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 |
| 2021. 1. 31. | $155.00 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $157.83 | $1.02 | 2.48% | 3,811.15 | 2.61% |
| 2. | 2021. 3. 31. | $169.99 | 7.70% | 3,972.89 | 4.24% | |
| 3. | 2021. 4. 30. | $203.86 | 19.92% | 4,181.17 | 5.24% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | $95.79 | $1.64 | 1.05% | 6,849.09 | 0.13% |
| 59. | 2025. 12. 31. | $99.19 | 3.55% | 6,845.50 | -0.05% | |
| 평균의 (R): | -0.10% | 1.14% | ||||
| 표준 편차: | 7.96% | 4.37% | ||||
| 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 |
| 2021. 1. 31. | $155.00 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $157.83 | $1.02 | 2.48% | 3,811.15 | 2.61% |
| 2. | 2021. 3. 31. | $169.99 | 7.70% | 3,972.89 | 4.24% | |
| 3. | 2021. 4. 30. | $203.86 | 19.92% | 4,181.17 | 5.24% | |
| 4. | 2021. 5. 31. | $214.60 | $1.02 | 5.77% | 4,204.11 | 0.55% |
| 5. | 2021. 6. 30. | $207.97 | -3.09% | 4,297.50 | 2.22% | |
| 6. | 2021. 7. 31. | $191.36 | -7.99% | 4,395.26 | 2.27% | |
| 7. | 2021. 8. 31. | $195.63 | $1.02 | 2.76% | 4,522.68 | 2.90% |
| 8. | 2021. 9. 30. | $182.10 | -6.92% | 4,307.54 | -4.76% | |
| 9. | 2021. 10. 31. | $213.47 | 17.23% | 4,605.38 | 6.91% | |
| 10. | 2021. 11. 30. | $198.37 | $1.02 | -6.60% | 4,567.00 | -0.83% |
| 11. | 2021. 12. 31. | $214.34 | 8.05% | 4,766.18 | 4.36% | |
| 12. | 2022. 1. 31. | $202.21 | -5.66% | 4,515.55 | -5.26% | |
| 13. | 2022. 2. 28. | $210.42 | $1.52 | 4.81% | 4,373.94 | -3.14% |
| 14. | 2022. 3. 31. | $214.46 | 1.92% | 4,530.41 | 3.58% | |
| 15. | 2022. 4. 30. | $179.98 | -16.08% | 4,131.93 | -8.80% | |
| 16. | 2022. 5. 31. | $182.25 | $1.52 | 2.11% | 4,132.15 | 0.01% |
| 17. | 2022. 6. 30. | $182.54 | 0.16% | 3,785.38 | -8.39% | |
| 18. | 2022. 7. 31. | $194.89 | 6.77% | 4,130.29 | 9.11% | |
| 19. | 2022. 8. 31. | $194.51 | $1.52 | 0.58% | 3,955.00 | -4.24% |
| 20. | 2022. 9. 30. | $161.54 | -16.95% | 3,585.62 | -9.34% | |
| 21. | 2022. 10. 31. | $167.77 | 3.86% | 3,871.98 | 7.99% | |
| 22. | 2022. 11. 30. | $189.73 | $1.52 | 14.00% | 4,080.11 | 5.38% |
| 23. | 2022. 12. 31. | $173.84 | -8.38% | 3,839.50 | -5.90% | |
| 24. | 2023. 1. 31. | $185.23 | 6.55% | 4,076.60 | 6.18% | |
| 25. | 2023. 2. 28. | $182.49 | $1.62 | -0.60% | 3,970.15 | -2.61% |
| 26. | 2023. 3. 31. | $193.99 | 6.30% | 4,109.31 | 3.51% | |
| 27. | 2023. 4. 30. | $179.81 | -7.31% | 4,169.48 | 1.46% | |
| 28. | 2023. 5. 31. | $167.00 | $1.62 | -6.22% | 4,179.83 | 0.25% |
