자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Ford보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Ford Motor Co., 월별 수익률
| Ford Motor Co. (F) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값F,t1 | 피제수F,t1 | RF,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2020. 1. 31. | $8.82 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $6.96 | -21.09% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $4.83 | -30.60% | 2,584.59 | -12.51% | |
| 3. | 2020. 4. 30. | $5.09 | 5.38% | 2,912.43 | 12.68% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | $11.13 | $0.15 | 9.62% | 6,032.38 | 5.73% |
| 59. | 2024. 12. 31. | $9.90 | -11.05% | 5,881.63 | -2.50% | |
| 평균의 (R): | 1.42% | 1.16% | ||||
| 표준 편차: | 13.21% | 5.28% | ||||
| Ford Motor Co. (F) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값F,t1 | 피제수F,t1 | RF,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2020. 1. 31. | $8.82 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $6.96 | -21.09% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $4.83 | -30.60% | 2,584.59 | -12.51% | |
| 3. | 2020. 4. 30. | $5.09 | 5.38% | 2,912.43 | 12.68% | |
| 4. | 2020. 5. 31. | $5.71 | 12.18% | 3,044.31 | 4.53% | |
| 5. | 2020. 6. 30. | $6.08 | 6.48% | 3,100.29 | 1.84% | |
| 6. | 2020. 7. 31. | $6.61 | 8.72% | 3,271.12 | 5.51% | |
| 7. | 2020. 8. 31. | $6.82 | 3.18% | 3,500.31 | 7.01% | |
| 8. | 2020. 9. 30. | $6.66 | -2.35% | 3,363.00 | -3.92% | |
| 9. | 2020. 10. 31. | $7.73 | 16.07% | 3,269.96 | -2.77% | |
| 10. | 2020. 11. 30. | $9.08 | 17.46% | 3,621.63 | 10.75% | |
| 11. | 2020. 12. 31. | $8.79 | -3.19% | 3,756.07 | 3.71% | |
| 12. | 2021. 1. 31. | $10.53 | 19.80% | 3,714.24 | -1.11% | |
| 13. | 2021. 2. 28. | $11.70 | 11.11% | 3,811.15 | 2.61% | |
| 14. | 2021. 3. 31. | $12.25 | 4.70% | 3,972.89 | 4.24% | |
| 15. | 2021. 4. 30. | $11.54 | -5.80% | 4,181.17 | 5.24% | |
| 16. | 2021. 5. 31. | $14.53 | 25.91% | 4,204.11 | 0.55% | |
| 17. | 2021. 6. 30. | $14.86 | 2.27% | 4,297.50 | 2.22% | |
| 18. | 2021. 7. 31. | $13.95 | -6.12% | 4,395.26 | 2.27% | |
| 19. | 2021. 8. 31. | $13.03 | -6.59% | 4,522.68 | 2.90% | |
| 20. | 2021. 9. 30. | $14.16 | 8.67% | 4,307.54 | -4.76% | |
| 21. | 2021. 10. 31. | $17.08 | 20.62% | 4,605.38 | 6.91% | |
| 22. | 2021. 11. 30. | $19.19 | $0.10 | 12.94% | 4,567.00 | -0.83% |
| 23. | 2021. 12. 31. | $20.77 | 8.23% | 4,766.18 | 4.36% | |
| 24. | 2022. 1. 31. | $20.30 | $0.10 | -1.78% | 4,515.55 | -5.26% |
| 25. | 2022. 2. 28. | $17.56 | -13.50% | 4,373.94 | -3.14% | |
| 26. | 2022. 3. 31. | $16.91 | -3.70% | 4,530.41 | 3.58% | |
