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 |
| 2021. 1. 31. | $10.53 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $11.70 | 11.11% | 3,811.15 | 2.61% | |
| 2. | 2021. 3. 31. | $12.25 | 4.70% | 3,972.89 | 4.24% | |
| 3. | 2021. 4. 30. | $11.54 | -5.80% | 4,181.17 | 5.24% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | $13.28 | $0.15 | 2.28% | 6,849.09 | 0.13% |
| 59. | 2025. 12. 31. | $13.12 | -1.20% | 6,845.50 | -0.05% | |
| 평균의 (R): | 1.49% | 1.14% | ||||
| 표준 편차: | 11.53% | 4.37% | ||||
| 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 |
| 2021. 1. 31. | $10.53 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $11.70 | 11.11% | 3,811.15 | 2.61% | |
| 2. | 2021. 3. 31. | $12.25 | 4.70% | 3,972.89 | 4.24% | |
| 3. | 2021. 4. 30. | $11.54 | -5.80% | 4,181.17 | 5.24% | |
| 4. | 2021. 5. 31. | $14.53 | 25.91% | 4,204.11 | 0.55% | |
| 5. | 2021. 6. 30. | $14.86 | 2.27% | 4,297.50 | 2.22% | |
| 6. | 2021. 7. 31. | $13.95 | -6.12% | 4,395.26 | 2.27% | |
| 7. | 2021. 8. 31. | $13.03 | -6.59% | 4,522.68 | 2.90% | |
| 8. | 2021. 9. 30. | $14.16 | 8.67% | 4,307.54 | -4.76% | |
| 9. | 2021. 10. 31. | $17.08 | 20.62% | 4,605.38 | 6.91% | |
| 10. | 2021. 11. 30. | $19.19 | $0.10 | 12.94% | 4,567.00 | -0.83% |
| 11. | 2021. 12. 31. | $20.77 | 8.23% | 4,766.18 | 4.36% | |
| 12. | 2022. 1. 31. | $20.30 | $0.10 | -1.78% | 4,515.55 | -5.26% |
| 13. | 2022. 2. 28. | $17.56 | -13.50% | 4,373.94 | -3.14% | |
| 14. | 2022. 3. 31. | $16.91 | -3.70% | 4,530.41 | 3.58% | |
| 15. | 2022. 4. 30. | $14.16 | $0.10 | -15.67% | 4,131.93 | -8.80% |
| 16. | 2022. 5. 31. | $13.68 | -3.39% | 4,132.15 | 0.01% | |
| 17. | 2022. 6. 30. | $11.13 | -18.64% | 3,785.38 | -8.39% | |
| 18. | 2022. 7. 31. | $14.69 | 31.99% | 4,130.29 | 9.11% | |
| 19. | 2022. 8. 31. | $15.24 | $0.15 | 4.77% | 3,955.00 | -4.24% |
| 20. | 2022. 9. 30. | $11.20 | -26.51% | 3,585.62 | -9.34% | |
| 21. | 2022. 10. 31. | $13.37 | 19.38% | 3,871.98 | 7.99% | |
| 22. | 2022. 11. 30. | $13.90 | $0.15 | 5.09% | 4,080.11 | 5.38% |
| 23. | 2022. 12. 31. | $11.63 | -16.33% | 3,839.50 | -5.90% | |
| 24. | 2023. 1. 31. | $13.51 | 16.17% | 4,076.60 | 6.18% | |
| 25. | 2023. 2. 28. | $12.07 | $0.80 | -4.74% | 3,970.15 | -2.61% |
| 26. | 2023. 3. 31. | $12.60 | 4.39% | 4,109.31 | 3.51% | |
| 27. | 2023. 4. 30. | $11.88 | $0.15 | -4.52% | 4,169.48 | 1.46% |
| 28. | 2023. 5. 31. | $12.00 | 1.01% | 4,179.83 | 0.25% | |
