자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 United Rentals보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
United Rentals Inc., 월별 수익률
| United Rentals Inc. (URI) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값URI,t1 | 피제수URI,t1 | RURI,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2018. 1. 31. | $181.11 | 2,823.81 | ||||
| 1. | 2018. 2. 28. | $175.09 | -3.32% | 2,713.83 | -3.89% | |
| 2. | 2018. 3. 31. | $172.73 | -1.35% | 2,640.87 | -2.69% | |
| 3. | 2018. 4. 30. | $150.00 | -13.16% | 2,648.05 | 0.27% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2022. 11. 30. | $353.03 | 11.82% | 4,080.11 | 5.38% | |
| 59. | 2022. 12. 31. | $355.42 | 0.68% | 3,839.50 | -5.90% | |
| 평균의 (R): | 1.95% | 0.67% | ||||
| 표준 편차: | 12.83% | 5.40% | ||||
| United Rentals Inc. (URI) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값URI,t1 | 피제수URI,t1 | RURI,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2018. 1. 31. | $181.11 | 2,823.81 | ||||
| 1. | 2018. 2. 28. | $175.09 | -3.32% | 2,713.83 | -3.89% | |
| 2. | 2018. 3. 31. | $172.73 | -1.35% | 2,640.87 | -2.69% | |
| 3. | 2018. 4. 30. | $150.00 | -13.16% | 2,648.05 | 0.27% | |
| 4. | 2018. 5. 31. | $159.57 | 6.38% | 2,705.27 | 2.16% | |
| 5. | 2018. 6. 30. | $147.62 | -7.49% | 2,718.37 | 0.48% | |
| 6. | 2018. 7. 31. | $148.80 | 0.80% | 2,816.29 | 3.60% | |
| 7. | 2018. 8. 31. | $155.87 | 4.75% | 2,901.52 | 3.03% | |
| 8. | 2018. 9. 30. | $163.60 | 4.96% | 2,913.98 | 0.43% | |
| 9. | 2018. 10. 31. | $120.07 | -26.61% | 2,711.74 | -6.94% | |
| 10. | 2018. 11. 30. | $117.13 | -2.45% | 2,760.17 | 1.79% | |
| 11. | 2018. 12. 31. | $102.53 | -12.46% | 2,506.85 | -9.18% | |
| 12. | 2019. 1. 31. | $125.26 | 22.17% | 2,704.10 | 7.87% | |
| 13. | 2019. 2. 28. | $134.59 | 7.45% | 2,784.49 | 2.97% | |
| 14. | 2019. 3. 31. | $114.25 | -15.11% | 2,834.40 | 1.79% | |
| 15. | 2019. 4. 30. | $140.92 | 23.34% | 2,945.83 | 3.93% | |
| 16. | 2019. 5. 31. | $110.10 | -21.87% | 2,752.06 | -6.58% | |
| 17. | 2019. 6. 30. | $132.63 | 20.46% | 2,941.76 | 6.89% | |
| 18. | 2019. 7. 31. | $126.55 | -4.58% | 2,980.38 | 1.31% | |
| 19. | 2019. 8. 31. | $112.56 | -11.05% | 2,926.46 | -1.81% | |
| 20. | 2019. 9. 30. | $124.64 | 10.73% | 2,976.74 | 1.72% | |
| 21. | 2019. 10. 31. | $133.57 | 7.16% | 3,037.56 | 2.04% | |
| 22. | 2019. 11. 30. | $153.05 | 14.58% | 3,140.98 | 3.40% | |
| 23. | 2019. 12. 31. | $166.77 | 8.96% | 3,230.78 | 2.86% | |
| 24. | 2020. 1. 31. | $135.69 | -18.64% | 3,225.52 | -0.16% | |
| 25. | 2020. 2. 29. | $132.48 | -2.37% | 2,954.22 | -8.41% | |
| 26. | 2020. 3. 31. | $102.90 | -22.33% | 2,584.59 | -12.51% | |
