자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Tesla보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Tesla Inc., 월별 수익률
| Tesla Inc. (TSLA) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값TSLA,t1 | 피제수TSLA,t1 | RTSLA,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $20.47 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $21.33 | 4.20% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $18.66 | -12.52% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $15.91 | -14.74% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $240.08 | 19.54% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $248.48 | 3.50% | 4,769.83 | 4.42% | |
| 평균의 (R): | 6.48% | 1.11% | ||||
| 표준 편차: | 22.26% | 5.31% | ||||
| Tesla Inc. (TSLA) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값TSLA,t1 | 피제수TSLA,t1 | RTSLA,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $20.47 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $21.33 | 4.20% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $18.66 | -12.52% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $15.91 | -14.74% | 2,945.83 | 3.93% | |
| 4. | 2019. 5. 31. | $12.34 | -22.44% | 2,752.06 | -6.58% | |
| 5. | 2019. 6. 30. | $14.90 | 20.75% | 2,941.76 | 6.89% | |
| 6. | 2019. 7. 31. | $16.11 | 8.12% | 2,980.38 | 1.31% | |
| 7. | 2019. 8. 31. | $15.04 | -6.64% | 2,926.46 | -1.81% | |
| 8. | 2019. 9. 30. | $16.06 | 6.78% | 2,976.74 | 1.72% | |
| 9. | 2019. 10. 31. | $20.99 | 30.70% | 3,037.56 | 2.04% | |
| 10. | 2019. 11. 30. | $22.00 | 4.81% | 3,140.98 | 3.40% | |
| 11. | 2019. 12. 31. | $27.89 | 26.77% | 3,230.78 | 2.86% | |
| 12. | 2020. 1. 31. | $43.37 | 55.50% | 3,225.52 | -0.16% | |
| 13. | 2020. 2. 29. | $44.53 | 2.67% | 2,954.22 | -8.41% | |
| 14. | 2020. 3. 31. | $34.93 | -21.56% | 2,584.59 | -12.51% | |
| 15. | 2020. 4. 30. | $52.13 | 49.24% | 2,912.43 | 12.68% | |
| 16. | 2020. 5. 31. | $55.67 | 6.79% | 3,044.31 | 4.53% | |
| 17. | 2020. 6. 30. | $71.99 | 29.32% | 3,100.29 | 1.84% | |
| 18. | 2020. 7. 31. | $95.38 | 32.49% | 3,271.12 | 5.51% | |
| 19. | 2020. 8. 31. | $166.11 | 74.16% | 3,500.31 | 7.01% | |
| 20. | 2020. 9. 30. | $143.00 | -13.91% | 3,363.00 | -3.92% | |
| 21. | 2020. 10. 31. | $129.35 | -9.55% | 3,269.96 | -2.77% | |
| 22. | 2020. 11. 30. | $189.20 | 46.27% | 3,621.63 | 10.75% | |
| 23. | 2020. 12. 31. | $235.22 | 24.32% | 3,756.07 | 3.71% | |
| 24. | 2021. 1. 31. | $264.51 | 12.45% | 3,714.24 | -1.11% | |
| 25. | 2021. 2. 28. | $225.17 | -14.87% | 3,811.15 | 2.61% | |
| 26. | 2021. 3. 31. | $222.64 | -1.12% | 3,972.89 | 4.24% | |
| 27. | 2021. 4. 30. | $236.48 | 6.22% | 4,181.17 | 5.24% | |
