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 |
| 2019. 1. 31. | $112.67 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $115.64 | $0.9275 | 3.46% | 2,784.49 | 2.97% |
| 2. | 2019. 3. 31. | $122.55 | 5.98% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $128.05 | 4.49% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $168.29 | $1.265 | 3.84% | 4,567.80 | 8.92% |
| 59. | 2023. 12. 31. | $169.84 | 0.92% | 4,769.83 | 4.42% | |
| 평균의 (R): | 1.04% | 1.11% | ||||
| 표준 편차: | 4.63% | 5.31% | ||||
| 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 |
| 2019. 1. 31. | $112.67 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $115.64 | $0.9275 | 3.46% | 2,784.49 | 2.97% |
| 2. | 2019. 3. 31. | $122.55 | 5.98% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $128.05 | 4.49% | 2,945.83 | 3.93% | |
| 4. | 2019. 5. 31. | $128.00 | -0.04% | 2,752.06 | -6.58% | |
| 5. | 2019. 6. 30. | $131.13 | $0.955 | 3.19% | 2,941.76 | 6.89% |
| 6. | 2019. 7. 31. | $127.81 | -2.53% | 2,980.38 | 1.31% | |
| 7. | 2019. 8. 31. | $136.73 | 6.98% | 2,926.46 | -1.81% | |
| 8. | 2019. 9. 30. | $137.10 | $0.955 | 0.97% | 2,976.74 | 1.72% |
| 9. | 2019. 10. 31. | $137.17 | 0.05% | 3,037.56 | 2.04% | |
| 10. | 2019. 11. 30. | $135.83 | -0.98% | 3,140.98 | 3.40% | |
| 11. | 2019. 12. 31. | $136.67 | $0.955 | 1.32% | 3,230.78 | 2.86% |
| 12. | 2020. 1. 31. | $142.02 | 3.91% | 3,225.52 | -0.16% | |
| 13. | 2020. 2. 29. | $132.03 | -7.03% | 2,954.22 | -8.41% | |
| 14. | 2020. 3. 31. | $120.10 | $0.955 | -8.31% | 2,584.59 | -12.51% |
| 15. | 2020. 4. 30. | $132.29 | 10.15% | 2,912.43 | 12.68% | |
| 16. | 2020. 5. 31. | $131.55 | -0.56% | 3,044.31 | 4.53% | |
| 17. | 2020. 6. 30. | $132.26 | $1.0225 | 1.32% | 3,100.29 | 1.84% |
| 18. | 2020. 7. 31. | $137.66 | 4.08% | 3,271.12 | 5.51% | |
| 19. | 2020. 8. 31. | $140.06 | 1.74% | 3,500.31 | 7.01% | |
| 20. | 2020. 9. 30. | $138.60 | $1.0225 | -0.31% | 3,363.00 | -3.92% |
| 21. | 2020. 10. 31. | $133.29 | -3.83% | 3,269.96 | -2.77% | |
| 22. | 2020. 11. 30. | $144.23 | 8.21% | 3,621.63 | 10.75% | |
| 23. | 2020. 12. 31. | $148.30 | $1.0225 | 3.53% | 3,756.07 | 3.71% |
| 24. | 2021. 1. 31. | $136.57 | -7.91% | 3,714.24 | -1.11% | |
| 25. | 2021. 2. 28. | $129.19 | -5.40% | 3,811.15 | 2.61% | |
| 26. | 2021. 3. 31. | $141.45 | $1.0225 | 10.28% | 3,972.89 | 4.24% |
