자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Kellanova의 보통주와 같은 위험 자산에 대한 기대 또는 필요한 수익률을 나타냅니다.
수익률
Kellanova, 월별 수익률
| Kellanova (K) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값K,t1 | 피제수K,t1 | RK,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $59.01 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $56.26 | -4.66% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $57.38 | $0.56 | 2.99% | 2,834.40 | 1.79% |
| 3. | 2019. 4. 30. | $60.30 | 5.09% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $52.54 | $0.56 | 5.21% | 4,567.80 | 8.92% |
| 59. | 2023. 12. 31. | $55.91 | 6.41% | 4,769.83 | 4.42% | |
| 평균의 (R): | 0.36% | 1.11% | ||||
| 표준 편차: | 5.31% | 5.31% | ||||
| Kellanova (K) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값K,t1 | 피제수K,t1 | RK,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $59.01 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $56.26 | -4.66% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $57.38 | $0.56 | 2.99% | 2,834.40 | 1.79% |
| 3. | 2019. 4. 30. | $60.30 | 5.09% | 2,945.83 | 3.93% | |
| 4. | 2019. 5. 31. | $52.56 | $0.56 | -11.91% | 2,752.06 | -6.58% |
| 5. | 2019. 6. 30. | $53.57 | 1.92% | 2,941.76 | 6.89% | |
| 6. | 2019. 7. 31. | $58.22 | 8.68% | 2,980.38 | 1.31% | |
| 7. | 2019. 8. 31. | $62.80 | $0.57 | 8.85% | 2,926.46 | -1.81% |
| 8. | 2019. 9. 30. | $64.35 | 2.47% | 2,976.74 | 1.72% | |
| 9. | 2019. 10. 31. | $63.53 | -1.27% | 3,037.56 | 2.04% | |
| 10. | 2019. 11. 30. | $65.12 | $0.57 | 3.40% | 3,140.98 | 3.40% |
| 11. | 2019. 12. 31. | $69.16 | 6.20% | 3,230.78 | 2.86% | |
| 12. | 2020. 1. 31. | $68.21 | -1.37% | 3,225.52 | -0.16% | |
| 13. | 2020. 2. 29. | $60.47 | -11.35% | 2,954.22 | -8.41% | |
| 14. | 2020. 3. 31. | $59.99 | $0.57 | 0.15% | 2,584.59 | -12.51% |
| 15. | 2020. 4. 30. | $65.50 | 9.18% | 2,912.43 | 12.68% | |
| 16. | 2020. 5. 31. | $65.31 | $0.57 | 0.58% | 3,044.31 | 4.53% |
| 17. | 2020. 6. 30. | $66.06 | 1.15% | 3,100.29 | 1.84% | |
| 18. | 2020. 7. 31. | $68.99 | 4.44% | 3,271.12 | 5.51% | |
| 19. | 2020. 8. 31. | $70.91 | $0.57 | 3.61% | 3,500.31 | 7.01% |
| 20. | 2020. 9. 30. | $64.59 | -8.91% | 3,363.00 | -3.92% | |
| 21. | 2020. 10. 31. | $62.89 | -2.63% | 3,269.96 | -2.77% | |
| 22. | 2020. 11. 30. | $63.91 | $0.57 | 2.53% | 3,621.63 | 10.75% |
| 23. | 2020. 12. 31. | $62.23 | -2.63% | 3,756.07 | 3.71% | |
| 24. | 2021. 1. 31. | $58.94 | -5.29% | 3,714.24 | -1.11% | |
| 25. | 2021. 2. 28. | $57.71 | -2.09% | 3,811.15 | 2.61% | |
| 26. | 2021. 3. 31. | $63.30 | $0.57 | 10.67% | 3,972.89 | 4.24% |
