자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Twitter보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Twitter Inc., 월별 수익률
| Twitter Inc. (TWTR) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값TWTR,t1 | 피제수TWTR,t1 | RTWTR,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 1. 31. | $17.62 | 2,278.87 | ||||
| 1. | 2017. 2. 28. | $15.77 | -10.50% | 2,363.64 | 3.72% | |
| 2. | 2017. 3. 31. | $14.95 | -5.20% | 2,362.72 | -0.04% | |
| 3. | 2017. 4. 30. | $16.48 | 10.23% | 2,384.20 | 0.91% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2021. 11. 30. | $43.94 | -17.93% | 4,567.00 | -0.83% | |
| 59. | 2021. 12. 31. | $43.22 | -1.64% | 4,766.18 | 4.36% | |
| 평균의 (R): | 2.59% | 1.36% | ||||
| 표준 편차: | 14.93% | 4.48% | ||||
| Twitter Inc. (TWTR) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값TWTR,t1 | 피제수TWTR,t1 | RTWTR,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 1. 31. | $17.62 | 2,278.87 | ||||
| 1. | 2017. 2. 28. | $15.77 | -10.50% | 2,363.64 | 3.72% | |
| 2. | 2017. 3. 31. | $14.95 | -5.20% | 2,362.72 | -0.04% | |
| 3. | 2017. 4. 30. | $16.48 | 10.23% | 2,384.20 | 0.91% | |
| 4. | 2017. 5. 31. | $18.32 | 11.17% | 2,411.80 | 1.16% | |
| 5. | 2017. 6. 30. | $17.87 | -2.46% | 2,423.41 | 0.48% | |
| 6. | 2017. 7. 31. | $16.09 | -9.96% | 2,470.30 | 1.93% | |
| 7. | 2017. 8. 31. | $16.91 | 5.10% | 2,471.65 | 0.05% | |
| 8. | 2017. 9. 30. | $16.87 | -0.24% | 2,519.36 | 1.93% | |
| 9. | 2017. 10. 31. | $20.62 | 22.23% | 2,575.26 | 2.22% | |
| 10. | 2017. 11. 30. | $20.58 | -0.19% | 2,647.58 | 2.81% | |
| 11. | 2017. 12. 31. | $24.01 | 16.67% | 2,673.61 | 0.98% | |
| 12. | 2018. 1. 31. | $25.81 | 7.50% | 2,823.81 | 5.62% | |
| 13. | 2018. 2. 28. | $31.86 | 23.44% | 2,713.83 | -3.89% | |
| 14. | 2018. 3. 31. | $29.01 | -8.95% | 2,640.87 | -2.69% | |
| 15. | 2018. 4. 30. | $30.31 | 4.48% | 2,648.05 | 0.27% | |
| 16. | 2018. 5. 31. | $34.70 | 14.48% | 2,705.27 | 2.16% | |
| 17. | 2018. 6. 30. | $43.67 | 25.85% | 2,718.37 | 0.48% | |
| 18. | 2018. 7. 31. | $31.87 | -27.02% | 2,816.29 | 3.60% | |
| 19. | 2018. 8. 31. | $35.18 | 10.39% | 2,901.52 | 3.03% | |
| 20. | 2018. 9. 30. | $28.46 | -19.10% | 2,913.98 | 0.43% | |
| 21. | 2018. 10. 31. | $34.75 | 22.10% | 2,711.74 | -6.94% | |
| 22. | 2018. 11. 30. | $31.45 | -9.50% | 2,760.17 | 1.79% | |
| 23. | 2018. 12. 31. | $28.74 | -8.62% | 2,506.85 | -9.18% | |
| 24. | 2019. 1. 31. | $33.56 | 16.77% | 2,704.10 | 7.87% | |
| 25. | 2019. 2. 28. | $30.78 | -8.28% | 2,784.49 | 2.97% | |
| 26. | 2019. 3. 31. | $32.88 | 6.82% | 2,834.40 | 1.79% | |
| 27. | 2019. 4. 30. | $39.91 | 21.38% | 2,945.83 | 3.93% | |
