자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Alphabet보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Alphabet Inc., 월별 수익률
| Alphabet Inc. (GOOG) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값GOOG,t1 | 피제수GOOG,t1 | RGOOG,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2020. 1. 31. | $71.71 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $66.97 | -6.61% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $58.14 | -13.19% | 2,584.59 | -12.51% | |
| 3. | 2020. 4. 30. | $67.43 | 15.98% | 2,912.43 | 12.68% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | $170.49 | -1.27% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $190.44 | $0.20 | 11.82% | 5,881.63 | -2.50% |
| 평균의 (R): | 1.98% | 1.16% | ||||
| 표준 편차: | 7.90% | 5.28% | ||||
| Alphabet Inc. (GOOG) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값GOOG,t1 | 피제수GOOG,t1 | RGOOG,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2020. 1. 31. | $71.71 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $66.97 | -6.61% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $58.14 | -13.19% | 2,584.59 | -12.51% | |
| 3. | 2020. 4. 30. | $67.43 | 15.98% | 2,912.43 | 12.68% | |
| 4. | 2020. 5. 31. | $71.45 | 5.96% | 3,044.31 | 4.53% | |
| 5. | 2020. 6. 30. | $70.68 | -1.08% | 3,100.29 | 1.84% | |
| 6. | 2020. 7. 31. | $74.15 | 4.91% | 3,271.12 | 5.51% | |
| 7. | 2020. 8. 31. | $81.71 | 10.20% | 3,500.31 | 7.01% | |
| 8. | 2020. 9. 30. | $73.48 | -10.07% | 3,363.00 | -3.92% | |
| 9. | 2020. 10. 31. | $81.05 | 10.30% | 3,269.96 | -2.77% | |
| 10. | 2020. 11. 30. | $88.04 | 8.62% | 3,621.63 | 10.75% | |
| 11. | 2020. 12. 31. | $87.59 | -0.51% | 3,756.07 | 3.71% | |
| 12. | 2021. 1. 31. | $91.79 | 4.80% | 3,714.24 | -1.11% | |
| 13. | 2021. 2. 28. | $101.84 | 10.95% | 3,811.15 | 2.61% | |
| 14. | 2021. 3. 31. | $103.43 | 1.56% | 3,972.89 | 4.24% | |
| 15. | 2021. 4. 30. | $120.51 | 16.51% | 4,181.17 | 5.24% | |
| 16. | 2021. 5. 31. | $120.58 | 0.06% | 4,204.11 | 0.55% | |
| 17. | 2021. 6. 30. | $125.32 | 3.93% | 4,297.50 | 2.22% | |
| 18. | 2021. 7. 31. | $135.22 | 7.90% | 4,395.26 | 2.27% | |
| 19. | 2021. 8. 31. | $145.46 | 7.57% | 4,522.68 | 2.90% | |
| 20. | 2021. 9. 30. | $133.27 | -8.38% | 4,307.54 | -4.76% | |
| 21. | 2021. 10. 31. | $148.27 | 11.26% | 4,605.38 | 6.91% | |
| 22. | 2021. 11. 30. | $142.45 | -3.93% | 4,567.00 | -0.83% | |
| 23. | 2021. 12. 31. | $144.68 | 1.57% | 4,766.18 | 4.36% | |
| 24. | 2022. 1. 31. | $135.70 | -6.21% | 4,515.55 | -5.26% | |
| 25. | 2022. 2. 28. | $134.89 | -0.60% | 4,373.94 | -3.14% | |
| 26. | 2022. 3. 31. | $139.65 | 3.53% | 4,530.41 | 3.58% | |
