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 |
| 2019. 1. 31. | $55.82 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $56.00 | 0.32% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $58.67 | 4.77% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $59.42 | 1.28% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $133.92 | 6.88% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $140.93 | 5.23% | 4,769.83 | 4.42% | |
| 평균의 (R): | 1.88% | 1.11% | ||||
| 표준 편차: | 7.83% | 5.31% | ||||
| 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 |
| 2019. 1. 31. | $55.82 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $56.00 | 0.32% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $58.67 | 4.77% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $59.42 | 1.28% | 2,945.83 | 3.93% | |
| 4. | 2019. 5. 31. | $55.18 | -7.14% | 2,752.06 | -6.58% | |
| 5. | 2019. 6. 30. | $54.05 | -2.05% | 2,941.76 | 6.89% | |
| 6. | 2019. 7. 31. | $60.83 | 12.54% | 2,980.38 | 1.31% | |
| 7. | 2019. 8. 31. | $59.41 | -2.33% | 2,926.46 | -1.81% | |
| 8. | 2019. 9. 30. | $60.95 | 2.59% | 2,976.74 | 1.72% | |
| 9. | 2019. 10. 31. | $63.01 | 3.38% | 3,037.56 | 2.04% | |
| 10. | 2019. 11. 30. | $65.25 | 3.55% | 3,140.98 | 3.40% | |
| 11. | 2019. 12. 31. | $66.85 | 2.45% | 3,230.78 | 2.86% | |
| 12. | 2020. 1. 31. | $71.71 | 7.27% | 3,225.52 | -0.16% | |
| 13. | 2020. 2. 29. | $66.97 | -6.61% | 2,954.22 | -8.41% | |
| 14. | 2020. 3. 31. | $58.14 | -13.19% | 2,584.59 | -12.51% | |
| 15. | 2020. 4. 30. | $67.43 | 15.98% | 2,912.43 | 12.68% | |
| 16. | 2020. 5. 31. | $71.45 | 5.96% | 3,044.31 | 4.53% | |
| 17. | 2020. 6. 30. | $70.68 | -1.08% | 3,100.29 | 1.84% | |
| 18. | 2020. 7. 31. | $74.15 | 4.91% | 3,271.12 | 5.51% | |
| 19. | 2020. 8. 31. | $81.71 | 10.20% | 3,500.31 | 7.01% | |
| 20. | 2020. 9. 30. | $73.48 | -10.07% | 3,363.00 | -3.92% | |
| 21. | 2020. 10. 31. | $81.05 | 10.30% | 3,269.96 | -2.77% | |
| 22. | 2020. 11. 30. | $88.04 | 8.62% | 3,621.63 | 10.75% | |
| 23. | 2020. 12. 31. | $87.59 | -0.51% | 3,756.07 | 3.71% | |
| 24. | 2021. 1. 31. | $91.79 | 4.80% | 3,714.24 | -1.11% | |
| 25. | 2021. 2. 28. | $101.84 | 10.95% | 3,811.15 | 2.61% | |
| 26. | 2021. 3. 31. | $103.43 | 1.56% | 3,972.89 | 4.24% | |
| 27. | 2021. 4. 30. | $120.51 | 16.51% | 4,181.17 | 5.24% | |
| 28. | 2021. 5. 31. | $120.58 | 0.06% | 4,204.11 | 0.55% | |
| 29. | 2021. 6. 30. | $125.32 | 3.93% | 4,297.50 | 2.22% | |