| 27. | 2021. 4. 30. | $62.42 | -1.39% | 4,181.17 | 5.24% | |
| 28. | 2021. 5. 31. | $65.49 | $0.58 | 5.85% | 4,204.11 | 0.55% |
| 29. | 2021. 6. 30. | $64.33 | -1.77% | 4,297.50 | 2.22% | |
| 30. | 2021. 7. 31. | $63.36 | -1.51% | 4,395.26 | 2.27% | |
| 31. | 2021. 8. 31. | $63.14 | $0.58 | 0.57% | 4,522.68 | 2.90% |
| 32. | 2021. 9. 30. | $63.92 | 1.24% | 4,307.54 | -4.76% | |
| 33. | 2021. 10. 31. | $61.30 | -4.10% | 4,605.38 | 6.91% | |
| 34. | 2021. 11. 30. | $61.18 | $0.58 | 0.75% | 4,567.00 | -0.83% |
| 35. | 2021. 12. 31. | $64.42 | 5.30% | 4,766.18 | 4.36% | |
| 36. | 2022. 1. 31. | $63.00 | -2.20% | 4,515.55 | -5.26% | |
| 37. | 2022. 2. 28. | $63.94 | $0.58 | 2.41% | 4,373.94 | -3.14% |
| 38. | 2022. 3. 31. | $64.49 | 0.86% | 4,530.41 | 3.58% | |
| 39. | 2022. 4. 30. | $68.50 | 6.22% | 4,131.93 | -8.80% | |
| 40. | 2022. 5. 31. | $69.74 | $0.58 | 2.66% | 4,132.15 | 0.01% |
| 41. | 2022. 6. 30. | $71.34 | 2.29% | 3,785.38 | -8.39% | |
| 42. | 2022. 7. 31. | $73.92 | 3.62% | 4,130.29 | 9.11% | |
| 43. | 2022. 8. 31. | $72.74 | $0.59 | -0.80% | 3,955.00 | -4.24% |
| 44. | 2022. 9. 30. | $69.66 | -4.23% | 3,585.62 | -9.34% | |
| 45. | 2022. 10. 31. | $76.82 | 10.28% | 3,871.98 | 7.99% | |
| 46. | 2022. 11. 30. | $72.95 | $0.59 | -4.27% | 4,080.11 | 5.38% |
| 47. | 2022. 12. 31. | $71.24 | -2.34% | 3,839.50 | -5.90% | |
| 48. | 2023. 1. 31. | $68.58 | -3.73% | 4,076.60 | 6.18% | |
| 49. | 2023. 2. 28. | $65.94 | $0.59 | -2.99% | 3,970.15 | -2.61% |
| 50. | 2023. 3. 31. | $66.96 | 1.55% | 4,109.31 | 3.51% | |
| 51. | 2023. 4. 30. | $69.77 | 4.20% | 4,169.48 | 1.46% | |
| 52. | 2023. 5. 31. | $66.77 | $0.59 | -3.45% | 4,179.83 | 0.25% |
| 53. | 2023. 6. 30. | $67.40 | 0.94% | 4,376.86 | 4.71% | |
| 54. | 2023. 7. 31. | $66.89 | -0.76% | 4,588.96 | 4.85% | |
| 55. | 2023. 8. 31. | $61.02 | $0.60 | -7.88% | 4,507.66 | -1.77% |
| 56. | 2023. 9. 30. | $59.51 | -2.47% | 4,288.05 | -4.87% | |
| 57. | 2023. 10. 31. | $50.47 | -15.19% | 4,193.80 | -2.20% | |
| 58. | 2023. 11. 30. | $52.54 | $0.56 | 5.21% | 4,567.80 | 8.92% |
| 59. | 2023. 12. 31. | $55.91 | 6.41% | 4,769.83 | 4.42% | |
| 평균의 (R): | 0.36% | 1.11% | ||||
| 표준 편차: | 5.31% | 5.31% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 K의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Kellanova, 수익률의 분산 및 공분산 계산
| t | 날짜 | RK,t | RS&P 500,t | (RK,t–RK)2 | (RS&P 500,t–RS&P 500)2 | (RK,t–RK)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | -4.66% | 2.97% | 25.17 | 3.49 | -9.37 |