| 27. | 2022. 4. 30. | $114.97 | -17.67% | 4,131.93 | -8.80% | |
| 28. | 2022. 5. 31. | $114.04 | -0.81% | 4,132.15 | 0.01% | |
| 29. | 2022. 6. 30. | $109.37 | -4.10% | 3,785.38 | -8.39% | |
| 30. | 2022. 7. 31. | $116.64 | 6.65% | 4,130.29 | 9.11% | |
| 31. | 2022. 8. 31. | $109.15 | -6.42% | 3,955.00 | -4.24% | |
| 32. | 2022. 9. 30. | $96.15 | -11.91% | 3,585.62 | -9.34% | |
| 33. | 2022. 10. 31. | $94.66 | -1.55% | 3,871.98 | 7.99% | |
| 34. | 2022. 11. 30. | $101.45 | 7.17% | 4,080.11 | 5.38% | |
| 35. | 2022. 12. 31. | $88.73 | -12.54% | 3,839.50 | -5.90% | |
| 36. | 2023. 1. 31. | $99.87 | 12.55% | 4,076.60 | 6.18% | |
| 37. | 2023. 2. 28. | $90.30 | -9.58% | 3,970.15 | -2.61% | |
| 38. | 2023. 3. 31. | $104.00 | 15.17% | 4,109.31 | 3.51% | |
| 39. | 2023. 4. 30. | $108.22 | 4.06% | 4,169.48 | 1.46% | |
| 40. | 2023. 5. 31. | $123.37 | 14.00% | 4,179.83 | 0.25% | |
| 41. | 2023. 6. 30. | $120.97 | -1.95% | 4,376.86 | 4.71% | |
| 42. | 2023. 7. 31. | $133.11 | 10.04% | 4,588.96 | 4.85% | |
| 43. | 2023. 8. 31. | $137.35 | 3.19% | 4,507.66 | -1.77% | |
| 44. | 2023. 9. 30. | $131.85 | -4.00% | 4,288.05 | -4.87% | |
| 45. | 2023. 10. 31. | $125.30 | -4.97% | 4,193.80 | -2.20% | |
| 46. | 2023. 11. 30. | $133.92 | 6.88% | 4,567.80 | 8.92% | |
| 47. | 2023. 12. 31. | $140.93 | 5.23% | 4,769.83 | 4.42% | |
| 48. | 2024. 1. 31. | $141.80 | 0.62% | 4,845.65 | 1.59% | |
| 49. | 2024. 2. 29. | $139.78 | -1.42% | 5,096.27 | 5.17% | |
| 50. | 2024. 3. 31. | $152.26 | 8.93% | 5,254.35 | 3.10% | |
| 51. | 2024. 4. 30. | $164.64 | 8.13% | 5,035.69 | -4.16% | |
| 52. | 2024. 5. 31. | $173.96 | 5.66% | 5,277.51 | 4.80% | |
| 53. | 2024. 6. 30. | $183.42 | $0.20 | 5.55% | 5,460.48 | 3.47% |
| 54. | 2024. 7. 31. | $173.15 | -5.60% | 5,522.30 | 1.13% | |
| 55. | 2024. 8. 31. | $165.11 | -4.64% | 5,648.40 | 2.28% | |
| 56. | 2024. 9. 30. | $167.19 | $0.20 | 1.38% | 5,762.48 | 2.02% |
| 57. | 2024. 10. 31. | $172.69 | 3.29% | 5,705.45 | -0.99% | |
| 58. | 2024. 11. 30. | $170.49 | -1.27% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $190.44 | $0.20 | 11.82% | 5,881.63 | -2.50% |
| 평균의 (R): | 1.98% | 1.16% | ||||
| 표준 편차: | 7.90% | 5.28% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 t기간 동안 GOOG의 보통주 수익률
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Alphabet Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RGOOG,t | RS&P 500,t | (RGOOG,t–RGOOG)2 | (RS&P 500,t–RS&P 500)2 | (RGOOG,t–RGOOG)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2020. 2. 29. | -6.61% | -8.41% | 73.82 | 91.63 | 82.24 |
| 2. | 2020. 3. 31. | -13.19% | -12.51% | 230.03 | 186.96 | 207.38 |
