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 |
| 2019. 1. 31. | $8.80 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $8.77 | -0.34% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $8.78 | 0.11% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $10.45 | $0.15 | 20.73% | 2,945.83 | 3.93% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $10.26 | 5.23% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $12.19 | 18.81% | 4,769.83 | 4.42% | |
| 평균의 (R): | 1.76% | 1.11% | ||||
| 표준 편차: | 13.16% | 5.31% | ||||
| 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 |
| 2019. 1. 31. | $8.80 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $8.77 | -0.34% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $8.78 | 0.11% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $10.45 | $0.15 | 20.73% | 2,945.83 | 3.93% |
| 4. | 2019. 5. 31. | $9.52 | -8.90% | 2,752.06 | -6.58% | |
| 5. | 2019. 6. 30. | $10.23 | 7.46% | 2,941.76 | 6.89% | |
| 6. | 2019. 7. 31. | $9.53 | $0.15 | -5.38% | 2,980.38 | 1.31% |
| 7. | 2019. 8. 31. | $9.17 | -3.78% | 2,926.46 | -1.81% | |
| 8. | 2019. 9. 30. | $9.16 | -0.11% | 2,976.74 | 1.72% | |
| 9. | 2019. 10. 31. | $8.59 | $0.15 | -4.59% | 3,037.56 | 2.04% |
| 10. | 2019. 11. 30. | $9.06 | 5.47% | 3,140.98 | 3.40% | |
| 11. | 2019. 12. 31. | $9.30 | 2.65% | 3,230.78 | 2.86% | |
| 12. | 2020. 1. 31. | $8.82 | $0.15 | -3.55% | 3,225.52 | -0.16% |
| 13. | 2020. 2. 29. | $6.96 | -21.09% | 2,954.22 | -8.41% | |
| 14. | 2020. 3. 31. | $4.83 | -30.60% | 2,584.59 | -12.51% | |
| 15. | 2020. 4. 30. | $5.09 | 5.38% | 2,912.43 | 12.68% | |
| 16. | 2020. 5. 31. | $5.71 | 12.18% | 3,044.31 | 4.53% | |
| 17. | 2020. 6. 30. | $6.08 | 6.48% | 3,100.29 | 1.84% | |
| 18. | 2020. 7. 31. | $6.61 | 8.72% | 3,271.12 | 5.51% | |
| 19. | 2020. 8. 31. | $6.82 | 3.18% | 3,500.31 | 7.01% | |
| 20. | 2020. 9. 30. | $6.66 | -2.35% | 3,363.00 | -3.92% | |
| 21. | 2020. 10. 31. | $7.73 | 16.07% | 3,269.96 | -2.77% | |
| 22. | 2020. 11. 30. | $9.08 | 17.46% | 3,621.63 | 10.75% | |
| 23. | 2020. 12. 31. | $8.79 | -3.19% | 3,756.07 | 3.71% | |
| 24. | 2021. 1. 31. | $10.53 | 19.80% | 3,714.24 | -1.11% | |
| 25. | 2021. 2. 28. | $11.70 | 11.11% | 3,811.15 | 2.61% | |
| 26. | 2021. 3. 31. | $12.25 | 4.70% | 3,972.89 | 4.24% | |
| 27. | 2021. 4. 30. | $11.54 | -5.80% | 4,181.17 | 5.24% | |
| 28. | 2021. 5. 31. | $14.53 | 25.91% | 4,204.11 | 0.55% | |
