자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 PepsiCo보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
PepsiCo Inc., 월별 수익률
| PepsiCo Inc. (PEP) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값PEP,t1 | 피제수PEP,t1 | RPEP,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2020. 1. 31. | $142.02 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $132.03 | -7.03% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $120.10 | $0.955 | -8.31% | 2,584.59 | -12.51% |
| 3. | 2020. 4. 30. | $132.29 | 10.15% | 2,912.43 | 12.68% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | $163.45 | -1.58% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $152.06 | $1.355 | -6.14% | 5,881.63 | -2.50% |
| 평균의 (R): | 0.47% | 1.16% | ||||
| 표준 편차: | 4.67% | 5.28% | ||||
| PepsiCo Inc. (PEP) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값PEP,t1 | 피제수PEP,t1 | RPEP,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2020. 1. 31. | $142.02 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $132.03 | -7.03% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $120.10 | $0.955 | -8.31% | 2,584.59 | -12.51% |
| 3. | 2020. 4. 30. | $132.29 | 10.15% | 2,912.43 | 12.68% | |
| 4. | 2020. 5. 31. | $131.55 | -0.56% | 3,044.31 | 4.53% | |
| 5. | 2020. 6. 30. | $132.26 | $1.0225 | 1.32% | 3,100.29 | 1.84% |
| 6. | 2020. 7. 31. | $137.66 | 4.08% | 3,271.12 | 5.51% | |
| 7. | 2020. 8. 31. | $140.06 | 1.74% | 3,500.31 | 7.01% | |
| 8. | 2020. 9. 30. | $138.60 | $1.0225 | -0.31% | 3,363.00 | -3.92% |
| 9. | 2020. 10. 31. | $133.29 | -3.83% | 3,269.96 | -2.77% | |
| 10. | 2020. 11. 30. | $144.23 | 8.21% | 3,621.63 | 10.75% | |
| 11. | 2020. 12. 31. | $148.30 | $1.0225 | 3.53% | 3,756.07 | 3.71% |
| 12. | 2021. 1. 31. | $136.57 | -7.91% | 3,714.24 | -1.11% | |
| 13. | 2021. 2. 28. | $129.19 | -5.40% | 3,811.15 | 2.61% | |
| 14. | 2021. 3. 31. | $141.45 | $1.0225 | 10.28% | 3,972.89 | 4.24% |
| 15. | 2021. 4. 30. | $144.16 | 1.92% | 4,181.17 | 5.24% | |
| 16. | 2021. 5. 31. | $147.94 | 2.62% | 4,204.11 | 0.55% | |
| 17. | 2021. 6. 30. | $148.17 | $1.075 | 0.88% | 4,297.50 | 2.22% |
| 18. | 2021. 7. 31. | $156.95 | 5.93% | 4,395.26 | 2.27% | |
| 19. | 2021. 8. 31. | $156.39 | -0.36% | 4,522.68 | 2.90% | |
| 20. | 2021. 9. 30. | $150.41 | $1.075 | -3.14% | 4,307.54 | -4.76% |
| 21. | 2021. 10. 31. | $161.60 | 7.44% | 4,605.38 | 6.91% | |
| 22. | 2021. 11. 30. | $159.78 | -1.13% | 4,567.00 | -0.83% | |
| 23. | 2021. 12. 31. | $173.71 | $1.075 | 9.39% | 4,766.18 | 4.36% |
| 24. | 2022. 1. 31. | $173.52 | -0.11% | 4,515.55 | -5.26% | |
| 25. | 2022. 2. 28. | $163.74 | -5.64% | 4,373.94 | -3.14% | |
