자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 HP보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
HP Inc., 월별 수익률
| HP Inc. (HPQ) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값HPQ,t1 | 피제수HPQ,t1 | RHPQ,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2012. 11. 30. | $12.99 | 1,416.18 | ||||
| 1. | 2012. 12. 31. | $14.25 | $0.132 | 10.72% | 1,426.19 | 0.71% |
| 2. | 2013. 1. 31. | $16.51 | 15.86% | 1,498.11 | 5.04% | |
| 3. | 2013. 2. 28. | $20.14 | 21.99% | 1,514.68 | 1.11% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2018. 9. 30. | $25.77 | $0.139 | 5.11% | 2,913.98 | 0.43% |
| 71. | 2018. 10. 31. | $24.14 | -6.33% | 2,711.74 | -6.94% | |
| 평균의 (R): | 1.77% | 0.96% | ||||
| 표준 편차: | 10.53% | 2.87% | ||||
| HP Inc. (HPQ) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값HPQ,t1 | 피제수HPQ,t1 | RHPQ,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2012. 11. 30. | $12.99 | 1,416.18 | ||||
| 1. | 2012. 12. 31. | $14.25 | $0.132 | 10.72% | 1,426.19 | 0.71% |
| 2. | 2013. 1. 31. | $16.51 | 15.86% | 1,498.11 | 5.04% | |
| 3. | 2013. 2. 28. | $20.14 | 21.99% | 1,514.68 | 1.11% | |
| 4. | 2013. 3. 31. | $23.84 | $0.132 | 19.03% | 1,569.19 | 3.60% |
| 5. | 2013. 4. 30. | $20.60 | -13.59% | 1,597.57 | 1.81% | |
| 6. | 2013. 5. 31. | $24.42 | 18.54% | 1,630.74 | 2.08% | |
| 7. | 2013. 6. 30. | $24.80 | $0.1452 | 2.15% | 1,606.28 | -1.50% |
| 8. | 2013. 7. 31. | $25.68 | 3.55% | 1,685.73 | 4.95% | |
| 9. | 2013. 8. 31. | $22.34 | -13.01% | 1,632.97 | -3.13% | |
| 10. | 2013. 9. 30. | $20.99 | $0.1452 | -5.39% | 1,681.55 | 2.97% |
| 11. | 2013. 10. 31. | $24.37 | 16.10% | 1,756.54 | 4.46% | |
| 12. | 2013. 11. 30. | $27.35 | 12.23% | 1,805.81 | 2.80% | |
| 13. | 2013. 12. 31. | $27.98 | $0.1452 | 2.83% | 1,848.36 | 2.36% |
| 14. | 2014. 1. 31. | $29.00 | 3.65% | 1,782.59 | -3.56% | |
| 15. | 2014. 2. 28. | $29.88 | 3.03% | 1,859.45 | 4.31% | |
| 16. | 2014. 3. 31. | $32.36 | $0.1452 | 8.79% | 1,872.34 | 0.69% |
| 17. | 2014. 4. 30. | $33.06 | 2.16% | 1,883.95 | 0.62% | |
| 18. | 2014. 5. 31. | $33.50 | 1.33% | 1,923.57 | 2.10% | |
| 19. | 2014. 6. 30. | $33.68 | $0.16 | 1.01% | 1,960.23 | 1.91% |
| 20. | 2014. 7. 31. | $35.61 | 5.73% | 1,930.67 | -1.51% | |
| 21. | 2014. 8. 31. | $38.00 | 6.71% | 2,003.37 | 3.77% | |
| 22. | 2014. 9. 30. | $35.47 | $0.16 | -6.24% | 1,972.29 | -1.55% |