| 30. | 2021. 7. 31. | $135.22 | 7.90% | 4,395.26 | 2.27% | |
| 31. | 2021. 8. 31. | $145.46 | 7.57% | 4,522.68 | 2.90% | |
| 32. | 2021. 9. 30. | $133.27 | -8.38% | 4,307.54 | -4.76% | |
| 33. | 2021. 10. 31. | $148.27 | 11.26% | 4,605.38 | 6.91% | |
| 34. | 2021. 11. 30. | $142.45 | -3.93% | 4,567.00 | -0.83% | |
| 35. | 2021. 12. 31. | $144.68 | 1.57% | 4,766.18 | 4.36% | |
| 36. | 2022. 1. 31. | $135.70 | -6.21% | 4,515.55 | -5.26% | |
| 37. | 2022. 2. 28. | $134.89 | -0.60% | 4,373.94 | -3.14% | |
| 38. | 2022. 3. 31. | $139.65 | 3.53% | 4,530.41 | 3.58% | |
| 39. | 2022. 4. 30. | $114.97 | -17.67% | 4,131.93 | -8.80% | |
| 40. | 2022. 5. 31. | $114.04 | -0.81% | 4,132.15 | 0.01% | |
| 41. | 2022. 6. 30. | $109.37 | -4.10% | 3,785.38 | -8.39% | |
| 42. | 2022. 7. 31. | $116.64 | 6.65% | 4,130.29 | 9.11% | |
| 43. | 2022. 8. 31. | $109.15 | -6.42% | 3,955.00 | -4.24% | |
| 44. | 2022. 9. 30. | $96.15 | -11.91% | 3,585.62 | -9.34% | |
| 45. | 2022. 10. 31. | $94.66 | -1.55% | 3,871.98 | 7.99% | |
| 46. | 2022. 11. 30. | $101.45 | 7.17% | 4,080.11 | 5.38% | |
| 47. | 2022. 12. 31. | $88.73 | -12.54% | 3,839.50 | -5.90% | |
| 48. | 2023. 1. 31. | $99.87 | 12.55% | 4,076.60 | 6.18% | |
| 49. | 2023. 2. 28. | $90.30 | -9.58% | 3,970.15 | -2.61% | |
| 50. | 2023. 3. 31. | $104.00 | 15.17% | 4,109.31 | 3.51% | |
| 51. | 2023. 4. 30. | $108.22 | 4.06% | 4,169.48 | 1.46% | |
| 52. | 2023. 5. 31. | $123.37 | 14.00% | 4,179.83 | 0.25% | |
| 53. | 2023. 6. 30. | $120.97 | -1.95% | 4,376.86 | 4.71% | |
| 54. | 2023. 7. 31. | $133.11 | 10.04% | 4,588.96 | 4.85% | |
| 55. | 2023. 8. 31. | $137.35 | 3.19% | 4,507.66 | -1.77% | |
| 56. | 2023. 9. 30. | $131.85 | -4.00% | 4,288.05 | -4.87% | |
| 57. | 2023. 10. 31. | $125.30 | -4.97% | 4,193.80 | -2.20% | |
| 58. | 2023. 11. 30. | $133.92 | 6.88% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $140.93 | 5.23% | 4,769.83 | 4.42% | |
| 평균의 (R): | 1.88% | 1.11% | ||||
| 표준 편차: | 7.83% | 5.31% | ||||
모두 표시
1 보통주 주당 US$ 단위의 데이터로, 분할 및 주식 배당금에 맞게 조정됩니다.
2 기간 t 동안 GOOG의 보통주에 대한 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)에 대한 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. | 2019. 2. 28. | 0.32% | 2.97% | 2.44 | 3.49 | -2.91 |
| 2. | 2019. 3. 31. | 4.77% | 1.79% | 8.32 | 0.47 | 1.98 |
| 3. | 2019. 4. 30. | 1.28% | 3.93% | 0.37 | 7.98 | -1.71 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | 6.88% | 8.92% | 24.96 | 61.03 | 39.03 |
| 59. | 2023. 12. 31. | 5.23% | 4.42% | 11.23 | 11.00 | 11.12 |