| 26. | 2022. 3. 31. | $167.38 | $1.075 | 2.88% | 4,530.41 | 3.58% |
| 27. | 2022. 4. 30. | $171.71 | 2.59% | 4,131.93 | -8.80% | |
| 28. | 2022. 5. 31. | $167.75 | -2.31% | 4,132.15 | 0.01% | |
| 29. | 2022. 6. 30. | $166.66 | $1.15 | 0.04% | 3,785.38 | -8.39% |
| 30. | 2022. 7. 31. | $174.96 | 4.98% | 4,130.29 | 9.11% | |
| 31. | 2022. 8. 31. | $172.27 | -1.54% | 3,955.00 | -4.24% | |
| 32. | 2022. 9. 30. | $163.26 | $1.15 | -4.56% | 3,585.62 | -9.34% |
| 33. | 2022. 10. 31. | $181.58 | 11.22% | 3,871.98 | 7.99% | |
| 34. | 2022. 11. 30. | $185.51 | 2.16% | 4,080.11 | 5.38% | |
| 35. | 2022. 12. 31. | $180.66 | $1.15 | -1.99% | 3,839.50 | -5.90% |
| 36. | 2023. 1. 31. | $171.02 | -5.34% | 4,076.60 | 6.18% | |
| 37. | 2023. 2. 28. | $173.53 | 1.47% | 3,970.15 | -2.61% | |
| 38. | 2023. 3. 31. | $182.30 | $1.15 | 5.72% | 4,109.31 | 3.51% |
| 39. | 2023. 4. 30. | $190.89 | 4.71% | 4,169.48 | 1.46% | |
| 40. | 2023. 5. 31. | $182.35 | -4.47% | 4,179.83 | 0.25% | |
| 41. | 2023. 6. 30. | $185.22 | $1.265 | 2.27% | 4,376.86 | 4.71% |
| 42. | 2023. 7. 31. | $187.46 | 1.21% | 4,588.96 | 4.85% | |
| 43. | 2023. 8. 31. | $177.92 | $1.265 | -4.41% | 4,507.66 | -1.77% |
| 44. | 2023. 9. 30. | $169.44 | -4.77% | 4,288.05 | -4.87% | |
| 45. | 2023. 10. 31. | $163.28 | -3.64% | 4,193.80 | -2.20% | |
| 46. | 2023. 11. 30. | $168.29 | $1.265 | 3.84% | 4,567.80 | 8.92% |
| 47. | 2023. 12. 31. | $169.84 | 0.92% | 4,769.83 | 4.42% | |
| 48. | 2024. 1. 31. | $168.53 | -0.77% | 4,845.65 | 1.59% | |
| 49. | 2024. 2. 29. | $165.34 | $1.265 | -1.14% | 5,096.27 | 5.17% |
| 50. | 2024. 3. 31. | $175.01 | 5.85% | 5,254.35 | 3.10% | |
| 51. | 2024. 4. 30. | $175.91 | 0.51% | 5,035.69 | -4.16% | |
| 52. | 2024. 5. 31. | $172.90 | -1.71% | 5,277.51 | 4.80% | |
| 53. | 2024. 6. 30. | $164.93 | $1.355 | -3.83% | 5,460.48 | 3.47% |
| 54. | 2024. 7. 31. | $172.67 | 4.69% | 5,522.30 | 1.13% | |
| 55. | 2024. 8. 31. | $172.88 | 0.12% | 5,648.40 | 2.28% | |
| 56. | 2024. 9. 30. | $170.05 | $1.355 | -0.85% | 5,762.48 | 2.02% |
| 57. | 2024. 10. 31. | $166.08 | -2.33% | 5,705.45 | -0.99% | |
| 58. | 2024. 11. 30. | $163.45 | -1.58% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $152.06 | $1.355 | -6.14% | 5,881.63 | -2.50% |
| 평균의 (R): | 0.47% | 1.16% | ||||
| 표준 편차: | 4.67% | 5.28% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 PEP의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
PepsiCo Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RPEP,t | RS&P 500,t | (RPEP,t–RPEP)2 | (RS&P 500,t–RS&P 500)2 | (RPEP,t–RPEP)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2020. 2. 29. | -7.03% | -8.41% | 56.27 | 91.63 | 71.80 |
