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 |
| 2021. 1. 31. | $165.69 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $172.27 | 3.97% | 3,811.15 | 2.61% | |
| 2. | 2021. 3. 31. | $188.99 | 9.71% | 3,972.89 | 4.24% | |
| 3. | 2021. 4. 30. | $180.51 | $1.02 | -3.95% | 4,181.17 | 5.24% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | $168.27 | 4.22% | 6,849.09 | 0.13% | |
| 59. | 2025. 12. 31. | $173.49 | 3.10% | 6,845.50 | -0.05% | |
| 평균의 (R): | 0.58% | 1.14% | ||||
| 표준 편차: | 7.45% | 4.37% | ||||
| 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 |
| 2021. 1. 31. | $165.69 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $172.27 | 3.97% | 3,811.15 | 2.61% | |
| 2. | 2021. 3. 31. | $188.99 | 9.71% | 3,972.89 | 4.24% | |
| 3. | 2021. 4. 30. | $180.51 | $1.02 | -3.95% | 4,181.17 | 5.24% |
| 4. | 2021. 5. 31. | $189.82 | 5.16% | 4,204.11 | 0.55% | |
| 5. | 2021. 6. 30. | $192.30 | 1.31% | 4,297.50 | 2.22% | |
| 6. | 2021. 7. 31. | $190.62 | $1.02 | -0.34% | 4,395.26 | 2.27% |
| 7. | 2021. 8. 31. | $190.91 | 0.15% | 4,522.68 | 2.90% | |
| 8. | 2021. 9. 30. | $192.21 | 0.68% | 4,307.54 | -4.76% | |
| 9. | 2021. 10. 31. | $187.48 | $1.15 | -1.86% | 4,605.38 | 6.91% |
| 10. | 2021. 11. 30. | $192.37 | 2.61% | 4,567.00 | -0.83% | |
| 11. | 2021. 12. 31. | $188.47 | -2.03% | 4,766.18 | 4.36% | |
| 12. | 2022. 1. 31. | $179.49 | $1.15 | -4.15% | 4,515.55 | -5.26% |
| 13. | 2022. 2. 28. | $169.99 | -5.29% | 4,373.94 | -3.14% | |
| 14. | 2022. 3. 31. | $183.48 | 7.94% | 4,530.41 | 3.58% | |
| 15. | 2022. 4. 30. | $170.25 | -7.21% | 4,131.93 | -8.80% | |
| 16. | 2022. 5. 31. | $176.76 | $1.15 | 4.50% | 4,132.15 | 0.01% |
| 17. | 2022. 6. 30. | $153.65 | -13.07% | 3,785.38 | -8.39% | |
| 18. | 2022. 7. 31. | $178.89 | $1.15 | 17.18% | 4,130.29 | 9.11% |
| 19. | 2022. 8. 31. | $165.21 | -7.65% | 3,955.00 | -4.24% | |
| 20. | 2022. 9. 30. | $154.78 | -6.31% | 3,585.62 | -9.34% | |
| 21. | 2022. 10. 31. | $160.63 | $1.24 | 4.58% | 3,871.98 | 7.99% |
| 22. | 2022. 11. 30. | $180.46 | 12.35% | 4,080.11 | 5.38% | |
| 23. | 2022. 12. 31. | $165.22 | -8.45% | 3,839.50 | -5.90% | |
| 24. | 2023. 1. 31. | $177.21 | $1.24 | 8.01% | 4,076.60 | 6.18% |
| 25. | 2023. 2. 28. | $171.45 | -3.25% | 3,970.15 | -2.61% | |
| 26. | 2023. 3. 31. | $186.01 | 8.49% | 4,109.31 | 3.51% | |
| 27. | 2023. 4. 30. | $167.20 | -10.11% | 4,169.48 | 1.46% | |
| 28. | 2023. 5. 31. | $173.88 | $1.24 | 4.74% | 4,179.83 | 0.25% |
