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 |
| 2020. 1. 31. | $33.39 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $30.50 | -8.66% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $20.78 | $0.38 | -30.62% | 2,584.59 | -12.51% |
| 3. | 2020. 4. 30. | $22.29 | 7.27% | 2,912.43 | 12.68% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | $55.59 | 9.52% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $53.27 | $0.12 | -3.96% | 5,881.63 | -2.50% |
| 평균의 (R): | 1.54% | 1.16% | ||||
| 표준 편차: | 11.64% | 5.28% | ||||
| 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 |
| 2020. 1. 31. | $33.39 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $30.50 | -8.66% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $20.78 | $0.38 | -30.62% | 2,584.59 | -12.51% |
| 3. | 2020. 4. 30. | $22.29 | 7.27% | 2,912.43 | 12.68% | |
| 4. | 2020. 5. 31. | $25.88 | 16.11% | 3,044.31 | 4.53% | |
| 5. | 2020. 6. 30. | $25.30 | -2.24% | 3,100.29 | 1.84% | |
| 6. | 2020. 7. 31. | $24.89 | -1.62% | 3,271.12 | 5.51% | |
| 7. | 2020. 8. 31. | $29.63 | 19.04% | 3,500.31 | 7.01% | |
| 8. | 2020. 9. 30. | $29.59 | -0.13% | 3,363.00 | -3.92% | |
| 9. | 2020. 10. 31. | $34.53 | 16.69% | 3,269.96 | -2.77% | |
| 10. | 2020. 11. 30. | $43.84 | 26.96% | 3,621.63 | 10.75% | |
| 11. | 2020. 12. 31. | $41.64 | -5.02% | 3,756.07 | 3.71% | |
| 12. | 2021. 1. 31. | $50.68 | 21.71% | 3,714.24 | -1.11% | |
| 13. | 2021. 2. 28. | $51.33 | 1.28% | 3,811.15 | 2.61% | |
| 14. | 2021. 3. 31. | $57.46 | 11.94% | 3,972.89 | 4.24% | |
| 15. | 2021. 4. 30. | $57.22 | -0.42% | 4,181.17 | 5.24% | |
| 16. | 2021. 5. 31. | $59.31 | 3.65% | 4,204.11 | 0.55% | |
| 17. | 2021. 6. 30. | $59.17 | -0.24% | 4,297.50 | 2.22% | |
| 18. | 2021. 7. 31. | $56.84 | -3.94% | 4,395.26 | 2.27% | |
| 19. | 2021. 8. 31. | $49.01 | -13.78% | 4,522.68 | 2.90% | |
| 20. | 2021. 9. 30. | $52.71 | 7.55% | 4,307.54 | -4.76% | |
| 21. | 2021. 10. 31. | $54.43 | 3.26% | 4,605.38 | 6.91% | |
| 22. | 2021. 11. 30. | $57.87 | 6.32% | 4,567.00 | -0.83% | |
| 23. | 2021. 12. 31. | $58.63 | 1.31% | 4,766.18 | 4.36% | |
| 24. | 2022. 1. 31. | $52.73 | -10.06% | 4,515.55 | -5.26% | |
| 25. | 2022. 2. 28. | $46.72 | -11.40% | 4,373.94 | -3.14% | |
| 26. | 2022. 3. 31. | $43.74 | -6.38% | 4,530.41 | 3.58% | |
| 27. | 2022. 4. 30. | $37.91 | -13.33% | 4,131.93 | -8.80% | |
| 28. | 2022. 5. 31. | $38.68 | 2.03% | 4,132.15 | 0.01% | |
| 29. | 2022. 6. 30. | $31.76 | -17.89% | 3,785.38 | -8.39% | |