| 27. | 2022. 4. 30. | $14.16 | $0.10 | -15.67% | 4,131.93 | -8.80% |
| 28. | 2022. 5. 31. | $13.68 | -3.39% | 4,132.15 | 0.01% | |
| 29. | 2022. 6. 30. | $11.13 | -18.64% | 3,785.38 | -8.39% | |
| 30. | 2022. 7. 31. | $14.69 | 31.99% | 4,130.29 | 9.11% | |
| 31. | 2022. 8. 31. | $15.24 | $0.15 | 4.77% | 3,955.00 | -4.24% |
| 32. | 2022. 9. 30. | $11.20 | -26.51% | 3,585.62 | -9.34% | |
| 33. | 2022. 10. 31. | $13.37 | 19.38% | 3,871.98 | 7.99% | |
| 34. | 2022. 11. 30. | $13.90 | $0.15 | 5.09% | 4,080.11 | 5.38% |
| 35. | 2022. 12. 31. | $11.63 | -16.33% | 3,839.50 | -5.90% | |
| 36. | 2023. 1. 31. | $13.51 | 16.17% | 4,076.60 | 6.18% | |
| 37. | 2023. 2. 28. | $12.07 | $0.80 | -4.74% | 3,970.15 | -2.61% |
| 38. | 2023. 3. 31. | $12.60 | 4.39% | 4,109.31 | 3.51% | |
| 39. | 2023. 4. 30. | $11.88 | $0.15 | -4.52% | 4,169.48 | 1.46% |
| 40. | 2023. 5. 31. | $12.00 | 1.01% | 4,179.83 | 0.25% | |
| 41. | 2023. 6. 30. | $15.13 | 26.08% | 4,376.86 | 4.71% | |
| 42. | 2023. 7. 31. | $13.21 | $0.15 | -11.70% | 4,588.96 | 4.85% |
| 43. | 2023. 8. 31. | $12.13 | -8.18% | 4,507.66 | -1.77% | |
| 44. | 2023. 9. 30. | $12.42 | 2.39% | 4,288.05 | -4.87% | |
| 45. | 2023. 10. 31. | $9.75 | $0.15 | -20.29% | 4,193.80 | -2.20% |
| 46. | 2023. 11. 30. | $10.26 | 5.23% | 4,567.80 | 8.92% | |
| 47. | 2023. 12. 31. | $12.19 | 18.81% | 4,769.83 | 4.42% | |
| 48. | 2024. 1. 31. | $11.72 | -3.86% | 4,845.65 | 1.59% | |
| 49. | 2024. 2. 29. | $12.44 | $0.33 | 8.96% | 5,096.27 | 5.17% |
| 50. | 2024. 3. 31. | $13.28 | 6.75% | 5,254.35 | 3.10% | |
| 51. | 2024. 4. 30. | $12.15 | -8.51% | 5,035.69 | -4.16% | |
| 52. | 2024. 5. 31. | $12.13 | $0.15 | 1.07% | 5,277.51 | 4.80% |
| 53. | 2024. 6. 30. | $12.54 | 3.38% | 5,460.48 | 3.47% | |
| 54. | 2024. 7. 31. | $10.82 | -13.72% | 5,522.30 | 1.13% | |
| 55. | 2024. 8. 31. | $11.19 | $0.15 | 4.81% | 5,648.40 | 2.28% |
| 56. | 2024. 9. 30. | $10.56 | -5.63% | 5,762.48 | 2.02% | |
| 57. | 2024. 10. 31. | $10.29 | -2.56% | 5,705.45 | -0.99% | |
| 58. | 2024. 11. 30. | $11.13 | $0.15 | 9.62% | 6,032.38 | 5.73% |
| 59. | 2024. 12. 31. | $9.90 | -11.05% | 5,881.63 | -2.50% | |
| 평균의 (R): | 1.42% | 1.16% | ||||
| 표준 편차: | 13.21% | 5.28% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 F의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Ford Motor Co., 수익률의 분산 및 공분산 계산
| t | 날짜 | RF,t | RS&P 500,t | (RF,t–RF)2 | (RS&P 500,t–RS&P 500)2 | (RF,t–RF)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2020. 2. 29. | -21.09% | -8.41% | 506.49 | 91.63 | 215.43 |
| 2. | 2020. 3. 31. | -30.60% | -12.51% | 1,025.30 | 186.96 | 437.82 |