| 23. | 2014. 10. 31. | $35.88 | 1.16% | 2,018.05 | 2.32% | |
| 24. | 2014. 11. 30. | $39.06 | 8.86% | 2,067.56 | 2.45% | |
| 25. | 2014. 12. 31. | $40.13 | $0.16 | 3.15% | 2,058.90 | -0.42% |
| 26. | 2015. 1. 31. | $36.13 | -9.97% | 1,994.99 | -3.10% | |
| 27. | 2015. 2. 28. | $34.84 | -3.57% | 2,104.50 | 5.49% | |
| 28. | 2015. 3. 31. | $31.16 | $0.16 | -10.10% | 2,067.89 | -1.74% |
| 29. | 2015. 4. 30. | $32.97 | 5.81% | 2,085.51 | 0.85% | |
| 30. | 2015. 5. 31. | $33.40 | 1.30% | 2,107.39 | 1.05% | |
| 31. | 2015. 6. 30. | $30.01 | $0.176 | -9.62% | 2,063.11 | -2.10% |
| 32. | 2015. 7. 31. | $30.52 | 1.70% | 2,103.84 | 1.97% | |
| 33. | 2015. 8. 31. | $28.06 | -8.06% | 1,972.18 | -6.26% | |
| 34. | 2015. 9. 30. | $25.61 | $0.176 | -8.10% | 1,920.03 | -2.64% |
| 35. | 2015. 10. 31. | $26.96 | 5.27% | 2,079.36 | 8.30% | |
| 36. | 2015. 11. 30. | $12.54 | -53.49% | 2,080.41 | 0.05% | |
| 37. | 2015. 12. 31. | $11.84 | $0.124 | -4.59% | 2,043.94 | -1.75% |
| 38. | 2016. 1. 31. | $9.71 | -17.99% | 1,940.24 | -5.07% | |
| 39. | 2016. 2. 29. | $10.69 | 10.09% | 1,932.23 | -0.41% | |
| 40. | 2016. 3. 31. | $12.32 | $0.124 | 16.41% | 2,059.74 | 6.60% |
| 41. | 2016. 4. 30. | $12.27 | -0.41% | 2,065.30 | 0.27% | |
| 42. | 2016. 5. 31. | $13.38 | 9.05% | 2,096.95 | 1.53% | |
| 43. | 2016. 6. 30. | $12.55 | $0.124 | -5.28% | 2,098.86 | 0.09% |
| 44. | 2016. 7. 31. | $14.01 | 11.63% | 2,173.60 | 3.56% | |
| 45. | 2016. 8. 31. | $14.37 | 2.57% | 2,170.95 | -0.12% | |
| 46. | 2016. 9. 30. | $15.53 | $0.124 | 8.94% | 2,168.27 | -0.12% |
| 47. | 2016. 10. 31. | $14.49 | -6.70% | 2,126.15 | -1.94% | |
| 48. | 2016. 11. 30. | $15.40 | 6.28% | 2,198.81 | 3.42% | |
| 49. | 2016. 12. 31. | $14.84 | $0.133 | -2.77% | 2,238.83 | 1.82% |
| 50. | 2017. 1. 31. | $15.05 | 1.42% | 2,278.87 | 1.79% | |
| 51. | 2017. 2. 28. | $17.37 | 15.42% | 2,363.64 | 3.72% | |
| 52. | 2017. 3. 31. | $17.88 | $0.133 | 3.70% | 2,362.72 | -0.04% |
| 53. | 2017. 4. 30. | $18.82 | 5.26% | 2,384.20 | 0.91% | |
| 54. | 2017. 5. 31. | $18.76 | -0.32% | 2,411.80 | 1.16% | |
| 55. | 2017. 6. 30. | $17.48 | $0.133 | -6.11% | 2,423.41 | 0.48% |
| 56. | 2017. 7. 31. | $19.10 | 9.27% | 2,470.30 | 1.93% | |
| 57. | 2017. 8. 31. | $19.08 | -0.10% | 2,471.65 | 0.05% | |
| 58. | 2017. 9. 30. | $19.96 | $0.133 | 5.31% | 2,519.36 | 1.93% |
| 59. | 2017. 10. 31. | $21.55 | 7.97% | 2,575.26 | 2.22% | |