| 합계 (Σ): | 3,552.13 | 1,634.30 | 1,765.97 | |||
| 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. | 2019. 2. 28. | 0.32% | 2.97% | 2.44 | 3.49 | -2.91 |
| 2. | 2019. 3. 31. | 4.77% | 1.79% | 8.32 | 0.47 | 1.98 |
| 3. | 2019. 4. 30. | 1.28% | 3.93% | 0.37 | 7.98 | -1.71 |
| 4. | 2019. 5. 31. | -7.14% | -6.58% | 81.34 | 59.04 | 69.30 |
| 5. | 2019. 6. 30. | -2.05% | 6.89% | 15.45 | 33.49 | -22.75 |
| 6. | 2019. 7. 31. | 12.54% | 1.31% | 113.65 | 0.04 | 2.21 |
| 7. | 2019. 8. 31. | -2.33% | -1.81% | 17.79 | 8.50 | 12.29 |
| 8. | 2019. 9. 30. | 2.59% | 1.72% | 0.50 | 0.37 | 0.43 |
| 9. | 2019. 10. 31. | 3.38% | 2.04% | 2.24 | 0.88 | 1.40 |
| 10. | 2019. 11. 30. | 3.55% | 3.40% | 2.79 | 5.28 | 3.84 |
| 11. | 2019. 12. 31. | 2.45% | 2.86% | 0.32 | 3.07 | 1.00 |
| 12. | 2020. 1. 31. | 7.27% | -0.16% | 29.02 | 1.61 | -6.83 |
| 13. | 2020. 2. 29. | -6.61% | -8.41% | 72.14 | 90.57 | 80.83 |
| 14. | 2020. 3. 31. | -13.19% | -12.51% | 227.06 | 185.44 | 205.20 |
| 15. | 2020. 4. 30. | 15.98% | 12.68% | 198.68 | 134.06 | 163.20 |
| 16. | 2020. 5. 31. | 5.96% | 4.53% | 16.63 | 11.71 | 13.96 |
| 17. | 2020. 6. 30. | -1.08% | 1.84% | 8.77 | 0.54 | -2.17 |
| 18. | 2020. 7. 31. | 4.91% | 5.51% | 9.16 | 19.40 | 13.33 |
| 19. | 2020. 8. 31. | 10.20% | 7.01% | 69.09 | 34.82 | 49.05 |
| 20. | 2020. 9. 30. | -10.07% | -3.92% | 142.94 | 25.29 | 60.12 |
| 21. | 2020. 10. 31. | 10.30% | -2.77% | 70.87 | 15.00 | -32.60 |
| 22. | 2020. 11. 30. | 8.62% | 10.75% | 45.44 | 93.10 | 65.04 |
| 23. | 2020. 12. 31. | -0.51% | 3.71% | 5.73 | 6.79 | -6.24 |
| 24. | 2021. 1. 31. | 4.80% | -1.11% | 8.48 | 4.93 | -6.46 |
| 25. | 2021. 2. 28. | 10.95% | 2.61% | 82.18 | 2.26 | 13.63 |
| 26. | 2021. 3. 31. | 1.56% | 4.24% | 0.10 | 9.85 | -1.01 |
| 27. | 2021. 4. 30. | 16.51% | 5.24% | 214.04 | 17.11 | 60.52 |
| 28. | 2021. 5. 31. | 0.06% | 0.55% | 3.33 | 0.31 | 1.02 |
| 29. | 2021. 6. 30. | 3.93% | 2.22% | 4.19 | 1.24 | 2.28 |
| 30. | 2021. 7. 31. | 7.90% | 2.27% | 36.20 | 1.37 | 7.03 |
| 31. | 2021. 8. 31. | 7.57% | 2.90% | 32.37 | 3.22 | 10.20 |
| 32. | 2021. 9. 30. | -8.38% | -4.76% | 105.34 | 34.37 | 60.17 |
| 33. | 2021. 10. 31. | 11.26% | 6.91% | 87.83 | 33.74 | 54.44 |
| 34. | 2021. 11. 30. | -3.93% | -0.83% | 33.74 | 3.76 | 11.26 |
| 35. | 2021. 12. 31. | 1.57% | 4.36% | 0.10 | 10.60 | -1.04 |
| 36. | 2022. 1. 31. | -6.21% | -5.26% | 65.45 | 40.51 | 51.49 |
| 37. | 2022. 2. 28. | -0.60% | -3.14% | 6.15 | 17.99 | 10.52 |