| 2. | 2019. 3. 31. | 2.99% | 1.79% | 6.91 | 0.47 | 1.81 |
| 3. | 2019. 4. 30. | 5.09% | 3.93% | 22.39 | 7.98 | 13.37 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | 5.21% | 8.92% | 23.56 | 61.03 | 37.92 |
| 59. | 2023. 12. 31. | 6.41% | 4.42% | 36.69 | 11.00 | 20.09 |
| 합계 (Σ): | 1,636.89 | 1,634.30 | 667.29 | |||
| t | 날짜 | RK,t | RS&P 500,t | (RK,t–RK)2 | (RS&P 500,t–RS&P 500)2 | (RK,t–RK)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | -4.66% | 2.97% | 25.17 | 3.49 | -9.37 |
| 2. | 2019. 3. 31. | 2.99% | 1.79% | 6.91 | 0.47 | 1.81 |
| 3. | 2019. 4. 30. | 5.09% | 3.93% | 22.39 | 7.98 | 13.37 |
| 4. | 2019. 5. 31. | -11.91% | -6.58% | 150.40 | 59.04 | 94.23 |
| 5. | 2019. 6. 30. | 1.92% | 6.89% | 2.45 | 33.49 | 9.06 |
| 6. | 2019. 7. 31. | 8.68% | 1.31% | 69.28 | 0.04 | 1.72 |
| 7. | 2019. 8. 31. | 8.85% | -1.81% | 72.06 | 8.50 | -24.75 |
| 8. | 2019. 9. 30. | 2.47% | 1.72% | 4.46 | 0.37 | 1.29 |
| 9. | 2019. 10. 31. | -1.27% | 2.04% | 2.66 | 0.88 | -1.53 |
| 10. | 2019. 11. 30. | 3.40% | 3.40% | 9.26 | 5.28 | 7.00 |
| 11. | 2019. 12. 31. | 6.20% | 2.86% | 34.19 | 3.07 | 10.25 |
| 12. | 2020. 1. 31. | -1.37% | -0.16% | 2.99 | 1.61 | 2.20 |
| 13. | 2020. 2. 29. | -11.35% | -8.41% | 136.98 | 90.57 | 111.39 |
| 14. | 2020. 3. 31. | 0.15% | -12.51% | 0.04 | 185.44 | 2.83 |
| 15. | 2020. 4. 30. | 9.18% | 12.68% | 77.94 | 134.06 | 102.22 |
| 16. | 2020. 5. 31. | 0.58% | 4.53% | 0.05 | 11.71 | 0.76 |
| 17. | 2020. 6. 30. | 1.15% | 1.84% | 0.63 | 0.54 | 0.58 |
| 18. | 2020. 7. 31. | 4.44% | 5.51% | 16.64 | 19.40 | 17.96 |
| 19. | 2020. 8. 31. | 3.61% | 7.01% | 10.58 | 34.82 | 19.19 |
| 20. | 2020. 9. 30. | -8.91% | -3.92% | 85.92 | 25.29 | 46.61 |
| 21. | 2020. 10. 31. | -2.63% | -2.77% | 8.93 | 15.00 | 11.57 |
| 22. | 2020. 11. 30. | 2.53% | 10.75% | 4.72 | 93.10 | 20.95 |
| 23. | 2020. 12. 31. | -2.63% | 3.71% | 8.91 | 6.79 | -7.78 |
| 24. | 2021. 1. 31. | -5.29% | -1.11% | 31.85 | 4.93 | 12.53 |
| 25. | 2021. 2. 28. | -2.09% | 2.61% | 5.97 | 2.26 | -3.67 |
| 26. | 2021. 3. 31. | 10.67% | 4.24% | 106.45 | 9.85 | 32.38 |
| 27. | 2021. 4. 30. | -1.39% | 5.24% | 3.05 | 17.11 | -7.23 |
| 28. | 2021. 5. 31. | 5.85% | 0.55% | 30.15 | 0.31 | -3.06 |
| 29. | 2021. 6. 30. | -1.77% | 2.22% | 4.53 | 1.24 | -2.37 |
| 30. | 2021. 7. 31. | -1.51% | 2.27% | 3.48 | 1.37 | -2.18 |
| 31. | 2021. 8. 31. | 0.57% | 2.90% | 0.04 | 3.22 | 0.38 |
| 32. | 2021. 9. 30. | 1.24% | -4.76% | 0.77 | 34.37 | -5.15 |
| 33. | 2021. 10. 31. | -4.10% | 6.91% | 19.85 | 33.74 | -25.88 |
| 34. | 2021. 11. 30. | 0.75% | -0.83% | 0.16 | 3.76 | -0.76 |