| 28. | 2021. 5. 31. | $208.41 | -11.87% | 4,204.11 | 0.55% | |
| 29. | 2021. 6. 30. | $226.57 | 8.71% | 4,297.50 | 2.22% | |
| 30. | 2021. 7. 31. | $229.07 | 1.10% | 4,395.26 | 2.27% | |
| 31. | 2021. 8. 31. | $245.24 | 7.06% | 4,522.68 | 2.90% | |
| 32. | 2021. 9. 30. | $258.49 | 5.40% | 4,307.54 | -4.76% | |
| 33. | 2021. 10. 31. | $371.33 | 43.65% | 4,605.38 | 6.91% | |
| 34. | 2021. 11. 30. | $381.59 | 2.76% | 4,567.00 | -0.83% | |
| 35. | 2021. 12. 31. | $352.26 | -7.69% | 4,766.18 | 4.36% | |
| 36. | 2022. 1. 31. | $312.24 | -11.36% | 4,515.55 | -5.26% | |
| 37. | 2022. 2. 28. | $290.14 | -7.08% | 4,373.94 | -3.14% | |
| 38. | 2022. 3. 31. | $359.20 | 23.80% | 4,530.41 | 3.58% | |
| 39. | 2022. 4. 30. | $290.25 | -19.20% | 4,131.93 | -8.80% | |
| 40. | 2022. 5. 31. | $252.75 | -12.92% | 4,132.15 | 0.01% | |
| 41. | 2022. 6. 30. | $224.47 | -11.19% | 3,785.38 | -8.39% | |
| 42. | 2022. 7. 31. | $297.15 | 32.38% | 4,130.29 | 9.11% | |
| 43. | 2022. 8. 31. | $275.61 | -7.25% | 3,955.00 | -4.24% | |
| 44. | 2022. 9. 30. | $265.25 | -3.76% | 3,585.62 | -9.34% | |
| 45. | 2022. 10. 31. | $227.54 | -14.22% | 3,871.98 | 7.99% | |
| 46. | 2022. 11. 30. | $194.70 | -14.43% | 4,080.11 | 5.38% | |
| 47. | 2022. 12. 31. | $123.18 | -36.73% | 3,839.50 | -5.90% | |
| 48. | 2023. 1. 31. | $173.22 | 40.62% | 4,076.60 | 6.18% | |
| 49. | 2023. 2. 28. | $205.71 | 18.76% | 3,970.15 | -2.61% | |
| 50. | 2023. 3. 31. | $207.46 | 0.85% | 4,109.31 | 3.51% | |
| 51. | 2023. 4. 30. | $164.31 | -20.80% | 4,169.48 | 1.46% | |
| 52. | 2023. 5. 31. | $203.93 | 24.11% | 4,179.83 | 0.25% | |
| 53. | 2023. 6. 30. | $261.77 | 28.36% | 4,376.86 | 4.71% | |
| 54. | 2023. 7. 31. | $267.43 | 2.16% | 4,588.96 | 4.85% | |
| 55. | 2023. 8. 31. | $258.08 | -3.50% | 4,507.66 | -1.77% | |
| 56. | 2023. 9. 30. | $250.22 | -3.05% | 4,288.05 | -4.87% | |
| 57. | 2023. 10. 31. | $200.84 | -19.73% | 4,193.80 | -2.20% | |
| 58. | 2023. 11. 30. | $240.08 | 19.54% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $248.48 | 3.50% | 4,769.83 | 4.42% | |
| 평균의 (R): | 6.48% | 1.11% | ||||
| 표준 편차: | 22.26% | 5.31% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 TSLA의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Tesla Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RTSLA,t | RS&P 500,t | (RTSLA,t–RTSLA)2 | (RS&P 500,t–RS&P 500)2 | (RTSLA,t–RTSLA)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 4.20% | 2.97% | 5.19 | 3.49 | -4.25 |
| 2. | 2019. 3. 31. | -12.52% | 1.79% | 360.85 | 0.47 | -13.04 |