| 29. | 2023. 6. 30. | $179.25 | 7.34% | 4,376.86 | 4.71% | |
| 30. | 2023. 7. 31. | $187.13 | 4.40% | 4,588.96 | 4.85% | |
| 31. | 2023. 8. 31. | $169.40 | $1.62 | -8.61% | 4,507.66 | -1.77% |
| 32. | 2023. 9. 30. | $155.87 | -7.99% | 4,288.05 | -4.87% | |
| 33. | 2023. 10. 31. | $141.25 | -9.38% | 4,193.80 | -2.20% | |
| 34. | 2023. 11. 30. | $151.61 | $1.62 | 8.48% | 4,567.80 | 8.92% |
| 35. | 2023. 12. 31. | $157.23 | 3.71% | 4,769.83 | 4.42% | |
| 36. | 2024. 1. 31. | $141.90 | -9.75% | 4,845.65 | 1.59% | |
| 37. | 2024. 2. 29. | $148.26 | $1.63 | 5.63% | 5,096.27 | 5.17% |
| 38. | 2024. 3. 31. | $148.63 | 0.25% | 5,254.35 | 3.10% | |
| 39. | 2024. 4. 30. | $147.48 | -0.77% | 5,035.69 | -4.16% | |
| 40. | 2024. 5. 31. | $138.93 | $1.63 | -4.69% | 5,277.51 | 4.80% |
| 41. | 2024. 6. 30. | $136.85 | -1.50% | 5,460.48 | 3.47% | |
| 42. | 2024. 7. 31. | $130.37 | -4.74% | 5,522.30 | 1.13% | |
| 43. | 2024. 8. 31. | $128.55 | $1.63 | -0.15% | 5,648.40 | 2.28% |
| 44. | 2024. 9. 30. | $136.34 | 6.06% | 5,762.48 | 2.02% | |
| 45. | 2024. 10. 31. | $134.06 | -1.67% | 5,705.45 | -0.99% | |
| 46. | 2024. 11. 30. | $135.72 | $1.63 | 2.45% | 6,032.38 | 5.73% |
| 47. | 2024. 12. 31. | $126.10 | -7.09% | 5,881.63 | -2.50% | |
| 48. | 2025. 1. 31. | $114.23 | -9.41% | 6,040.53 | 2.70% | |
| 49. | 2025. 2. 28. | $119.03 | $1.64 | 5.64% | 5,954.50 | -1.42% |
| 50. | 2025. 3. 31. | $109.99 | -7.59% | 5,611.85 | -5.75% | |
| 51. | 2025. 4. 30. | $95.30 | -13.36% | 5,569.06 | -0.76% | |
| 52. | 2025. 5. 31. | $97.54 | $1.64 | 4.07% | 5,911.69 | 6.15% |
| 53. | 2025. 6. 30. | $100.94 | 3.49% | 6,204.95 | 4.96% | |
| 54. | 2025. 7. 31. | $86.16 | -14.64% | 6,339.39 | 2.17% | |
| 55. | 2025. 8. 31. | $87.44 | $1.64 | 3.39% | 6,460.26 | 1.91% |
| 56. | 2025. 9. 30. | $83.53 | -4.47% | 6,688.46 | 3.53% | |
| 57. | 2025. 10. 31. | $96.42 | 15.43% | 6,840.20 | 2.27% | |
| 58. | 2025. 11. 30. | $95.79 | $1.64 | 1.05% | 6,849.09 | 0.13% |
| 59. | 2025. 12. 31. | $99.19 | 3.55% | 6,845.50 | -0.05% | |
| 평균의 (R): | -0.10% | 1.14% | ||||
| 표준 편차: | 7.96% | 4.37% | ||||
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. | 2021. 2. 28. | 2.48% | 2.61% | 6.66 | 2.17 | 3.80 |
| 2. | 2021. 3. 31. | 7.70% | 4.24% | 60.86 | 9.66 | 24.24 |
| 3. | 2021. 4. 30. | 19.92% | 5.24% | 400.85 | 16.86 | 82.21 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | 1.05% | 0.13% | 1.31 | 1.01 | -1.15 |