| 29. | 2023. 6. 30. | $180.02 | 3.53% | 4,376.86 | 4.71% | |
| 30. | 2023. 7. 31. | $180.00 | $1.24 | 0.68% | 4,588.96 | 4.85% |
| 31. | 2023. 8. 31. | $168.06 | -6.63% | 4,507.66 | -1.77% | |
| 32. | 2023. 9. 30. | $159.01 | -5.38% | 4,288.05 | -4.87% | |
| 33. | 2023. 10. 31. | $142.01 | $1.30 | -9.87% | 4,193.80 | -2.20% |
| 34. | 2023. 11. 30. | $152.71 | 7.53% | 4,567.80 | 8.92% | |
| 35. | 2023. 12. 31. | $170.46 | 11.62% | 4,769.83 | 4.42% | |
| 36. | 2024. 1. 31. | $160.12 | $1.30 | -5.30% | 4,845.65 | 1.59% |
| 37. | 2024. 2. 29. | $167.33 | 4.50% | 5,096.27 | 5.17% | |
| 38. | 2024. 3. 31. | $174.21 | 4.11% | 5,254.35 | 3.10% | |
| 39. | 2024. 4. 30. | $176.42 | 1.27% | 5,035.69 | -4.16% | |
| 40. | 2024. 5. 31. | $195.01 | $1.30 | 11.27% | 5,277.51 | 4.80% |
| 41. | 2024. 6. 30. | $194.53 | -0.25% | 5,460.48 | 3.47% | |
| 42. | 2024. 7. 31. | $203.81 | $1.30 | 5.44% | 5,522.30 | 1.13% |
| 43. | 2024. 8. 31. | $214.34 | 5.17% | 5,648.40 | 2.28% | |
| 44. | 2024. 9. 30. | $206.57 | -3.63% | 5,762.48 | 2.02% | |
| 45. | 2024. 10. 31. | $203.16 | $1.36 | -0.99% | 5,705.45 | -0.99% |
| 46. | 2024. 11. 30. | $201.03 | -1.05% | 6,032.38 | 5.73% | |
| 47. | 2024. 12. 31. | $187.51 | -6.73% | 5,881.63 | -2.50% | |
| 48. | 2025. 1. 31. | $184.61 | $1.36 | -0.82% | 6,040.53 | 2.70% |
| 49. | 2025. 2. 28. | $195.99 | 6.16% | 5,954.50 | -1.42% | |
| 50. | 2025. 3. 31. | $179.70 | -8.31% | 5,611.85 | -5.75% | |
| 51. | 2025. 4. 30. | $160.05 | $1.36 | -10.18% | 5,569.06 | -0.76% |
| 52. | 2025. 5. 31. | $182.85 | 14.25% | 5,911.69 | 6.15% | |
| 53. | 2025. 6. 30. | $207.62 | 13.55% | 6,204.95 | 4.96% | |
| 54. | 2025. 7. 31. | $181.06 | $1.36 | -12.14% | 6,339.39 | 2.17% |
| 55. | 2025. 8. 31. | $202.48 | 11.83% | 6,460.26 | 1.91% | |
| 56. | 2025. 9. 30. | $183.73 | -9.26% | 6,688.46 | 3.53% | |
| 57. | 2025. 10. 31. | $161.46 | $1.42 | -11.35% | 6,840.20 | 2.27% |
| 58. | 2025. 11. 30. | $168.27 | 4.22% | 6,849.09 | 0.13% | |
| 59. | 2025. 12. 31. | $173.49 | 3.10% | 6,845.50 | -0.05% | |
| 평균의 (R): | 0.58% | 1.14% | ||||
| 표준 편차: | 7.45% | 4.37% | ||||
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. | 2021. 2. 28. | 3.97% | 2.61% | 11.52 | 2.17 | 5.00 |
| 2. | 2021. 3. 31. | 9.71% | 4.24% | 83.34 | 9.66 | 28.37 |
| 3. | 2021. 4. 30. | -3.95% | 5.24% | 20.47 | 16.86 | -18.58 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | 4.22% | 0.13% | 13.26 | 1.01 | -3.66 |
