자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 TI보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Texas Instruments Inc., 월별 수익률
| Texas Instruments Inc. (TXN) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값TXN,t1 | 피제수TXN,t1 | RTXN,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2020. 1. 31. | $120.65 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $114.14 | -5.40% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $99.93 | -12.45% | 2,584.59 | -12.51% | |
| 3. | 2020. 4. 30. | $116.07 | 16.15% | 2,912.43 | 12.68% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | $201.03 | -1.05% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $187.51 | -6.73% | 5,881.63 | -2.50% | |
| 평균의 (R): | 1.21% | 1.16% | ||||
| 표준 편차: | 6.96% | 5.28% | ||||
| Texas Instruments Inc. (TXN) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값TXN,t1 | 피제수TXN,t1 | RTXN,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2020. 1. 31. | $120.65 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $114.14 | -5.40% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $99.93 | -12.45% | 2,584.59 | -12.51% | |
| 3. | 2020. 4. 30. | $116.07 | 16.15% | 2,912.43 | 12.68% | |
| 4. | 2020. 5. 31. | $118.74 | $0.90 | 3.08% | 3,044.31 | 4.53% |
| 5. | 2020. 6. 30. | $126.97 | 6.93% | 3,100.29 | 1.84% | |
| 6. | 2020. 7. 31. | $127.55 | $0.90 | 1.17% | 3,271.12 | 5.51% |
| 7. | 2020. 8. 31. | $142.15 | 11.45% | 3,500.31 | 7.01% | |
| 8. | 2020. 9. 30. | $142.79 | 0.45% | 3,363.00 | -3.92% | |
| 9. | 2020. 10. 31. | $144.59 | $1.02 | 1.97% | 3,269.96 | -2.77% |
| 10. | 2020. 11. 30. | $161.25 | 11.52% | 3,621.63 | 10.75% | |
| 11. | 2020. 12. 31. | $164.13 | 1.79% | 3,756.07 | 3.71% | |
| 12. | 2021. 1. 31. | $165.69 | $1.02 | 1.57% | 3,714.24 | -1.11% |
| 13. | 2021. 2. 28. | $172.27 | 3.97% | 3,811.15 | 2.61% | |
| 14. | 2021. 3. 31. | $188.99 | 9.71% | 3,972.89 | 4.24% | |
| 15. | 2021. 4. 30. | $180.51 | $1.02 | -3.95% | 4,181.17 | 5.24% |
| 16. | 2021. 5. 31. | $189.82 | 5.16% | 4,204.11 | 0.55% | |
| 17. | 2021. 6. 30. | $192.30 | 1.31% | 4,297.50 | 2.22% | |
| 18. | 2021. 7. 31. | $190.62 | $1.02 | -0.34% | 4,395.26 | 2.27% |
| 19. | 2021. 8. 31. | $190.91 | 0.15% | 4,522.68 | 2.90% | |
| 20. | 2021. 9. 30. | $192.21 | 0.68% | 4,307.54 | -4.76% | |
| 21. | 2021. 10. 31. | $187.48 | $1.15 | -1.86% | 4,605.38 | 6.91% |
| 22. | 2021. 11. 30. | $192.37 | 2.61% | 4,567.00 | -0.83% | |
| 23. | 2021. 12. 31. | $188.47 | -2.03% | 4,766.18 | 4.36% | |
| 24. | 2022. 1. 31. | $179.49 | $1.15 | -4.15% | 4,515.55 | -5.26% |
| 25. | 2022. 2. 28. | $169.99 | -5.29% | 4,373.94 | -3.14% | |