| 2. | 2020. 3. 31. | -8.31% | -12.51% | 77.08 | 186.96 | 120.04 |
| 3. | 2020. 4. 30. | 10.15% | 12.68% | 93.76 | 132.78 | 111.58 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | -1.58% | 5.73% | 4.21 | 20.87 | -9.37 |
| 59. | 2024. 12. 31. | -6.14% | -2.50% | 43.65 | 13.40 | 24.18 |
| 합계 (Σ): | 1,263.94 | 1,618.62 | 876.02 | |||
| t | 날짜 | RPEP,t | RS&P 500,t | (RPEP,t–RPEP)2 | (RS&P 500,t–RS&P 500)2 | (RPEP,t–RPEP)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2020. 2. 29. | -7.03% | -8.41% | 56.27 | 91.63 | 71.80 |
| 2. | 2020. 3. 31. | -8.31% | -12.51% | 77.08 | 186.96 | 120.04 |
| 3. | 2020. 4. 30. | 10.15% | 12.68% | 93.76 | 132.78 | 111.58 |
| 4. | 2020. 5. 31. | -0.56% | 4.53% | 1.05 | 11.34 | -3.46 |
| 5. | 2020. 6. 30. | 1.32% | 1.84% | 0.72 | 0.46 | 0.58 |
| 6. | 2020. 7. 31. | 4.08% | 5.51% | 13.07 | 18.91 | 15.72 |
| 7. | 2020. 8. 31. | 1.74% | 7.01% | 1.63 | 34.17 | 7.46 |
| 8. | 2020. 9. 30. | -0.31% | -3.92% | 0.61 | 25.85 | 3.96 |
| 9. | 2020. 10. 31. | -3.83% | -2.77% | 18.47 | 15.43 | 16.88 |
| 10. | 2020. 11. 30. | 8.21% | 10.75% | 59.92 | 92.03 | 74.26 |
| 11. | 2020. 12. 31. | 3.53% | 3.71% | 9.39 | 6.51 | 7.82 |
| 12. | 2021. 1. 31. | -7.91% | -1.11% | 70.17 | 5.18 | 19.06 |
| 13. | 2021. 2. 28. | -5.40% | 2.61% | 34.47 | 2.10 | -8.50 |
| 14. | 2021. 3. 31. | 10.28% | 4.24% | 96.32 | 9.50 | 30.25 |
| 15. | 2021. 4. 30. | 1.92% | 5.24% | 2.10 | 16.66 | 5.91 |
| 16. | 2021. 5. 31. | 2.62% | 0.55% | 4.64 | 0.38 | -1.32 |
| 17. | 2021. 6. 30. | 0.88% | 2.22% | 0.17 | 1.12 | 0.44 |
| 18. | 2021. 7. 31. | 5.93% | 2.27% | 29.80 | 1.24 | 6.08 |
| 19. | 2021. 8. 31. | -0.36% | 2.90% | 0.68 | 3.02 | -1.43 |
| 20. | 2021. 9. 30. | -3.14% | -4.76% | 12.98 | 35.02 | 21.33 |
| 21. | 2021. 10. 31. | 7.44% | 6.91% | 48.62 | 33.10 | 40.11 |
| 22. | 2021. 11. 30. | -1.13% | -0.83% | 2.54 | 3.98 | 3.18 |
| 23. | 2021. 12. 31. | 9.39% | 4.36% | 79.64 | 10.24 | 28.56 |
| 24. | 2022. 1. 31. | -0.11% | -5.26% | 0.33 | 41.21 | 3.70 |
| 25. | 2022. 2. 28. | -5.64% | -3.14% | 37.25 | 18.47 | 26.23 |
| 26. | 2022. 3. 31. | 2.88% | 3.58% | 5.82 | 5.84 | 5.83 |
| 27. | 2022. 4. 30. | 2.59% | -8.80% | 4.49 | 99.14 | -21.11 |
| 28. | 2022. 5. 31. | -2.31% | 0.01% | 7.69 | 1.34 | 3.21 |
| 29. | 2022. 6. 30. | 0.04% | -8.39% | 0.19 | 91.26 | 4.12 |
| 30. | 2022. 7. 31. | 4.98% | 9.11% | 20.37 | 63.21 | 35.88 |
| 31. | 2022. 8. 31. | -1.54% | -4.24% | 4.02 | 29.22 | 10.84 |
| 32. | 2022. 9. 30. | -4.56% | -9.34% | 25.30 | 110.27 | 52.82 |
| 33. | 2022. 10. 31. | 11.22% | 7.99% | 115.66 | 46.58 | 73.40 |