| 28. | 2019. 5. 31. | $36.44 | -8.69% | 2,752.06 | -6.58% | |
| 29. | 2019. 6. 30. | $34.90 | -4.23% | 2,941.76 | 6.89% | |
| 30. | 2019. 7. 31. | $42.31 | 21.23% | 2,980.38 | 1.31% | |
| 31. | 2019. 8. 31. | $42.65 | 0.80% | 2,926.46 | -1.81% | |
| 32. | 2019. 9. 30. | $41.20 | -3.40% | 2,976.74 | 1.72% | |
| 33. | 2019. 10. 31. | $29.97 | -27.26% | 3,037.56 | 2.04% | |
| 34. | 2019. 11. 30. | $30.91 | 3.14% | 3,140.98 | 3.40% | |
| 35. | 2019. 12. 31. | $32.05 | 3.69% | 3,230.78 | 2.86% | |
| 36. | 2020. 1. 31. | $32.48 | 1.34% | 3,225.52 | -0.16% | |
| 37. | 2020. 2. 29. | $33.20 | 2.22% | 2,954.22 | -8.41% | |
| 38. | 2020. 3. 31. | $24.56 | -26.02% | 2,584.59 | -12.51% | |
| 39. | 2020. 4. 30. | $28.68 | 16.78% | 2,912.43 | 12.68% | |
| 40. | 2020. 5. 31. | $30.97 | 7.98% | 3,044.31 | 4.53% | |
| 41. | 2020. 6. 30. | $29.79 | -3.81% | 3,100.29 | 1.84% | |
| 42. | 2020. 7. 31. | $36.40 | 22.19% | 3,271.12 | 5.51% | |
| 43. | 2020. 8. 31. | $40.58 | 11.48% | 3,500.31 | 7.01% | |
| 44. | 2020. 9. 30. | $44.50 | 9.66% | 3,363.00 | -3.92% | |
| 45. | 2020. 10. 31. | $41.36 | -7.06% | 3,269.96 | -2.77% | |
| 46. | 2020. 11. 30. | $46.51 | 12.45% | 3,621.63 | 10.75% | |
| 47. | 2020. 12. 31. | $54.15 | 16.43% | 3,756.07 | 3.71% | |
| 48. | 2021. 1. 31. | $50.53 | -6.69% | 3,714.24 | -1.11% | |
| 49. | 2021. 2. 28. | $77.06 | 52.50% | 3,811.15 | 2.61% | |
| 50. | 2021. 3. 31. | $63.63 | -17.43% | 3,972.89 | 4.24% | |
| 51. | 2021. 4. 30. | $55.22 | -13.22% | 4,181.17 | 5.24% | |
| 52. | 2021. 5. 31. | $58.00 | 5.03% | 4,204.11 | 0.55% | |
| 53. | 2021. 6. 30. | $68.81 | 18.64% | 4,297.50 | 2.22% | |
| 54. | 2021. 7. 31. | $69.75 | 1.37% | 4,395.26 | 2.27% | |
| 55. | 2021. 8. 31. | $64.50 | -7.53% | 4,522.68 | 2.90% | |
| 56. | 2021. 9. 30. | $60.39 | -6.37% | 4,307.54 | -4.76% | |
| 57. | 2021. 10. 31. | $53.54 | -11.34% | 4,605.38 | 6.91% | |
| 58. | 2021. 11. 30. | $43.94 | -17.93% | 4,567.00 | -0.83% | |
| 59. | 2021. 12. 31. | $43.22 | -1.64% | 4,766.18 | 4.36% | |
| 평균의 (R): | 2.59% | 1.36% | ||||
| 표준 편차: | 14.93% | 4.48% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 TWTR의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Twitter Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RTWTR,t | RS&P 500,t | (RTWTR,t–RTWTR)2 | (RS&P 500,t–RS&P 500)2 | (RTWTR,t–RTWTR)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 2. 28. | -10.50% | 3.72% | 171.38 | 5.58 | -30.92 |
| 2. | 2017. 3. 31. | -5.20% | -0.04% | 60.71 | 1.95 | 10.88 |