| 3. | 2020. 4. 30. | 5.38% | 12.68% | 15.73 | 132.78 | 45.70 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | 9.62% | 5.73% | 67.31 | 20.87 | 37.48 |
| 59. | 2024. 12. 31. | -11.05% | -2.50% | 155.45 | 13.40 | 45.64 |
| 합계 (Σ): | 10,128.34 | 1,618.62 | 2,596.17 | |||
| t | 날짜 | RF,t | RS&P 500,t | (RF,t–RF)2 | (RS&P 500,t–RS&P 500)2 | (RF,t–RF)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2020. 2. 29. | -21.09% | -8.41% | 506.49 | 91.63 | 215.43 |
| 2. | 2020. 3. 31. | -30.60% | -12.51% | 1,025.30 | 186.96 | 437.82 |
| 3. | 2020. 4. 30. | 5.38% | 12.68% | 15.73 | 132.78 | 45.70 |
| 4. | 2020. 5. 31. | 12.18% | 4.53% | 115.86 | 11.34 | 36.24 |
| 5. | 2020. 6. 30. | 6.48% | 1.84% | 25.63 | 0.46 | 3.43 |
| 6. | 2020. 7. 31. | 8.72% | 5.51% | 53.29 | 18.91 | 31.75 |
| 7. | 2020. 8. 31. | 3.18% | 7.01% | 3.10 | 34.17 | 10.29 |
| 8. | 2020. 9. 30. | -2.35% | -3.92% | 14.16 | 25.85 | 19.13 |
| 9. | 2020. 10. 31. | 16.07% | -2.77% | 214.60 | 15.43 | -57.54 |
| 10. | 2020. 11. 30. | 17.46% | 10.75% | 257.53 | 92.03 | 153.95 |
| 11. | 2020. 12. 31. | -3.19% | 3.71% | 21.26 | 6.51 | -11.76 |
| 12. | 2021. 1. 31. | 19.80% | -1.11% | 337.77 | 5.18 | -41.81 |
| 13. | 2021. 2. 28. | 11.11% | 2.61% | 93.98 | 2.10 | 14.04 |
| 14. | 2021. 3. 31. | 4.70% | 4.24% | 10.78 | 9.50 | 10.12 |
| 15. | 2021. 4. 30. | -5.80% | 5.24% | 52.02 | 16.66 | -29.44 |
| 16. | 2021. 5. 31. | 25.91% | 0.55% | 599.91 | 0.38 | -15.00 |
| 17. | 2021. 6. 30. | 2.27% | 2.22% | 0.73 | 1.12 | 0.91 |
| 18. | 2021. 7. 31. | -6.12% | 2.27% | 56.86 | 1.24 | -8.40 |
| 19. | 2021. 8. 31. | -6.59% | 2.90% | 64.19 | 3.02 | -13.92 |
| 20. | 2021. 9. 30. | 8.67% | -4.76% | 52.64 | 35.02 | -42.94 |
| 21. | 2021. 10. 31. | 20.62% | 6.91% | 368.82 | 33.10 | 110.49 |
| 22. | 2021. 11. 30. | 12.94% | -0.83% | 132.76 | 3.98 | -22.98 |
| 23. | 2021. 12. 31. | 8.23% | 4.36% | 46.47 | 10.24 | 21.81 |
| 24. | 2022. 1. 31. | -1.78% | -5.26% | 10.23 | 41.21 | 20.53 |
| 25. | 2022. 2. 28. | -13.50% | -3.14% | 222.44 | 18.47 | 64.09 |
| 26. | 2022. 3. 31. | -3.70% | 3.58% | 26.20 | 5.84 | -12.37 |
| 27. | 2022. 4. 30. | -15.67% | -8.80% | 292.00 | 99.14 | 170.14 |
| 28. | 2022. 5. 31. | -3.39% | 0.01% | 23.10 | 1.34 | 5.56 |
| 29. | 2022. 6. 30. | -18.64% | -8.39% | 402.29 | 91.26 | 191.61 |
| 30. | 2022. 7. 31. | 31.99% | 9.11% | 934.45 | 63.21 | 243.03 |
| 31. | 2022. 8. 31. | 4.77% | -4.24% | 11.21 | 29.22 | -18.10 |
| 32. | 2022. 9. 30. | -26.51% | -9.34% | 779.86 | 110.27 | 293.25 |
| 33. | 2022. 10. 31. | 19.38% | 7.99% | 322.50 | 46.58 | 122.57 |