| 3. | 2020. 4. 30. | 15.98% | 12.68% | 195.92 | 132.78 | 161.29 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | -1.27% | 5.73% | 10.60 | 20.87 | -14.87 |
| 59. | 2024. 12. 31. | 11.82% | -2.50% | 96.77 | 13.40 | -36.01 |
| 합계 (Σ): | 3,615.77 | 1,618.62 | 1,635.41 | |||
| t | 날짜 | RGOOG,t | RS&P 500,t | (RGOOG,t–RGOOG)2 | (RS&P 500,t–RS&P 500)2 | (RGOOG,t–RGOOG)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2020. 2. 29. | -6.61% | -8.41% | 73.82 | 91.63 | 82.24 |
| 2. | 2020. 3. 31. | -13.19% | -12.51% | 230.03 | 186.96 | 207.38 |
| 3. | 2020. 4. 30. | 15.98% | 12.68% | 195.92 | 132.78 | 161.29 |
| 4. | 2020. 5. 31. | 5.96% | 4.53% | 15.84 | 11.34 | 13.40 |
| 5. | 2020. 6. 30. | -1.08% | 1.84% | 9.36 | 0.46 | -2.07 |
| 6. | 2020. 7. 31. | 4.91% | 5.51% | 8.57 | 18.91 | 12.73 |
| 7. | 2020. 8. 31. | 10.20% | 7.01% | 67.47 | 34.17 | 48.01 |
| 8. | 2020. 9. 30. | -10.07% | -3.92% | 145.30 | 25.85 | 61.28 |
| 9. | 2020. 10. 31. | 10.30% | -2.77% | 69.23 | 15.43 | -32.68 |
| 10. | 2020. 11. 30. | 8.62% | 10.75% | 44.12 | 92.03 | 63.72 |
| 11. | 2020. 12. 31. | -0.51% | 3.71% | 6.21 | 6.51 | -6.36 |
| 12. | 2021. 1. 31. | 4.80% | -1.11% | 7.92 | 5.18 | -6.40 |
| 13. | 2021. 2. 28. | 10.95% | 2.61% | 80.41 | 2.10 | 12.98 |
| 14. | 2021. 3. 31. | 1.56% | 4.24% | 0.18 | 9.50 | -1.30 |
| 15. | 2021. 4. 30. | 16.51% | 5.24% | 211.18 | 16.66 | 59.31 |
| 16. | 2021. 5. 31. | 0.06% | 0.55% | 3.70 | 0.38 | 1.18 |
| 17. | 2021. 6. 30. | 3.93% | 2.22% | 3.80 | 1.12 | 2.07 |
| 18. | 2021. 7. 31. | 7.90% | 2.27% | 35.02 | 1.24 | 6.59 |
| 19. | 2021. 8. 31. | 7.57% | 2.90% | 31.26 | 3.02 | 9.72 |
| 20. | 2021. 9. 30. | -8.38% | -4.76% | 107.37 | 35.02 | 61.32 |
| 21. | 2021. 10. 31. | 11.26% | 6.91% | 86.00 | 33.10 | 53.35 |
| 22. | 2021. 11. 30. | -3.93% | -0.83% | 34.89 | 3.98 | 11.78 |
| 23. | 2021. 12. 31. | 1.57% | 4.36% | 0.17 | 10.24 | -1.33 |
| 24. | 2022. 1. 31. | -6.21% | -5.26% | 67.05 | 41.21 | 52.57 |
| 25. | 2022. 2. 28. | -0.60% | -3.14% | 6.65 | 18.47 | 11.08 |
| 26. | 2022. 3. 31. | 3.53% | 3.58% | 2.39 | 5.84 | 3.74 |
| 27. | 2022. 4. 30. | -17.67% | -8.80% | 386.30 | 99.14 | 195.70 |
| 28. | 2022. 5. 31. | -0.81% | 0.01% | 7.79 | 1.34 | 3.23 |
| 29. | 2022. 6. 30. | -4.10% | -8.39% | 36.93 | 91.26 | 58.05 |
| 30. | 2022. 7. 31. | 6.65% | 9.11% | 21.77 | 63.21 | 37.09 |
| 31. | 2022. 8. 31. | -6.42% | -4.24% | 70.61 | 29.22 | 45.42 |
| 32. | 2022. 9. 30. | -11.91% | -9.34% | 192.98 | 110.27 | 145.88 |
| 33. | 2022. 10. 31. | -1.55% | 7.99% | 12.47 | 46.58 | -24.10 |
| 34. | 2022. 11. 30. | 7.17% | 5.38% | 26.95 | 17.76 | 21.88 |
