자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Zoetis보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Zoetis Inc., 월별 수익률
| Zoetis Inc. (ZTS) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값ZTS,t1 | 피제수ZTS,t1 | RZTS,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $86.16 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $94.23 | 9.37% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $100.67 | 6.83% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $101.84 | $0.164 | 1.33% | 2,945.83 | 3.93% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $176.67 | 12.53% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $197.37 | 11.72% | 4,769.83 | 4.42% | |
| 평균의 (R): | 1.72% | 1.11% | ||||
| 표준 편차: | 7.08% | 5.31% | ||||
| Zoetis Inc. (ZTS) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값ZTS,t1 | 피제수ZTS,t1 | RZTS,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $86.16 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $94.23 | 9.37% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $100.67 | 6.83% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $101.84 | $0.164 | 1.33% | 2,945.83 | 3.93% |
| 4. | 2019. 5. 31. | $101.05 | -0.78% | 2,752.06 | -6.58% | |
| 5. | 2019. 6. 30. | $113.49 | 12.31% | 2,941.76 | 6.89% | |
| 6. | 2019. 7. 31. | $114.89 | $0.164 | 1.38% | 2,980.38 | 1.31% |
| 7. | 2019. 8. 31. | $126.42 | 10.04% | 2,926.46 | -1.81% | |
| 8. | 2019. 9. 30. | $124.59 | -1.45% | 2,976.74 | 1.72% | |
| 9. | 2019. 10. 31. | $127.92 | $0.164 | 2.80% | 3,037.56 | 2.04% |
| 10. | 2019. 11. 30. | $120.52 | -5.78% | 3,140.98 | 3.40% | |
| 11. | 2019. 12. 31. | $132.35 | 9.82% | 3,230.78 | 2.86% | |
| 12. | 2020. 1. 31. | $134.21 | $0.20 | 1.56% | 3,225.52 | -0.16% |
| 13. | 2020. 2. 29. | $133.23 | -0.73% | 2,954.22 | -8.41% | |
| 14. | 2020. 3. 31. | $117.69 | -11.66% | 2,584.59 | -12.51% | |
| 15. | 2020. 4. 30. | $129.31 | $0.20 | 10.04% | 2,912.43 | 12.68% |
| 16. | 2020. 5. 31. | $139.39 | 7.80% | 3,044.31 | 4.53% | |
| 17. | 2020. 6. 30. | $137.04 | -1.69% | 3,100.29 | 1.84% | |
| 18. | 2020. 7. 31. | $151.68 | $0.20 | 10.83% | 3,271.12 | 5.51% |
| 19. | 2020. 8. 31. | $160.10 | 5.55% | 3,500.31 | 7.01% | |
| 20. | 2020. 9. 30. | $165.37 | 3.29% | 3,363.00 | -3.92% | |
| 21. | 2020. 10. 31. | $158.55 | $0.20 | -4.00% | 3,269.96 | -2.77% |
| 22. | 2020. 11. 30. | $160.38 | 1.15% | 3,621.63 | 10.75% | |
| 23. | 2020. 12. 31. | $165.50 | 3.19% | 3,756.07 | 3.71% | |
| 24. | 2021. 1. 31. | $154.25 | $0.25 | -6.65% | 3,714.24 | -1.11% |
| 25. | 2021. 2. 28. | $155.24 | 0.64% | 3,811.15 | 2.61% | |