| 29. | 2021. 6. 30. | $14.86 | 2.27% | 4,297.50 | 2.22% | |
| 30. | 2021. 7. 31. | $13.95 | -6.12% | 4,395.26 | 2.27% | |
| 31. | 2021. 8. 31. | $13.03 | -6.59% | 4,522.68 | 2.90% | |
| 32. | 2021. 9. 30. | $14.16 | 8.67% | 4,307.54 | -4.76% | |
| 33. | 2021. 10. 31. | $17.08 | 20.62% | 4,605.38 | 6.91% | |
| 34. | 2021. 11. 30. | $19.19 | $0.10 | 12.94% | 4,567.00 | -0.83% |
| 35. | 2021. 12. 31. | $20.77 | 8.23% | 4,766.18 | 4.36% | |
| 36. | 2022. 1. 31. | $20.30 | $0.10 | -1.78% | 4,515.55 | -5.26% |
| 37. | 2022. 2. 28. | $17.56 | -13.50% | 4,373.94 | -3.14% | |
| 38. | 2022. 3. 31. | $16.91 | -3.70% | 4,530.41 | 3.58% | |
| 39. | 2022. 4. 30. | $14.16 | $0.10 | -15.67% | 4,131.93 | -8.80% |
| 40. | 2022. 5. 31. | $13.68 | -3.39% | 4,132.15 | 0.01% | |
| 41. | 2022. 6. 30. | $11.13 | -18.64% | 3,785.38 | -8.39% | |
| 42. | 2022. 7. 31. | $14.69 | 31.99% | 4,130.29 | 9.11% | |
| 43. | 2022. 8. 31. | $15.24 | $0.15 | 4.77% | 3,955.00 | -4.24% |
| 44. | 2022. 9. 30. | $11.20 | -26.51% | 3,585.62 | -9.34% | |
| 45. | 2022. 10. 31. | $13.37 | 19.38% | 3,871.98 | 7.99% | |
| 46. | 2022. 11. 30. | $13.90 | $0.15 | 5.09% | 4,080.11 | 5.38% |
| 47. | 2022. 12. 31. | $11.63 | -16.33% | 3,839.50 | -5.90% | |
| 48. | 2023. 1. 31. | $13.51 | 16.17% | 4,076.60 | 6.18% | |
| 49. | 2023. 2. 28. | $12.07 | $0.80 | -4.74% | 3,970.15 | -2.61% |
| 50. | 2023. 3. 31. | $12.60 | 4.39% | 4,109.31 | 3.51% | |
| 51. | 2023. 4. 30. | $11.88 | $0.15 | -4.52% | 4,169.48 | 1.46% |
| 52. | 2023. 5. 31. | $12.00 | 1.01% | 4,179.83 | 0.25% | |
| 53. | 2023. 6. 30. | $15.13 | 26.08% | 4,376.86 | 4.71% | |
| 54. | 2023. 7. 31. | $13.21 | $0.15 | -11.70% | 4,588.96 | 4.85% |
| 55. | 2023. 8. 31. | $12.13 | -8.18% | 4,507.66 | -1.77% | |
| 56. | 2023. 9. 30. | $12.42 | 2.39% | 4,288.05 | -4.87% | |
| 57. | 2023. 10. 31. | $9.75 | $0.15 | -20.29% | 4,193.80 | -2.20% |
| 58. | 2023. 11. 30. | $10.26 | 5.23% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $12.19 | 18.81% | 4,769.83 | 4.42% | |
| 평균의 (R): | 1.76% | 1.11% | ||||
| 표준 편차: | 13.16% | 5.31% | ||||
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. | 2019. 2. 28. | -0.34% | 2.97% | 4.43 | 3.49 | -3.93 |
| 2. | 2019. 3. 31. | 0.11% | 1.79% | 2.72 | 0.47 | -1.13 |
| 3. | 2019. 4. 30. | 20.73% | 3.93% | 359.65 | 7.98 | 53.58 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | 5.23% | 8.92% | 12.01 | 61.03 | 27.08 |
| 59. | 2023. 12. 31. | 18.81% | 4.42% | 290.58 | 11.00 | 56.54 |