| 35. | 2022. 12. 31. | -12.54% | -5.90% | 210.83 | 49.82 | 102.49 |
| 36. | 2023. 1. 31. | 12.55% | 6.18% | 111.79 | 25.14 | 53.01 |
| 37. | 2023. 2. 28. | -9.58% | -2.61% | 133.73 | 14.23 | 43.63 |
| 38. | 2023. 3. 31. | 15.17% | 3.51% | 173.98 | 5.49 | 30.92 |
| 39. | 2023. 4. 30. | 4.06% | 1.46% | 4.31 | 0.09 | 0.63 |
| 40. | 2023. 5. 31. | 14.00% | 0.25% | 144.42 | 0.83 | -10.97 |
| 41. | 2023. 6. 30. | -1.95% | 4.71% | 15.42 | 12.62 | -13.95 |
| 42. | 2023. 7. 31. | 10.04% | 4.85% | 64.87 | 13.58 | 29.68 |
| 43. | 2023. 8. 31. | 3.19% | -1.77% | 1.45 | 8.60 | -3.53 |
| 44. | 2023. 9. 30. | -4.00% | -4.87% | 35.83 | 36.40 | 36.11 |
| 45. | 2023. 10. 31. | -4.97% | -2.20% | 48.29 | 11.28 | 23.34 |
| 46. | 2023. 11. 30. | 6.88% | 8.92% | 23.99 | 60.17 | 37.99 |
| 47. | 2023. 12. 31. | 5.23% | 4.42% | 10.58 | 10.64 | 10.61 |
| 48. | 2024. 1. 31. | 0.62% | 1.59% | 1.86 | 0.18 | -0.58 |
| 49. | 2024. 2. 29. | -1.42% | 5.17% | 11.60 | 16.09 | -13.66 |
| 50. | 2024. 3. 31. | 8.93% | 3.10% | 48.26 | 3.77 | 13.48 |
| 51. | 2024. 4. 30. | 8.13% | -4.16% | 37.81 | 28.33 | -32.73 |
| 52. | 2024. 5. 31. | 5.66% | 4.80% | 13.54 | 13.26 | 13.40 |
| 53. | 2024. 6. 30. | 5.55% | 3.47% | 12.75 | 5.32 | 8.23 |
| 54. | 2024. 7. 31. | -5.60% | 1.13% | 57.47 | 0.00 | 0.22 |
| 55. | 2024. 8. 31. | -4.64% | 2.28% | 43.89 | 1.26 | -7.43 |
| 56. | 2024. 9. 30. | 1.38% | 2.02% | 0.36 | 0.74 | -0.52 |
| 57. | 2024. 10. 31. | 3.29% | -0.99% | 1.71 | 4.63 | -2.81 |
| 58. | 2024. 11. 30. | -1.27% | 5.73% | 10.60 | 20.87 | -14.87 |
| 59. | 2024. 12. 31. | 11.82% | -2.50% | 96.77 | 13.40 | -36.01 |
| 합계 (Σ): | 3,615.77 | 1,618.62 | 1,635.41 | |||
모두 보기
분산GOOG = Σ(RGOOG,t–RGOOG)2 ÷ (59 – 1)
= 3,615.77 ÷ (59 – 1)
= 62.34
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91
공분산GOOG, S&P 500 = Σ(RGOOG,t–RGOOG)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,635.41 ÷ (59 – 1)
= 28.20
체계적인 위험 추정 (β)
| 분산GOOG | 62.34 |
| 분산S&P 500 | 27.91 |
| 공분산GOOG, S&P 500 | 28.20 |
| 상관 계수GOOG, S&P 5001 | 0.68 |
| βGOOG2 | 1.01 |
| αGOOG3 | 0.81% |
계산
1 상관 계수GOOG, S&P 500
= 공분산GOOG, S&P 500 ÷ (표준 편차GOOG × 표준 편차S&P 500)
= 28.20 ÷ (7.90% × 5.28%)
= 0.68
2 βGOOG
= 공분산GOOG, S&P 500 ÷ 분산S&P 500
= 28.20 ÷ 27.91
= 1.01
3 αGOOG
= 평균의GOOG – βGOOG × 평균의S&P 500
= 1.98% – 1.01 × 1.16%
= 0.81%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.60% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.89% |
| 보통주의 체계적 위험Alphabet | βGOOG | 1.01 |
| 알파벳 보통주 예상 수익률3 | E(RGOOG) | 14.99% |
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(RGOOG) = RF + βGOOG [E(RM) – RF]
= 4.60% + 1.01 [14.89% – 4.60%]
= 14.99%