9.80% | 2,945.83 | 3.93% | |
| 4. | 2019. 5. 31. | $115.94 | $0.645 | -0.39% | 2,752.06 | -6.58% |
| 5. | 2019. 6. 30. | $110.79 | -4.44% | 2,941.76 | 6.89% | |
| 6. | 2019. 7. 31. | $108.95 | -1.66% | 2,980.38 | 1.31% | |
| 7. | 2019. 8. 31. | $112.97 | $0.645 | 4.28% | 2,926.46 | -1.81% |
| 8. | 2019. 9. 30. | $111.83 | -1.01% | 2,976.74 | 1.72% | |
| 9. | 2019. 10. 31. | $113.95 | 1.90% | 3,037.56 | 2.04% | |
| 10. | 2019. 11. 30. | $117.35 | $0.645 | 3.55% | 3,140.98 | 3.40% |
| 11. | 2019. 12. 31. | $131.43 | 12.00% | 3,230.78 | 2.86% | |
| 12. | 2020. 1. 31. | $139.64 | 6.25% | 3,225.52 | -0.16% | |
| 13. | 2020. 2. 29. | $126.13 | $0.74 | -9.14% | 2,954.22 | -8.41% |
| 14. | 2020. 3. 31. | $138.72 | 9.98% | 2,584.59 | -12.51% | |
| 15. | 2020. 4. 30. | $154.64 | 11.48% | 2,912.43 | 12.68% | |
| 16. | 2020. 5. 31. | $152.95 | $0.74 | -0.61% | 3,044.31 | 4.53% |
| 17. | 2020. 6. 30. | $164.18 | 7.34% | 3,100.29 | 1.84% | |
| 18. | 2020. 7. 31. | $150.29 | -8.46% | 3,271.12 | 5.51% | |
| 19. | 2020. 8. 31. | $148.39 | $0.74 | -0.77% | 3,500.31 | 7.01% |
| 20. | 2020. 9. 30. | $148.02 | -0.25% | 3,363.00 | -3.92% | |
| 21. | 2020. 10. 31. | $130.46 | -11.86% | 3,269.96 | -2.77% | |
| 22. | 2020. 11. 30. | $145.65 | $0.74 | 12.21% | 3,621.63 | 10.75% |
| 23. | 2020. 12. 31. | $168.84 | 15.92% | 3,756.07 | 3.71% | |
| 24. | 2021. 1. 31. | $207.97 | 23.18% | 3,714.24 | -1.11% | |
| 25. | 2021. 2. 28. | $204.89 | $0.85 | -1.07% | 3,811.15 | 2.61% |
| 26. | 2021. 3. 31. | $186.82 | -8.82% | 3,972.89 | 4.24% | |
| 27. | 2021. 4. 30. | $182.77 | -2.17% | 4,181.17 | 5.24% | |
| 28. | 2021. 5. 31. | $199.74 | $0.85 | 9.75% | 4,204.11 | 0.55% |
| 29. | 2021. 6. 30. | $229.52 | 14.91% | 4,297.50 | 2.22% | |
| 30. | 2021. 7. 31. | $243.50 | 6.09% | 4,395.26 | 2.27% | |
| 31. | 2021. 8. 31. | $258.29 | $0.85 | 6.42% | 4,522.68 | 2.90% |
| 32. | 2021. 9. 30. | $231.05 | -10.55% | 4,307.54 | -4.76% | |
| 33. | 2021. 10. 31. | $254.76 | 10.26% | 4,605.38 | 6.91% | |
| 34. | 2021. 11. 30. | $248.04 | $0.85 | -2.30% | 4,567.00 | -0.83% |
| 35. | 2021. 12. 31. | $276.22 | 11.36% | 4,766.18 | 4.36% | |
| 36. | 2022. 1. 31. | $245.39 | -11.16% | 4,515.55 | -5.26% | |
| 37. | 2022. 2. 28. | $249.95 | $0.98 | 2.26% | 4,373.94 | -3.14% |
| 38. | 2022. 3. 31. | $286.37 | 14.57% | 4,530.41 | 3.58% | |