| 29. | 2023. 6. 30. | $15.13 | 26.08% | 4,376.86 | 4.71% | |
| 30. | 2023. 7. 31. | $13.21 | $0.15 | -11.70% | 4,588.96 | 4.85% |
| 31. | 2023. 8. 31. | $12.13 | -8.18% | 4,507.66 | -1.77% | |
| 32. | 2023. 9. 30. | $12.42 | 2.39% | 4,288.05 | -4.87% | |
| 33. | 2023. 10. 31. | $9.75 | $0.15 | -20.29% | 4,193.80 | -2.20% |
| 34. | 2023. 11. 30. | $10.26 | 5.23% | 4,567.80 | 8.92% | |
| 35. | 2023. 12. 31. | $12.19 | 18.81% | 4,769.83 | 4.42% | |
| 36. | 2024. 1. 31. | $11.72 | -3.86% | 4,845.65 | 1.59% | |
| 37. | 2024. 2. 29. | $12.44 | $0.33 | 8.96% | 5,096.27 | 5.17% |
| 38. | 2024. 3. 31. | $13.28 | 6.75% | 5,254.35 | 3.10% | |
| 39. | 2024. 4. 30. | $12.15 | -8.51% | 5,035.69 | -4.16% | |
| 40. | 2024. 5. 31. | $12.13 | $0.15 | 1.07% | 5,277.51 | 4.80% |
| 41. | 2024. 6. 30. | $12.54 | 3.38% | 5,460.48 | 3.47% | |
| 42. | 2024. 7. 31. | $10.82 | -13.72% | 5,522.30 | 1.13% | |
| 43. | 2024. 8. 31. | $11.19 | $0.15 | 4.81% | 5,648.40 | 2.28% |
| 44. | 2024. 9. 30. | $10.56 | -5.63% | 5,762.48 | 2.02% | |
| 45. | 2024. 10. 31. | $10.29 | -2.56% | 5,705.45 | -0.99% | |
| 46. | 2024. 11. 30. | $11.13 | $0.15 | 9.62% | 6,032.38 | 5.73% |
| 47. | 2024. 12. 31. | $9.90 | -11.05% | 5,881.63 | -2.50% | |
| 48. | 2025. 1. 31. | $10.08 | 1.82% | 6,040.53 | 2.70% | |
| 49. | 2025. 2. 28. | $9.55 | $0.30 | -2.28% | 5,954.50 | -1.42% |
| 50. | 2025. 3. 31. | $10.03 | 5.03% | 5,611.85 | -5.75% | |
| 51. | 2025. 4. 30. | $10.01 | -0.20% | 5,569.06 | -0.76% | |
| 52. | 2025. 5. 31. | $10.38 | $0.15 | 5.19% | 5,911.69 | 6.15% |
| 53. | 2025. 6. 30. | $10.85 | 4.53% | 6,204.95 | 4.96% | |
| 54. | 2025. 7. 31. | $11.07 | 2.03% | 6,339.39 | 2.17% | |
| 55. | 2025. 8. 31. | $11.77 | $0.15 | 7.68% | 6,460.26 | 1.91% |
| 56. | 2025. 9. 30. | $11.96 | 1.61% | 6,688.46 | 3.53% | |
| 57. | 2025. 10. 31. | $13.13 | 9.78% | 6,840.20 | 2.27% | |
| 58. | 2025. 11. 30. | $13.28 | $0.15 | 2.28% | 6,849.09 | 0.13% |
| 59. | 2025. 12. 31. | $13.12 | -1.20% | 6,845.50 | -0.05% | |
| 평균의 (R): | 1.49% | 1.14% | ||||
| 표준 편차: | 11.53% | 4.37% | ||||
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. | 2021. 2. 28. | 11.11% | 2.61% | 92.59 | 2.17 | 14.17 |
| 2. | 2021. 3. 31. | 4.70% | 4.24% | 10.32 | 9.66 | 9.98 |
| 3. | 2021. 4. 30. | -5.80% | 5.24% | 53.06 | 16.86 | -29.91 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | 2.28% | 0.13% | 0.63 | 1.01 | -0.80 |
| 59. | 2025. 12. 31. | -1.20% | -0.05% | 7.25 | 1.41 | 3.20 |