| 26. | 2022. 3. 31. | $183.48 | 7.94% | 4,530.41 | 3.58% | |
| 27. | 2022. 4. 30. | $170.25 | -7.21% | 4,131.93 | -8.80% | |
| 28. | 2022. 5. 31. | $176.76 | $1.15 | 4.50% | 4,132.15 | 0.01% |
| 29. | 2022. 6. 30. | $153.65 | -13.07% | 3,785.38 | -8.39% | |
| 30. | 2022. 7. 31. | $178.89 | $1.15 | 17.18% | 4,130.29 | 9.11% |
| 31. | 2022. 8. 31. | $165.21 | -7.65% | 3,955.00 | -4.24% | |
| 32. | 2022. 9. 30. | $154.78 | -6.31% | 3,585.62 | -9.34% | |
| 33. | 2022. 10. 31. | $160.63 | $1.24 | 4.58% | 3,871.98 | 7.99% |
| 34. | 2022. 11. 30. | $180.46 | 12.35% | 4,080.11 | 5.38% | |
| 35. | 2022. 12. 31. | $165.22 | -8.45% | 3,839.50 | -5.90% | |
| 36. | 2023. 1. 31. | $177.21 | $1.24 | 8.01% | 4,076.60 | 6.18% |
| 37. | 2023. 2. 28. | $171.45 | -3.25% | 3,970.15 | -2.61% | |
| 38. | 2023. 3. 31. | $186.01 | 8.49% | 4,109.31 | 3.51% | |
| 39. | 2023. 4. 30. | $167.20 | -10.11% | 4,169.48 | 1.46% | |
| 40. | 2023. 5. 31. | $173.88 | $1.24 | 4.74% | 4,179.83 | 0.25% |
| 41. | 2023. 6. 30. | $180.02 | 3.53% | 4,376.86 | 4.71% | |
| 42. | 2023. 7. 31. | $180.00 | $1.24 | 0.68% | 4,588.96 | 4.85% |
| 43. | 2023. 8. 31. | $168.06 | -6.63% | 4,507.66 | -1.77% | |
| 44. | 2023. 9. 30. | $159.01 | -5.38% | 4,288.05 | -4.87% | |
| 45. | 2023. 10. 31. | $142.01 | $1.30 | -9.87% | 4,193.80 | -2.20% |
| 46. | 2023. 11. 30. | $152.71 | 7.53% | 4,567.80 | 8.92% | |
| 47. | 2023. 12. 31. | $170.46 | 11.62% | 4,769.83 | 4.42% | |
| 48. | 2024. 1. 31. | $160.12 | $1.30 | -5.30% | 4,845.65 | 1.59% |
| 49. | 2024. 2. 29. | $167.33 | 4.50% | 5,096.27 | 5.17% | |
| 50. | 2024. 3. 31. | $174.21 | 4.11% | 5,254.35 | 3.10% | |
| 51. | 2024. 4. 30. | $176.42 | 1.27% | 5,035.69 | -4.16% | |
| 52. | 2024. 5. 31. | $195.01 | $1.30 | 11.27% | 5,277.51 | 4.80% |
| 53. | 2024. 6. 30. | $194.53 | -0.25% | 5,460.48 | 3.47% | |
| 54. | 2024. 7. 31. | $203.81 | $1.30 | 5.44% | 5,522.30 | 1.13% |
| 55. | 2024. 8. 31. | $214.34 | 5.17% | 5,648.40 | 2.28% | |
| 56. | 2024. 9. 30. | $206.57 | -3.63% | 5,762.48 | 2.02% | |
| 57. | 2024. 10. 31. | $203.16 | $1.36 | -0.99% | 5,705.45 | -0.99% |
| 58. | 2024. 11. 30. | $201.03 | -1.05% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $187.51 | -6.73% | 5,881.63 | -2.50% | |
| 평균의 (R): | 1.21% | 1.16% | ||||
| 표준 편차: | 6.96% | 5.28% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 t 기간 동안 TXN의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Texas Instruments Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RTXN,t | RS&P 500,t | (RTXN,t–RTXN)2 | (RS&P 500,t–RS&P 500)2 | (RTXN,t–RTXN)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2020. 2. 29. | -5.40% | -8.41% | 43.59 | 91.63 | 63.20 |