| 39. | 2022. 4. 30. | $292.13 | 2.01% | 4,131.93 | -8.80% | |
| 40. | 2022. 5. 31. | $313.44 | $0.98 | 7.63% | 4,132.15 | 0.01% |
| 41. | 2022. 6. 30. | $324.23 | 3.44% | 3,785.38 | -8.39% | |
| 42. | 2022. 7. 31. | $329.69 | 1.68% | 4,130.29 | 9.11% | |
| 43. | 2022. 8. 31. | $301.23 | $0.98 | -8.34% | 3,955.00 | -4.24% |
| 44. | 2022. 9. 30. | $323.35 | 7.34% | 3,585.62 | -9.34% | |
| 45. | 2022. 10. 31. | $362.09 | 11.98% | 3,871.98 | 7.99% | |
| 46. | 2022. 11. 30. | $371.08 | $0.98 | 2.75% | 4,080.11 | 5.38% |
| 47. | 2022. 12. 31. | $365.84 | -1.41% | 3,839.50 | -5.90% | |
| 48. | 2023. 1. 31. | $344.15 | -5.93% | 4,076.60 | 6.18% | |
| 49. | 2023. 2. 28. | $311.22 | $1.13 | -9.24% | 3,970.15 | -2.61% |
| 50. | 2023. 3. 31. | $343.42 | 10.35% | 4,109.31 | 3.51% | |
| 51. | 2023. 4. 30. | $395.86 | 15.27% | 4,169.48 | 1.46% | |
| 52. | 2023. 5. 31. | $429.46 | $1.13 | 8.77% | 4,179.83 | 0.25% |
| 53. | 2023. 6. 30. | $468.98 | 9.20% | 4,376.86 | 4.71% | |
| 54. | 2023. 7. 31. | $454.55 | -3.08% | 4,588.96 | 4.85% | |
| 55. | 2023. 8. 31. | $554.20 | $1.13 | 22.17% | 4,507.66 | -1.77% |
| 56. | 2023. 9. 30. | $537.13 | -3.08% | 4,288.05 | -4.87% | |
| 57. | 2023. 10. 31. | $553.93 | 3.13% | 4,193.80 | -2.20% | |
| 58. | 2023. 11. 30. | $591.04 | $1.13 | 6.90% | 4,567.80 | 8.92% |
| 59. | 2023. 12. 31. | $582.92 | -1.37% | 4,769.83 | 4.42% | |
| 평균의 (R): | 3.19% | 1.11% | ||||
| 표준 편차: | 8.33% | 5.31% | ||||
모두 표시
1 보통주 주당 US$ 단위의 데이터로, 분할 및 주식 배당금에 맞게 조정됩니다.
2 기간 t 동안 LLY의 보통주에 대한 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)에 대한 수익률.
분산과 공분산
Eli Lilly & Co., 수익률의 분산 및 공분산 계산
| t | 날짜 | RLLY,t | RS&P 500,t | (RLLY,t–RLLY)2 | (RS&P 500,t–RS&P 500)2 | (RLLY,t–RLLY)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 5.90% | 2.97% | 7.37 | 3.49 | 5.07 |
| 2. | 2019. 3. 31. | 2.75% | 1.79% | 0.19 | 0.47 | -0.30 |
| 3. | 2019. 4. 30. | -9.80% | 3.93% | 168.75 | 7.98 | -36.70 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | 6.90% | 8.92% | 13.81 | 61.03 | 29.03 |
| 59. | 2023. 12. 31. | -1.37% | 4.42% | 20.81 | 11.00 | -15.13 |
| 합계 (Σ): | 4,020.05 | 1,634.30 | 491.40 | |||
| t | 날짜 | RLLY,t | RS&P 500,t | (RLLY,t–RLLY)2 | (RS&P 500,t–RS&P 500)2 | (RLLY,t–RLLY)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 5.90% | 2.97% | 7.37 | 3.49 | 5.07 |
| 2. | 2019. 3. 31. | 2.75% | 1.79% | 0.19 | 0.47 | -0.30 |
