자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 UPS보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
United Parcel Service Inc., 월별 수익률
| United Parcel Service Inc. (UPS) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값UPS,t1 | 피제수UPS,t1 | RUPS,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $105.40 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $110.20 | $0.96 | 5.46% | 2,784.49 | 2.97% |
| 2. | 2019. 3. 31. | $111.74 | 1.40% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $106.22 | -4.94% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $151.61 | $1.62 | 8.48% | 4,567.80 | 8.92% |
| 59. | 2023. 12. 31. | $157.23 | 3.71% | 4,769.83 | 4.42% | |
| 평균의 (R): | 1.34% | 1.11% | ||||
| 표준 편차: | 9.01% | 5.31% | ||||
| United Parcel Service Inc. (UPS) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값UPS,t1 | 피제수UPS,t1 | RUPS,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $105.40 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $110.20 | $0.96 | 5.46% | 2,784.49 | 2.97% |
| 2. | 2019. 3. 31. | $111.74 | 1.40% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $106.22 | -4.94% | 2,945.83 | 3.93% | |
| 4. | 2019. 5. 31. | $92.92 | $0.96 | -11.62% | 2,752.06 | -6.58% |
| 5. | 2019. 6. 30. | $103.27 | 11.14% | 2,941.76 | 6.89% | |
| 6. | 2019. 7. 31. | $119.47 | 15.69% | 2,980.38 | 1.31% | |
| 7. | 2019. 8. 31. | $118.66 | $0.96 | 0.13% | 2,926.46 | -1.81% |
| 8. | 2019. 9. 30. | $119.82 | 0.98% | 2,976.74 | 1.72% | |
| 9. | 2019. 10. 31. | $115.17 | -3.88% | 3,037.56 | 2.04% | |
| 10. | 2019. 11. 30. | $119.73 | $0.96 | 4.79% | 3,140.98 | 3.40% |
| 11. | 2019. 12. 31. | $117.06 | -2.23% | 3,230.78 | 2.86% | |
| 12. | 2020. 1. 31. | $103.52 | -11.57% | 3,225.52 | -0.16% | |
| 13. | 2020. 2. 29. | $90.49 | $1.01 | -11.61% | 2,954.22 | -8.41% |
| 14. | 2020. 3. 31. | $93.42 | 3.24% | 2,584.59 | -12.51% | |
| 15. | 2020. 4. 30. | $94.66 | 1.33% | 2,912.43 | 12.68% | |
| 16. | 2020. 5. 31. | $99.71 | $1.01 | 6.40% | 3,044.31 | 4.53% |
| 17. | 2020. 6. 30. | $111.18 | 11.50% | 3,100.29 | 1.84% | |
| 18. | 2020. 7. 31. | $142.76 | 28.40% | 3,271.12 | 5.51% | |
| 19. | 2020. 8. 31. | $163.62 | $1.01 | 15.32% | 3,500.31 | 7.01% |
| 20. | 2020. 9. 30. | $166.63 | 1.84% | 3,363.00 | -3.92% | |
| 21. | 2020. 10. 31. | $157.11 | -5.71% | 3,269.96 | -2.77% | |
| 22. | 2020. 11. 30. | $171.07 | $1.01 | 9.53% | 3,621.63 | 10.75% |
| 23. | 2020. 12. 31. | $168.40 | -1.56% | 3,756.07 | 3.71% | |
| 24. | 2021. 1. 31. | $155.00 | -7.96% | 3,714.24 | -1.11% | |
| 25. | 2021. 2. 28. | $157.83 | $1.02 | 2.48% | 3,811.15 | 2.61% |