| 34. | 2022. 11. 30. | 5.09% | 5.38% | 13.46 | 17.76 | 15.46 |
| 35. | 2022. 12. 31. | -16.33% | -5.90% | 314.98 | 49.82 | 125.27 |
| 36. | 2023. 1. 31. | 16.17% | 6.18% | 217.51 | 25.14 | 73.95 |
| 37. | 2023. 2. 28. | -4.74% | -2.61% | 37.87 | 14.23 | 23.22 |
| 38. | 2023. 3. 31. | 4.39% | 3.51% | 8.85 | 5.49 | 6.97 |
| 39. | 2023. 4. 30. | -4.52% | 1.46% | 35.29 | 0.09 | -1.80 |
| 40. | 2023. 5. 31. | 1.01% | 0.25% | 0.17 | 0.83 | 0.37 |
| 41. | 2023. 6. 30. | 26.08% | 4.71% | 608.44 | 12.62 | 87.63 |
| 42. | 2023. 7. 31. | -11.70% | 4.85% | 172.01 | 13.58 | -48.33 |
| 43. | 2023. 8. 31. | -8.18% | -1.77% | 92.02 | 8.60 | 28.13 |
| 44. | 2023. 9. 30. | 2.39% | -4.87% | 0.95 | 36.40 | -5.88 |
| 45. | 2023. 10. 31. | -20.29% | -2.20% | 471.18 | 11.28 | 72.92 |
| 46. | 2023. 11. 30. | 5.23% | 8.92% | 14.55 | 60.17 | 29.58 |
| 47. | 2023. 12. 31. | 18.81% | 4.42% | 302.55 | 10.64 | 56.73 |
| 48. | 2024. 1. 31. | -3.86% | 1.59% | 27.80 | 0.18 | -2.26 |
| 49. | 2024. 2. 29. | 8.96% | 5.17% | 56.89 | 16.09 | 30.25 |
| 50. | 2024. 3. 31. | 6.75% | 3.10% | 28.47 | 3.77 | 10.35 |
| 51. | 2024. 4. 30. | -8.51% | -4.16% | 98.52 | 28.33 | 52.83 |
| 52. | 2024. 5. 31. | 1.07% | 4.80% | 0.12 | 13.26 | -1.26 |
| 53. | 2024. 6. 30. | 3.38% | 3.47% | 3.85 | 5.32 | 4.53 |
| 54. | 2024. 7. 31. | -13.72% | 1.13% | 229.01 | 0.00 | 0.44 |
| 55. | 2024. 8. 31. | 4.81% | 2.28% | 11.49 | 1.26 | 3.80 |
| 56. | 2024. 9. 30. | -5.63% | 2.02% | 49.66 | 0.74 | -6.05 |
| 57. | 2024. 10. 31. | -2.56% | -0.99% | 15.79 | 4.63 | 8.55 |
| 58. | 2024. 11. 30. | 9.62% | 5.73% | 67.31 | 20.87 | 37.48 |
| 59. | 2024. 12. 31. | -11.05% | -2.50% | 155.45 | 13.40 | 45.64 |
| 합계 (Σ): | 10,128.34 | 1,618.62 | 2,596.17 | |||
모두 보기
분산F = Σ(RF,t–RF)2 ÷ (59 – 1)
= 10,128.34 ÷ (59 – 1)
= 174.63
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91
공분산F, S&P 500 = Σ(RF,t–RF)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,596.17 ÷ (59 – 1)
= 44.76
체계적인 위험 추정 (β)
| 분산F | 174.63 |
| 분산S&P 500 | 27.91 |
| 공분산F, S&P 500 | 44.76 |
| 상관 계수F, S&P 5001 | 0.64 |
| βF2 | 1.60 |
| αF3 | -0.45% |
계산
1 상관 계수F, S&P 500
= 공분산F, S&P 500 ÷ (표준 편차F × 표준 편차S&P 500)
= 44.76 ÷ (13.21% × 5.28%)
= 0.64
2 βF
= 공분산F, S&P 500 ÷ 분산S&P 500
= 44.76 ÷ 27.91
= 1.60
3 αF
= 평균의F – βF × 평균의S&P 500
= 1.42% – 1.60 × 1.16%
= -0.45%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.88% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.88% |
| 보통주의 체계적 위험Ford | βF | 1.60 |
| 포드 보통주에 대한 예상 수익률3 | E(RF) | 20.92% |
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(RF) = RF + βF [E(RM) – RF]
= 4.88% + 1.60 [14.88% – 4.88%]
= 20.92%