| 38. | 2022. 3. 31. | 3.53% | 3.58% | 2.71 | 6.11 | 4.07 |
| 39. | 2022. 4. 30. | -17.67% | -8.80% | 382.44 | 98.04 | 193.64 |
| 40. | 2022. 5. 31. | -0.81% | 0.01% | 7.25 | 1.21 | 2.96 |
| 41. | 2022. 6. 30. | -4.10% | -8.39% | 35.74 | 90.21 | 56.78 |
| 42. | 2022. 7. 31. | 6.65% | 9.11% | 22.69 | 64.09 | 38.14 |
| 43. | 2022. 8. 31. | -6.42% | -4.24% | 68.97 | 28.62 | 44.43 |
| 44. | 2022. 9. 30. | -11.91% | -9.34% | 190.26 | 109.11 | 144.08 |
| 45. | 2022. 10. 31. | -1.55% | 7.99% | 11.79 | 47.34 | -23.62 |
| 46. | 2022. 11. 30. | 7.17% | 5.38% | 27.98 | 18.23 | 22.58 |
| 47. | 2022. 12. 31. | -12.54% | -5.90% | 207.98 | 49.04 | 100.99 |
| 48. | 2023. 1. 31. | 12.55% | 6.18% | 113.88 | 25.70 | 54.10 |
| 49. | 2023. 2. 28. | -9.58% | -2.61% | 131.47 | 13.82 | 42.62 |
| 50. | 2023. 3. 31. | 15.17% | 3.51% | 176.58 | 5.76 | 31.88 |
| 51. | 2023. 4. 30. | 4.06% | 1.46% | 4.73 | 0.13 | 0.78 |
| 52. | 2023. 5. 31. | 14.00% | 0.25% | 146.79 | 0.74 | -10.39 |
| 53. | 2023. 6. 30. | -1.95% | 4.71% | 14.66 | 13.02 | -13.81 |
| 54. | 2023. 7. 31. | 10.04% | 4.85% | 66.46 | 13.99 | 30.49 |
| 55. | 2023. 8. 31. | 3.19% | -1.77% | 1.69 | 8.28 | -3.75 |
| 56. | 2023. 9. 30. | -4.00% | -4.87% | 34.67 | 35.73 | 35.20 |
| 57. | 2023. 10. 31. | -4.97% | -2.20% | 46.94 | 10.92 | 22.64 |
| 58. | 2023. 11. 30. | 6.88% | 8.92% | 24.96 | 61.03 | 39.03 |
| 59. | 2023. 12. 31. | 5.23% | 4.42% | 11.23 | 11.00 | 11.12 |
| 합계 (Σ): | 3,552.13 | 1,634.30 | 1,765.97 | |||
모두 표시
분산GOOG = Σ(RGOOG,t–RGOOG)2 ÷ (59 – 1)
= 3,552.13 ÷ (59 – 1)
= 61.24
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산GOOG, S&P 500 = Σ(RGOOG,t–RGOOG)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,765.97 ÷ (59 – 1)
= 30.45
체계적인 위험 추정 (β)
| 분산GOOG | 61.24 |
| 분산S&P 500 | 28.18 |
| 공분산GOOG, S&P 500 | 30.45 |
| 상관 계수GOOG, S&P 5001 | 0.73 |
| βGOOG2 | 1.08 |
| αGOOG3 | 0.69% |
계산
1 상관 계수GOOG, S&P 500
= 공분산GOOG, S&P 500 ÷ (표준 편차GOOG × 표준 편차S&P 500)
= 30.45 ÷ (7.83% × 5.31%)
= 0.73
2 βGOOG
= 공분산GOOG, S&P 500 ÷ 분산S&P 500
= 30.45 ÷ 28.18
= 1.08
3 αGOOG
= 평균의GOOG – βGOOG × 평균의S&P 500
= 1.88% – 1.08 × 1.11%
= 0.69%
예상 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.90% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.55% |
| 보통주의 체계적 위험Alphabet | βGOOG | 1.08 |
| 알파벳 보통주 예상 수익률3 | E(RGOOG) | 14.24% |
1 10년 이내에 만기가 되지 않거나 콜 가능하지 않은 모든 미결제 고정 쿠폰 미국 재무부 채권에 대한 입찰 수익률의 가중 평균(무위험 수익률 프록시).
2 자세히 보기 »
3 E(RGOOG) = RF + βGOOG [E(RM) – RF]
= 4.90% + 1.08 [13.55% – 4.90%]
= 14.24%