| 59. | 2025. 12. 31. | 3.55% | -0.05% | 13.29 | 1.41 | -4.33 |
| 합계 (Σ): | 3,677.92 | 1,108.23 | 1,224.50 | |||
| 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. | 2021. 2. 28. | 2.48% | 2.61% | 6.66 | 2.17 | 3.80 |
| 2. | 2021. 3. 31. | 7.70% | 4.24% | 60.86 | 9.66 | 24.24 |
| 3. | 2021. 4. 30. | 19.92% | 5.24% | 400.85 | 16.86 | 82.21 |
| 4. | 2021. 5. 31. | 5.77% | 0.55% | 34.40 | 0.35 | -3.45 |
| 5. | 2021. 6. 30. | -3.09% | 2.22% | 8.96 | 1.18 | -3.25 |
| 6. | 2021. 7. 31. | -7.99% | 2.27% | 62.26 | 1.30 | -8.98 |
| 7. | 2021. 8. 31. | 2.76% | 2.90% | 8.18 | 3.11 | 5.04 |
| 8. | 2021. 9. 30. | -6.92% | -4.76% | 46.51 | 34.73 | 40.19 |
| 9. | 2021. 10. 31. | 17.23% | 6.91% | 300.10 | 33.39 | 100.10 |
| 10. | 2021. 11. 30. | -6.60% | -0.83% | 42.24 | 3.88 | 12.80 |
| 11. | 2021. 12. 31. | 8.05% | 4.36% | 66.38 | 10.40 | 26.28 |
| 12. | 2022. 1. 31. | -5.66% | -5.26% | 30.94 | 40.89 | 35.57 |
| 13. | 2022. 2. 28. | 4.81% | -3.14% | 24.09 | 18.25 | -20.97 |
| 14. | 2022. 3. 31. | 1.92% | 3.58% | 4.07 | 5.96 | 4.92 |
| 15. | 2022. 4. 30. | -16.08% | -8.80% | 255.40 | 98.64 | 158.72 |
| 16. | 2022. 5. 31. | 2.11% | 0.01% | 4.85 | 1.28 | -2.49 |
| 17. | 2022. 6. 30. | 0.16% | -8.39% | 0.07 | 90.79 | -2.44 |
| 18. | 2022. 7. 31. | 6.77% | 9.11% | 47.09 | 63.61 | 54.73 |
| 19. | 2022. 8. 31. | 0.58% | -4.24% | 0.46 | 28.95 | -3.67 |
| 20. | 2022. 9. 30. | -16.95% | -9.34% | 284.05 | 109.74 | 176.56 |
| 21. | 2022. 10. 31. | 3.86% | 7.99% | 15.63 | 46.93 | 27.08 |
| 22. | 2022. 11. 30. | 14.00% | 5.38% | 198.58 | 17.97 | 59.74 |
| 23. | 2022. 12. 31. | -8.38% | -5.90% | 68.53 | 49.47 | 58.23 |
| 24. | 2023. 1. 31. | 6.55% | 6.18% | 44.20 | 25.39 | 33.50 |
| 25. | 2023. 2. 28. | -0.60% | -2.61% | 0.26 | 14.04 | 1.90 |
| 26. | 2023. 3. 31. | 6.30% | 3.51% | 40.94 | 5.61 | 15.16 |
| 27. | 2023. 4. 30. | -7.31% | 1.46% | 52.03 | 0.11 | -2.37 |
| 28. | 2023. 5. 31. | -6.22% | 0.25% | 37.54 | 0.79 | 5.44 |
| 29. | 2023. 6. 30. | 7.34% | 4.71% | 55.23 | 12.80 | 26.59 |
| 30. | 2023. 7. 31. | 4.40% | 4.85% | 20.18 | 13.76 | 16.67 |
| 31. | 2023. 8. 31. | -8.61% | -1.77% | 72.46 | 8.46 | 24.75 |
| 32. | 2023. 9. 30. | -7.99% | -4.87% | 62.26 | 36.10 | 47.41 |
| 33. | 2023. 10. 31. | -9.38% | -2.20% | 86.18 | 11.12 | 30.95 |
| 34. | 2023. 11. 30. | 8.48% | 8.92% | 73.58 | 60.56 | 66.75 |
| 35. | 2023. 12. 31. | 3.71% | 4.42% | 14.47 | 10.80 | 12.50 |
| 36. | 2024. 1. 31. | -9.75% | 1.59% | 93.19 | 0.21 | -4.38 |