| 합계 (Σ): | 7,707.99 | 1,108.23 | 1,789.95 | |||
| 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. | 2021. 2. 28. | 11.11% | 2.61% | 92.59 | 2.17 | 14.17 |
| 2. | 2021. 3. 31. | 4.70% | 4.24% | 10.32 | 9.66 | 9.98 |
| 3. | 2021. 4. 30. | -5.80% | 5.24% | 53.06 | 16.86 | -29.91 |
| 4. | 2021. 5. 31. | 25.91% | 0.55% | 596.40 | 0.35 | -14.35 |
| 5. | 2021. 6. 30. | 2.27% | 2.22% | 0.61 | 1.18 | 0.85 |
| 6. | 2021. 7. 31. | -6.12% | 2.27% | 57.95 | 1.30 | -8.67 |
| 7. | 2021. 8. 31. | -6.59% | 2.90% | 65.34 | 3.11 | -14.25 |
| 8. | 2021. 9. 30. | 8.67% | -4.76% | 51.60 | 34.73 | -42.33 |
| 9. | 2021. 10. 31. | 20.62% | 6.91% | 366.07 | 33.39 | 110.55 |
| 10. | 2021. 11. 30. | 12.94% | -0.83% | 131.11 | 3.88 | -22.55 |
| 11. | 2021. 12. 31. | 8.23% | 4.36% | 45.49 | 10.40 | 21.75 |
| 12. | 2022. 1. 31. | -1.78% | -5.26% | 10.69 | 40.89 | 20.91 |
| 13. | 2022. 2. 28. | -13.50% | -3.14% | 224.59 | 18.25 | 64.02 |
| 14. | 2022. 3. 31. | -3.70% | 3.58% | 26.94 | 5.96 | -12.67 |
| 15. | 2022. 4. 30. | -15.67% | -8.80% | 294.46 | 98.64 | 170.43 |
| 16. | 2022. 5. 31. | -3.39% | 0.01% | 23.80 | 1.28 | 5.52 |
| 17. | 2022. 6. 30. | -18.64% | -8.39% | 405.18 | 90.79 | 191.79 |
| 18. | 2022. 7. 31. | 31.99% | 9.11% | 930.07 | 63.61 | 243.23 |
| 19. | 2022. 8. 31. | 4.77% | -4.24% | 10.74 | 28.95 | -17.63 |
| 20. | 2022. 9. 30. | -26.51% | -9.34% | 783.88 | 109.74 | 293.30 |
| 21. | 2022. 10. 31. | 19.38% | 7.99% | 319.92 | 46.93 | 122.53 |
| 22. | 2022. 11. 30. | 5.09% | 5.38% | 12.94 | 17.97 | 15.25 |
| 23. | 2022. 12. 31. | -16.33% | -5.90% | 317.54 | 49.47 | 125.33 |
| 24. | 2023. 1. 31. | 16.17% | 6.18% | 215.40 | 25.39 | 73.96 |
| 25. | 2023. 2. 28. | -4.74% | -2.61% | 38.76 | 14.04 | 23.33 |
| 26. | 2023. 3. 31. | 4.39% | 3.51% | 8.42 | 5.61 | 6.88 |
| 27. | 2023. 4. 30. | -4.52% | 1.46% | 36.15 | 0.11 | -1.97 |
| 28. | 2023. 5. 31. | 1.01% | 0.25% | 0.23 | 0.79 | 0.42 |
| 29. | 2023. 6. 30. | 26.08% | 4.71% | 604.90 | 12.80 | 87.99 |
| 30. | 2023. 7. 31. | -11.70% | 4.85% | 173.90 | 13.76 | -48.92 |
| 31. | 2023. 8. 31. | -8.18% | -1.77% | 93.40 | 8.46 | 28.10 |
| 32. | 2023. 9. 30. | 2.39% | -4.87% | 0.81 | 36.10 | -5.42 |
| 33. | 2023. 10. 31. | -20.29% | -2.20% | 474.30 | 11.12 | 72.61 |
| 34. | 2023. 11. 30. | 5.23% | 8.92% | 14.00 | 60.56 | 29.12 |
| 35. | 2023. 12. 31. | 18.81% | 4.42% | 300.06 | 10.80 | 56.93 |