| 30. | 2022. 7. 31. | $36.26 | 14.17% | 4,130.29 | 9.11% | |
| 31. | 2022. 8. 31. | $38.21 | $0.09 | 5.63% | 3,955.00 | -4.24% |
| 32. | 2022. 9. 30. | $32.09 | -16.02% | 3,585.62 | -9.34% | |
| 33. | 2022. 10. 31. | $39.25 | 22.31% | 3,871.98 | 7.99% | |
| 34. | 2022. 11. 30. | $40.56 | 3.34% | 4,080.11 | 5.38% | |
| 35. | 2022. 12. 31. | $33.64 | $0.09 | -16.84% | 3,839.50 | -5.90% |
| 36. | 2023. 1. 31. | $39.32 | 16.88% | 4,076.60 | 6.18% | |
| 37. | 2023. 2. 28. | $38.74 | -1.48% | 3,970.15 | -2.61% | |
| 38. | 2023. 3. 31. | $36.68 | $0.09 | -5.09% | 4,109.31 | 3.51% |
| 39. | 2023. 4. 30. | $33.04 | -9.92% | 4,169.48 | 1.46% | |
| 40. | 2023. 5. 31. | $32.41 | -1.91% | 4,179.83 | 0.25% | |
| 41. | 2023. 6. 30. | $38.56 | $0.09 | 19.25% | 4,376.86 | 4.71% |
| 42. | 2023. 7. 31. | $38.37 | -0.49% | 4,588.96 | 4.85% | |
| 43. | 2023. 8. 31. | $33.51 | $0.09 | -12.43% | 4,507.66 | -1.77% |
| 44. | 2023. 9. 30. | $32.97 | -1.61% | 4,288.05 | -4.87% | |
| 45. | 2023. 10. 31. | $28.20 | -14.47% | 4,193.80 | -2.20% | |
| 46. | 2023. 11. 30. | $31.60 | $0.09 | 12.38% | 4,567.80 | 8.92% |
| 47. | 2023. 12. 31. | $35.92 | 13.67% | 4,769.83 | 4.42% | |
| 48. | 2024. 1. 31. | $38.80 | 8.02% | 4,845.65 | 1.59% | |
| 49. | 2024. 2. 29. | $40.98 | $0.12 | 5.93% | 5,096.27 | 5.17% |
| 50. | 2024. 3. 31. | $45.35 | 10.66% | 5,254.35 | 3.10% | |
| 51. | 2024. 4. 30. | $44.53 | -1.81% | 5,035.69 | -4.16% | |
| 52. | 2024. 5. 31. | $44.99 | 1.03% | 5,277.51 | 4.80% | |
| 53. | 2024. 6. 30. | $46.46 | $0.12 | 3.53% | 5,460.48 | 3.47% |
| 54. | 2024. 7. 31. | $44.32 | -4.61% | 5,522.30 | 1.13% | |
| 55. | 2024. 8. 31. | $49.78 | 12.32% | 5,648.40 | 2.28% | |
| 56. | 2024. 9. 30. | $44.84 | $0.12 | -9.68% | 5,762.48 | 2.02% |
| 57. | 2024. 10. 31. | $50.76 | 13.20% | 5,705.45 | -0.99% | |
| 58. | 2024. 11. 30. | $55.59 | 9.52% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $53.27 | $0.12 | -3.96% | 5,881.63 | -2.50% |
| 평균의 (R): | 1.54% | 1.16% | ||||
| 표준 편차: | 11.64% | 5.28% | ||||
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. | 2020. 2. 29. | -8.66% | -8.41% | 103.98 | 91.63 | 97.61 |
| 2. | 2020. 3. 31. | -30.62% | -12.51% | 1,034.56 | 186.96 | 439.79 |
| 3. | 2020. 4. 30. | 7.27% | 12.68% | 32.78 | 132.78 | 65.97 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | 9.52% | 5.73% | 63.58 | 20.87 | 36.43 |
| 59. | 2024. 12. 31. | -3.96% | -2.50% | 30.24 | 13.40 | 20.13 |