| 2. | 2020. 3. 31. | -12.45% | -12.51% | 186.50 | 186.96 | 186.73 |
| 3. | 2020. 4. 30. | 16.15% | 12.68% | 223.34 | 132.78 | 172.21 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | -1.05% | 5.73% | 5.09 | 20.87 | -10.30 |
| 59. | 2024. 12. 31. | -6.73% | -2.50% | 62.92 | 13.40 | 29.03 |
| 합계 (Σ): | 2,807.36 | 1,618.62 | 1,578.30 | |||
| t | 날짜 | RTXN,t | RS&P 500,t | (RTXN,t–RTXN)2 | (RS&P 500,t–RS&P 500)2 | (RTXN,t–RTXN)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2020. 2. 29. | -5.40% | -8.41% | 43.59 | 91.63 | 63.20 |
| 2. | 2020. 3. 31. | -12.45% | -12.51% | 186.50 | 186.96 | 186.73 |
| 3. | 2020. 4. 30. | 16.15% | 12.68% | 223.34 | 132.78 | 172.21 |
| 4. | 2020. 5. 31. | 3.08% | 4.53% | 3.49 | 11.34 | 6.29 |
| 5. | 2020. 6. 30. | 6.93% | 1.84% | 32.77 | 0.46 | 3.88 |
| 6. | 2020. 7. 31. | 1.17% | 5.51% | 0.00 | 18.91 | -0.18 |
| 7. | 2020. 8. 31. | 11.45% | 7.01% | 104.85 | 34.17 | 59.85 |
| 8. | 2020. 9. 30. | 0.45% | -3.92% | 0.57 | 25.85 | 3.85 |
| 9. | 2020. 10. 31. | 1.97% | -2.77% | 0.59 | 15.43 | -3.02 |
| 10. | 2020. 11. 30. | 11.52% | 10.75% | 106.41 | 92.03 | 98.96 |
| 11. | 2020. 12. 31. | 1.79% | 3.71% | 0.34 | 6.51 | 1.48 |
| 12. | 2021. 1. 31. | 1.57% | -1.11% | 0.13 | 5.18 | -0.83 |
| 13. | 2021. 2. 28. | 3.97% | 2.61% | 7.64 | 2.10 | 4.00 |
| 14. | 2021. 3. 31. | 9.71% | 4.24% | 72.23 | 9.50 | 26.20 |
| 15. | 2021. 4. 30. | -3.95% | 5.24% | 26.56 | 16.66 | -21.04 |
| 16. | 2021. 5. 31. | 5.16% | 0.55% | 15.61 | 0.38 | -2.42 |
| 17. | 2021. 6. 30. | 1.31% | 2.22% | 0.01 | 1.12 | 0.11 |
| 18. | 2021. 7. 31. | -0.34% | 2.27% | 2.40 | 1.24 | -1.73 |
| 19. | 2021. 8. 31. | 0.15% | 2.90% | 1.11 | 3.02 | -1.83 |
| 20. | 2021. 9. 30. | 0.68% | -4.76% | 0.28 | 35.02 | 3.11 |
| 21. | 2021. 10. 31. | -1.86% | 6.91% | 9.42 | 33.10 | -17.66 |
| 22. | 2021. 11. 30. | 2.61% | -0.83% | 1.96 | 3.98 | -2.80 |
| 23. | 2021. 12. 31. | -2.03% | 4.36% | 10.46 | 10.24 | -10.35 |
| 24. | 2022. 1. 31. | -4.15% | -5.26% | 28.74 | 41.21 | 34.42 |
| 25. | 2022. 2. 28. | -5.29% | -3.14% | 42.24 | 18.47 | 27.93 |
| 26. | 2022. 3. 31. | 7.94% | 3.58% | 45.28 | 5.84 | 16.26 |
| 27. | 2022. 4. 30. | -7.21% | -8.80% | 70.85 | 99.14 | 83.81 |
| 28. | 2022. 5. 31. | 4.50% | 0.01% | 10.84 | 1.34 | -3.81 |
| 29. | 2022. 6. 30. | -13.07% | -8.39% | 203.95 | 91.26 | 136.43 |
| 30. | 2022. 7. 31. | 17.18% | 9.11% | 255.00 | 63.21 | 126.96 |
| 31. | 2022. 8. 31. | -7.65% | -4.24% | 78.39 | 29.22 | 47.86 |
| 32. | 2022. 9. 30. | -6.31% | -9.34% | 56.55 | 110.27 | 78.97 |
| 33. | 2022. 10. 31. | 4.58% | 7.99% | 11.38 | 46.58 | 23.03 |