| 3. | 2017. 4. 30. | 10.23% | 0.91% | 58.41 | 0.20 | -3.43 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2021. 11. 30. | -17.93% | -0.83% | 421.16 | 4.80 | 44.97 |
| 59. | 2021. 12. 31. | -1.64% | 4.36% | 17.90 | 9.02 | -12.71 |
| 합계 (Σ): | 12,929.79 | 1,164.17 | 806.82 | |||
| t | 날짜 | RTWTR,t | RS&P 500,t | (RTWTR,t–RTWTR)2 | (RS&P 500,t–RS&P 500)2 | (RTWTR,t–RTWTR)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 2. 28. | -10.50% | 3.72% | 171.38 | 5.58 | -30.92 |
| 2. | 2017. 3. 31. | -5.20% | -0.04% | 60.71 | 1.95 | 10.88 |
| 3. | 2017. 4. 30. | 10.23% | 0.91% | 58.41 | 0.20 | -3.43 |
| 4. | 2017. 5. 31. | 11.17% | 1.16% | 73.50 | 0.04 | -1.72 |
| 5. | 2017. 6. 30. | -2.46% | 0.48% | 25.48 | 0.77 | 4.42 |
| 6. | 2017. 7. 31. | -9.96% | 1.93% | 157.57 | 0.33 | -7.24 |
| 7. | 2017. 8. 31. | 5.10% | 0.05% | 6.27 | 1.70 | -3.26 |
| 8. | 2017. 9. 30. | -0.24% | 1.93% | 8.00 | 0.33 | -1.62 |
| 9. | 2017. 10. 31. | 22.23% | 2.22% | 385.61 | 0.74 | 16.91 |
| 10. | 2017. 11. 30. | -0.19% | 2.81% | 7.76 | 2.10 | -4.04 |
| 11. | 2017. 12. 31. | 16.67% | 0.98% | 198.10 | 0.14 | -5.27 |
| 12. | 2018. 1. 31. | 7.50% | 5.62% | 24.06 | 18.15 | 20.90 |
| 13. | 2018. 2. 28. | 23.44% | -3.89% | 434.67 | 27.59 | -109.51 |
| 14. | 2018. 3. 31. | -8.95% | -2.69% | 133.11 | 16.37 | 46.68 |
| 15. | 2018. 4. 30. | 4.48% | 0.27% | 3.57 | 1.18 | -2.05 |
| 16. | 2018. 5. 31. | 14.48% | 2.16% | 141.42 | 0.64 | 9.55 |
| 17. | 2018. 6. 30. | 25.85% | 0.48% | 540.95 | 0.76 | -20.32 |
| 18. | 2018. 7. 31. | -27.02% | 3.60% | 876.91 | 5.04 | -66.46 |
| 19. | 2018. 8. 31. | 10.39% | 3.03% | 60.75 | 2.78 | 13.00 |
| 20. | 2018. 9. 30. | -19.10% | 0.43% | 470.61 | 0.86 | 20.14 |
| 21. | 2018. 10. 31. | 22.10% | -6.94% | 380.62 | 68.86 | -161.89 |
| 22. | 2018. 11. 30. | -9.50% | 1.79% | 146.12 | 0.18 | -5.17 |
| 23. | 2018. 12. 31. | -8.62% | -9.18% | 125.63 | 111.00 | 118.09 |
| 24. | 2019. 1. 31. | 16.77% | 7.87% | 201.05 | 42.39 | 92.31 |
| 25. | 2019. 2. 28. | -8.28% | 2.97% | 118.28 | 2.61 | -17.56 |
| 26. | 2019. 3. 31. | 6.82% | 1.79% | 17.90 | 0.19 | 1.84 |
| 27. | 2019. 4. 30. | 21.38% | 3.93% | 353.03 | 6.62 | 48.35 |
| 28. | 2019. 5. 31. | -8.69% | -6.58% | 127.38 | 62.97 | 89.56 |
| 29. | 2019. 6. 30. | -4.23% | 6.89% | 46.48 | 30.64 | -37.74 |
| 30. | 2019. 7. 31. | 21.23% | 1.31% | 347.46 | 0.00 | -0.84 |
| 31. | 2019. 8. 31. | 0.80% | -1.81% | 3.20 | 10.03 | 5.66 |
| 32. | 2019. 9. 30. | -3.40% | 1.72% | 35.90 | 0.13 | -2.16 |
| 33. | 2019. 10. 31. | -27.26% | 2.04% | 890.97 | 0.47 | -20.45 |
| 34. | 2019. 11. 30. | 3.14% | 3.40% | 0.30 | 4.19 | 1.11 |
| 35. | 2019. 12. 31. | 3.69% | 2.86% | 1.20 | 2.25 | 1.65 |
