자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Hilton의 보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Hilton Worldwide Holdings Inc., 월별 수익률
| Hilton Worldwide Holdings Inc. (HLT) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값HLT,t1 | 피제수HLT,t1 | RHLT,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $74.48 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $83.10 | $0.15 | 11.77% | 2,784.49 | 2.97% |
| 2. | 2019. 3. 31. | $83.11 | 0.01% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $86.99 | 4.67% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $167.52 | $0.15 | 10.65% | 4,567.80 | 8.92% |
| 59. | 2023. 12. 31. | $182.09 | 8.70% | 4,769.83 | 4.42% | |
| 평균의 (R): | 1.99% | 1.11% | ||||
| 표준 편차: | 9.31% | 5.31% | ||||
| Hilton Worldwide Holdings Inc. (HLT) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값HLT,t1 | 피제수HLT,t1 | RHLT,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $74.48 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $83.10 | $0.15 | 11.77% | 2,784.49 | 2.97% |
| 2. | 2019. 3. 31. | $83.11 | 0.01% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $86.99 | 4.67% | 2,945.83 | 3.93% | |
| 4. | 2019. 5. 31. | $89.44 | $0.15 | 2.99% | 2,752.06 | -6.58% |
| 5. | 2019. 6. 30. | $97.74 | 9.28% | 2,941.76 | 6.89% | |
| 6. | 2019. 7. 31. | $96.55 | -1.22% | 2,980.38 | 1.31% | |
| 7. | 2019. 8. 31. | $92.37 | $0.15 | -4.17% | 2,926.46 | -1.81% |
| 8. | 2019. 9. 30. | $93.11 | 0.80% | 2,976.74 | 1.72% | |
| 9. | 2019. 10. 31. | $96.96 | 4.13% | 3,037.56 | 2.04% | |
| 10. | 2019. 11. 30. | $105.00 | $0.15 | 8.45% | 3,140.98 | 3.40% |
| 11. | 2019. 12. 31. | $110.91 | 5.63% | 3,230.78 | 2.86% | |
| 12. | 2020. 1. 31. | $107.80 | -2.80% | 3,225.52 | -0.16% | |
| 13. | 2020. 2. 29. | $97.20 | $0.15 | -9.69% | 2,954.22 | -8.41% |
| 14. | 2020. 3. 31. | $68.24 | -29.79% | 2,584.59 | -12.51% | |
| 15. | 2020. 4. 30. | $75.71 | 10.95% | 2,912.43 | 12.68% | |
| 16. | 2020. 5. 31. | $79.31 | 4.75% | 3,044.31 | 4.53% | |
| 17. | 2020. 6. 30. | $73.45 | -7.39% | 3,100.29 | 1.84% | |
| 18. | 2020. 7. 31. | $75.05 | 2.18% | 3,271.12 | 5.51% | |
| 19. | 2020. 8. 31. | $90.36 | 20.40% | 3,500.31 | 7.01% | |
| 20. | 2020. 9. 30. | $85.32 | -5.58% | 3,363.00 | -3.92% | |
| 21. | 2020. 10. 31. | $87.81 | 2.92% | 3,269.96 | -2.77% | |
| 22. | 2020. 11. 30. | $103.63 | 18.02% | 3,621.63 | 10.75% | |
| 23. | 2020. 12. 31. | $111.26 | 7.36% | 3,756.07 | 3.71% | |
| 24. | 2021. 1. 31. | $101.39 | -8.87% | 3,714.24 | -1.11% | |
| 25. | 2021. 2. 28. | $123.68 | 21.98% | 3,811.15 | 2.61% | |