| 59. | 2025. 12. 31. | 3.10% | -0.05% | 6.38 | 1.41 | -3.00 |
| 합계 (Σ): | 3,223.31 | 1,108.23 | 1,119.07 | |||
| 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. | 2021. 2. 28. | 3.97% | 2.61% | 11.52 | 2.17 | 5.00 |
| 2. | 2021. 3. 31. | 9.71% | 4.24% | 83.34 | 9.66 | 28.37 |
| 3. | 2021. 4. 30. | -3.95% | 5.24% | 20.47 | 16.86 | -18.58 |
| 4. | 2021. 5. 31. | 5.16% | 0.55% | 20.99 | 0.35 | -2.69 |
| 5. | 2021. 6. 30. | 1.31% | 2.22% | 0.53 | 1.18 | 0.79 |
| 6. | 2021. 7. 31. | -0.34% | 2.27% | 0.85 | 1.30 | -1.05 |
| 7. | 2021. 8. 31. | 0.15% | 2.90% | 0.18 | 3.11 | -0.75 |
| 8. | 2021. 9. 30. | 0.68% | -4.76% | 0.01 | 34.73 | -0.61 |
| 9. | 2021. 10. 31. | -1.86% | 6.91% | 5.95 | 33.39 | -14.09 |
| 10. | 2021. 11. 30. | 2.61% | -0.83% | 4.13 | 3.88 | -4.00 |
| 11. | 2021. 12. 31. | -2.03% | 4.36% | 6.78 | 10.40 | -8.40 |
| 12. | 2022. 1. 31. | -4.15% | -5.26% | 22.38 | 40.89 | 30.25 |
| 13. | 2022. 2. 28. | -5.29% | -3.14% | 34.45 | 18.25 | 25.08 |
| 14. | 2022. 3. 31. | 7.94% | 3.58% | 54.16 | 5.96 | 17.97 |
| 15. | 2022. 4. 30. | -7.21% | -8.80% | 60.64 | 98.64 | 77.34 |
| 16. | 2022. 5. 31. | 4.50% | 0.01% | 15.39 | 1.28 | -4.44 |
| 17. | 2022. 6. 30. | -13.07% | -8.39% | 186.35 | 90.79 | 130.07 |
| 18. | 2022. 7. 31. | 17.18% | 9.11% | 275.52 | 63.61 | 132.38 |
| 19. | 2022. 8. 31. | -7.65% | -4.24% | 67.63 | 28.95 | 44.25 |
| 20. | 2022. 9. 30. | -6.31% | -9.34% | 47.47 | 109.74 | 72.18 |
| 21. | 2022. 10. 31. | 4.58% | 7.99% | 16.03 | 46.93 | 27.43 |
| 22. | 2022. 11. 30. | 12.35% | 5.38% | 138.50 | 17.97 | 49.89 |
| 23. | 2022. 12. 31. | -8.45% | -5.90% | 81.39 | 49.47 | 63.45 |
| 24. | 2023. 1. 31. | 8.01% | 6.18% | 55.22 | 25.39 | 37.45 |
| 25. | 2023. 2. 28. | -3.25% | -2.61% | 14.65 | 14.04 | 14.34 |
| 26. | 2023. 3. 31. | 8.49% | 3.51% | 62.66 | 5.61 | 18.75 |
| 27. | 2023. 4. 30. | -10.11% | 1.46% | 114.25 | 0.11 | -3.51 |
| 28. | 2023. 5. 31. | 4.74% | 0.25% | 17.31 | 0.79 | -3.69 |
| 29. | 2023. 6. 30. | 3.53% | 4.71% | 8.73 | 12.80 | 10.57 |
| 30. | 2023. 7. 31. | 0.68% | 4.85% | 0.01 | 13.76 | 0.37 |
| 31. | 2023. 8. 31. | -6.63% | -1.77% | 51.98 | 8.46 | 20.96 |
| 32. | 2023. 9. 30. | -5.38% | -4.87% | 35.54 | 36.10 | 35.82 |
| 33. | 2023. 10. 31. | -9.87% | -2.20% | 109.21 | 11.12 | 34.84 |
| 34. | 2023. 11. 30. | 7.53% | 8.92% | 48.41 | 60.56 | 54.15 |
| 35. | 2023. 12. 31. | 11.62% | 4.42% | 122.03 | 10.80 | 36.31 |
| 36. | 2024. 1. 31. | -5.30% | 1.59% | 34.57 | 0.21 | -2.67 |