| 36. | 2024. 1. 31. | -3.86% | 1.59% | 28.56 | 0.21 | -2.42 |
| 37. | 2024. 2. 29. | 8.96% | 5.17% | 55.81 | 16.29 | 30.15 |
| 38. | 2024. 3. 31. | 6.75% | 3.10% | 27.71 | 3.86 | 10.35 |
| 39. | 2024. 4. 30. | -8.51% | -4.16% | 99.95 | 28.06 | 52.96 |
| 40. | 2024. 5. 31. | 1.07% | 4.80% | 0.18 | 13.44 | -1.53 |
| 41. | 2024. 6. 30. | 3.38% | 3.47% | 3.58 | 5.43 | 4.41 |
| 42. | 2024. 7. 31. | -13.72% | 1.13% | 231.18 | 0.00 | 0.06 |
| 43. | 2024. 8. 31. | 4.81% | 2.28% | 11.00 | 1.32 | 3.81 |
| 44. | 2024. 9. 30. | -5.63% | 2.02% | 50.68 | 0.78 | -6.29 |
| 45. | 2024. 10. 31. | -2.56% | -0.99% | 16.37 | 4.52 | 8.60 |
| 46. | 2024. 11. 30. | 9.62% | 5.73% | 66.14 | 21.10 | 37.36 |
| 47. | 2024. 12. 31. | -11.05% | -2.50% | 157.25 | 13.21 | 45.58 |
| 48. | 2025. 1. 31. | 1.82% | 2.70% | 0.11 | 2.45 | 0.52 |
| 49. | 2025. 2. 28. | -2.28% | -1.42% | 14.22 | 6.56 | 9.65 |
| 50. | 2025. 3. 31. | 5.03% | -5.75% | 12.51 | 47.48 | -24.38 |
| 51. | 2025. 4. 30. | -0.20% | -0.76% | 2.85 | 3.60 | 3.20 |
| 52. | 2025. 5. 31. | 5.19% | 6.15% | 13.74 | 25.16 | 18.59 |
| 53. | 2025. 6. 30. | 4.53% | 4.96% | 9.24 | 14.63 | 11.62 |
| 54. | 2025. 7. 31. | 2.03% | 2.17% | 0.29 | 1.06 | 0.56 |
| 55. | 2025. 8. 31. | 7.68% | 1.91% | 38.31 | 0.59 | 4.77 |
| 56. | 2025. 9. 30. | 1.61% | 3.53% | 0.02 | 5.74 | 0.30 |
| 57. | 2025. 10. 31. | 9.78% | 2.27% | 68.79 | 1.28 | 9.39 |
| 58. | 2025. 11. 30. | 2.28% | 0.13% | 0.63 | 1.01 | -0.80 |
| 59. | 2025. 12. 31. | -1.20% | -0.05% | 7.25 | 1.41 | 3.20 |
| 합계 (Σ): | 7,707.99 | 1,108.23 | 1,789.95 | |||
모두 보기
분산F = Σ(RF,t–RF)2 ÷ (59 – 1)
= 7,707.99 ÷ (59 – 1)
= 132.90
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,108.23 ÷ (59 – 1)
= 19.11
공분산F, S&P 500 = Σ(RF,t–RF)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,789.95 ÷ (59 – 1)
= 30.86
체계적인 위험 추정 (β)
| 분산F | 132.90 |
| 분산S&P 500 | 19.11 |
| 공분산F, S&P 500 | 30.86 |
| 상관 계수F, S&P 5001 | 0.61 |
| βF2 | 1.62 |
| αF3 | -0.35% |
계산
1 상관 계수F, S&P 500
= 공분산F, S&P 500 ÷ (표준 편차F × 표준 편차S&P 500)
= 30.86 ÷ (11.53% × 4.37%)
= 0.61
2 βF
= 공분산F, S&P 500 ÷ 분산S&P 500
= 30.86 ÷ 19.11
= 1.62
3 αF
= 평균의F – βF × 평균의S&P 500
= 1.49% – 1.62 × 1.14%
= -0.35%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.54% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 17.37% |
| 보통주의 체계적 위험Ford | βF | 1.62 |
| 포드 보통주에 대한 예상 수익률3 | E(RF) | 25.26% |
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]
= 4.54% + 1.62 [17.37% – 4.54%]
= 25.26%