| 26. | 2021. 3. 31. | $169.99 | 7.70% | 3,972.89 | 4.24% | |
| 27. | 2021. 4. 30. | $203.86 | 19.92% | 4,181.17 | 5.24% | |
| 28. | 2021. 5. 31. | $214.60 | $1.02 | 5.77% | 4,204.11 | 0.55% |
| 29. | 2021. 6. 30. | $207.97 | -3.09% | 4,297.50 | 2.22% | |
| 30. | 2021. 7. 31. | $191.36 | -7.99% | 4,395.26 | 2.27% | |
| 31. | 2021. 8. 31. | $195.63 | $1.02 | 2.76% | 4,522.68 | 2.90% |
| 32. | 2021. 9. 30. | $182.10 | -6.92% | 4,307.54 | -4.76% | |
| 33. | 2021. 10. 31. | $213.47 | 17.23% | 4,605.38 | 6.91% | |
| 34. | 2021. 11. 30. | $198.37 | $1.02 | -6.60% | 4,567.00 | -0.83% |
| 35. | 2021. 12. 31. | $214.34 | 8.05% | 4,766.18 | 4.36% | |
| 36. | 2022. 1. 31. | $202.21 | -5.66% | 4,515.55 | -5.26% | |
| 37. | 2022. 2. 28. | $210.42 | $1.52 | 4.81% | 4,373.94 | -3.14% |
| 38. | 2022. 3. 31. | $214.46 | 1.92% | 4,530.41 | 3.58% | |
| 39. | 2022. 4. 30. | $179.98 | -16.08% | 4,131.93 | -8.80% | |
| 40. | 2022. 5. 31. | $182.25 | $1.52 | 2.11% | 4,132.15 | 0.01% |
| 41. | 2022. 6. 30. | $182.54 | 0.16% | 3,785.38 | -8.39% | |
| 42. | 2022. 7. 31. | $194.89 | 6.77% | 4,130.29 | 9.11% | |
| 43. | 2022. 8. 31. | $194.51 | $1.52 | 0.58% | 3,955.00 | -4.24% |
| 44. | 2022. 9. 30. | $161.54 | -16.95% | 3,585.62 | -9.34% | |
| 45. | 2022. 10. 31. | $167.77 | 3.86% | 3,871.98 | 7.99% | |
| 46. | 2022. 11. 30. | $189.73 | $1.52 | 14.00% | 4,080.11 | 5.38% |
| 47. | 2022. 12. 31. | $173.84 | -8.38% | 3,839.50 | -5.90% | |
| 48. | 2023. 1. 31. | $185.23 | 6.55% | 4,076.60 | 6.18% | |
| 49. | 2023. 2. 28. | $182.49 | $1.62 | -0.60% | 3,970.15 | -2.61% |
| 50. | 2023. 3. 31. | $193.99 | 6.30% | 4,109.31 | 3.51% | |
| 51. | 2023. 4. 30. | $179.81 | -7.31% | 4,169.48 | 1.46% | |
| 52. | 2023. 5. 31. | $167.00 | $1.62 | -6.22% | 4,179.83 | 0.25% |
| 53. | 2023. 6. 30. | $179.25 | 7.34% | 4,376.86 | 4.71% | |
| 54. | 2023. 7. 31. | $187.13 | 4.40% | 4,588.96 | 4.85% | |
| 55. | 2023. 8. 31. | $169.40 | $1.62 | -8.61% | 4,507.66 | -1.77% |
| 56. | 2023. 9. 30. | $155.87 | -7.99% | 4,288.05 | -4.87% | |
| 57. | 2023. 10. 31. | $141.25 | -9.38% | 4,193.80 | -2.20% | |
| 58. | 2023. 11. 30. | $151.61 | $1.62 | 8.48% | 4,567.80 | 8.92% |
| 59. | 2023. 12. 31. | $157.23 | 3.71% | 4,769.83 | 4.42% | |
| 평균의 (R): | 1.34% | 1.11% | ||||
| 표준 편차: | 9.01% | 5.31% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 t 기간 동안 UPS의 보통주 수익률
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
United Parcel Service Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RUPS,t | RS&P 500,t | (RUPS,t–RUPS)2 | (RS&P 500,t–RS&P 500)2 | (RUPS,t–RUPS)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 5.46% | 2.97% | 16.99 | 3.49 | 7.70 |