| 26. | 2021. 3. 31. | $157.48 | 1.44% | 3,972.89 | 4.24% | |
| 27. | 2021. 4. 30. | $173.03 | $0.25 | 10.03% | 4,181.17 | 5.24% |
| 28. | 2021. 5. 31. | $176.68 | 2.11% | 4,204.11 | 0.55% | |
| 29. | 2021. 6. 30. | $186.36 | 5.48% | 4,297.50 | 2.22% | |
| 30. | 2021. 7. 31. | $202.70 | $0.25 | 8.90% | 4,395.26 | 2.27% |
| 31. | 2021. 8. 31. | $204.56 | 0.92% | 4,522.68 | 2.90% | |
| 32. | 2021. 9. 30. | $194.14 | -5.09% | 4,307.54 | -4.76% | |
| 33. | 2021. 10. 31. | $216.20 | $0.25 | 11.49% | 4,605.38 | 6.91% |
| 34. | 2021. 11. 30. | $222.04 | 2.70% | 4,567.00 | -0.83% | |
| 35. | 2021. 12. 31. | $244.03 | 9.90% | 4,766.18 | 4.36% | |
| 36. | 2022. 1. 31. | $199.79 | $0.33 | -17.99% | 4,515.55 | -5.26% |
| 37. | 2022. 2. 28. | $193.65 | -3.07% | 4,373.94 | -3.14% | |
| 38. | 2022. 3. 31. | $188.59 | -2.61% | 4,530.41 | 3.58% | |
| 39. | 2022. 4. 30. | $177.25 | $0.33 | -5.84% | 4,131.93 | -8.80% |
| 40. | 2022. 5. 31. | $170.93 | -3.57% | 4,132.15 | 0.01% | |
| 41. | 2022. 6. 30. | $171.89 | 0.56% | 3,785.38 | -8.39% | |
| 42. | 2022. 7. 31. | $182.55 | $0.33 | 6.39% | 4,130.29 | 9.11% |
| 43. | 2022. 8. 31. | $156.53 | -14.25% | 3,955.00 | -4.24% | |
| 44. | 2022. 9. 30. | $148.29 | -5.26% | 3,585.62 | -9.34% | |
| 45. | 2022. 10. 31. | $150.78 | $0.33 | 1.90% | 3,871.98 | 7.99% |
| 46. | 2022. 11. 30. | $154.14 | 2.23% | 4,080.11 | 5.38% | |
| 47. | 2022. 12. 31. | $146.55 | -4.92% | 3,839.50 | -5.90% | |
| 48. | 2023. 1. 31. | $165.49 | $0.38 | 13.18% | 4,076.60 | 6.18% |
| 49. | 2023. 2. 28. | $167.00 | 0.91% | 3,970.15 | -2.61% | |
| 50. | 2023. 3. 31. | $166.44 | -0.34% | 4,109.31 | 3.51% | |
| 51. | 2023. 4. 30. | $175.78 | $0.38 | 5.84% | 4,169.48 | 1.46% |
| 52. | 2023. 5. 31. | $163.01 | -7.26% | 4,179.83 | 0.25% | |
| 53. | 2023. 6. 30. | $172.21 | 5.64% | 4,376.86 | 4.71% | |
| 54. | 2023. 7. 31. | $188.09 | $0.38 | 9.44% | 4,588.96 | 4.85% |
| 55. | 2023. 8. 31. | $190.51 | 1.29% | 4,507.66 | -1.77% | |
| 56. | 2023. 9. 30. | $173.98 | -8.68% | 4,288.05 | -4.87% | |
| 57. | 2023. 10. 31. | $157.00 | $0.38 | -9.54% | 4,193.80 | -2.20% |
| 58. | 2023. 11. 30. | $176.67 | 12.53% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $197.37 | 11.72% | 4,769.83 | 4.42% | |
| 평균의 (R): | 1.72% | 1.11% | ||||
| 표준 편차: | 7.08% | 5.31% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 t 기간 동안 ZTS의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Zoetis Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RZTS,t | RS&P 500,t | (RZTS,t–RZTS)2 | (RS&P 500,t–RS&P 500)2 | (RZTS,t–RZTS)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 9.37% | 2.97% | 58.49 | 3.49 | 14.28 |