| 34. | 2022. 11. 30. | 12.35% | 5.38% | 124.06 | 17.76 | 46.94 |
| 35. | 2022. 12. 31. | -8.45% | -5.90% | 93.16 | 49.82 | 68.13 |
| 36. | 2023. 1. 31. | 8.01% | 6.18% | 46.25 | 25.14 | 34.10 |
| 37. | 2023. 2. 28. | -3.25% | -2.61% | 19.87 | 14.23 | 16.81 |
| 38. | 2023. 3. 31. | 8.49% | 3.51% | 53.08 | 5.49 | 17.08 |
| 39. | 2023. 4. 30. | -10.11% | 1.46% | 128.12 | 0.09 | -3.43 |
| 40. | 2023. 5. 31. | 4.74% | 0.25% | 12.46 | 0.83 | -3.22 |
| 41. | 2023. 6. 30. | 3.53% | 4.71% | 5.40 | 12.62 | 8.26 |
| 42. | 2023. 7. 31. | 0.68% | 4.85% | 0.28 | 13.58 | -1.95 |
| 43. | 2023. 8. 31. | -6.63% | -1.77% | 61.47 | 8.60 | 22.99 |
| 44. | 2023. 9. 30. | -5.38% | -4.87% | 43.45 | 36.40 | 39.77 |
| 45. | 2023. 10. 31. | -9.87% | -2.20% | 122.78 | 11.28 | 37.22 |
| 46. | 2023. 11. 30. | 7.53% | 8.92% | 40.04 | 60.17 | 49.08 |
| 47. | 2023. 12. 31. | 11.62% | 4.42% | 108.50 | 10.64 | 33.98 |
| 48. | 2024. 1. 31. | -5.30% | 1.59% | 42.38 | 0.18 | -2.79 |
| 49. | 2024. 2. 29. | 4.50% | 5.17% | 10.86 | 16.09 | 13.22 |
| 50. | 2024. 3. 31. | 4.11% | 3.10% | 8.44 | 3.77 | 5.64 |
| 51. | 2024. 4. 30. | 1.27% | -4.16% | 0.00 | 28.33 | -0.33 |
| 52. | 2024. 5. 31. | 11.27% | 4.80% | 101.35 | 13.26 | 36.65 |
| 53. | 2024. 6. 30. | -0.25% | 3.47% | 2.11 | 5.32 | -3.35 |
| 54. | 2024. 7. 31. | 5.44% | 1.13% | 17.91 | 0.00 | -0.12 |
| 55. | 2024. 8. 31. | 5.17% | 2.28% | 15.68 | 1.26 | 4.44 |
| 56. | 2024. 9. 30. | -3.63% | 2.02% | 23.35 | 0.74 | -4.15 |
| 57. | 2024. 10. 31. | -0.99% | -0.99% | 4.84 | 4.63 | 4.73 |
| 58. | 2024. 11. 30. | -1.05% | 5.73% | 5.09 | 20.87 | -10.30 |
| 59. | 2024. 12. 31. | -6.73% | -2.50% | 62.92 | 13.40 | 29.03 |
| 합계 (Σ): | 2,807.36 | 1,618.62 | 1,578.30 | |||
모두 보기
분산TXN = Σ(RTXN,t–RTXN)2 ÷ (59 – 1)
= 2,807.36 ÷ (59 – 1)
= 48.40
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91
공분산TXN, S&P 500 = Σ(RTXN,t–RTXN)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,578.30 ÷ (59 – 1)
= 27.21
체계적인 위험 추정 (β)
| 분산TXN | 48.40 |
| 분산S&P 500 | 27.91 |
| 공분산TXN, S&P 500 | 27.21 |
| 상관 계수TXN, S&P 5001 | 0.74 |
| βTXN2 | 0.98 |
| αTXN3 | 0.07% |
계산
1 상관 계수TXN, S&P 500
= 공분산TXN, S&P 500 ÷ (표준 편차TXN × 표준 편차S&P 500)
= 27.21 ÷ (6.96% × 5.28%)
= 0.74
2 βTXN
= 공분산TXN, S&P 500 ÷ 분산S&P 500
= 27.21 ÷ 27.91
= 0.98
3 αTXN
= 평균의TXN – βTXN × 평균의S&P 500
= 1.21% – 0.98 × 1.16%
= 0.07%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.74% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.86% |
| 보통주의 체계적 위험TI | βTXN | 0.98 |
| TI 보통주에 대한 예상 수익률3 | E(RTXN) | 14.61% |
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(RTXN) = RF + βTXN [E(RM) – RF]
= 4.74% + 0.98 [14.86% – 4.74%]
= 14.61%