| 3. | 2019. 4. 30. | -9.80% | 3.93% | 168.75 | 7.98 | -36.70 |
| 4. | 2019. 5. 31. | -0.39% | -6.58% | 12.79 | 59.04 | 27.48 |
| 5. | 2019. 6. 30. | -4.44% | 6.89% | 58.21 | 33.49 | -44.15 |
| 6. | 2019. 7. 31. | -1.66% | 1.31% | 23.51 | 0.04 | -1.00 |
| 7. | 2019. 8. 31. | 4.28% | -1.81% | 1.20 | 8.50 | -3.19 |
| 8. | 2019. 9. 30. | -1.01% | 1.72% | 17.61 | 0.37 | -2.57 |
| 9. | 2019. 10. 31. | 1.90% | 2.04% | 1.67 | 0.88 | -1.21 |
| 10. | 2019. 11. 30. | 3.55% | 3.40% | 0.13 | 5.28 | 0.83 |
| 11. | 2019. 12. 31. | 12.00% | 2.86% | 77.63 | 3.07 | 15.45 |
| 12. | 2020. 1. 31. | 6.25% | -0.16% | 9.36 | 1.61 | -3.88 |
| 13. | 2020. 2. 29. | -9.14% | -8.41% | 152.09 | 90.57 | 117.37 |
| 14. | 2020. 3. 31. | 9.98% | -12.51% | 46.16 | 185.44 | -92.52 |
| 15. | 2020. 4. 30. | 11.48% | 12.68% | 68.70 | 134.06 | 95.97 |
| 16. | 2020. 5. 31. | -0.61% | 4.53% | 14.45 | 11.71 | -13.01 |
| 17. | 2020. 6. 30. | 7.34% | 1.84% | 17.26 | 0.54 | 3.05 |
| 18. | 2020. 7. 31. | -8.46% | 5.51% | 135.67 | 19.40 | -51.30 |
| 19. | 2020. 8. 31. | -0.77% | 7.01% | 15.68 | 34.82 | -23.36 |
| 20. | 2020. 9. 30. | -0.25% | -3.92% | 11.81 | 25.29 | 17.28 |
| 21. | 2020. 10. 31. | -11.86% | -2.77% | 226.53 | 15.00 | 58.28 |
| 22. | 2020. 11. 30. | 12.21% | 10.75% | 81.41 | 93.10 | 87.06 |
| 23. | 2020. 12. 31. | 15.92% | 3.71% | 162.16 | 6.79 | 33.19 |
| 24. | 2021. 1. 31. | 23.18% | -1.11% | 399.53 | 4.93 | -44.36 |
| 25. | 2021. 2. 28. | -1.07% | 2.61% | 18.15 | 2.26 | -6.40 |
| 26. | 2021. 3. 31. | -8.82% | 4.24% | 144.17 | 9.85 | -37.68 |
| 27. | 2021. 4. 30. | -2.17% | 5.24% | 28.68 | 17.11 | -22.15 |
| 28. | 2021. 5. 31. | 9.75% | 0.55% | 43.06 | 0.31 | -3.66 |
| 29. | 2021. 6. 30. | 14.91% | 2.22% | 137.40 | 1.24 | 13.08 |
| 30. | 2021. 7. 31. | 6.09% | 2.27% | 8.43 | 1.37 | 3.39 |
| 31. | 2021. 8. 31. | 6.42% | 2.90% | 10.47 | 3.22 | 5.80 |
| 32. | 2021. 9. 30. | -10.55% | -4.76% | 188.62 | 34.37 | 80.52 |
| 33. | 2021. 10. 31. | 10.26% | 6.91% | 50.04 | 33.74 | 41.09 |
| 34. | 2021. 11. 30. | -2.30% | -0.83% | 30.16 | 3.76 | 10.65 |
| 35. | 2021. 12. 31. | 11.36% | 4.36% | 66.81 | 10.60 | 26.61 |
| 36. | 2022. 1. 31. | -11.16% | -5.26% | 205.89 | 40.51 | 91.32 |
| 37. | 2022. 2. 28. | 2.26% | -3.14% | 0.86 | 17.99 | 3.94 |
| 38. | 2022. 3. 31. | 14.57% | 3.58% | 129.58 | 6.11 | 28.13 |