| 26. | 2021. 3. 31. | $120.92 | -2.23% | 3,972.89 | 4.24% | |
| 27. | 2021. 4. 30. | $128.70 | 6.43% | 4,181.17 | 5.24% | |
| 28. | 2021. 5. 31. | $125.27 | -2.67% | 4,204.11 | 0.55% | |
| 29. | 2021. 6. 30. | $120.62 | -3.71% | 4,297.50 | 2.22% | |
| 30. | 2021. 7. 31. | $131.45 | 8.98% | 4,395.26 | 2.27% | |
| 31. | 2021. 8. 31. | $124.86 | -5.01% | 4,522.68 | 2.90% | |
| 32. | 2021. 9. 30. | $132.11 | 5.81% | 4,307.54 | -4.76% | |
| 33. | 2021. 10. 31. | $143.95 | 8.96% | 4,605.38 | 6.91% | |
| 34. | 2021. 11. 30. | $135.07 | -6.17% | 4,567.00 | -0.83% | |
| 35. | 2021. 12. 31. | $155.99 | 15.49% | 4,766.18 | 4.36% | |
| 36. | 2022. 1. 31. | $145.11 | -6.97% | 4,515.55 | -5.26% | |
| 37. | 2022. 2. 28. | $148.86 | 2.58% | 4,373.94 | -3.14% | |
| 38. | 2022. 3. 31. | $151.74 | 1.93% | 4,530.41 | 3.58% | |
| 39. | 2022. 4. 30. | $155.29 | 2.34% | 4,131.93 | -8.80% | |
| 40. | 2022. 5. 31. | $140.86 | $0.15 | -9.20% | 4,132.15 | 0.01% |
| 41. | 2022. 6. 30. | $111.44 | -20.89% | 3,785.38 | -8.39% | |
| 42. | 2022. 7. 31. | $128.07 | 14.92% | 4,130.29 | 9.11% | |
| 43. | 2022. 8. 31. | $127.36 | $0.15 | -0.44% | 3,955.00 | -4.24% |
| 44. | 2022. 9. 30. | $120.62 | -5.29% | 3,585.62 | -9.34% | |
| 45. | 2022. 10. 31. | $135.26 | 12.14% | 3,871.98 | 7.99% | |
| 46. | 2022. 11. 30. | $142.62 | $0.15 | 5.55% | 4,080.11 | 5.38% |
| 47. | 2022. 12. 31. | $126.36 | -11.40% | 3,839.50 | -5.90% | |
| 48. | 2023. 1. 31. | $145.09 | 14.82% | 4,076.60 | 6.18% | |
| 49. | 2023. 2. 28. | $144.51 | $0.15 | -0.30% | 3,970.15 | -2.61% |
| 50. | 2023. 3. 31. | $140.87 | -2.52% | 4,109.31 | 3.51% | |
| 51. | 2023. 4. 30. | $144.02 | 2.24% | 4,169.48 | 1.46% | |
| 52. | 2023. 5. 31. | $136.12 | $0.15 | -5.38% | 4,179.83 | 0.25% |
| 53. | 2023. 6. 30. | $145.55 | 6.93% | 4,376.86 | 4.71% | |
| 54. | 2023. 7. 31. | $155.49 | 6.83% | 4,588.96 | 4.85% | |
| 55. | 2023. 8. 31. | $148.65 | $0.15 | -4.30% | 4,507.66 | -1.77% |
| 56. | 2023. 9. 30. | $150.18 | 1.03% | 4,288.05 | -4.87% | |
| 57. | 2023. 10. 31. | $151.53 | 0.90% | 4,193.80 | -2.20% | |
| 58. | 2023. 11. 30. | $167.52 | $0.15 | 10.65% | 4,567.80 | 8.92% |
| 59. | 2023. 12. 31. | $182.09 | 8.70% | 4,769.83 | 4.42% | |
| 평균의 (R): | 1.99% | 1.11% | ||||
| 표준 편차: | 9.31% | 5.31% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 HLT의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Hilton Worldwide Holdings Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RHLT,t | RS&P 500,t | (RHLT,t–RHLT)2 | (RS&P 500,t–RS&P 500)2 | (RHLT,t–RHLT)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 11.77% | 2.97% | 95.70 | 3.49 | 18.27 |
