자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 General Motors보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
General Motors Co., 월별 수익률
| General Motors Co. (GM) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값GM,t1 | 피제수GM,t1 | RGM,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2021. 1. 31. | $50.68 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $51.33 | 1.28% | 3,811.15 | 2.61% | |
| 2. | 2021. 3. 31. | $57.46 | 11.94% | 3,972.89 | 4.24% | |
| 3. | 2021. 4. 30. | $57.22 | -0.42% | 4,181.17 | 5.24% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | $73.52 | 6.41% | 6,849.09 | 0.13% | |
| 59. | 2025. 12. 31. | $81.32 | $0.15 | 10.81% | 6,845.50 | -0.05% |
| 평균의 (R): | 1.32% | 1.14% | ||||
| 표준 편차: | 9.64% | 4.37% | ||||
| General Motors Co. (GM) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값GM,t1 | 피제수GM,t1 | RGM,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2021. 1. 31. | $50.68 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $51.33 | 1.28% | 3,811.15 | 2.61% | |
| 2. | 2021. 3. 31. | $57.46 | 11.94% | 3,972.89 | 4.24% | |
| 3. | 2021. 4. 30. | $57.22 | -0.42% | 4,181.17 | 5.24% | |
| 4. | 2021. 5. 31. | $59.31 | 3.65% | 4,204.11 | 0.55% | |
| 5. | 2021. 6. 30. | $59.17 | -0.24% | 4,297.50 | 2.22% | |
| 6. | 2021. 7. 31. | $56.84 | -3.94% | 4,395.26 | 2.27% | |
| 7. | 2021. 8. 31. | $49.01 | -13.78% | 4,522.68 | 2.90% | |
| 8. | 2021. 9. 30. | $52.71 | 7.55% | 4,307.54 | -4.76% | |
| 9. | 2021. 10. 31. | $54.43 | 3.26% | 4,605.38 | 6.91% | |
| 10. | 2021. 11. 30. | $57.87 | 6.32% | 4,567.00 | -0.83% | |
| 11. | 2021. 12. 31. | $58.63 | 1.31% | 4,766.18 | 4.36% | |
| 12. | 2022. 1. 31. | $52.73 | -10.06% | 4,515.55 | -5.26% | |
| 13. | 2022. 2. 28. | $46.72 | -11.40% | 4,373.94 | -3.14% | |
| 14. | 2022. 3. 31. | $43.74 | -6.38% | 4,530.41 | 3.58% | |
| 15. | 2022. 4. 30. | $37.91 | -13.33% | 4,131.93 | -8.80% | |
| 16. | 2022. 5. 31. | $38.68 | 2.03% | 4,132.15 | 0.01% | |
| 17. | 2022. 6. 30. | $31.76 | -17.89% | 3,785.38 | -8.39% | |
| 18. | 2022. 7. 31. | $36.26 | 14.17% | 4,130.29 | 9.11% | |
| 19. | 2022. 8. 31. | $38.21 | $0.09 | 5.63% | 3,955.00 | -4.24% |
| 20. | 2022. 9. 30. | $32.09 | -16.02% | 3,585.62 | -9.34% | |
| 21. | 2022. 10. 31. | $39.25 | 22.31% | 3,871.98 | 7.99% | |
| 22. | 2022. 11. 30. | $40.56 | 3.34% | 4,080.11 | 5.38% | |
| 23. | 2022. 12. 31. | $33.64 | $0.09 | -16.84% | 3,839.50 | -5.90% |
| 24. | 2023. 1. 31. | $39.32 | 16.88% | 4,076.60 | 6.18% | |
| 25. | 2023. 2. 28. | $38.74 | -1.48% | 3,970.15 | -2.61% | |
| 26. | 2023. 3. 31. | $36.68 | $0.09 | -5.09% | 4,109.31 | 3.51% |