| 27. | 2021. 4. 30. | $144.16 | 1.92% | 4,181.17 | 5.24% | |
| 28. | 2021. 5. 31. | $147.94 | 2.62% | 4,204.11 | 0.55% | |
| 29. | 2021. 6. 30. | $148.17 | $1.075 | 0.88% | 4,297.50 | 2.22% |
| 30. | 2021. 7. 31. | $156.95 | 5.93% | 4,395.26 | 2.27% | |
| 31. | 2021. 8. 31. | $156.39 | -0.36% | 4,522.68 | 2.90% | |
| 32. | 2021. 9. 30. | $150.41 | $1.075 | -3.14% | 4,307.54 | -4.76% |
| 33. | 2021. 10. 31. | $161.60 | 7.44% | 4,605.38 | 6.91% | |
| 34. | 2021. 11. 30. | $159.78 | -1.13% | 4,567.00 | -0.83% | |
| 35. | 2021. 12. 31. | $173.71 | $1.075 | 9.39% | 4,766.18 | 4.36% |
| 36. | 2022. 1. 31. | $173.52 | -0.11% | 4,515.55 | -5.26% | |
| 37. | 2022. 2. 28. | $163.74 | -5.64% | 4,373.94 | -3.14% | |
| 38. | 2022. 3. 31. | $167.38 | $1.075 | 2.88% | 4,530.41 | 3.58% |
| 39. | 2022. 4. 30. | $171.71 | 2.59% | 4,131.93 | -8.80% | |
| 40. | 2022. 5. 31. | $167.75 | -2.31% | 4,132.15 | 0.01% | |
| 41. | 2022. 6. 30. | $166.66 | $1.15 | 0.04% | 3,785.38 | -8.39% |
| 42. | 2022. 7. 31. | $174.96 | 4.98% | 4,130.29 | 9.11% | |
| 43. | 2022. 8. 31. | $172.27 | -1.54% | 3,955.00 | -4.24% | |
| 44. | 2022. 9. 30. | $163.26 | $1.15 | -4.56% | 3,585.62 | -9.34% |
| 45. | 2022. 10. 31. | $181.58 | 11.22% | 3,871.98 | 7.99% | |
| 46. | 2022. 11. 30. | $185.51 | 2.16% | 4,080.11 | 5.38% | |
| 47. | 2022. 12. 31. | $180.66 | $1.15 | -1.99% | 3,839.50 | -5.90% |
| 48. | 2023. 1. 31. | $171.02 | -5.34% | 4,076.60 | 6.18% | |
| 49. | 2023. 2. 28. | $173.53 | 1.47% | 3,970.15 | -2.61% | |
| 50. | 2023. 3. 31. | $182.30 | $1.15 | 5.72% | 4,109.31 | 3.51% |
| 51. | 2023. 4. 30. | $190.89 | 4.71% | 4,169.48 | 1.46% | |
| 52. | 2023. 5. 31. | $182.35 | -4.47% | 4,179.83 | 0.25% | |
| 53. | 2023. 6. 30. | $185.22 | $1.265 | 2.27% | 4,376.86 | 4.71% |
| 54. | 2023. 7. 31. | $187.46 | 1.21% | 4,588.96 | 4.85% | |
| 55. | 2023. 8. 31. | $177.92 | $1.265 | -4.41% | 4,507.66 | -1.77% |
| 56. | 2023. 9. 30. | $169.44 | -4.77% | 4,288.05 | -4.87% | |
| 57. | 2023. 10. 31. | $163.28 | -3.64% | 4,193.80 | -2.20% | |
| 58. | 2023. 11. 30. | $168.29 | $1.265 | 3.84% | 4,567.80 | 8.92% |
| 59. | 2023. 12. 31. | $169.84 | 0.92% | 4,769.83 | 4.42% | |
| 평균의 (R): | 1.04% | 1.11% | ||||
| 표준 편차: | 4.63% | 5.31% | ||||
모두 표시
1 보통주 주당 US$ 단위의 데이터로, 분할 및 주식 배당금에 맞게 조정됩니다.