| 2. | 2019. 3. 31. | 0.01% | 1.79% | 3.92 | 0.47 | -1.36 |
| 3. | 2019. 4. 30. | 4.67% | 3.93% | 7.16 | 7.98 | 7.56 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | 10.65% | 8.92% | 74.98 | 61.03 | 67.65 |
| 59. | 2023. 12. 31. | 8.70% | 4.42% | 44.96 | 11.00 | 22.24 |
| 합계 (Σ): | 5,022.46 | 1,634.30 | 2,071.12 | |||
| t | 날짜 | RHLT,t | RS&P 500,t | (RHLT,t–RHLT)2 | (RS&P 500,t–RS&P 500)2 | (RHLT,t–RHLT)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 11.77% | 2.97% | 95.70 | 3.49 | 18.27 |
| 2. | 2019. 3. 31. | 0.01% | 1.79% | 3.92 | 0.47 | -1.36 |
| 3. | 2019. 4. 30. | 4.67% | 3.93% | 7.16 | 7.98 | 7.56 |
| 4. | 2019. 5. 31. | 2.99% | -6.58% | 0.99 | 59.04 | -7.66 |
| 5. | 2019. 6. 30. | 9.28% | 6.89% | 53.11 | 33.49 | 42.18 |
| 6. | 2019. 7. 31. | -1.22% | 1.31% | 10.30 | 0.04 | -0.66 |
| 7. | 2019. 8. 31. | -4.17% | -1.81% | 38.02 | 8.50 | 17.97 |
| 8. | 2019. 9. 30. | 0.80% | 1.72% | 1.42 | 0.37 | -0.73 |
| 9. | 2019. 10. 31. | 4.13% | 2.04% | 4.59 | 0.88 | 2.01 |
| 10. | 2019. 11. 30. | 8.45% | 3.40% | 41.66 | 5.28 | 14.84 |
| 11. | 2019. 12. 31. | 5.63% | 2.86% | 13.22 | 3.07 | 6.38 |
| 12. | 2020. 1. 31. | -2.80% | -0.16% | 23.00 | 1.61 | 6.08 |
| 13. | 2020. 2. 29. | -9.69% | -8.41% | 136.56 | 90.57 | 111.21 |
| 14. | 2020. 3. 31. | -29.79% | -12.51% | 1,010.37 | 185.44 | 432.86 |
| 15. | 2020. 4. 30. | 10.95% | 12.68% | 80.18 | 134.06 | 103.68 |
| 16. | 2020. 5. 31. | 4.75% | 4.53% | 7.63 | 11.71 | 9.46 |
| 17. | 2020. 6. 30. | -7.39% | 1.84% | 88.00 | 0.54 | -6.88 |
| 18. | 2020. 7. 31. | 2.18% | 5.51% | 0.03 | 19.40 | 0.82 |
| 19. | 2020. 8. 31. | 20.40% | 7.01% | 338.84 | 34.82 | 108.62 |
| 20. | 2020. 9. 30. | -5.58% | -3.92% | 57.30 | 25.29 | 38.07 |
| 21. | 2020. 10. 31. | 2.92% | -2.77% | 0.86 | 15.00 | -3.59 |
| 22. | 2020. 11. 30. | 18.02% | 10.75% | 256.77 | 93.10 | 154.61 |
| 23. | 2020. 12. 31. | 7.36% | 3.71% | 28.84 | 6.79 | 14.00 |
| 24. | 2021. 1. 31. | -8.87% | -1.11% | 118.01 | 4.93 | 24.11 |
| 25. | 2021. 2. 28. | 21.98% | 2.61% | 399.69 | 2.26 | 30.05 |
| 26. | 2021. 3. 31. | -2.23% | 4.24% | 17.84 | 9.85 | -13.25 |
| 27. | 2021. 4. 30. | 6.43% | 5.24% | 19.73 | 17.11 | 18.37 |
| 28. | 2021. 5. 31. | -2.67% | 0.55% | 21.69 | 0.31 | 2.59 |
| 29. | 2021. 6. 30. | -3.71% | 2.22% | 32.54 | 1.24 | -6.36 |
| 30. | 2021. 7. 31. | 8.98% | 2.27% | 48.81 | 1.37 | 8.17 |
| 31. | 2021. 8. 31. | -5.01% | 2.90% | 49.08 | 3.22 | -12.56 |
| 32. | 2021. 9. 30. | 5.81% | -4.76% | 14.55 | 34.37 | -22.36 |
| 33. | 2021. 10. 31. | 8.96% | 6.91% | 48.58 | 33.74 | 40.49 |
| 34. | 2021. 11. 30. | -6.17% | -0.83% | 66.60 | 3.76 | 15.83 |