| 합계 (Σ): | 7,854.66 | 1,618.62 | 2,264.42 | |||
| 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. | 2020. 2. 29. | -8.66% | -8.41% | 103.98 | 91.63 | 97.61 |
| 2. | 2020. 3. 31. | -30.62% | -12.51% | 1,034.56 | 186.96 | 439.79 |
| 3. | 2020. 4. 30. | 7.27% | 12.68% | 32.78 | 132.78 | 65.97 |
| 4. | 2020. 5. 31. | 16.11% | 4.53% | 212.12 | 11.34 | 49.04 |
| 5. | 2020. 6. 30. | -2.24% | 1.84% | 14.31 | 0.46 | -2.56 |
| 6. | 2020. 7. 31. | -1.62% | 5.51% | 10.00 | 18.91 | -13.75 |
| 7. | 2020. 8. 31. | 19.04% | 7.01% | 306.32 | 34.17 | 102.30 |
| 8. | 2020. 9. 30. | -0.13% | -3.92% | 2.81 | 25.85 | 8.52 |
| 9. | 2020. 10. 31. | 16.69% | -2.77% | 229.62 | 15.43 | -59.52 |
| 10. | 2020. 11. 30. | 26.96% | 10.75% | 646.20 | 92.03 | 243.87 |
| 11. | 2020. 12. 31. | -5.02% | 3.71% | 43.03 | 6.51 | -16.73 |
| 12. | 2021. 1. 31. | 21.71% | -1.11% | 406.76 | 5.18 | -45.88 |
| 13. | 2021. 2. 28. | 1.28% | 2.61% | 0.07 | 2.10 | -0.38 |
| 14. | 2021. 3. 31. | 11.94% | 4.24% | 108.17 | 9.50 | 32.06 |
| 15. | 2021. 4. 30. | -0.42% | 5.24% | 3.84 | 16.66 | -8.00 |
| 16. | 2021. 5. 31. | 3.65% | 0.55% | 4.46 | 0.38 | -1.29 |
| 17. | 2021. 6. 30. | -0.24% | 2.22% | 3.16 | 1.12 | -1.88 |
| 18. | 2021. 7. 31. | -3.94% | 2.27% | 30.02 | 1.24 | -6.10 |
| 19. | 2021. 8. 31. | -13.78% | 2.90% | 234.62 | 3.02 | -26.62 |
| 20. | 2021. 9. 30. | 7.55% | -4.76% | 36.09 | 35.02 | -35.56 |
| 21. | 2021. 10. 31. | 3.26% | 6.91% | 2.96 | 33.10 | 9.90 |
| 22. | 2021. 11. 30. | 6.32% | -0.83% | 22.83 | 3.98 | -9.53 |
| 23. | 2021. 12. 31. | 1.31% | 4.36% | 0.05 | 10.24 | -0.73 |
| 24. | 2022. 1. 31. | -10.06% | -5.26% | 134.67 | 41.21 | 74.50 |
| 25. | 2022. 2. 28. | -11.40% | -3.14% | 167.43 | 18.47 | 55.60 |
| 26. | 2022. 3. 31. | -6.38% | 3.58% | 62.73 | 5.84 | -19.14 |
| 27. | 2022. 4. 30. | -13.33% | -8.80% | 221.13 | 99.14 | 148.06 |
| 28. | 2022. 5. 31. | 2.03% | 0.01% | 0.24 | 1.34 | -0.57 |
| 29. | 2022. 6. 30. | -17.89% | -8.39% | 377.60 | 91.26 | 185.64 |
| 30. | 2022. 7. 31. | 14.17% | 9.11% | 159.44 | 63.21 | 100.39 |
| 31. | 2022. 8. 31. | 5.63% | -4.24% | 16.68 | 29.22 | -22.08 |
| 32. | 2022. 9. 30. | -16.02% | -9.34% | 308.30 | 110.27 | 184.38 |
| 33. | 2022. 10. 31. | 22.31% | 7.99% | 431.42 | 46.58 | 141.76 |
| 34. | 2022. 11. 30. | 3.34% | 5.38% | 3.23 | 17.76 | 7.57 |
| 35. | 2022. 12. 31. | -16.84% | -5.90% | 337.86 | 49.82 | 129.74 |
| 36. | 2023. 1. 31. | 16.88% | 6.18% | 235.41 | 25.14 | 76.93 |