| 27. | 2023. 4. 30. | $33.04 | -9.92% | 4,169.48 | 1.46% | |
| 28. | 2023. 5. 31. | $32.41 | -1.91% | 4,179.83 | 0.25% | |
| 29. | 2023. 6. 30. | $38.56 | $0.09 | 19.25% | 4,376.86 | 4.71% |
| 30. | 2023. 7. 31. | $38.37 | -0.49% | 4,588.96 | 4.85% | |
| 31. | 2023. 8. 31. | $33.51 | $0.09 | -12.43% | 4,507.66 | -1.77% |
| 32. | 2023. 9. 30. | $32.97 | -1.61% | 4,288.05 | -4.87% | |
| 33. | 2023. 10. 31. | $28.20 | -14.47% | 4,193.80 | -2.20% | |
| 34. | 2023. 11. 30. | $31.60 | $0.09 | 12.38% | 4,567.80 | 8.92% |
| 35. | 2023. 12. 31. | $35.92 | 13.67% | 4,769.83 | 4.42% | |
| 36. | 2024. 1. 31. | $38.80 | 8.02% | 4,845.65 | 1.59% | |
| 37. | 2024. 2. 29. | $40.98 | $0.12 | 5.93% | 5,096.27 | 5.17% |
| 38. | 2024. 3. 31. | $45.35 | 10.66% | 5,254.35 | 3.10% | |
| 39. | 2024. 4. 30. | $44.53 | -1.81% | 5,035.69 | -4.16% | |
| 40. | 2024. 5. 31. | $44.99 | 1.03% | 5,277.51 | 4.80% | |
| 41. | 2024. 6. 30. | $46.46 | $0.12 | 3.53% | 5,460.48 | 3.47% |
| 42. | 2024. 7. 31. | $44.32 | -4.61% | 5,522.30 | 1.13% | |
| 43. | 2024. 8. 31. | $49.78 | 12.32% | 5,648.40 | 2.28% | |
| 44. | 2024. 9. 30. | $44.84 | $0.12 | -9.68% | 5,762.48 | 2.02% |
| 45. | 2024. 10. 31. | $50.76 | 13.20% | 5,705.45 | -0.99% | |
| 46. | 2024. 11. 30. | $55.59 | 9.52% | 6,032.38 | 5.73% | |
| 47. | 2024. 12. 31. | $53.27 | $0.12 | -3.96% | 5,881.63 | -2.50% |
| 48. | 2025. 1. 31. | $49.46 | -7.15% | 6,040.53 | 2.70% | |
| 49. | 2025. 2. 28. | $49.13 | -0.67% | 5,954.50 | -1.42% | |
| 50. | 2025. 3. 31. | $47.03 | $0.12 | -4.03% | 5,611.85 | -5.75% |
| 51. | 2025. 4. 30. | $45.24 | -3.81% | 5,569.06 | -0.76% | |
| 52. | 2025. 5. 31. | $49.61 | 9.66% | 5,911.69 | 6.15% | |
| 53. | 2025. 6. 30. | $49.21 | $0.15 | -0.50% | 6,204.95 | 4.96% |
| 54. | 2025. 7. 31. | $53.34 | 8.39% | 6,339.39 | 2.17% | |
| 55. | 2025. 8. 31. | $58.59 | 9.84% | 6,460.26 | 1.91% | |
| 56. | 2025. 9. 30. | $60.97 | $0.15 | 4.32% | 6,688.46 | 3.53% |
| 57. | 2025. 10. 31. | $69.09 | 13.32% | 6,840.20 | 2.27% | |
| 58. | 2025. 11. 30. | $73.52 | 6.41% | 6,849.09 | 0.13% | |
| 59. | 2025. 12. 31. | $81.32 | $0.15 | 10.81% | 6,845.50 | -0.05% |
| 평균의 (R): | 1.32% | 1.14% | ||||
| 표준 편차: | 9.64% | 4.37% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 GM의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
General Motors Co., 수익률의 분산 및 공분산 계산
| t | 날짜 | RGM,t | RS&P 500,t | (RGM,t–RGM)2 | (RS&P 500,t–RS&P 500)2 | (RGM,t–RGM)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021. 2. 28. | 1.28% | 2.61% | 0.00 | 2.17 | -0.06 |
| 2. | 2021. 3. 31. | 11.94% | 4.24% | 112.77 | 9.66 | 33.00 |