| 합계 (Σ): | 10,051.61 | 1,634.30 | 2,602.97 | |||
| 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. | 2019. 2. 28. | -0.34% | 2.97% | 4.43 | 3.49 | -3.93 |
| 2. | 2019. 3. 31. | 0.11% | 1.79% | 2.72 | 0.47 | -1.13 |
| 3. | 2019. 4. 30. | 20.73% | 3.93% | 359.65 | 7.98 | 53.58 |
| 4. | 2019. 5. 31. | -8.90% | -6.58% | 113.72 | 59.04 | 81.94 |
| 5. | 2019. 6. 30. | 7.46% | 6.89% | 32.42 | 33.49 | 32.95 |
| 6. | 2019. 7. 31. | -5.38% | 1.31% | 50.99 | 0.04 | -1.48 |
| 7. | 2019. 8. 31. | -3.78% | -1.81% | 30.71 | 8.50 | 16.16 |
| 8. | 2019. 9. 30. | -0.11% | 1.72% | 3.51 | 0.37 | -1.15 |
| 9. | 2019. 10. 31. | -4.59% | 2.04% | 40.32 | 0.88 | -5.95 |
| 10. | 2019. 11. 30. | 5.47% | 3.40% | 13.74 | 5.28 | 8.52 |
| 11. | 2019. 12. 31. | 2.65% | 2.86% | 0.78 | 3.07 | 1.55 |
| 12. | 2020. 1. 31. | -3.55% | -0.16% | 28.23 | 1.61 | 6.74 |
| 13. | 2020. 2. 29. | -21.09% | -8.41% | 522.26 | 90.57 | 217.49 |
| 14. | 2020. 3. 31. | -30.60% | -12.51% | 1,047.69 | 185.44 | 440.78 |
| 15. | 2020. 4. 30. | 5.38% | 12.68% | 13.09 | 134.06 | 41.90 |
| 16. | 2020. 5. 31. | 12.18% | 4.53% | 108.50 | 11.71 | 35.65 |
| 17. | 2020. 6. 30. | 6.48% | 1.84% | 22.23 | 0.54 | 3.46 |
| 18. | 2020. 7. 31. | 8.72% | 5.51% | 48.34 | 19.40 | 30.62 |
| 19. | 2020. 8. 31. | 3.18% | 7.01% | 2.00 | 34.82 | 8.33 |
| 20. | 2020. 9. 30. | -2.35% | -3.92% | 16.90 | 25.29 | 20.67 |
| 21. | 2020. 10. 31. | 16.07% | -2.77% | 204.53 | 15.00 | -55.38 |
| 22. | 2020. 11. 30. | 17.46% | 10.75% | 246.49 | 93.10 | 151.48 |
| 23. | 2020. 12. 31. | -3.19% | 3.71% | 24.59 | 6.79 | -12.92 |
| 24. | 2021. 1. 31. | 19.80% | -1.11% | 325.11 | 4.93 | -40.02 |
| 25. | 2021. 2. 28. | 11.11% | 2.61% | 87.36 | 2.26 | 14.05 |
| 26. | 2021. 3. 31. | 4.70% | 4.24% | 8.62 | 9.85 | 9.21 |
| 27. | 2021. 4. 30. | -5.80% | 5.24% | 57.16 | 17.11 | -31.28 |
| 28. | 2021. 5. 31. | 25.91% | 0.55% | 583.00 | 0.31 | -13.45 |
| 29. | 2021. 6. 30. | 2.27% | 2.22% | 0.26 | 1.24 | 0.57 |
| 30. | 2021. 7. 31. | -6.12% | 2.27% | 62.23 | 1.37 | -9.22 |
| 31. | 2021. 8. 31. | -6.59% | 2.90% | 69.88 | 3.22 | -14.99 |
| 32. | 2021. 9. 30. | 8.67% | -4.76% | 47.72 | 34.37 | -40.50 |
| 33. | 2021. 10. 31. | 20.62% | 6.91% | 355.58 | 33.74 | 109.53 |
| 34. | 2021. 11. 30. | 12.94% | -0.83% | 124.87 | 3.76 | -21.67 |
| 35. | 2021. 12. 31. | 8.23% | 4.36% | 41.85 | 10.60 | 21.06 |
| 36. | 2022. 1. 31. | -1.78% | -5.26% | 12.57 | 40.51 | 22.57 |