| 2. | 2019. 3. 31. | 1.40% | 1.79% | 0.00 | 0.47 | 0.04 |
| 3. | 2019. 4. 30. | -4.94% | 3.93% | 39.47 | 7.98 | -17.75 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | 8.48% | 8.92% | 50.97 | 61.03 | 55.77 |
| 59. | 2023. 12. 31. | 3.71% | 4.42% | 5.59 | 11.00 | 7.84 |
| 합계 (Σ): | 4,712.90 | 1,634.30 | 1,724.48 | |||
| t | 날짜 | RUPS,t | RS&P 500,t | (RUPS,t–RUPS)2 | (RS&P 500,t–RS&P 500)2 | (RUPS,t–RUPS)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 5.46% | 2.97% | 16.99 | 3.49 | 7.70 |
| 2. | 2019. 3. 31. | 1.40% | 1.79% | 0.00 | 0.47 | 0.04 |
| 3. | 2019. 4. 30. | -4.94% | 3.93% | 39.47 | 7.98 | -17.75 |
| 4. | 2019. 5. 31. | -11.62% | -6.58% | 167.96 | 59.04 | 99.58 |
| 5. | 2019. 6. 30. | 11.14% | 6.89% | 95.97 | 33.49 | 56.69 |
| 6. | 2019. 7. 31. | 15.69% | 1.31% | 205.77 | 0.04 | 2.97 |
| 7. | 2019. 8. 31. | 0.13% | -1.81% | 1.48 | 8.50 | 3.55 |
| 8. | 2019. 9. 30. | 0.98% | 1.72% | 0.13 | 0.37 | -0.22 |
| 9. | 2019. 10. 31. | -3.88% | 2.04% | 27.28 | 0.88 | -4.90 |
| 10. | 2019. 11. 30. | 4.79% | 3.40% | 11.91 | 5.28 | 7.93 |
| 11. | 2019. 12. 31. | -2.23% | 2.86% | 12.76 | 3.07 | -6.26 |
| 12. | 2020. 1. 31. | -11.57% | -0.16% | 166.65 | 1.61 | 16.38 |
| 13. | 2020. 2. 29. | -11.61% | -8.41% | 167.80 | 90.57 | 123.28 |
| 14. | 2020. 3. 31. | 3.24% | -12.51% | 3.59 | 185.44 | -25.81 |
| 15. | 2020. 4. 30. | 1.33% | 12.68% | 0.00 | 134.06 | -0.17 |
| 16. | 2020. 5. 31. | 6.40% | 4.53% | 25.60 | 11.71 | 17.32 |
| 17. | 2020. 6. 30. | 11.50% | 1.84% | 103.25 | 0.54 | 7.45 |
| 18. | 2020. 7. 31. | 28.40% | 5.51% | 732.35 | 19.40 | 119.19 |
| 19. | 2020. 8. 31. | 15.32% | 7.01% | 195.36 | 34.82 | 82.47 |
| 20. | 2020. 9. 30. | 1.84% | -3.92% | 0.25 | 25.29 | -2.50 |
| 21. | 2020. 10. 31. | -5.71% | -2.77% | 49.78 | 15.00 | 27.32 |
| 22. | 2020. 11. 30. | 9.53% | 10.75% | 67.01 | 93.10 | 78.98 |
| 23. | 2020. 12. 31. | -1.56% | 3.71% | 8.43 | 6.79 | -7.57 |
| 24. | 2021. 1. 31. | -7.96% | -1.11% | 86.48 | 4.93 | 20.64 |
| 25. | 2021. 2. 28. | 2.48% | 2.61% | 1.30 | 2.26 | 1.72 |
| 26. | 2021. 3. 31. | 7.70% | 4.24% | 40.48 | 9.85 | 19.96 |
| 27. | 2021. 4. 30. | 19.92% | 5.24% | 345.30 | 17.11 | 76.87 |
| 28. | 2021. 5. 31. | 5.77% | 0.55% | 19.59 | 0.31 | -2.47 |
| 29. | 2021. 6. 30. | -3.09% | 2.22% | 19.64 | 1.24 | -4.94 |
| 30. | 2021. 7. 31. | -7.99% | 2.27% | 87.03 | 1.37 | -10.91 |
| 31. | 2021. 8. 31. | 2.76% | 2.90% | 2.02 | 3.22 | 2.55 |
| 32. | 2021. 9. 30. | -6.92% | -4.76% | 68.20 | 34.37 | 48.42 |
| 33. | 2021. 10. 31. | 17.23% | 6.91% | 252.31 | 33.74 | 92.27 |
| 34. | 2021. 11. 30. | -6.60% | -0.83% | 63.01 | 3.76 | 15.39 |