| 37. | 2024. 2. 29. | 4.50% | 5.17% | 15.42 | 16.29 | 15.85 |
| 38. | 2024. 3. 31. | 4.11% | 3.10% | 12.50 | 3.86 | 6.95 |
| 39. | 2024. 4. 30. | 1.27% | -4.16% | 0.48 | 28.06 | -3.67 |
| 40. | 2024. 5. 31. | 11.27% | 4.80% | 114.44 | 13.44 | 39.22 |
| 41. | 2024. 6. 30. | -0.25% | 3.47% | 0.68 | 5.43 | -1.92 |
| 42. | 2024. 7. 31. | 5.44% | 1.13% | 23.64 | 0.00 | -0.02 |
| 43. | 2024. 8. 31. | 5.17% | 2.28% | 21.07 | 1.32 | 5.27 |
| 44. | 2024. 9. 30. | -3.63% | 2.02% | 17.65 | 0.78 | -3.71 |
| 45. | 2024. 10. 31. | -0.99% | -0.99% | 2.46 | 4.52 | 3.34 |
| 46. | 2024. 11. 30. | -1.05% | 5.73% | 2.64 | 21.10 | -7.47 |
| 47. | 2024. 12. 31. | -6.73% | -2.50% | 53.32 | 13.21 | 26.54 |
| 48. | 2025. 1. 31. | -0.82% | 2.70% | 1.95 | 2.45 | -2.19 |
| 49. | 2025. 2. 28. | 6.16% | -1.42% | 31.22 | 6.56 | -14.31 |
| 50. | 2025. 3. 31. | -8.31% | -5.75% | 79.00 | 47.48 | 61.25 |
| 51. | 2025. 4. 30. | -10.18% | -0.76% | 115.66 | 3.60 | 20.42 |
| 52. | 2025. 5. 31. | 14.25% | 6.15% | 186.84 | 25.16 | 68.57 |
| 53. | 2025. 6. 30. | 13.55% | 4.96% | 168.22 | 14.63 | 49.60 |
| 54. | 2025. 7. 31. | -12.14% | 2.17% | 161.65 | 1.06 | -13.10 |
| 55. | 2025. 8. 31. | 11.83% | 1.91% | 126.65 | 0.59 | 8.67 |
| 56. | 2025. 9. 30. | -9.26% | 3.53% | 96.76 | 5.74 | -23.57 |
| 57. | 2025. 10. 31. | -11.35% | 2.27% | 142.20 | 1.28 | -13.51 |
| 58. | 2025. 11. 30. | 4.22% | 0.13% | 13.26 | 1.01 | -3.66 |
| 59. | 2025. 12. 31. | 3.10% | -0.05% | 6.38 | 1.41 | -3.00 |
| 합계 (Σ): | 3,223.31 | 1,108.23 | 1,119.07 | |||
모두 보기
분산TXN = Σ(RTXN,t–RTXN)2 ÷ (59 – 1)
= 3,223.31 ÷ (59 – 1)
= 55.57
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,108.23 ÷ (59 – 1)
= 19.11
공분산TXN, S&P 500 = Σ(RTXN,t–RTXN)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,119.07 ÷ (59 – 1)
= 19.29
체계적인 위험 추정 (β)
| 분산TXN | 55.57 |
| 분산S&P 500 | 19.11 |
| 공분산TXN, S&P 500 | 19.29 |
| 상관 계수TXN, S&P 5001 | 0.59 |
| βTXN2 | 1.01 |
| αTXN3 | -0.57% |
계산
1 상관 계수TXN, S&P 500
= 공분산TXN, S&P 500 ÷ (표준 편차TXN × 표준 편차S&P 500)
= 19.29 ÷ (7.45% × 4.37%)
= 0.59
2 βTXN
= 공분산TXN, S&P 500 ÷ 분산S&P 500
= 19.29 ÷ 19.11
= 1.01
3 αTXN
= 평균의TXN – βTXN × 평균의S&P 500
= 0.58% – 1.01 × 1.14%
= -0.57%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.54% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 17.37% |
| 보통주의 체계적 위험TI | βTXN | 1.01 |
| TI 보통주에 대한 예상 수익률3 | E(RTXN) | 17.49% |
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]
= 4.54% + 1.01 [17.37% – 4.54%]
= 17.49%