| 27. | 2020. 4. 30. | $128.50 | 24.88% | 2,912.43 | 12.68% | |
| 28. | 2020. 5. 31. | $138.89 | 8.09% | 3,044.31 | 4.53% | |
| 29. | 2020. 6. 30. | $149.04 | 7.31% | 3,100.29 | 1.84% | |
| 30. | 2020. 7. 31. | $155.37 | 4.25% | 3,271.12 | 5.51% | |
| 31. | 2020. 8. 31. | $177.05 | 13.95% | 3,500.31 | 7.01% | |
| 32. | 2020. 9. 30. | $174.50 | -1.44% | 3,363.00 | -3.92% | |
| 33. | 2020. 10. 31. | $178.29 | 2.17% | 3,269.96 | -2.77% | |
| 34. | 2020. 11. 30. | $226.98 | 27.31% | 3,621.63 | 10.75% | |
| 35. | 2020. 12. 31. | $231.91 | 2.17% | 3,756.07 | 3.71% | |
| 36. | 2021. 1. 31. | $243.01 | 4.79% | 3,714.24 | -1.11% | |
| 37. | 2021. 2. 28. | $297.38 | 22.37% | 3,811.15 | 2.61% | |
| 38. | 2021. 3. 31. | $329.31 | 10.74% | 3,972.89 | 4.24% | |
| 39. | 2021. 4. 30. | $319.95 | -2.84% | 4,181.17 | 5.24% | |
| 40. | 2021. 5. 31. | $333.96 | 4.38% | 4,204.11 | 0.55% | |
| 41. | 2021. 6. 30. | $319.01 | -4.48% | 4,297.50 | 2.22% | |
| 42. | 2021. 7. 31. | $329.55 | 3.30% | 4,395.26 | 2.27% | |
| 43. | 2021. 8. 31. | $352.65 | 7.01% | 4,522.68 | 2.90% | |
| 44. | 2021. 9. 30. | $350.93 | -0.49% | 4,307.54 | -4.76% | |
| 45. | 2021. 10. 31. | $379.11 | 8.03% | 4,605.38 | 6.91% | |
| 46. | 2021. 11. 30. | $338.74 | -10.65% | 4,567.00 | -0.83% | |
| 47. | 2021. 12. 31. | $332.29 | -1.90% | 4,766.18 | 4.36% | |
| 48. | 2022. 1. 31. | $320.12 | -3.66% | 4,515.55 | -5.26% | |
| 49. | 2022. 2. 28. | $321.62 | 0.47% | 4,373.94 | -3.14% | |
| 50. | 2022. 3. 31. | $355.21 | 10.44% | 4,530.41 | 3.58% | |
| 51. | 2022. 4. 30. | $316.52 | -10.89% | 4,131.93 | -8.80% | |
| 52. | 2022. 5. 31. | $298.18 | -5.79% | 4,132.15 | 0.01% | |
| 53. | 2022. 6. 30. | $242.91 | -18.54% | 3,785.38 | -8.39% | |
| 54. | 2022. 7. 31. | $322.67 | 32.84% | 4,130.29 | 9.11% | |
| 55. | 2022. 8. 31. | $292.04 | -9.49% | 3,955.00 | -4.24% | |
| 56. | 2022. 9. 30. | $270.12 | -7.51% | 3,585.62 | -9.34% | |
| 57. | 2022. 10. 31. | $315.71 | 16.88% | 3,871.98 | 7.99% | |
| 58. | 2022. 11. 30. | $353.03 | 11.82% | 4,080.11 | 5.38% | |
| 59. | 2022. 12. 31. | $355.42 | 0.68% | 3,839.50 | -5.90% | |
| 평균의 (R): | 1.95% | 0.67% | ||||
| 표준 편차: | 12.83% | 5.40% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 URI의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
United Rentals Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RURI,t | RS&P 500,t | (RURI,t–RURI)2 | (RS&P 500,t–RS&P 500)2 | (RURI,t–RURI)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018. 2. 28. | -3.32% | -3.89% | 27.83 | 20.81 | 24.06 |
| 2. | 2018. 3. 31. | -1.35% | -2.69% | 10.89 | 11.26 | 11.07 |