| 60. | 2017. 11. 30. | $21.45 | -0.46% | 2,647.58 | 2.81% | |
| 61. | 2017. 12. 31. | $21.01 | $0.139 | -1.40% | 2,673.61 | 0.98% |
| 62. | 2018. 1. 31. | $23.32 | 10.99% | 2,823.81 | 5.62% | |
| 63. | 2018. 2. 28. | $23.39 | 0.30% | 2,713.83 | -3.89% | |
| 64. | 2018. 3. 31. | $21.92 | $0.139 | -5.69% | 2,640.87 | -2.69% |
| 65. | 2018. 4. 30. | $21.49 | -1.96% | 2,648.05 | 0.27% | |
| 66. | 2018. 5. 31. | $22.03 | 2.51% | 2,705.27 | 2.16% | |
| 67. | 2018. 6. 30. | $22.69 | $0.139 | 3.63% | 2,718.37 | 0.48% |
| 68. | 2018. 7. 31. | $23.08 | 1.72% | 2,816.29 | 3.60% | |
| 69. | 2018. 8. 31. | $24.65 | 6.80% | 2,901.52 | 3.03% | |
| 70. | 2018. 9. 30. | $25.77 | $0.139 | 5.11% | 2,913.98 | 0.43% |
| 71. | 2018. 10. 31. | $24.14 | -6.33% | 2,711.74 | -6.94% | |
| 평균의 (R): | 1.77% | 0.96% | ||||
| 표준 편차: | 10.53% | 2.87% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 HPQ의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
HP Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RHPQ,t | RS&P 500,t | (RHPQ,t–RHPQ)2 | (RS&P 500,t–RS&P 500)2 | (RHPQ,t–RHPQ)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2012. 12. 31. | 10.72% | 0.71% | 80.01 | 0.06 | -2.26 |
| 2. | 2013. 1. 31. | 15.86% | 5.04% | 198.48 | 16.67 | 57.52 |
| 3. | 2013. 2. 28. | 21.99% | 1.11% | 408.66 | 0.02 | 2.96 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2018. 9. 30. | 5.11% | 0.43% | 11.13 | 0.28 | -1.77 |
| 71. | 2018. 10. 31. | -6.33% | -6.94% | 65.55 | 62.41 | 63.96 |
| 합계 (Σ): | 7,757.62 | 576.08 | 1,004.69 | |||
| t | 날짜 | RHPQ,t | RS&P 500,t | (RHPQ,t–RHPQ)2 | (RS&P 500,t–RS&P 500)2 | (RHPQ,t–RHPQ)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2012. 12. 31. | 10.72% | 0.71% | 80.01 | 0.06 | -2.26 |
| 2. | 2013. 1. 31. | 15.86% | 5.04% | 198.48 | 16.67 | 57.52 |
| 3. | 2013. 2. 28. | 21.99% | 1.11% | 408.66 | 0.02 | 2.96 |
| 4. | 2013. 3. 31. | 19.03% | 3.60% | 297.75 | 6.97 | 45.54 |
| 5. | 2013. 4. 30. | -13.59% | 1.81% | 235.99 | 0.72 | -13.04 |
| 6. | 2013. 5. 31. | 18.54% | 2.08% | 281.31 | 1.25 | 18.73 |
| 7. | 2013. 6. 30. | 2.15% | -1.50% | 0.14 | 6.05 | -0.93 |
| 8. | 2013. 7. 31. | 3.55% | 4.95% | 3.16 | 15.89 | 7.08 |
| 9. | 2013. 8. 31. | -13.01% | -3.13% | 218.38 | 16.72 | 60.43 |
| 10. | 2013. 9. 30. | -5.39% | 2.97% | 51.33 | 4.06 | -14.44 |
| 11. | 2013. 10. 31. | 16.10% | 4.46% | 205.39 | 12.25 | 50.16 |
