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 |
| 2021. 1. 31. | $91.79 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $101.84 | 10.95% | 3,811.15 | 2.61% | |
| 2. | 2021. 3. 31. | $103.43 | 1.56% | 3,972.89 | 4.24% | |
| 3. | 2021. 4. 30. | $120.51 | 16.51% | 4,181.17 | 5.24% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | $320.12 | 13.59% | 6,849.09 | 0.13% | |
| 59. | 2025. 12. 31. | $313.80 | $0.21 | -1.91% | 6,845.50 | -0.05% |
| 평균의 (R): | 2.45% | 1.14% | ||||
| 표준 편차: | 8.16% | 4.37% | ||||
| 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 |
| 2021. 1. 31. | $91.79 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $101.84 | 10.95% | 3,811.15 | 2.61% | |
| 2. | 2021. 3. 31. | $103.43 | 1.56% | 3,972.89 | 4.24% | |
| 3. | 2021. 4. 30. | $120.51 | 16.51% | 4,181.17 | 5.24% | |
| 4. | 2021. 5. 31. | $120.58 | 0.06% | 4,204.11 | 0.55% | |
| 5. | 2021. 6. 30. | $125.32 | 3.93% | 4,297.50 | 2.22% | |
| 6. | 2021. 7. 31. | $135.22 | 7.90% | 4,395.26 | 2.27% | |
| 7. | 2021. 8. 31. | $145.46 | 7.57% | 4,522.68 | 2.90% | |
| 8. | 2021. 9. 30. | $133.27 | -8.38% | 4,307.54 | -4.76% | |
| 9. | 2021. 10. 31. | $148.27 | 11.26% | 4,605.38 | 6.91% | |
| 10. | 2021. 11. 30. | $142.45 | -3.93% | 4,567.00 | -0.83% | |
| 11. | 2021. 12. 31. | $144.68 | 1.57% | 4,766.18 | 4.36% | |
| 12. | 2022. 1. 31. | $135.70 | -6.21% | 4,515.55 | -5.26% | |
| 13. | 2022. 2. 28. | $134.89 | -0.60% | 4,373.94 | -3.14% | |
| 14. | 2022. 3. 31. | $139.65 | 3.53% | 4,530.41 | 3.58% | |
| 15. | 2022. 4. 30. | $114.97 | -17.67% | 4,131.93 | -8.80% | |
| 16. | 2022. 5. 31. | $114.04 | -0.81% | 4,132.15 | 0.01% | |
| 17. | 2022. 6. 30. | $109.37 | -4.10% | 3,785.38 | -8.39% | |
| 18. | 2022. 7. 31. | $116.64 | 6.65% | 4,130.29 | 9.11% | |
| 19. | 2022. 8. 31. | $109.15 | -6.42% | 3,955.00 | -4.24% | |
| 20. | 2022. 9. 30. | $96.15 | -11.91% | 3,585.62 | -9.34% | |
| 21. | 2022. 10. 31. | $94.66 | -1.55% | 3,871.98 | 7.99% | |
| 22. | 2022. 11. 30. | $101.45 | 7.17% | 4,080.11 | 5.38% | |
| 23. | 2022. 12. 31. | $88.73 | -12.54% | 3,839.50 | -5.90% | |
| 24. | 2023. 1. 31. | $99.87 | 12.55% | 4,076.60 | 6.18% | |
| 25. | 2023. 2. 28. | $90.30 | -9.58% | 3,970.15 | -2.61% | |
| 26. | 2023. 3. 31. | $104.00 | 15.17% | 4,109.31 | 3.51% | |
| 27. | 2023. 4. 30. | $108.22 | 4.06% | 4,169.48 | 1.46% | |
| 28. | 2023. 5. 31. | $123.37 | 14.00% | 4,179.83 | 0.25% | |