| 3. | 2018. 4. 30. | -13.16% | 0.27% | 228.34 | 0.16 | 5.97 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2022. 11. 30. | 11.82% | 5.38% | 97.40 | 22.17 | 46.47 |
| 59. | 2022. 12. 31. | 0.68% | -5.90% | 1.62 | 43.08 | 8.37 |
| 합계 (Σ): | 9,550.56 | 1,691.48 | 3,092.28 | |||
| t | 날짜 | RURI,t | RS&P 500,t | (RURI,t–RURI)2 | (RS&P 500,t–RS&P 500)2 | (RURI,t–RURI)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018. 2. 28. | -3.32% | -3.89% | 27.83 | 20.81 | 24.06 |
| 2. | 2018. 3. 31. | -1.35% | -2.69% | 10.89 | 11.26 | 11.07 |
| 3. | 2018. 4. 30. | -13.16% | 0.27% | 228.34 | 0.16 | 5.97 |
| 4. | 2018. 5. 31. | 6.38% | 2.16% | 19.61 | 2.23 | 6.62 |
| 5. | 2018. 6. 30. | -7.49% | 0.48% | 89.13 | 0.03 | 1.72 |
| 6. | 2018. 7. 31. | 0.80% | 3.60% | 1.33 | 8.62 | -3.38 |
| 7. | 2018. 8. 31. | 4.75% | 3.03% | 7.84 | 5.57 | 6.61 |
| 8. | 2018. 9. 30. | 4.96% | 0.43% | 9.05 | 0.06 | -0.71 |
| 9. | 2018. 10. 31. | -26.61% | -6.94% | 815.63 | 57.87 | 217.25 |
| 10. | 2018. 11. 30. | -2.45% | 1.79% | 19.36 | 1.25 | -4.93 |
| 11. | 2018. 12. 31. | -12.46% | -9.18% | 207.84 | 96.91 | 141.92 |
| 12. | 2019. 1. 31. | 22.17% | 7.87% | 408.74 | 51.87 | 145.60 |
| 13. | 2019. 2. 28. | 7.45% | 2.97% | 30.21 | 5.32 | 12.68 |
| 14. | 2019. 3. 31. | -15.11% | 1.79% | 291.19 | 1.27 | -19.21 |
| 15. | 2019. 4. 30. | 23.34% | 3.93% | 457.61 | 10.66 | 69.84 |
| 16. | 2019. 5. 31. | -21.87% | -6.58% | 567.50 | 52.48 | 172.58 |
| 17. | 2019. 6. 30. | 20.46% | 6.89% | 342.67 | 38.77 | 115.26 |
| 18. | 2019. 7. 31. | -4.58% | 1.31% | 42.72 | 0.42 | -4.22 |
| 19. | 2019. 8. 31. | -11.05% | -1.81% | 169.17 | 6.13 | 32.20 |
| 20. | 2019. 9. 30. | 10.73% | 1.72% | 77.09 | 1.11 | 9.23 |
| 21. | 2019. 10. 31. | 7.16% | 2.04% | 27.17 | 1.89 | 7.18 |
| 22. | 2019. 11. 30. | 14.58% | 3.40% | 159.58 | 7.50 | 34.59 |
| 23. | 2019. 12. 31. | 8.96% | 2.86% | 49.18 | 4.81 | 15.37 |
| 24. | 2020. 1. 31. | -18.64% | -0.16% | 423.87 | 0.69 | 17.08 |
| 25. | 2020. 2. 29. | -2.37% | -8.41% | 18.64 | 82.40 | 39.19 |
| 26. | 2020. 3. 31. | -22.33% | -12.51% | 589.50 | 173.67 | 319.97 |
| 27. | 2020. 4. 30. | 24.88% | 12.68% | 525.64 | 144.43 | 275.53 |
| 28. | 2020. 5. 31. | 8.09% | 4.53% | 37.62 | 14.91 | 23.69 |
| 29. | 2020. 6. 30. | 7.31% | 1.84% | 28.69 | 1.37 | 6.28 |
| 30. | 2020. 7. 31. | 4.25% | 5.51% | 5.27 | 23.46 | 11.12 |
| 31. | 2020. 8. 31. | 13.95% | 7.01% | 144.05 | 40.19 | 76.09 |
| 32. | 2020. 9. 30. | -1.44% | -3.92% | 11.51 | 21.06 | 15.57 |
| 33. | 2020. 10. 31. | 2.17% | -2.77% | 0.05 | 11.79 | -0.76 |
| 34. | 2020. 11. 30. | 27.31% | 10.75% | 643.01 | 101.77 | 255.81 |