2 기간 t 동안 PEP의 보통주에 대한 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)에 대한 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. | 2019. 2. 28. | 3.46% | 2.97% | 5.84 | 3.49 | 4.51 |
| 2. | 2019. 3. 31. | 5.98% | 1.79% | 24.33 | 0.47 | 3.39 |
| 3. | 2019. 4. 30. | 4.49% | 3.93% | 11.87 | 7.98 | 9.73 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | 3.84% | 8.92% | 7.84 | 61.03 | 21.87 |
| 59. | 2023. 12. 31. | 0.92% | 4.42% | 0.01 | 11.00 | -0.40 |
| 합계 (Σ): | 1,242.35 | 1,634.30 | 886.66 | |||
| 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. | 2019. 2. 28. | 3.46% | 2.97% | 5.84 | 3.49 | 4.51 |
| 2. | 2019. 3. 31. | 5.98% | 1.79% | 24.33 | 0.47 | 3.39 |
| 3. | 2019. 4. 30. | 4.49% | 3.93% | 11.87 | 7.98 | 9.73 |
| 4. | 2019. 5. 31. | -0.04% | -6.58% | 1.17 | 59.04 | 8.31 |
| 5. | 2019. 6. 30. | 3.19% | 6.89% | 4.62 | 33.49 | 12.43 |
| 6. | 2019. 7. 31. | -2.53% | 1.31% | 12.78 | 0.04 | -0.74 |
| 7. | 2019. 8. 31. | 6.98% | -1.81% | 35.24 | 8.50 | -17.30 |
| 8. | 2019. 9. 30. | 0.97% | 1.72% | 0.01 | 0.37 | -0.05 |
| 9. | 2019. 10. 31. | 0.05% | 2.04% | 0.98 | 0.88 | -0.93 |
| 10. | 2019. 11. 30. | -0.98% | 3.40% | 4.08 | 5.28 | -4.64 |
| 11. | 2019. 12. 31. | 1.32% | 2.86% | 0.08 | 3.07 | 0.49 |
| 12. | 2020. 1. 31. | 3.91% | -0.16% | 8.25 | 1.61 | -3.64 |
| 13. | 2020. 2. 29. | -7.03% | -8.41% | 65.24 | 90.57 | 76.87 |
| 14. | 2020. 3. 31. | -8.31% | -12.51% | 87.53 | 185.44 | 127.40 |
| 15. | 2020. 4. 30. | 10.15% | 12.68% | 82.93 | 134.06 | 105.44 |
| 16. | 2020. 5. 31. | -0.56% | 4.53% | 2.57 | 11.71 | -5.48 |
| 17. | 2020. 6. 30. | 1.32% | 1.84% | 0.08 | 0.54 | 0.20 |
| 18. | 2020. 7. 31. | 4.08% | 5.51% | 9.24 | 19.40 | 13.39 |
| 19. | 2020. 8. 31. | 1.74% | 7.01% | 0.49 | 34.82 | 4.13 |
| 20. | 2020. 9. 30. | -0.31% | -3.92% | 1.84 | 25.29 | 6.82 |
| 21. | 2020. 10. 31. | -3.83% | -2.77% | 23.76 | 15.00 | 18.88 |
| 22. | 2020. 11. 30. | 8.21% | 10.75% | 51.33 | 93.10 | 69.13 |
| 23. | 2020. 12. 31. | 3.53% | 3.71% | 6.19 | 6.79 | 6.48 |
| 24. | 2021. 1. 31. | -7.91% | -1.11% | 80.15 | 4.93 | 19.87 |
| 25. | 2021. 2. 28. | -5.40% | 2.61% | 41.56 | 2.26 | -9.69 |
| 26. | 2021. 3. 31. | 10.28% | 4.24% | 85.35 | 9.85 | 28.99 |
| 27. | 2021. 4. 30. | 1.92% | 5.24% | 0.76 | 17.11 | 3.61 |
| 28. | 2021. 5. 31. | 2.62% | 0.55% | 2.49 | 0.31 | -0.88 |
| 29. | 2021. 6. 30. | 0.88% | 2.22% | 0.03 | 1.24 | -0.18 |
| 30. | 2021. 7. 31. | 5.93% | 2.27% | 23.84 | 1.37 | 5.71 |
| 31. | 2021. 8. 31. | -0.36% | 2.90% | 1.96 | 3.22 | -2.51 |
| 32. | 2021. 9. 30. | -3.14% | -4.76% | 17.47 | 34.37 | 24.50 |
| 33. | 2021. 10. 31. | 7.44% | 6.91% | 40.92 | 33.74 | 37.15 |