| 34. | 2022. 11. 30. | 2.16% | 5.38% | 2.88 | 17.76 | 7.15 |
| 35. | 2022. 12. 31. | -1.99% | -5.90% | 6.06 | 49.82 | 17.37 |
| 36. | 2023. 1. 31. | -5.34% | 6.18% | 33.68 | 25.14 | -29.10 |
| 37. | 2023. 2. 28. | 1.47% | -2.61% | 1.00 | 14.23 | -3.77 |
| 38. | 2023. 3. 31. | 5.72% | 3.51% | 27.56 | 5.49 | 12.30 |
| 39. | 2023. 4. 30. | 4.71% | 1.46% | 18.02 | 0.09 | 1.29 |
| 40. | 2023. 5. 31. | -4.47% | 0.25% | 24.41 | 0.83 | 4.51 |
| 41. | 2023. 6. 30. | 2.27% | 4.71% | 3.24 | 12.62 | 6.40 |
| 42. | 2023. 7. 31. | 1.21% | 4.85% | 0.55 | 13.58 | 2.74 |
| 43. | 2023. 8. 31. | -4.41% | -1.77% | 23.83 | 8.60 | 14.32 |
| 44. | 2023. 9. 30. | -4.77% | -4.87% | 27.39 | 36.40 | 31.57 |
| 45. | 2023. 10. 31. | -3.64% | -2.20% | 16.83 | 11.28 | 13.78 |
| 46. | 2023. 11. 30. | 3.84% | 8.92% | 11.40 | 60.17 | 26.19 |
| 47. | 2023. 12. 31. | 0.92% | 4.42% | 0.21 | 10.64 | 1.48 |
| 48. | 2024. 1. 31. | -0.77% | 1.59% | 1.53 | 0.18 | -0.53 |
| 49. | 2024. 2. 29. | -1.14% | 5.17% | 2.59 | 16.09 | -6.45 |
| 50. | 2024. 3. 31. | 5.85% | 3.10% | 28.96 | 3.77 | 10.44 |
| 51. | 2024. 4. 30. | 0.51% | -4.16% | 0.00 | 28.33 | -0.25 |
| 52. | 2024. 5. 31. | -1.71% | 4.80% | 4.74 | 13.26 | -7.93 |
| 53. | 2024. 6. 30. | -3.83% | 3.47% | 18.43 | 5.32 | -9.90 |
| 54. | 2024. 7. 31. | 4.69% | 1.13% | 17.86 | 0.00 | -0.12 |
| 55. | 2024. 8. 31. | 0.12% | 2.28% | 0.12 | 1.26 | -0.39 |
| 56. | 2024. 9. 30. | -0.85% | 2.02% | 1.74 | 0.74 | -1.13 |
| 57. | 2024. 10. 31. | -2.33% | -0.99% | 7.85 | 4.63 | 6.03 |
| 58. | 2024. 11. 30. | -1.58% | 5.73% | 4.21 | 20.87 | -9.37 |
| 59. | 2024. 12. 31. | -6.14% | -2.50% | 43.65 | 13.40 | 24.18 |
| 합계 (Σ): | 1,263.94 | 1,618.62 | 876.02 | |||
모두 보기
분산PEP = Σ(RPEP,t–RPEP)2 ÷ (59 – 1)
= 1,263.94 ÷ (59 – 1)
= 21.79
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91
공분산PEP, S&P 500 = Σ(RPEP,t–RPEP)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 876.02 ÷ (59 – 1)
= 15.10
체계적인 위험 추정 (β)
| 분산PEP | 21.79 |
| 분산S&P 500 | 27.91 |
| 공분산PEP, S&P 500 | 15.10 |
| 상관 계수PEP, S&P 5001 | 0.61 |
| βPEP2 | 0.54 |
| αPEP3 | -0.16% |
계산
1 상관 계수PEP, S&P 500
= 공분산PEP, S&P 500 ÷ (표준 편차PEP × 표준 편차S&P 500)
= 15.10 ÷ (4.67% × 5.28%)
= 0.61
2 βPEP
= 공분산PEP, S&P 500 ÷ 분산S&P 500
= 15.10 ÷ 27.91
= 0.54
3 αPEP
= 평균의PEP – βPEP × 평균의S&P 500
= 0.47% – 0.54 × 1.16%
= -0.16%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.83% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.88% |
| 보통주의 체계적 위험PepsiCo | βPEP | 0.54 |
| PepsiCo 보통주 예상 수익률3 | E(RPEP) | 10.27% |
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(RPEP) = RF + βPEP [E(RM) – RF]
= 4.83% + 0.54 [14.88% – 4.83%]
= 10.27%