| 37. | 2024. 2. 29. | 5.63% | 5.17% | 32.80 | 16.29 | 23.11 |
| 38. | 2024. 3. 31. | 0.25% | 3.10% | 0.12 | 3.86 | 0.68 |
| 39. | 2024. 4. 30. | -0.77% | -4.16% | 0.46 | 28.06 | 3.59 |
| 40. | 2024. 5. 31. | -4.69% | 4.80% | 21.12 | 13.44 | -16.85 |
| 41. | 2024. 6. 30. | -1.50% | 3.47% | 1.96 | 5.43 | -3.26 |
| 42. | 2024. 7. 31. | -4.74% | 1.13% | 21.52 | 0.00 | 0.02 |
| 43. | 2024. 8. 31. | -0.15% | 2.28% | 0.00 | 1.32 | -0.06 |
| 44. | 2024. 9. 30. | 6.06% | 2.02% | 37.90 | 0.78 | 5.44 |
| 45. | 2024. 10. 31. | -1.67% | -0.99% | 2.48 | 4.52 | 3.35 |
| 46. | 2024. 11. 30. | 2.45% | 5.73% | 6.51 | 21.10 | 11.72 |
| 47. | 2024. 12. 31. | -7.09% | -2.50% | 48.88 | 13.21 | 25.42 |
| 48. | 2025. 1. 31. | -9.41% | 2.70% | 86.80 | 2.45 | -14.59 |
| 49. | 2025. 2. 28. | 5.64% | -1.42% | 32.88 | 6.56 | -14.68 |
| 50. | 2025. 3. 31. | -7.59% | -5.75% | 56.22 | 47.48 | 51.67 |
| 51. | 2025. 4. 30. | -13.36% | -0.76% | 175.81 | 3.60 | 25.17 |
| 52. | 2025. 5. 31. | 4.07% | 6.15% | 17.37 | 25.16 | 20.91 |
| 53. | 2025. 6. 30. | 3.49% | 4.96% | 12.83 | 14.63 | 13.70 |
| 54. | 2025. 7. 31. | -14.64% | 2.17% | 211.58 | 1.06 | -14.99 |
| 55. | 2025. 8. 31. | 3.39% | 1.91% | 12.15 | 0.59 | 2.69 |
| 56. | 2025. 9. 30. | -4.47% | 3.53% | 19.14 | 5.74 | -10.48 |
| 57. | 2025. 10. 31. | 15.43% | 2.27% | 241.12 | 1.28 | 17.59 |
| 58. | 2025. 11. 30. | 1.05% | 0.13% | 1.31 | 1.01 | -1.15 |
| 59. | 2025. 12. 31. | 3.55% | -0.05% | 13.29 | 1.41 | -4.33 |
| 합계 (Σ): | 3,677.92 | 1,108.23 | 1,224.50 | |||
모두 보기
분산UPS = Σ(RUPS,t–RUPS)2 ÷ (59 – 1)
= 3,677.92 ÷ (59 – 1)
= 63.41
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,108.23 ÷ (59 – 1)
= 19.11
공분산UPS, S&P 500 = Σ(RUPS,t–RUPS)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,224.50 ÷ (59 – 1)
= 21.11
체계적인 위험 추정 (β)
| 분산UPS | 63.41 |
| 분산S&P 500 | 19.11 |
| 공분산UPS, S&P 500 | 21.11 |
| 상관 계수UPS, S&P 5001 | 0.61 |
| βUPS2 | 1.10 |
| αUPS3 | -1.35% |
계산
1 상관 계수UPS, S&P 500
= 공분산UPS, S&P 500 ÷ (표준 편차UPS × 표준 편차S&P 500)
= 21.11 ÷ (7.96% × 4.37%)
= 0.61
2 βUPS
= 공분산UPS, S&P 500 ÷ 분산S&P 500
= 21.11 ÷ 19.11
= 1.10
3 αUPS
= 평균의UPS – βUPS × 평균의S&P 500
= -0.10% – 1.10 × 1.14%
= -1.35%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.54% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 17.37% |
| 보통주의 체계적 위험UPS | βUPS | 1.10 |
| UPS 보통주에 대한 예상 수익률3 | E(RUPS) | 18.71% |
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]
= 4.54% + 1.10 [17.37% – 4.54%]
= 18.71%