| 34. | 2021. 11. 30. | -1.13% | -0.83% | 4.71 | 3.76 | 4.21 |
| 35. | 2021. 12. 31. | 9.39% | 4.36% | 69.69 | 10.60 | 27.18 |
| 36. | 2022. 1. 31. | -0.11% | -5.26% | 1.33 | 40.51 | 7.33 |
| 37. | 2022. 2. 28. | -5.64% | -3.14% | 44.61 | 17.99 | 28.33 |
| 38. | 2022. 3. 31. | 2.88% | 3.58% | 3.37 | 6.11 | 4.54 |
| 39. | 2022. 4. 30. | 2.59% | -8.80% | 2.38 | 98.04 | -15.29 |
| 40. | 2022. 5. 31. | -2.31% | 0.01% | 11.22 | 1.21 | 3.69 |
| 41. | 2022. 6. 30. | 0.04% | -8.39% | 1.01 | 90.21 | 9.57 |
| 42. | 2022. 7. 31. | 4.98% | 9.11% | 15.50 | 64.09 | 31.52 |
| 43. | 2022. 8. 31. | -1.54% | -4.24% | 6.66 | 28.62 | 13.81 |
| 44. | 2022. 9. 30. | -4.56% | -9.34% | 31.42 | 109.11 | 58.55 |
| 45. | 2022. 10. 31. | 11.22% | 7.99% | 103.60 | 47.34 | 70.03 |
| 46. | 2022. 11. 30. | 2.16% | 5.38% | 1.26 | 18.23 | 4.79 |
| 47. | 2022. 12. 31. | -1.99% | -5.90% | 9.23 | 49.04 | 21.27 |
| 48. | 2023. 1. 31. | -5.34% | 6.18% | 40.69 | 25.70 | -32.34 |
| 49. | 2023. 2. 28. | 1.47% | -2.61% | 0.18 | 13.82 | -1.58 |
| 50. | 2023. 3. 31. | 5.72% | 3.51% | 21.84 | 5.76 | 11.21 |
| 51. | 2023. 4. 30. | 4.71% | 1.46% | 13.46 | 0.13 | 1.31 |
| 52. | 2023. 5. 31. | -4.47% | 0.25% | 30.44 | 0.74 | 4.73 |
| 53. | 2023. 6. 30. | 2.27% | 4.71% | 1.50 | 13.02 | 4.42 |
| 54. | 2023. 7. 31. | 1.21% | 4.85% | 0.03 | 13.99 | 0.62 |
| 55. | 2023. 8. 31. | -4.41% | -1.77% | 29.78 | 8.28 | 15.70 |
| 56. | 2023. 9. 30. | -4.77% | -4.87% | 33.75 | 35.73 | 34.73 |
| 57. | 2023. 10. 31. | -3.64% | -2.20% | 21.89 | 10.92 | 15.46 |
| 58. | 2023. 11. 30. | 3.84% | 8.92% | 7.84 | 61.03 | 21.87 |
| 59. | 2023. 12. 31. | 0.92% | 4.42% | 0.01 | 11.00 | -0.40 |
| 합계 (Σ): | 1,242.35 | 1,634.30 | 886.66 | |||
모두 표시
분산PEP = Σ(RPEP,t–RPEP)2 ÷ (59 – 1)
= 1,242.35 ÷ (59 – 1)
= 21.42
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산PEP, S&P 500 = Σ(RPEP,t–RPEP)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 886.66 ÷ (59 – 1)
= 15.29
체계적인 위험 추정 (β)
| 분산PEP | 21.42 |
| 분산S&P 500 | 28.18 |
| 공분산PEP, S&P 500 | 15.29 |
| 상관 계수PEP, S&P 5001 | 0.62 |
| βPEP2 | 0.54 |
| αPEP3 | 0.44% |
계산
1 상관 계수PEP, S&P 500
= 공분산PEP, S&P 500 ÷ (표준 편차PEP × 표준 편차S&P 500)
= 15.29 ÷ (4.63% × 5.31%)
= 0.62
2 βPEP
= 공분산PEP, S&P 500 ÷ 분산S&P 500
= 15.29 ÷ 28.18
= 0.54
3 αPEP
= 평균의PEP – βPEP × 평균의S&P 500
= 1.04% – 0.54 × 1.11%
= 0.44%
예상 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.56% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.77% |
| 보통주의 체계적 위험PepsiCo | βPEP | 0.54 |
| PepsiCo 보통주 예상 수익률3 | E(RPEP) | 9.55% |
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(RPEP) = RF + βPEP [E(RM) – RF]
= 4.56% + 0.54 [13.77% – 4.56%]
= 9.55%