| 2. | 2019. 3. 31. | 6.83% | 1.79% | 26.18 | 0.47 | 3.51 |
| 3. | 2019. 4. 30. | 1.33% | 3.93% | 0.15 | 7.98 | -1.11 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | 12.53% | 8.92% | 116.87 | 61.03 | 84.45 |
| 59. | 2023. 12. 31. | 11.72% | 4.42% | 99.97 | 11.00 | 33.17 |
| 합계 (Σ): | 2,908.39 | 1,634.30 | 1,446.63 | |||
| t | 날짜 | RZTS,t | RS&P 500,t | (RZTS,t–RZTS)2 | (RS&P 500,t–RS&P 500)2 | (RZTS,t–RZTS)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 9.37% | 2.97% | 58.49 | 3.49 | 14.28 |
| 2. | 2019. 3. 31. | 6.83% | 1.79% | 26.18 | 0.47 | 3.51 |
| 3. | 2019. 4. 30. | 1.33% | 3.93% | 0.15 | 7.98 | -1.11 |
| 4. | 2019. 5. 31. | -0.78% | -6.58% | 6.22 | 59.04 | 19.16 |
| 5. | 2019. 6. 30. | 12.31% | 6.89% | 112.20 | 33.49 | 61.30 |
| 6. | 2019. 7. 31. | 1.38% | 1.31% | 0.12 | 0.04 | -0.07 |
| 7. | 2019. 8. 31. | 10.04% | -1.81% | 69.18 | 8.50 | -24.25 |
| 8. | 2019. 9. 30. | -1.45% | 1.72% | 10.02 | 0.37 | -1.94 |
| 9. | 2019. 10. 31. | 2.80% | 2.04% | 1.18 | 0.88 | 1.02 |
| 10. | 2019. 11. 30. | -5.78% | 3.40% | 56.29 | 5.28 | -17.25 |
| 11. | 2019. 12. 31. | 9.82% | 2.86% | 65.57 | 3.07 | 14.20 |
| 12. | 2020. 1. 31. | 1.56% | -0.16% | 0.03 | 1.61 | 0.21 |
| 13. | 2020. 2. 29. | -0.73% | -8.41% | 5.99 | 90.57 | 23.30 |
| 14. | 2020. 3. 31. | -11.66% | -12.51% | 179.08 | 185.44 | 182.24 |
| 15. | 2020. 4. 30. | 10.04% | 12.68% | 69.31 | 134.06 | 96.39 |
| 16. | 2020. 5. 31. | 7.80% | 4.53% | 36.93 | 11.71 | 20.80 |
| 17. | 2020. 6. 30. | -1.69% | 1.84% | 11.59 | 0.54 | -2.50 |
| 18. | 2020. 7. 31. | 10.83% | 5.51% | 83.01 | 19.40 | 40.13 |
| 19. | 2020. 8. 31. | 5.55% | 7.01% | 14.69 | 34.82 | 22.62 |
| 20. | 2020. 9. 30. | 3.29% | -3.92% | 2.48 | 25.29 | -7.91 |
| 21. | 2020. 10. 31. | -4.00% | -2.77% | 32.73 | 15.00 | 22.16 |
| 22. | 2020. 11. 30. | 1.15% | 10.75% | 0.32 | 93.10 | -5.44 |
| 23. | 2020. 12. 31. | 3.19% | 3.71% | 2.17 | 6.79 | 3.84 |
| 24. | 2021. 1. 31. | -6.65% | -1.11% | 69.97 | 4.93 | 18.57 |
| 25. | 2021. 2. 28. | 0.64% | 2.61% | 1.16 | 2.26 | -1.62 |
| 26. | 2021. 3. 31. | 1.44% | 4.24% | 0.08 | 9.85 | -0.86 |
| 27. | 2021. 4. 30. | 10.03% | 5.24% | 69.14 | 17.11 | 34.40 |
| 28. | 2021. 5. 31. | 2.11% | 0.55% | 0.15 | 0.31 | -0.22 |
| 29. | 2021. 6. 30. | 5.48% | 2.22% | 14.14 | 1.24 | 4.20 |
| 30. | 2021. 7. 31. | 8.90% | 2.27% | 51.61 | 1.37 | 8.40 |
| 31. | 2021. 8. 31. | 0.92% | 2.90% | 0.64 | 3.22 | -1.44 |
| 32. | 2021. 9. 30. | -5.09% | -4.76% | 46.40 | 34.37 | 39.94 |
| 33. | 2021. 10. 31. | 11.49% | 6.91% | 95.52 | 33.74 | 56.77 |
| 34. | 2021. 11. 30. | 2.70% | -0.83% | 0.97 | 3.76 | -1.91 |