| 29. | 2023. 6. 30. | $120.97 | -1.95% | 4,376.86 | 4.71% | |
| 30. | 2023. 7. 31. | $133.11 | 10.04% | 4,588.96 | 4.85% | |
| 31. | 2023. 8. 31. | $137.35 | 3.19% | 4,507.66 | -1.77% | |
| 32. | 2023. 9. 30. | $131.85 | -4.00% | 4,288.05 | -4.87% | |
| 33. | 2023. 10. 31. | $125.30 | -4.97% | 4,193.80 | -2.20% | |
| 34. | 2023. 11. 30. | $133.92 | 6.88% | 4,567.80 | 8.92% | |
| 35. | 2023. 12. 31. | $140.93 | 5.23% | 4,769.83 | 4.42% | |
| 36. | 2024. 1. 31. | $141.80 | 0.62% | 4,845.65 | 1.59% | |
| 37. | 2024. 2. 29. | $139.78 | -1.42% | 5,096.27 | 5.17% | |
| 38. | 2024. 3. 31. | $152.26 | 8.93% | 5,254.35 | 3.10% | |
| 39. | 2024. 4. 30. | $164.64 | 8.13% | 5,035.69 | -4.16% | |
| 40. | 2024. 5. 31. | $173.96 | 5.66% | 5,277.51 | 4.80% | |
| 41. | 2024. 6. 30. | $183.42 | $0.20 | 5.55% | 5,460.48 | 3.47% |
| 42. | 2024. 7. 31. | $173.15 | -5.60% | 5,522.30 | 1.13% | |
| 43. | 2024. 8. 31. | $165.11 | -4.64% | 5,648.40 | 2.28% | |
| 44. | 2024. 9. 30. | $167.19 | $0.20 | 1.38% | 5,762.48 | 2.02% |
| 45. | 2024. 10. 31. | $172.69 | 3.29% | 5,705.45 | -0.99% | |
| 46. | 2024. 11. 30. | $170.49 | -1.27% | 6,032.38 | 5.73% | |
| 47. | 2024. 12. 31. | $190.44 | $0.20 | 11.82% | 5,881.63 | -2.50% |
| 48. | 2025. 1. 31. | $205.60 | 7.96% | 6,040.53 | 2.70% | |
| 49. | 2025. 2. 28. | $172.22 | -16.24% | 5,954.50 | -1.42% | |
| 50. | 2025. 3. 31. | $156.23 | $0.20 | -9.17% | 5,611.85 | -5.75% |
| 51. | 2025. 4. 30. | $160.89 | 2.98% | 5,569.06 | -0.76% | |
| 52. | 2025. 5. 31. | $172.85 | 7.43% | 5,911.69 | 6.15% | |
| 53. | 2025. 6. 30. | $177.39 | $0.21 | 2.75% | 6,204.95 | 4.96% |
| 54. | 2025. 7. 31. | $192.86 | 8.72% | 6,339.39 | 2.17% | |
| 55. | 2025. 8. 31. | $213.53 | 10.72% | 6,460.26 | 1.91% | |
| 56. | 2025. 9. 30. | $243.55 | $0.21 | 14.16% | 6,688.46 | 3.53% |
| 57. | 2025. 10. 31. | $281.82 | 15.71% | 6,840.20 | 2.27% | |
| 58. | 2025. 11. 30. | $320.12 | 13.59% | 6,849.09 | 0.13% | |
| 59. | 2025. 12. 31. | $313.80 | $0.21 | -1.91% | 6,845.50 | -0.05% |
| 평균의 (R): | 2.45% | 1.14% | ||||
| 표준 편차: | 8.16% | 4.37% | ||||
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. | 2021. 2. 28. | 10.95% | 2.61% | 72.30 | 2.17 | 12.52 |
| 2. | 2021. 3. 31. | 1.56% | 4.24% | 0.78 | 9.66 | -2.75 |
| 3. | 2021. 4. 30. | 16.51% | 5.24% | 197.89 | 16.86 | 57.77 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | 13.59% | 0.13% | 124.19 | 1.01 | -11.21 |
| 59. | 2025. 12. 31. | -1.91% | -0.05% | 18.96 | 1.41 | 5.18 |