| 3. | 2019. 4. 30. | -14.74% | 3.93% | 450.12 | 7.98 | -59.95 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | 19.54% | 8.92% | 170.55 | 61.03 | 102.02 |
| 59. | 2023. 12. 31. | 3.50% | 4.42% | 8.88 | 11.00 | -9.88 |
| 합계 (Σ): | 28,739.73 | 1,634.30 | 3,951.06 | |||
| t | 날짜 | RTSLA,t | RS&P 500,t | (RTSLA,t–RTSLA)2 | (RS&P 500,t–RS&P 500)2 | (RTSLA,t–RTSLA)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 4.20% | 2.97% | 5.19 | 3.49 | -4.25 |
| 2. | 2019. 3. 31. | -12.52% | 1.79% | 360.85 | 0.47 | -13.04 |
| 3. | 2019. 4. 30. | -14.74% | 3.93% | 450.12 | 7.98 | -59.95 |
| 4. | 2019. 5. 31. | -22.44% | -6.58% | 836.21 | 59.04 | 222.19 |
| 5. | 2019. 6. 30. | 20.75% | 6.89% | 203.55 | 33.49 | 82.57 |
| 6. | 2019. 7. 31. | 8.12% | 1.31% | 2.70 | 0.04 | 0.34 |
| 7. | 2019. 8. 31. | -6.64% | -1.81% | 172.14 | 8.50 | 38.25 |
| 8. | 2019. 9. 30. | 6.78% | 1.72% | 0.09 | 0.37 | 0.19 |
| 9. | 2019. 10. 31. | 30.70% | 2.04% | 586.55 | 0.88 | 22.70 |
| 10. | 2019. 11. 30. | 4.81% | 3.40% | 2.78 | 5.28 | -3.83 |
| 11. | 2019. 12. 31. | 26.77% | 2.86% | 411.85 | 3.07 | 35.58 |
| 12. | 2020. 1. 31. | 55.50% | -0.16% | 2,403.47 | 1.61 | -62.20 |
| 13. | 2020. 2. 29. | 2.67% | -8.41% | 14.47 | 90.57 | 36.20 |
| 14. | 2020. 3. 31. | -21.56% | -12.51% | 786.08 | 185.44 | 381.80 |
| 15. | 2020. 4. 30. | 49.24% | 12.68% | 1,828.66 | 134.06 | 495.13 |
| 16. | 2020. 5. 31. | 6.79% | 4.53% | 0.10 | 11.71 | 1.07 |
| 17. | 2020. 6. 30. | 29.32% | 1.84% | 521.53 | 0.54 | 16.74 |
| 18. | 2020. 7. 31. | 32.49% | 5.51% | 676.63 | 19.40 | 114.56 |
| 19. | 2020. 8. 31. | 74.16% | 7.01% | 4,580.24 | 34.82 | 399.34 |
| 20. | 2020. 9. 30. | -13.91% | -3.92% | 415.79 | 25.29 | 102.54 |
| 21. | 2020. 10. 31. | -9.55% | -2.77% | 256.77 | 15.00 | 62.05 |
| 22. | 2020. 11. 30. | 46.27% | 10.75% | 1,583.35 | 93.10 | 383.93 |
| 23. | 2020. 12. 31. | 24.32% | 3.71% | 318.44 | 6.79 | 46.51 |
| 24. | 2021. 1. 31. | 12.45% | -1.11% | 35.68 | 4.93 | -13.26 |
| 25. | 2021. 2. 28. | -14.87% | 2.61% | 455.88 | 2.26 | -32.10 |
| 26. | 2021. 3. 31. | -1.12% | 4.24% | 57.79 | 9.85 | -23.86 |
| 27. | 2021. 4. 30. | 6.22% | 5.24% | 0.07 | 17.11 | -1.08 |
| 28. | 2021. 5. 31. | -11.87% | 0.55% | 336.67 | 0.31 | 10.22 |
| 29. | 2021. 6. 30. | 8.71% | 2.22% | 5.00 | 1.24 | 2.49 |
| 30. | 2021. 7. 31. | 1.10% | 2.27% | 28.89 | 1.37 | -6.28 |
| 31. | 2021. 8. 31. | 7.06% | 2.90% | 0.34 | 3.22 | 1.04 |
| 32. | 2021. 9. 30. | 5.40% | -4.76% | 1.16 | 34.37 | 6.31 |
| 33. | 2021. 10. 31. | 43.65% | 6.91% | 1,381.98 | 33.74 | 215.93 |
| 34. | 2021. 11. 30. | 2.76% | -0.83% | 13.80 | 3.76 | 7.21 |
| 35. | 2021. 12. 31. | -7.69% | 4.36% | 200.64 | 10.60 | -46.11 |