| 35. | 2021. 12. 31. | 9.90% | 4.36% | 67.00 | 10.60 | 26.65 |
| 36. | 2022. 1. 31. | -17.99% | -5.26% | 388.56 | 40.51 | 125.45 |
| 37. | 2022. 2. 28. | -3.07% | -3.14% | 22.96 | 17.99 | 20.32 |
| 38. | 2022. 3. 31. | -2.61% | 3.58% | 18.76 | 6.11 | -10.70 |
| 39. | 2022. 4. 30. | -5.84% | -8.80% | 57.10 | 98.04 | 74.82 |
| 40. | 2022. 5. 31. | -3.57% | 0.01% | 27.92 | 1.21 | 5.81 |
| 41. | 2022. 6. 30. | 0.56% | -8.39% | 1.34 | 90.21 | 10.98 |
| 42. | 2022. 7. 31. | 6.39% | 9.11% | 21.86 | 64.09 | 37.43 |
| 43. | 2022. 8. 31. | -14.25% | -4.24% | 255.10 | 28.62 | 85.45 |
| 44. | 2022. 9. 30. | -5.26% | -9.34% | 48.75 | 109.11 | 72.93 |
| 45. | 2022. 10. 31. | 1.90% | 7.99% | 0.03 | 47.34 | 1.26 |
| 46. | 2022. 11. 30. | 2.23% | 5.38% | 0.26 | 18.23 | 2.18 |
| 47. | 2022. 12. 31. | -4.92% | -5.90% | 44.12 | 49.04 | 46.52 |
| 48. | 2023. 1. 31. | 13.18% | 6.18% | 131.45 | 25.70 | 58.12 |
| 49. | 2023. 2. 28. | 0.91% | -2.61% | 0.65 | 13.82 | 2.99 |
| 50. | 2023. 3. 31. | -0.34% | 3.51% | 4.22 | 5.76 | -4.93 |
| 51. | 2023. 4. 30. | 5.84% | 1.46% | 16.99 | 0.13 | 1.48 |
| 52. | 2023. 5. 31. | -7.26% | 0.25% | 80.69 | 0.74 | 7.70 |
| 53. | 2023. 6. 30. | 5.64% | 4.71% | 15.41 | 13.02 | 14.16 |
| 54. | 2023. 7. 31. | 9.44% | 4.85% | 59.66 | 13.99 | 28.89 |
| 55. | 2023. 8. 31. | 1.29% | -1.77% | 0.19 | 8.28 | 1.24 |
| 56. | 2023. 9. 30. | -8.68% | -4.87% | 108.05 | 35.73 | 62.14 |
| 57. | 2023. 10. 31. | -9.54% | -2.20% | 126.78 | 10.92 | 37.20 |
| 58. | 2023. 11. 30. | 12.53% | 8.92% | 116.87 | 61.03 | 84.45 |
| 59. | 2023. 12. 31. | 11.72% | 4.42% | 99.97 | 11.00 | 33.17 |
| 합계 (Σ): | 2,908.39 | 1,634.30 | 1,446.63 | |||
모두 보기
분산ZTS = Σ(RZTS,t–RZTS)2 ÷ (59 – 1)
= 2,908.39 ÷ (59 – 1)
= 50.14
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산ZTS, S&P 500 = Σ(RZTS,t–RZTS)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,446.63 ÷ (59 – 1)
= 24.94
체계적인 위험 추정 (β)
| 분산ZTS | 50.14 |
| 분산S&P 500 | 28.18 |
| 공분산ZTS, S&P 500 | 24.94 |
| 상관 계수ZTS, S&P 5001 | 0.66 |
| βZTS2 | 0.89 |
| αZTS3 | 0.74% |
계산
1 상관 계수ZTS, S&P 500
= 공분산ZTS, S&P 500 ÷ (표준 편차ZTS × 표준 편차S&P 500)
= 24.94 ÷ (7.08% × 5.31%)
= 0.66
2 βZTS
= 공분산ZTS, S&P 500 ÷ 분산S&P 500
= 24.94 ÷ 28.18
= 0.89
3 αZTS
= 평균의ZTS – βZTS × 평균의S&P 500
= 1.72% – 0.89 × 1.11%
= 0.74%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.67% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.79% |
| 보통주의 체계적 위험Zoetis | βZTS | 0.89 |
| Zoetis 보통주에 대한 예상 수익률3 | E(RZTS) | 12.74% |
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(RZTS) = RF + βZTS [E(RM) – RF]
= 4.67% + 0.89 [13.79% – 4.67%]
= 12.74%