| 35. | 2020. 12. 31. | 2.17% | 3.71% | 0.05 | 9.28 | 0.67 |
| 36. | 2021. 1. 31. | 4.79% | -1.11% | 8.03 | 3.17 | -5.05 |
| 37. | 2021. 2. 28. | 22.37% | 2.61% | 417.05 | 3.77 | 39.67 |
| 38. | 2021. 3. 31. | 10.74% | 4.24% | 77.18 | 12.80 | 31.43 |
| 39. | 2021. 4. 30. | -2.84% | 5.24% | 22.98 | 20.94 | -21.94 |
| 40. | 2021. 5. 31. | 4.38% | 0.55% | 5.89 | 0.01 | -0.29 |
| 41. | 2021. 6. 30. | -4.48% | 2.22% | 41.32 | 2.42 | -9.99 |
| 42. | 2021. 7. 31. | 3.30% | 2.27% | 1.83 | 2.59 | 2.17 |
| 43. | 2021. 8. 31. | 7.01% | 2.90% | 25.58 | 4.98 | 11.29 |
| 44. | 2021. 9. 30. | -0.49% | -4.76% | 5.95 | 29.42 | 13.23 |
| 45. | 2021. 10. 31. | 8.03% | 6.91% | 36.95 | 39.03 | 37.98 |
| 46. | 2021. 11. 30. | -10.65% | -0.83% | 158.77 | 2.25 | 18.90 |
| 47. | 2021. 12. 31. | -1.90% | 4.36% | 14.87 | 13.65 | -14.25 |
| 48. | 2022. 1. 31. | -3.66% | -5.26% | 31.52 | 35.11 | 33.27 |
| 49. | 2022. 2. 28. | 0.47% | -3.14% | 2.20 | 14.46 | 5.64 |
| 50. | 2022. 3. 31. | 10.44% | 3.58% | 72.12 | 8.47 | 24.72 |
| 51. | 2022. 4. 30. | -10.89% | -8.80% | 164.97 | 89.54 | 121.53 |
| 52. | 2022. 5. 31. | -5.79% | 0.01% | 60.00 | 0.44 | 5.12 |
| 53. | 2022. 6. 30. | -18.54% | -8.39% | 419.74 | 82.06 | 185.59 |
| 54. | 2022. 7. 31. | 32.84% | 9.11% | 953.79 | 71.32 | 260.81 |
| 55. | 2022. 8. 31. | -9.49% | -4.24% | 130.97 | 24.11 | 56.20 |
| 56. | 2022. 9. 30. | -7.51% | -9.34% | 89.45 | 100.12 | 94.63 |
| 57. | 2022. 10. 31. | 16.88% | 7.99% | 222.78 | 53.58 | 109.25 |
| 58. | 2022. 11. 30. | 11.82% | 5.38% | 97.40 | 22.17 | 46.47 |
| 59. | 2022. 12. 31. | 0.68% | -5.90% | 1.62 | 43.08 | 8.37 |
| 합계 (Σ): | 9,550.56 | 1,691.48 | 3,092.28 | |||
모두 보기
분산URI = Σ(RURI,t–RURI)2 ÷ (59 – 1)
= 9,550.56 ÷ (59 – 1)
= 164.66
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,691.48 ÷ (59 – 1)
= 29.16
공분산URI, S&P 500 = Σ(RURI,t–RURI)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 3,092.28 ÷ (59 – 1)
= 53.32
체계적인 위험 추정 (β)
| 분산URI | 164.66 |
| 분산S&P 500 | 29.16 |
| 공분산URI, S&P 500 | 53.32 |
| 상관 계수URI, S&P 5001 | 0.77 |
| βURI2 | 1.83 |
| αURI3 | 0.73% |
계산
1 상관 계수URI, S&P 500
= 공분산URI, S&P 500 ÷ (표준 편차URI × 표준 편차S&P 500)
= 53.32 ÷ (12.83% × 5.40%)
= 0.77
2 βURI
= 공분산URI, S&P 500 ÷ 분산S&P 500
= 53.32 ÷ 29.16
= 1.83
3 αURI
= 평균의URI – βURI × 평균의S&P 500
= 1.95% – 1.83 × 0.67%
= 0.73%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.60% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.89% |
| 보통주의 체계적 위험United Rentals | βURI | 1.83 |
| United Rentals 보통주에 대한 예상 수익률3 | E(RURI) | 23.41% |
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(RURI) = RF + βURI [E(RM) – RF]
= 4.60% + 1.83 [14.89% – 4.60%]
= 23.41%