| 36. | 2020. 1. 31. | 1.34% | -0.16% | 1.56 | 2.31 | 1.90 |
| 37. | 2020. 2. 29. | 2.22% | -8.41% | 0.14 | 95.43 | 3.66 |
| 38. | 2020. 3. 31. | -26.02% | -12.51% | 818.87 | 192.37 | 396.90 |
| 39. | 2020. 4. 30. | 16.78% | 12.68% | 201.17 | 128.29 | 160.65 |
| 40. | 2020. 5. 31. | 7.98% | 4.53% | 29.08 | 10.05 | 17.10 |
| 41. | 2020. 6. 30. | -3.81% | 1.84% | 40.98 | 0.23 | -3.08 |
| 42. | 2020. 7. 31. | 22.19% | 5.51% | 384.04 | 17.24 | 81.37 |
| 43. | 2020. 8. 31. | 11.48% | 7.01% | 79.06 | 31.91 | 50.23 |
| 44. | 2020. 9. 30. | 9.66% | -3.92% | 49.96 | 27.89 | -37.32 |
| 45. | 2020. 10. 31. | -7.06% | -2.77% | 93.08 | 17.01 | 39.79 |
| 46. | 2020. 11. 30. | 12.45% | 10.75% | 97.22 | 88.30 | 92.65 |
| 47. | 2020. 12. 31. | 16.43% | 3.71% | 191.40 | 5.54 | 32.57 |
| 48. | 2021. 1. 31. | -6.69% | -1.11% | 86.06 | 6.11 | 22.93 |
| 49. | 2021. 2. 28. | 52.50% | 2.61% | 2,491.18 | 1.57 | 62.45 |
| 50. | 2021. 3. 31. | -17.43% | 4.24% | 400.79 | 8.33 | -57.78 |
| 51. | 2021. 4. 30. | -13.22% | 5.24% | 249.92 | 15.09 | -61.41 |
| 52. | 2021. 5. 31. | 5.03% | 0.55% | 5.97 | 0.65 | -1.98 |
| 53. | 2021. 6. 30. | 18.64% | 2.22% | 257.48 | 0.75 | 13.86 |
| 54. | 2021. 7. 31. | 1.37% | 2.27% | 1.50 | 0.84 | -1.12 |
| 55. | 2021. 8. 31. | -7.53% | 2.90% | 102.39 | 2.38 | -15.59 |
| 56. | 2021. 9. 30. | -6.37% | -4.76% | 80.35 | 37.39 | 54.81 |
| 57. | 2021. 10. 31. | -11.34% | 6.91% | 194.18 | 30.87 | -77.43 |
| 58. | 2021. 11. 30. | -17.93% | -0.83% | 421.16 | 4.80 | 44.97 |
| 59. | 2021. 12. 31. | -1.64% | 4.36% | 17.90 | 9.02 | -12.71 |
| 합계 (Σ): | 12,929.79 | 1,164.17 | 806.82 | |||
모두 보기
분산TWTR = Σ(RTWTR,t–RTWTR)2 ÷ (59 – 1)
= 12,929.79 ÷ (59 – 1)
= 222.93
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,164.17 ÷ (59 – 1)
= 20.07
공분산TWTR, S&P 500 = Σ(RTWTR,t–RTWTR)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 806.82 ÷ (59 – 1)
= 13.91
체계적인 위험 추정 (β)
| 분산TWTR | 222.93 |
| 분산S&P 500 | 20.07 |
| 공분산TWTR, S&P 500 | 13.91 |
| 상관 계수TWTR, S&P 5001 | 0.21 |
| βTWTR2 | 0.69 |
| αTWTR3 | 1.65% |
계산
1 상관 계수TWTR, S&P 500
= 공분산TWTR, S&P 500 ÷ (표준 편차TWTR × 표준 편차S&P 500)
= 13.91 ÷ (14.93% × 4.48%)
= 0.21
2 βTWTR
= 공분산TWTR, S&P 500 ÷ 분산S&P 500
= 13.91 ÷ 20.07
= 0.69
3 αTWTR
= 평균의TWTR – βTWTR × 평균의S&P 500
= 2.59% – 0.69 × 1.36%
= 1.65%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.60% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.89% |
| 보통주의 체계적 위험Twitter | βTWTR | 0.69 |
| 트위터 보통주 예상 수익률3 | E(RTWTR) | 11.73% |
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(RTWTR) = RF + βTWTR [E(RM) – RF]
= 4.60% + 0.69 [14.89% – 4.60%]
= 11.73%