| 37. | 2023. 2. 28. | -1.48% | -2.61% | 9.10 | 14.23 | 11.38 |
| 38. | 2023. 3. 31. | -5.09% | 3.51% | 43.91 | 5.49 | -15.53 |
| 39. | 2023. 4. 30. | -9.92% | 1.46% | 131.45 | 0.09 | -3.47 |
| 40. | 2023. 5. 31. | -1.91% | 0.25% | 11.89 | 0.83 | 3.15 |
| 41. | 2023. 6. 30. | 19.25% | 4.71% | 313.70 | 12.62 | 62.92 |
| 42. | 2023. 7. 31. | -0.49% | 4.85% | 4.14 | 13.58 | -7.50 |
| 43. | 2023. 8. 31. | -12.43% | -1.77% | 195.25 | 8.60 | 40.98 |
| 44. | 2023. 9. 30. | -1.61% | -4.87% | 9.94 | 36.40 | 19.02 |
| 45. | 2023. 10. 31. | -14.47% | -2.20% | 256.30 | 11.28 | 53.78 |
| 46. | 2023. 11. 30. | 12.38% | 8.92% | 117.38 | 60.17 | 84.04 |
| 47. | 2023. 12. 31. | 13.67% | 4.42% | 147.12 | 10.64 | 39.56 |
| 48. | 2024. 1. 31. | 8.02% | 1.59% | 41.94 | 0.18 | 2.77 |
| 49. | 2024. 2. 29. | 5.93% | 5.17% | 19.24 | 16.09 | 17.59 |
| 50. | 2024. 3. 31. | 10.66% | 3.10% | 83.21 | 3.77 | 17.70 |
| 51. | 2024. 4. 30. | -1.81% | -4.16% | 11.22 | 28.33 | 17.83 |
| 52. | 2024. 5. 31. | 1.03% | 4.80% | 0.26 | 13.26 | -1.85 |
| 53. | 2024. 6. 30. | 3.53% | 3.47% | 3.97 | 5.32 | 4.59 |
| 54. | 2024. 7. 31. | -4.61% | 1.13% | 37.80 | 0.00 | 0.18 |
| 55. | 2024. 8. 31. | 12.32% | 2.28% | 116.16 | 1.26 | 12.09 |
| 56. | 2024. 9. 30. | -9.68% | 2.02% | 125.98 | 0.74 | -9.64 |
| 57. | 2024. 10. 31. | 13.20% | -0.99% | 135.98 | 4.63 | -25.08 |
| 58. | 2024. 11. 30. | 9.52% | 5.73% | 63.58 | 20.87 | 36.43 |
| 59. | 2024. 12. 31. | -3.96% | -2.50% | 30.24 | 13.40 | 20.13 |
| 합계 (Σ): | 7,854.66 | 1,618.62 | 2,264.42 | |||
모두 보기
분산GM = Σ(RGM,t–RGM)2 ÷ (59 – 1)
= 7,854.66 ÷ (59 – 1)
= 135.43
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91
공분산GM, S&P 500 = Σ(RGM,t–RGM)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,264.42 ÷ (59 – 1)
= 39.04
체계적인 위험 추정 (β)
| 분산GM | 135.43 |
| 분산S&P 500 | 27.91 |
| 공분산GM, S&P 500 | 39.04 |
| 상관 계수GM, S&P 5001 | 0.64 |
| βGM2 | 1.40 |
| αGM3 | -0.08% |
계산
1 상관 계수GM, S&P 500
= 공분산GM, S&P 500 ÷ (표준 편차GM × 표준 편차S&P 500)
= 39.04 ÷ (11.64% × 5.28%)
= 0.64
2 βGM
= 공분산GM, S&P 500 ÷ 분산S&P 500
= 39.04 ÷ 27.91
= 1.40
3 αGM
= 평균의GM – βGM × 평균의S&P 500
= 1.54% – 1.40 × 1.16%
= -0.08%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.83% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.73% |
| 보통주의 체계적 위험General Motors | βGM | 1.40 |
| General Motors 보통주 예상 수익률3 | E(RGM) | 18.67% |
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(RGM) = RF + βGM [E(RM) – RF]
= 4.83% + 1.40 [14.73% – 4.83%]
= 18.67%