| 35. | 2021. 12. 31. | 5.30% | 4.36% | 24.40 | 10.60 | 16.08 |
| 36. | 2022. 1. 31. | -2.20% | -5.26% | 6.56 | 40.51 | 16.30 |
| 37. | 2022. 2. 28. | 2.41% | -3.14% | 4.23 | 17.99 | -8.72 |
| 38. | 2022. 3. 31. | 0.86% | 3.58% | 0.25 | 6.11 | 1.24 |
| 39. | 2022. 4. 30. | 6.22% | -8.80% | 34.36 | 98.04 | -58.04 |
| 40. | 2022. 5. 31. | 2.66% | 0.01% | 5.29 | 1.21 | -2.53 |
| 41. | 2022. 6. 30. | 2.29% | -8.39% | 3.75 | 90.21 | -18.40 |
| 42. | 2022. 7. 31. | 3.62% | 9.11% | 10.63 | 64.09 | 26.10 |
| 43. | 2022. 8. 31. | -0.80% | -4.24% | 1.33 | 28.62 | 6.18 |
| 44. | 2022. 9. 30. | -4.23% | -9.34% | 21.08 | 109.11 | 47.95 |
| 45. | 2022. 10. 31. | 10.28% | 7.99% | 98.44 | 47.34 | 68.27 |
| 46. | 2022. 11. 30. | -4.27% | 5.38% | 21.40 | 18.23 | -19.75 |
| 47. | 2022. 12. 31. | -2.34% | -5.90% | 7.29 | 49.04 | 18.91 |
| 48. | 2023. 1. 31. | -3.73% | 6.18% | 16.73 | 25.70 | -20.74 |
| 49. | 2023. 2. 28. | -2.99% | -2.61% | 11.19 | 13.82 | 12.44 |
| 50. | 2023. 3. 31. | 1.55% | 3.51% | 1.42 | 5.76 | 2.86 |
| 51. | 2023. 4. 30. | 4.20% | 1.46% | 14.74 | 0.13 | 1.38 |
| 52. | 2023. 5. 31. | -3.45% | 0.25% | 14.52 | 0.74 | 3.27 |
| 53. | 2023. 6. 30. | 0.94% | 4.71% | 0.34 | 13.02 | 2.12 |
| 54. | 2023. 7. 31. | -0.76% | 4.85% | 1.24 | 13.99 | -4.16 |
| 55. | 2023. 8. 31. | -7.88% | -1.77% | 67.82 | 8.28 | 23.70 |
| 56. | 2023. 9. 30. | -2.47% | -4.87% | 8.02 | 35.73 | 16.92 |
| 57. | 2023. 10. 31. | -15.19% | -2.20% | 241.72 | 10.92 | 51.37 |
| 58. | 2023. 11. 30. | 5.21% | 8.92% | 23.56 | 61.03 | 37.92 |
| 59. | 2023. 12. 31. | 6.41% | 4.42% | 36.69 | 11.00 | 20.09 |
| 합계 (Σ): | 1,636.89 | 1,634.30 | 667.29 | |||
모두 보기
분산K = Σ(RK,t–RK)2 ÷ (59 – 1)
= 1,636.89 ÷ (59 – 1)
= 28.22
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산K, S&P 500 = Σ(RK,t–RK)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 667.29 ÷ (59 – 1)
= 11.51
체계적인 위험 추정 (β)
| 분산K | 28.22 |
| 분산S&P 500 | 28.18 |
| 공분산K, S&P 500 | 11.51 |
| 상관 계수K, S&P 5001 | 0.41 |
| βK2 | 0.41 |
| αK3 | -0.09% |
계산
1 상관 계수K, S&P 500
= 공분산K, S&P 500 ÷ (표준 편차K × 표준 편차S&P 500)
= 11.51 ÷ (5.31% × 5.31%)
= 0.41
2 βK
= 공분산K, S&P 500 ÷ 분산S&P 500
= 11.51 ÷ 28.18
= 0.41
3 αK
= 평균의K – βK × 평균의S&P 500
= 0.36% – 0.41 × 1.11%
= -0.09%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.01% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.80% |
| 보통주의 체계적 위험Kellanova | βK | 0.41 |
| Kellanova 보통주의 예상 수익률3 | E(RK) | 8.01% |
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(RK) = RF + βK [E(RM) – RF]
= 4.01% + 0.41 [13.80% – 4.01%]
= 8.01%