| 35. | 2021. 12. 31. | 8.05% | 4.36% | 45.00 | 10.60 | 21.84 |
| 36. | 2022. 1. 31. | -5.66% | -5.26% | 49.02 | 40.51 | 44.56 |
| 37. | 2022. 2. 28. | 4.81% | -3.14% | 12.04 | 17.99 | -14.72 |
| 38. | 2022. 3. 31. | 1.92% | 3.58% | 0.33 | 6.11 | 1.43 |
| 39. | 2022. 4. 30. | -16.08% | -8.80% | 303.46 | 98.04 | 172.48 |
| 40. | 2022. 5. 31. | 2.11% | 0.01% | 0.58 | 1.21 | -0.84 |
| 41. | 2022. 6. 30. | 0.16% | -8.39% | 1.40 | 90.21 | 11.24 |
| 42. | 2022. 7. 31. | 6.77% | 9.11% | 29.41 | 64.09 | 43.42 |
| 43. | 2022. 8. 31. | 0.58% | -4.24% | 0.57 | 28.62 | 4.05 |
| 44. | 2022. 9. 30. | -16.95% | -9.34% | 334.62 | 109.11 | 191.07 |
| 45. | 2022. 10. 31. | 3.86% | 7.99% | 6.32 | 47.34 | 17.30 |
| 46. | 2022. 11. 30. | 14.00% | 5.38% | 160.10 | 18.23 | 54.02 |
| 47. | 2022. 12. 31. | -8.38% | -5.90% | 94.43 | 49.04 | 68.05 |
| 48. | 2023. 1. 31. | 6.55% | 6.18% | 27.14 | 25.70 | 26.41 |
| 49. | 2023. 2. 28. | -0.60% | -2.61% | 3.79 | 13.82 | 7.24 |
| 50. | 2023. 3. 31. | 6.30% | 3.51% | 24.59 | 5.76 | 11.90 |
| 51. | 2023. 4. 30. | -7.31% | 1.46% | 74.86 | 0.13 | -3.10 |
| 52. | 2023. 5. 31. | -6.22% | 0.25% | 57.24 | 0.74 | 6.49 |
| 53. | 2023. 6. 30. | 7.34% | 4.71% | 35.92 | 13.02 | 21.62 |
| 54. | 2023. 7. 31. | 4.40% | 4.85% | 9.33 | 13.99 | 11.42 |
| 55. | 2023. 8. 31. | -8.61% | -1.77% | 99.03 | 8.28 | 28.64 |
| 56. | 2023. 9. 30. | -7.99% | -4.87% | 87.04 | 35.73 | 55.77 |
| 57. | 2023. 10. 31. | -9.38% | -2.20% | 114.96 | 10.92 | 35.42 |
| 58. | 2023. 11. 30. | 8.48% | 8.92% | 50.97 | 61.03 | 55.77 |
| 59. | 2023. 12. 31. | 3.71% | 4.42% | 5.59 | 11.00 | 7.84 |
| 합계 (Σ): | 4,712.90 | 1,634.30 | 1,724.48 | |||
모두 보기
분산UPS = Σ(RUPS,t–RUPS)2 ÷ (59 – 1)
= 4,712.90 ÷ (59 – 1)
= 81.26
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산UPS, S&P 500 = Σ(RUPS,t–RUPS)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,724.48 ÷ (59 – 1)
= 29.73
체계적인 위험 추정 (β)
| 분산UPS | 81.26 |
| 분산S&P 500 | 28.18 |
| 공분산UPS, S&P 500 | 29.73 |
| 상관 계수UPS, S&P 5001 | 0.62 |
| βUPS2 | 1.06 |
| αUPS3 | 0.18% |
계산
1 상관 계수UPS, S&P 500
= 공분산UPS, S&P 500 ÷ (표준 편차UPS × 표준 편차S&P 500)
= 29.73 ÷ (9.01% × 5.31%)
= 0.62
2 βUPS
= 공분산UPS, S&P 500 ÷ 분산S&P 500
= 29.73 ÷ 28.18
= 1.06
3 αUPS
= 평균의UPS – βUPS × 평균의S&P 500
= 1.34% – 1.06 × 1.11%
= 0.18%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.67% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.79% |
| 보통주의 체계적 위험UPS | βUPS | 1.06 |
| UPS 보통주에 대한 예상 수익률3 | E(RUPS) | 14.29% |
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(RUPS) = RF + βUPS [E(RM) – RF]
= 4.67% + 1.06 [13.79% – 4.67%]
= 14.29%