| 39. | 2022. 4. 30. | 2.01% | -8.80% | 1.38 | 98.04 | 11.65 |
| 40. | 2022. 5. 31. | 7.63% | 0.01% | 19.74 | 1.21 | -4.89 |
| 41. | 2022. 6. 30. | 3.44% | -8.39% | 0.06 | 90.21 | -2.42 |
| 42. | 2022. 7. 31. | 1.68% | 9.11% | 2.26 | 64.09 | -12.04 |
| 43. | 2022. 8. 31. | -8.34% | -4.24% | 132.77 | 28.62 | 61.64 |
| 44. | 2022. 9. 30. | 7.34% | -9.34% | 17.27 | 109.11 | -43.41 |
| 45. | 2022. 10. 31. | 11.98% | 7.99% | 77.32 | 47.34 | 60.50 |
| 46. | 2022. 11. 30. | 2.75% | 5.38% | 0.19 | 18.23 | -1.85 |
| 47. | 2022. 12. 31. | -1.41% | -5.90% | 21.16 | 49.04 | 32.21 |
| 48. | 2023. 1. 31. | -5.93% | 6.18% | 83.11 | 25.70 | -46.22 |
| 49. | 2023. 2. 28. | -9.24% | -2.61% | 154.45 | 13.82 | 46.20 |
| 50. | 2023. 3. 31. | 10.35% | 3.51% | 51.25 | 5.76 | 17.18 |
| 51. | 2023. 4. 30. | 15.27% | 1.46% | 145.98 | 0.13 | 4.33 |
| 52. | 2023. 5. 31. | 8.77% | 0.25% | 31.20 | 0.74 | -4.79 |
| 53. | 2023. 6. 30. | 9.20% | 4.71% | 36.18 | 13.02 | 21.70 |
| 54. | 2023. 7. 31. | -3.08% | 4.85% | 39.24 | 13.99 | -23.43 |
| 55. | 2023. 8. 31. | 22.17% | -1.77% | 360.38 | 8.28 | -54.63 |
| 56. | 2023. 9. 30. | -3.08% | -4.87% | 39.28 | 35.73 | 37.47 |
| 57. | 2023. 10. 31. | 3.13% | -2.20% | 0.00 | 10.92 | 0.20 |
| 58. | 2023. 11. 30. | 6.90% | 8.92% | 13.81 | 61.03 | 29.03 |
| 59. | 2023. 12. 31. | -1.37% | 4.42% | 20.81 | 11.00 | -15.13 |
| 합계 (Σ): | 4,020.05 | 1,634.30 | 491.40 | |||
모두 표시
분산LLY = Σ(RLLY,t–RLLY)2 ÷ (59 – 1)
= 4,020.05 ÷ (59 – 1)
= 69.31
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산LLY, S&P 500 = Σ(RLLY,t–RLLY)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 491.40 ÷ (59 – 1)
= 8.47
체계적인 위험 추정 (β)
| 분산LLY | 69.31 |
| 분산S&P 500 | 28.18 |
| 공분산LLY, S&P 500 | 8.47 |
| 상관 계수LLY, S&P 5001 | 0.19 |
| βLLY2 | 0.30 |
| αLLY3 | 2.86% |
계산
1 상관 계수LLY, S&P 500
= 공분산LLY, S&P 500 ÷ (표준 편차LLY × 표준 편차S&P 500)
= 8.47 ÷ (8.33% × 5.31%)
= 0.19
2 βLLY
= 공분산LLY, S&P 500 ÷ 분산S&P 500
= 8.47 ÷ 28.18
= 0.30
3 αLLY
= 평균의LLY – βLLY × 평균의S&P 500
= 3.19% – 0.30 × 1.11%
= 2.86%
예상 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.83% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.48% |
| 보통주의 체계적 위험Lilly | βLLY | 0.30 |
| Lilly 보통주의 예상 수익률3 | E(RLLY) | 7.43% |
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(RLLY) = RF + βLLY [E(RM) – RF]
= 4.83% + 0.30 [13.48% – 4.83%]
= 7.43%