| 합계 (Σ): | 3,860.95 | 1,108.23 | 1,245.29 | |||
| 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. | 2021. 2. 28. | 10.95% | 2.61% | 72.30 | 2.17 | 12.52 |
| 2. | 2021. 3. 31. | 1.56% | 4.24% | 0.78 | 9.66 | -2.75 |
| 3. | 2021. 4. 30. | 16.51% | 5.24% | 197.89 | 16.86 | 57.77 |
| 4. | 2021. 5. 31. | 0.06% | 0.55% | 5.70 | 0.35 | 1.40 |
| 5. | 2021. 6. 30. | 3.93% | 2.22% | 2.20 | 1.18 | 1.61 |
| 6. | 2021. 7. 31. | 7.90% | 2.27% | 29.74 | 1.30 | 6.21 |
| 7. | 2021. 8. 31. | 7.57% | 2.90% | 26.28 | 3.11 | 9.04 |
| 8. | 2021. 9. 30. | -8.38% | -4.76% | 117.21 | 34.73 | 63.80 |
| 9. | 2021. 10. 31. | 11.26% | 6.91% | 77.60 | 33.39 | 50.90 |
| 10. | 2021. 11. 30. | -3.93% | -0.83% | 40.59 | 3.88 | 12.55 |
| 11. | 2021. 12. 31. | 1.57% | 4.36% | 0.78 | 10.40 | -2.84 |
| 12. | 2022. 1. 31. | -6.21% | -5.26% | 74.87 | 40.89 | 55.33 |
| 13. | 2022. 2. 28. | -0.60% | -3.14% | 9.26 | 18.25 | 13.00 |
| 14. | 2022. 3. 31. | 3.53% | 3.58% | 1.17 | 5.96 | 2.64 |
| 15. | 2022. 4. 30. | -17.67% | -8.80% | 404.77 | 98.64 | 199.82 |
| 16. | 2022. 5. 31. | -0.81% | 0.01% | 10.59 | 1.28 | 3.68 |
| 17. | 2022. 6. 30. | -4.10% | -8.39% | 42.79 | 90.79 | 62.32 |
| 18. | 2022. 7. 31. | 6.65% | 9.11% | 17.65 | 63.61 | 33.51 |
| 19. | 2022. 8. 31. | -6.42% | -4.24% | 78.63 | 28.95 | 47.71 |
| 20. | 2022. 9. 30. | -11.91% | -9.34% | 206.10 | 109.74 | 150.39 |
| 21. | 2022. 10. 31. | -1.55% | 7.99% | 15.97 | 46.93 | -27.37 |
| 22. | 2022. 11. 30. | 7.17% | 5.38% | 22.34 | 17.97 | 20.04 |
| 23. | 2022. 12. 31. | -12.54% | -5.90% | 224.53 | 49.47 | 105.39 |
| 24. | 2023. 1. 31. | 12.55% | 6.18% | 102.19 | 25.39 | 50.94 |
| 25. | 2023. 2. 28. | -9.58% | -2.61% | 144.69 | 14.04 | 45.08 |
| 26. | 2023. 3. 31. | 15.17% | 3.51% | 161.94 | 5.61 | 30.15 |
| 27. | 2023. 4. 30. | 4.06% | 1.46% | 2.60 | 0.11 | 0.53 |
| 28. | 2023. 5. 31. | 14.00% | 0.25% | 133.48 | 0.79 | -10.26 |
| 29. | 2023. 6. 30. | -1.95% | 4.71% | 19.28 | 12.80 | -15.71 |
| 30. | 2023. 7. 31. | 10.04% | 4.85% | 57.60 | 13.76 | 28.16 |
| 31. | 2023. 8. 31. | 3.19% | -1.77% | 0.55 | 8.46 | -2.15 |
| 32. | 2023. 9. 30. | -4.00% | -4.87% | 41.61 | 36.10 | 38.75 |
| 33. | 2023. 10. 31. | -4.97% | -2.20% | 54.97 | 11.12 | 24.72 |
| 34. | 2023. 11. 30. | 6.88% | 8.92% | 19.66 | 60.56 | 34.50 |
| 35. | 2023. 12. 31. | 5.23% | 4.42% | 7.78 | 10.80 | 9.16 |
| 36. | 2024. 1. 31. | 0.62% | 1.59% | 3.34 | 0.21 | -0.83 |