| 36. | 2022. 1. 31. | -11.36% | -5.26% | 318.25 | 40.51 | 113.54 |
| 37. | 2022. 2. 28. | -7.08% | -3.14% | 183.78 | 17.99 | 57.50 |
| 38. | 2022. 3. 31. | 23.80% | 3.58% | 300.11 | 6.11 | 42.82 |
| 39. | 2022. 4. 30. | -19.20% | -8.80% | 659.15 | 98.04 | 254.21 |
| 40. | 2022. 5. 31. | -12.92% | 0.01% | 376.30 | 1.21 | 21.35 |
| 41. | 2022. 6. 30. | -11.19% | -8.39% | 312.14 | 90.21 | 167.80 |
| 42. | 2022. 7. 31. | 32.38% | 9.11% | 670.81 | 64.09 | 207.35 |
| 43. | 2022. 8. 31. | -7.25% | -4.24% | 188.44 | 28.62 | 73.44 |
| 44. | 2022. 9. 30. | -3.76% | -9.34% | 104.81 | 109.11 | 106.93 |
| 45. | 2022. 10. 31. | -14.22% | 7.99% | 428.30 | 47.34 | -142.39 |
| 46. | 2022. 11. 30. | -14.43% | 5.38% | 437.28 | 18.23 | -89.28 |
| 47. | 2022. 12. 31. | -36.73% | -5.90% | 1,867.27 | 49.04 | 302.61 |
| 48. | 2023. 1. 31. | 40.62% | 6.18% | 1,165.88 | 25.70 | 173.10 |
| 49. | 2023. 2. 28. | 18.76% | -2.61% | 150.75 | 13.82 | -45.64 |
| 50. | 2023. 3. 31. | 0.85% | 3.51% | 31.67 | 5.76 | -13.50 |
| 51. | 2023. 4. 30. | -20.80% | 1.46% | 744.07 | 0.13 | -9.78 |
| 52. | 2023. 5. 31. | 24.11% | 0.25% | 310.97 | 0.74 | -15.12 |
| 53. | 2023. 6. 30. | 28.36% | 4.71% | 478.92 | 13.02 | 78.96 |
| 54. | 2023. 7. 31. | 2.16% | 4.85% | 18.63 | 13.99 | -16.14 |
| 55. | 2023. 8. 31. | -3.50% | -1.77% | 99.50 | 8.28 | 28.70 |
| 56. | 2023. 9. 30. | -3.05% | -4.87% | 90.71 | 35.73 | 56.93 |
| 57. | 2023. 10. 31. | -19.73% | -2.20% | 687.13 | 10.92 | 86.60 |
| 58. | 2023. 11. 30. | 19.54% | 8.92% | 170.55 | 61.03 | 102.02 |
| 59. | 2023. 12. 31. | 3.50% | 4.42% | 8.88 | 11.00 | -9.88 |
| 합계 (Σ): | 28,739.73 | 1,634.30 | 3,951.06 | |||
모두 보기
분산TSLA = Σ(RTSLA,t–RTSLA)2 ÷ (59 – 1)
= 28,739.73 ÷ (59 – 1)
= 495.51
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산TSLA, S&P 500 = Σ(RTSLA,t–RTSLA)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 3,951.06 ÷ (59 – 1)
= 68.12
체계적인 위험 추정 (β)
| 분산TSLA | 495.51 |
| 분산S&P 500 | 28.18 |
| 공분산TSLA, S&P 500 | 68.12 |
| 상관 계수TSLA, S&P 5001 | 0.58 |
| βTSLA2 | 2.42 |
| αTSLA3 | 3.81% |
계산
1 상관 계수TSLA, S&P 500
= 공분산TSLA, S&P 500 ÷ (표준 편차TSLA × 표준 편차S&P 500)
= 68.12 ÷ (22.26% × 5.31%)
= 0.58
2 βTSLA
= 공분산TSLA, S&P 500 ÷ 분산S&P 500
= 68.12 ÷ 28.18
= 2.42
3 αTSLA
= 평균의TSLA – βTSLA × 평균의S&P 500
= 6.48% – 2.42 × 1.11%
= 3.81%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.07% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.86% |
| 보통주의 체계적 위험Tesla | βTSLA | 2.42 |
| Tesla 보통주 예상 수익률3 | E(RTSLA) | 27.75% |
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(RTSLA) = RF + βTSLA [E(RM) – RF]
= 4.07% + 2.42 [13.86% – 4.07%]
= 27.75%