| 3. | 2021. 4. 30. | -0.42% | 5.24% | 3.03 | 16.86 | -7.15 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | 6.41% | 0.13% | 25.90 | 1.01 | -5.12 |
| 59. | 2025. 12. 31. | 10.81% | -0.05% | 90.07 | 1.41 | -11.28 |
| 합계 (Σ): | 5,391.47 | 1,108.23 | 1,485.75 | |||
| t | 날짜 | RGM,t | RS&P 500,t | (RGM,t–RGM)2 | (RS&P 500,t–RS&P 500)2 | (RGM,t–RGM)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021. 2. 28. | 1.28% | 2.61% | 0.00 | 2.17 | -0.06 |
| 2. | 2021. 3. 31. | 11.94% | 4.24% | 112.77 | 9.66 | 33.00 |
| 3. | 2021. 4. 30. | -0.42% | 5.24% | 3.03 | 16.86 | -7.15 |
| 4. | 2021. 5. 31. | 3.65% | 0.55% | 5.43 | 0.35 | -1.37 |
| 5. | 2021. 6. 30. | -0.24% | 2.22% | 2.43 | 1.18 | -1.69 |
| 6. | 2021. 7. 31. | -3.94% | 2.27% | 27.68 | 1.30 | -5.99 |
| 7. | 2021. 8. 31. | -13.78% | 2.90% | 227.97 | 3.11 | -26.62 |
| 8. | 2021. 9. 30. | 7.55% | -4.76% | 38.77 | 34.73 | -36.69 |
| 9. | 2021. 10. 31. | 3.26% | 6.91% | 3.76 | 33.39 | 11.21 |
| 10. | 2021. 11. 30. | 6.32% | -0.83% | 24.97 | 3.88 | -9.84 |
| 11. | 2021. 12. 31. | 1.31% | 4.36% | 0.00 | 10.40 | -0.03 |
| 12. | 2022. 1. 31. | -10.06% | -5.26% | 129.65 | 40.89 | 72.81 |
| 13. | 2022. 2. 28. | -11.40% | -3.14% | 161.82 | 18.25 | 54.35 |
| 14. | 2022. 3. 31. | -6.38% | 3.58% | 59.31 | 5.96 | -18.80 |
| 15. | 2022. 4. 30. | -13.33% | -8.80% | 214.68 | 98.64 | 145.52 |
| 16. | 2022. 5. 31. | 2.03% | 0.01% | 0.50 | 1.28 | -0.80 |
| 17. | 2022. 6. 30. | -17.89% | -8.39% | 369.16 | 90.79 | 183.07 |
| 18. | 2022. 7. 31. | 14.17% | 9.11% | 165.01 | 63.61 | 102.45 |
| 19. | 2022. 8. 31. | 5.63% | -4.24% | 18.52 | 28.95 | -23.15 |
| 20. | 2022. 9. 30. | -16.02% | -9.34% | 300.67 | 109.74 | 181.65 |
| 21. | 2022. 10. 31. | 22.31% | 7.99% | 440.54 | 46.93 | 143.78 |
| 22. | 2022. 11. 30. | 3.34% | 5.38% | 4.06 | 17.97 | 8.54 |
| 23. | 2022. 12. 31. | -16.84% | -5.90% | 329.87 | 49.47 | 127.74 |
| 24. | 2023. 1. 31. | 16.88% | 6.18% | 242.16 | 25.39 | 78.42 |
| 25. | 2023. 2. 28. | -1.48% | -2.61% | 7.83 | 14.04 | 10.49 |
| 26. | 2023. 3. 31. | -5.09% | 3.51% | 41.07 | 5.61 | -15.18 |
| 27. | 2023. 4. 30. | -9.92% | 1.46% | 126.49 | 0.11 | -3.69 |
| 28. | 2023. 5. 31. | -1.91% | 0.25% | 10.43 | 0.79 | 2.87 |
| 29. | 2023. 6. 30. | 19.25% | 4.71% | 321.49 | 12.80 | 64.15 |
| 30. | 2023. 7. 31. | -0.49% | 4.85% | 3.30 | 13.76 | -6.74 |
| 31. | 2023. 8. 31. | -12.43% | -1.77% | 189.19 | 8.46 | 40.00 |
| 32. | 2023. 9. 30. | -1.61% | -4.87% | 8.61 | 36.10 | 17.63 |
| 33. | 2023. 10. 31. | -14.47% | -2.20% | 249.35 | 11.12 | 52.65 |
| 34. | 2023. 11. 30. | 12.38% | 8.92% | 122.16 | 60.56 | 86.01 |