| 12. | 2013. 11. 30. | 12.23% | 2.80% | 109.34 | 3.41 | 19.30 |
| 13. | 2013. 12. 31. | 2.83% | 2.36% | 1.13 | 1.95 | 1.48 |
| 14. | 2014. 1. 31. | 3.65% | -3.56% | 3.51 | 20.41 | -8.47 |
| 15. | 2014. 2. 28. | 3.03% | 4.31% | 1.60 | 11.24 | 4.23 |
| 16. | 2014. 3. 31. | 8.79% | 0.69% | 49.20 | 0.07 | -1.87 |
| 17. | 2014. 4. 30. | 2.16% | 0.62% | 0.15 | 0.12 | -0.13 |
| 18. | 2014. 5. 31. | 1.33% | 2.10% | 0.19 | 1.31 | -0.50 |
| 19. | 2014. 6. 30. | 1.01% | 1.91% | 0.57 | 0.90 | -0.72 |
| 20. | 2014. 7. 31. | 5.73% | -1.51% | 15.67 | 6.09 | -9.77 |
| 21. | 2014. 8. 31. | 6.71% | 3.77% | 24.41 | 7.87 | 13.86 |
| 22. | 2014. 9. 30. | -6.24% | -1.55% | 64.13 | 6.31 | 20.11 |
| 23. | 2014. 10. 31. | 1.16% | 2.32% | 0.38 | 1.85 | -0.84 |
| 24. | 2014. 11. 30. | 8.86% | 2.45% | 50.29 | 2.23 | 10.59 |
| 25. | 2014. 12. 31. | 3.15% | -0.42% | 1.90 | 1.90 | -1.90 |
| 26. | 2015. 1. 31. | -9.97% | -3.10% | 137.80 | 16.51 | 47.70 |
| 27. | 2015. 2. 28. | -3.57% | 5.49% | 28.54 | 20.52 | -24.20 |
| 28. | 2015. 3. 31. | -10.10% | -1.74% | 141.01 | 7.29 | 32.05 |
| 29. | 2015. 4. 30. | 5.81% | 0.85% | 16.30 | 0.01 | -0.43 |
| 30. | 2015. 5. 31. | 1.30% | 1.05% | 0.22 | 0.01 | -0.04 |
| 31. | 2015. 6. 30. | -9.62% | -2.10% | 129.83 | 9.37 | 34.88 |
| 32. | 2015. 7. 31. | 1.70% | 1.97% | 0.01 | 1.03 | -0.07 |
| 33. | 2015. 8. 31. | -8.06% | -6.26% | 96.66 | 52.10 | 70.96 |
| 34. | 2015. 9. 30. | -8.10% | -2.64% | 97.52 | 12.99 | 35.59 |
| 35. | 2015. 10. 31. | 5.27% | 8.30% | 12.25 | 53.86 | 25.69 |
| 36. | 2015. 11. 30. | -53.49% | 0.05% | 3,053.45 | 0.83 | 50.24 |
| 37. | 2015. 12. 31. | -4.59% | -1.75% | 40.51 | 7.36 | 17.27 |
| 38. | 2016. 1. 31. | -17.99% | -5.07% | 390.51 | 36.40 | 119.22 |
| 39. | 2016. 2. 29. | 10.09% | -0.41% | 69.24 | 1.88 | -11.42 |
| 40. | 2016. 3. 31. | 16.41% | 6.60% | 214.23 | 31.80 | 82.54 |
| 41. | 2016. 4. 30. | -0.41% | 0.27% | 4.74 | 0.48 | 1.50 |
| 42. | 2016. 5. 31. | 9.05% | 1.53% | 52.93 | 0.33 | 4.17 |
| 43. | 2016. 6. 30. | -5.28% | 0.09% | 49.67 | 0.75 | 6.12 |
| 44. | 2016. 7. 31. | 11.63% | 3.56% | 97.26 | 6.77 | 25.65 |
| 45. | 2016. 8. 31. | 2.57% | -0.12% | 0.64 | 1.17 | -0.86 |
| 46. | 2016. 9. 30. | 8.94% | -0.12% | 51.32 | 1.17 | -7.76 |
| 47. | 2016. 10. 31. | -6.70% | -1.94% | 71.71 | 8.42 | 24.58 |
| 48. | 2016. 11. 30. | 6.28% | 3.42% | 20.33 | 6.04 | 11.08 |
| 49. | 2016. 12. 31. | -2.77% | 1.82% | 20.65 | 0.74 | -3.91 |