| 37. | 2024. 2. 29. | -1.42% | 5.17% | 14.98 | 16.29 | -15.62 |
| 38. | 2024. 3. 31. | 8.93% | 3.10% | 42.02 | 3.86 | 12.74 |
| 39. | 2024. 4. 30. | 8.13% | -4.16% | 32.32 | 28.06 | -30.12 |
| 40. | 2024. 5. 31. | 5.66% | 4.80% | 10.33 | 13.44 | 11.79 |
| 41. | 2024. 6. 30. | 5.55% | 3.47% | 9.65 | 5.43 | 7.24 |
| 42. | 2024. 7. 31. | -5.60% | 1.13% | 64.73 | 0.00 | 0.03 |
| 43. | 2024. 8. 31. | -4.64% | 2.28% | 50.26 | 1.32 | -8.13 |
| 44. | 2024. 9. 30. | 1.38% | 2.02% | 1.13 | 0.78 | -0.94 |
| 45. | 2024. 10. 31. | 3.29% | -0.99% | 0.71 | 4.52 | -1.79 |
| 46. | 2024. 11. 30. | -1.27% | 5.73% | 13.84 | 21.10 | -17.09 |
| 47. | 2024. 12. 31. | 11.82% | -2.50% | 87.85 | 13.21 | -34.07 |
| 48. | 2025. 1. 31. | 7.96% | 2.70% | 30.41 | 2.45 | 8.63 |
| 49. | 2025. 2. 28. | -16.24% | -1.42% | 349.00 | 6.56 | 47.83 |
| 50. | 2025. 3. 31. | -9.17% | -5.75% | 134.90 | 47.48 | 80.03 |
| 51. | 2025. 4. 30. | 2.98% | -0.76% | 0.29 | 3.60 | -1.02 |
| 52. | 2025. 5. 31. | 7.43% | 6.15% | 24.88 | 25.16 | 25.02 |
| 53. | 2025. 6. 30. | 2.75% | 4.96% | 0.09 | 14.63 | 1.15 |
| 54. | 2025. 7. 31. | 8.72% | 2.17% | 39.37 | 1.06 | 6.47 |
| 55. | 2025. 8. 31. | 10.72% | 1.91% | 68.42 | 0.59 | 6.37 |
| 56. | 2025. 9. 30. | 14.16% | 3.53% | 137.15 | 5.74 | 28.06 |
| 57. | 2025. 10. 31. | 15.71% | 2.27% | 176.02 | 1.28 | 15.03 |
| 58. | 2025. 11. 30. | 13.59% | 0.13% | 124.19 | 1.01 | -11.21 |
| 59. | 2025. 12. 31. | -1.91% | -0.05% | 18.96 | 1.41 | 5.18 |
| 합계 (Σ): | 3,860.95 | 1,108.23 | 1,245.29 | |||
모두 보기
분산GOOG = Σ(RGOOG,t–RGOOG)2 ÷ (59 – 1)
= 3,860.95 ÷ (59 – 1)
= 66.57
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,108.23 ÷ (59 – 1)
= 19.11
공분산GOOG, S&P 500 = Σ(RGOOG,t–RGOOG)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,245.29 ÷ (59 – 1)
= 21.47
체계적인 위험 추정 (β)
| 분산GOOG | 66.57 |
| 분산S&P 500 | 19.11 |
| 공분산GOOG, S&P 500 | 21.47 |
| 상관 계수GOOG, S&P 5001 | 0.60 |
| βGOOG2 | 1.12 |
| αGOOG3 | 1.17% |
계산
1 상관 계수GOOG, S&P 500
= 공분산GOOG, S&P 500 ÷ (표준 편차GOOG × 표준 편차S&P 500)
= 21.47 ÷ (8.16% × 4.37%)
= 0.60
2 βGOOG
= 공분산GOOG, S&P 500 ÷ 분산S&P 500
= 21.47 ÷ 19.11
= 1.12
3 αGOOG
= 평균의GOOG – βGOOG × 평균의S&P 500
= 2.45% – 1.12 × 1.14%
= 1.17%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.95% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 17.36% |
| 보통주의 체계적 위험Alphabet | βGOOG | 1.12 |
| 알파벳 보통주 예상 수익률3 | E(RGOOG) | 18.89% |
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]
= 4.95% + 1.12 [17.36% – 4.95%]
= 18.89%