| 35. | 2023. 12. 31. | 13.67% | 4.42% | 152.47 | 10.80 | 40.58 |
| 36. | 2024. 1. 31. | 8.02% | 1.59% | 44.82 | 0.21 | 3.04 |
| 37. | 2024. 2. 29. | 5.93% | 5.17% | 21.20 | 16.29 | 18.58 |
| 38. | 2024. 3. 31. | 10.66% | 3.10% | 87.25 | 3.86 | 18.36 |
| 39. | 2024. 4. 30. | -1.81% | -4.16% | 9.80 | 28.06 | 16.59 |
| 40. | 2024. 5. 31. | 1.03% | 4.80% | 0.08 | 13.44 | -1.06 |
| 41. | 2024. 6. 30. | 3.53% | 3.47% | 4.89 | 5.43 | 5.15 |
| 42. | 2024. 7. 31. | -4.61% | 1.13% | 35.16 | 0.00 | 0.02 |
| 43. | 2024. 8. 31. | 12.32% | 2.28% | 120.92 | 1.32 | 12.62 |
| 44. | 2024. 9. 30. | -9.68% | 2.02% | 121.13 | 0.78 | -9.72 |
| 45. | 2024. 10. 31. | 13.20% | -0.99% | 141.12 | 4.52 | -25.25 |
| 46. | 2024. 11. 30. | 9.52% | 5.73% | 67.11 | 21.10 | 37.64 |
| 47. | 2024. 12. 31. | -3.96% | -2.50% | 27.89 | 13.21 | 19.20 |
| 48. | 2025. 1. 31. | -7.15% | 2.70% | 71.83 | 2.45 | -13.27 |
| 49. | 2025. 2. 28. | -0.67% | -1.42% | 3.96 | 6.56 | 5.10 |
| 50. | 2025. 3. 31. | -4.03% | -5.75% | 28.66 | 47.48 | 36.89 |
| 51. | 2025. 4. 30. | -3.81% | -0.76% | 26.31 | 3.60 | 9.74 |
| 52. | 2025. 5. 31. | 9.66% | 6.15% | 69.50 | 25.16 | 41.82 |
| 53. | 2025. 6. 30. | -0.50% | 4.96% | 3.34 | 14.63 | -6.99 |
| 54. | 2025. 7. 31. | 8.39% | 2.17% | 49.98 | 1.06 | 7.29 |
| 55. | 2025. 8. 31. | 9.84% | 1.91% | 72.58 | 0.59 | 6.56 |
| 56. | 2025. 9. 30. | 4.32% | 3.53% | 8.97 | 5.74 | 7.18 |
| 57. | 2025. 10. 31. | 13.32% | 2.27% | 143.88 | 1.28 | 13.58 |
| 58. | 2025. 11. 30. | 6.41% | 0.13% | 25.90 | 1.01 | -5.12 |
| 59. | 2025. 12. 31. | 10.81% | -0.05% | 90.07 | 1.41 | -11.28 |
| 합계 (Σ): | 5,391.47 | 1,108.23 | 1,485.75 | |||
모두 보기
분산GM = Σ(RGM,t–RGM)2 ÷ (59 – 1)
= 5,391.47 ÷ (59 – 1)
= 92.96
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,108.23 ÷ (59 – 1)
= 19.11
공분산GM, S&P 500 = Σ(RGM,t–RGM)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,485.75 ÷ (59 – 1)
= 25.62
체계적인 위험 추정 (β)
| 분산GM | 92.96 |
| 분산S&P 500 | 19.11 |
| 공분산GM, S&P 500 | 25.62 |
| 상관 계수GM, S&P 5001 | 0.61 |
| βGM2 | 1.34 |
| αGM3 | -0.20% |
계산
1 상관 계수GM, S&P 500
= 공분산GM, S&P 500 ÷ (표준 편차GM × 표준 편차S&P 500)
= 25.62 ÷ (9.64% × 4.37%)
= 0.61
2 βGM
= 공분산GM, S&P 500 ÷ 분산S&P 500
= 25.62 ÷ 19.11
= 1.34
3 αGM
= 평균의GM – βGM × 평균의S&P 500
= 1.32% – 1.34 × 1.14%
= -0.20%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.84% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 17.37% |
| 보통주의 체계적 위험General Motors | βGM | 1.34 |
| General Motors 보통주 예상 수익률3 | E(RGM) | 21.63% |
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(RGM) = RF + βGM [E(RM) – RF]
= 4.84% + 1.34 [17.37% – 4.84%]
= 21.63%