| 35. | 2021. 12. 31. | 15.49% | 4.36% | 182.15 | 10.60 | 43.94 |
| 36. | 2022. 1. 31. | -6.97% | -5.26% | 80.41 | 40.51 | 57.07 |
| 37. | 2022. 2. 28. | 2.58% | -3.14% | 0.35 | 17.99 | -2.51 |
| 38. | 2022. 3. 31. | 1.93% | 3.58% | 0.00 | 6.11 | -0.14 |
| 39. | 2022. 4. 30. | 2.34% | -8.80% | 0.12 | 98.04 | -3.44 |
| 40. | 2022. 5. 31. | -9.20% | 0.01% | 125.17 | 1.21 | 12.31 |
| 41. | 2022. 6. 30. | -20.89% | -8.39% | 523.41 | 90.21 | 217.29 |
| 42. | 2022. 7. 31. | 14.92% | 9.11% | 167.20 | 64.09 | 103.52 |
| 43. | 2022. 8. 31. | -0.44% | -4.24% | 5.90 | 28.62 | 13.00 |
| 44. | 2022. 9. 30. | -5.29% | -9.34% | 53.06 | 109.11 | 76.09 |
| 45. | 2022. 10. 31. | 12.14% | 7.99% | 102.93 | 47.34 | 69.80 |
| 46. | 2022. 11. 30. | 5.55% | 5.38% | 12.67 | 18.23 | 15.20 |
| 47. | 2022. 12. 31. | -11.40% | -5.90% | 179.37 | 49.04 | 93.79 |
| 48. | 2023. 1. 31. | 14.82% | 6.18% | 164.63 | 25.70 | 65.04 |
| 49. | 2023. 2. 28. | -0.30% | -2.61% | 5.24 | 13.82 | 8.51 |
| 50. | 2023. 3. 31. | -2.52% | 3.51% | 20.35 | 5.76 | -10.82 |
| 51. | 2023. 4. 30. | 2.24% | 1.46% | 0.06 | 0.13 | 0.09 |
| 52. | 2023. 5. 31. | -5.38% | 0.25% | 54.37 | 0.74 | 6.32 |
| 53. | 2023. 6. 30. | 6.93% | 4.71% | 24.36 | 13.02 | 17.81 |
| 54. | 2023. 7. 31. | 6.83% | 4.85% | 23.40 | 13.99 | 18.09 |
| 55. | 2023. 8. 31. | -4.30% | -1.77% | 39.62 | 8.28 | 18.11 |
| 56. | 2023. 9. 30. | 1.03% | -4.87% | 0.93 | 35.73 | 5.76 |
| 57. | 2023. 10. 31. | 0.90% | -2.20% | 1.19 | 10.92 | 3.61 |
| 58. | 2023. 11. 30. | 10.65% | 8.92% | 74.98 | 61.03 | 67.65 |
| 59. | 2023. 12. 31. | 8.70% | 4.42% | 44.96 | 11.00 | 22.24 |
| 합계 (Σ): | 5,022.46 | 1,634.30 | 2,071.12 | |||
모두 보기
분산HLT = Σ(RHLT,t–RHLT)2 ÷ (59 – 1)
= 5,022.46 ÷ (59 – 1)
= 86.59
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산HLT, S&P 500 = Σ(RHLT,t–RHLT)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,071.12 ÷ (59 – 1)
= 35.71
체계적인 위험 추정 (β)
| 분산HLT | 86.59 |
| 분산S&P 500 | 28.18 |
| 공분산HLT, S&P 500 | 35.71 |
| 상관 계수HLT, S&P 5001 | 0.72 |
| βHLT2 | 1.27 |
| αHLT3 | 0.59% |
계산
1 상관 계수HLT, S&P 500
= 공분산HLT, S&P 500 ÷ (표준 편차HLT × 표준 편차S&P 500)
= 35.71 ÷ (9.31% × 5.31%)
= 0.72
2 βHLT
= 공분산HLT, S&P 500 ÷ 분산S&P 500
= 35.71 ÷ 28.18
= 1.27
3 αHLT
= 평균의HLT – βHLT × 평균의S&P 500
= 1.99% – 1.27 × 1.11%
= 0.59%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.67% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.79% |
| 보통주의 체계적 위험Hilton | βHLT | 1.27 |
| Hilton 보통주에 대한 예상 수익률3 | E(RHLT) | 16.22% |
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(RHLT) = RF + βHLT [E(RM) – RF]
= 4.67% + 1.27 [13.79% – 4.67%]
= 16.22%