| 37. | 2022. 2. 28. | -13.50% | -3.14% | 232.93 | 17.99 | 64.74 |
| 38. | 2022. 3. 31. | -3.70% | 3.58% | 29.88 | 6.11 | -13.51 |
| 39. | 2022. 4. 30. | -15.67% | -8.80% | 304.00 | 98.04 | 172.64 |
| 40. | 2022. 5. 31. | -3.39% | 0.01% | 26.57 | 1.21 | 5.67 |
| 41. | 2022. 6. 30. | -18.64% | -8.39% | 416.36 | 90.21 | 193.80 |
| 42. | 2022. 7. 31. | 31.99% | 9.11% | 913.31 | 64.09 | 241.94 |
| 43. | 2022. 8. 31. | 4.77% | -4.24% | 9.00 | 28.62 | -16.05 |
| 44. | 2022. 9. 30. | -26.51% | -9.34% | 799.40 | 109.11 | 295.33 |
| 45. | 2022. 10. 31. | 19.38% | 7.99% | 310.13 | 47.34 | 121.17 |
| 46. | 2022. 11. 30. | 5.09% | 5.38% | 11.03 | 18.23 | 14.18 |
| 47. | 2022. 12. 31. | -16.33% | -5.90% | 327.45 | 49.04 | 126.72 |
| 48. | 2023. 1. 31. | 16.17% | 6.18% | 207.38 | 25.70 | 73.00 |
| 49. | 2023. 2. 28. | -4.74% | -2.61% | 42.27 | 13.82 | 24.17 |
| 50. | 2023. 3. 31. | 4.39% | 3.51% | 6.90 | 5.76 | 6.30 |
| 51. | 2023. 4. 30. | -4.52% | 1.46% | 39.54 | 0.13 | -2.25 |
| 52. | 2023. 5. 31. | 1.01% | 0.25% | 0.57 | 0.74 | 0.65 |
| 53. | 2023. 6. 30. | 26.08% | 4.71% | 591.40 | 13.02 | 87.74 |
| 54. | 2023. 7. 31. | -11.70% | 4.85% | 181.26 | 13.99 | -50.35 |
| 55. | 2023. 8. 31. | -8.18% | -1.77% | 98.81 | 8.28 | 28.60 |
| 56. | 2023. 9. 30. | 2.39% | -4.87% | 0.39 | 35.73 | -3.74 |
| 57. | 2023. 10. 31. | -20.29% | -2.20% | 486.40 | 10.92 | 72.86 |
| 58. | 2023. 11. 30. | 5.23% | 8.92% | 12.01 | 61.03 | 27.08 |
| 59. | 2023. 12. 31. | 18.81% | 4.42% | 290.58 | 11.00 | 56.54 |
| 합계 (Σ): | 10,051.61 | 1,634.30 | 2,602.97 | |||
모두 보기
분산F = Σ(RF,t–RF)2 ÷ (59 – 1)
= 10,051.61 ÷ (59 – 1)
= 173.30
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산F, S&P 500 = Σ(RF,t–RF)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,602.97 ÷ (59 – 1)
= 44.88
체계적인 위험 추정 (β)
| 분산F | 173.30 |
| 분산S&P 500 | 28.18 |
| 공분산F, S&P 500 | 44.88 |
| 상관 계수F, S&P 5001 | 0.64 |
| βF2 | 1.59 |
| αF3 | 0.00% |
계산
1 상관 계수F, S&P 500
= 공분산F, S&P 500 ÷ (표준 편차F × 표준 편차S&P 500)
= 44.88 ÷ (13.16% × 5.31%)
= 0.64
2 βF
= 공분산F, S&P 500 ÷ 분산S&P 500
= 44.88 ÷ 28.18
= 1.59
3 αF
= 평균의F – βF × 평균의S&P 500
= 1.76% – 1.59 × 1.11%
= 0.00%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.07% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.86% |
| 보통주의 체계적 위험Ford | βF | 1.59 |
| 포드 보통주에 대한 예상 수익률3 | E(RF) | 19.67% |
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]
= 4.07% + 1.59 [13.86% – 4.07%]
= 19.67%