| 50. | 2017. 1. 31. | 1.42% | 1.79% | 0.13 | 0.69 | -0.30 |
| 51. | 2017. 2. 28. | 15.42% | 3.72% | 186.16 | 7.62 | 37.66 |
| 52. | 2017. 3. 31. | 3.70% | -0.04% | 3.73 | 1.00 | -1.93 |
| 53. | 2017. 4. 30. | 5.26% | 0.91% | 12.15 | 0.00 | -0.18 |
| 54. | 2017. 5. 31. | -0.32% | 1.16% | 4.37 | 0.04 | -0.41 |
| 55. | 2017. 6. 30. | -6.11% | 0.48% | 62.18 | 0.23 | 3.77 |
| 56. | 2017. 7. 31. | 9.27% | 1.93% | 56.20 | 0.95 | 7.31 |
| 57. | 2017. 8. 31. | -0.10% | 0.05% | 3.52 | 0.82 | 1.70 |
| 58. | 2017. 9. 30. | 5.31% | 1.93% | 12.52 | 0.94 | 3.43 |
| 59. | 2017. 10. 31. | 7.97% | 2.22% | 38.37 | 1.59 | 7.80 |
| 60. | 2017. 11. 30. | -0.46% | 2.81% | 5.00 | 3.42 | -4.13 |
| 61. | 2017. 12. 31. | -1.40% | 0.98% | 10.08 | 0.00 | -0.07 |
| 62. | 2018. 1. 31. | 10.99% | 5.62% | 85.07 | 21.70 | 42.96 |
| 63. | 2018. 2. 28. | 0.30% | -3.89% | 2.16 | 23.57 | 7.14 |
| 64. | 2018. 3. 31. | -5.69% | -2.69% | 55.68 | 13.31 | 27.22 |
| 65. | 2018. 4. 30. | -1.96% | 0.27% | 13.94 | 0.47 | 2.57 |
| 66. | 2018. 5. 31. | 2.51% | 2.16% | 0.55 | 1.44 | 0.89 |
| 67. | 2018. 6. 30. | 3.63% | 0.48% | 3.44 | 0.23 | -0.88 |
| 68. | 2018. 7. 31. | 1.72% | 3.60% | 0.00 | 6.98 | -0.14 |
| 69. | 2018. 8. 31. | 6.80% | 3.03% | 25.31 | 4.27 | 10.40 |
| 70. | 2018. 9. 30. | 5.11% | 0.43% | 11.13 | 0.28 | -1.77 |
| 71. | 2018. 10. 31. | -6.33% | -6.94% | 65.55 | 62.41 | 63.96 |
| 합계 (Σ): | 7,757.62 | 576.08 | 1,004.69 | |||
모두 보기
분산HPQ = Σ(RHPQ,t–RHPQ)2 ÷ (71 – 1)
= 7,757.62 ÷ (71 – 1)
= 110.82
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 576.08 ÷ (71 – 1)
= 8.23
공분산HPQ, S&P 500 = Σ(RHPQ,t–RHPQ)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 1,004.69 ÷ (71 – 1)
= 14.35
체계적인 위험 추정 (β)
| 분산HPQ | 110.82 |
| 분산S&P 500 | 8.23 |
| 공분산HPQ, S&P 500 | 14.35 |
| 상관 계수HPQ, S&P 5001 | 0.48 |
| βHPQ2 | 1.74 |
| αHPQ3 | 0.10% |
계산
1 상관 계수HPQ, S&P 500
= 공분산HPQ, S&P 500 ÷ (표준 편차HPQ × 표준 편차S&P 500)
= 14.35 ÷ (10.53% × 2.87%)
= 0.48
2 βHPQ
= 공분산HPQ, S&P 500 ÷ 분산S&P 500
= 14.35 ÷ 8.23
= 1.74
3 αHPQ
= 평균의HPQ – βHPQ × 평균의S&P 500
= 1.77% – 1.74 × 0.96%
= 0.10%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.81% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.72% |
| 보통주의 체계적 위험HP | βHPQ | 1.74 |
| HP 보통주에 대한 예상 수익률3 | E(RHPQ) | 22.09% |
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(RHPQ) = RF + βHPQ [E(RM) – RF]
= 4.81% + 1.74 [14.72% – 4.81%]
= 22.09%