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 |
| 2019. 1. 31. | $100.68 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $105.78 | 5.07% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $106.07 | 0.27% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $117.83 | 11.09% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $152.71 | 7.53% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $170.46 | 11.62% | 4,769.83 | 4.42% | |
| 평균의 (R): | 1.38% | 1.11% | ||||
| 표준 편차: | 7.30% | 5.31% | ||||
| 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 |
| 2019. 1. 31. | $100.68 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $105.78 | 5.07% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $106.07 | 0.27% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $117.83 | 11.09% | 2,945.83 | 3.93% | |
| 4. | 2019. 5. 31. | $104.31 | $0.77 | -10.82% | 2,752.06 | -6.58% |
| 5. | 2019. 6. 30. | $114.76 | 10.02% | 2,941.76 | 6.89% | |
| 6. | 2019. 7. 31. | $125.01 | $0.77 | 9.60% | 2,980.38 | 1.31% |
| 7. | 2019. 8. 31. | $123.75 | -1.01% | 2,926.46 | -1.81% | |
| 8. | 2019. 9. 30. | $129.24 | 4.44% | 2,976.74 | 1.72% | |
| 9. | 2019. 10. 31. | $117.99 | $0.90 | -8.01% | 3,037.56 | 2.04% |
| 10. | 2019. 11. 30. | $120.21 | 1.88% | 3,140.98 | 3.40% | |
| 11. | 2019. 12. 31. | $128.29 | 6.72% | 3,230.78 | 2.86% | |
| 12. | 2020. 1. 31. | $120.65 | $0.90 | -5.25% | 3,225.52 | -0.16% |
| 13. | 2020. 2. 29. | $114.14 | -5.40% | 2,954.22 | -8.41% | |
| 14. | 2020. 3. 31. | $99.93 | -12.45% | 2,584.59 | -12.51% | |
| 15. | 2020. 4. 30. | $116.07 | 16.15% | 2,912.43 | 12.68% | |
| 16. | 2020. 5. 31. | $118.74 | $0.90 | 3.08% | 3,044.31 | 4.53% |
| 17. | 2020. 6. 30. | $126.97 | 6.93% | 3,100.29 | 1.84% | |
| 18. | 2020. 7. 31. | $127.55 | $0.90 | 1.17% | 3,271.12 | 5.51% |
| 19. | 2020. 8. 31. | $142.15 | 11.45% | 3,500.31 | 7.01% | |
| 20. | 2020. 9. 30. | $142.79 | 0.45% | 3,363.00 | -3.92% | |
| 21. | 2020. 10. 31. | $144.59 | $1.02 | 1.97% | 3,269.96 | -2.77% |
| 22. | 2020. 11. 30. | $161.25 | 11.52% | 3,621.63 | 10.75% | |
| 23. | 2020. 12. 31. | $164.13 | 1.79% | 3,756.07 | 3.71% | |
| 24. | 2021. 1. 31. | $165.69 | $1.02 | 1.57% | 3,714.24 | -1.11% |
| 25. | 2021. 2. 28. | $172.27 | 3.97% | 3,811.15 | 2.61% | |
| 26. | 2021. 3. 31. | $188.99 | 9.71% | 3,972.89 | 4.24% | |
| 27. | 2021. 4. 30. | $180.51 | $1.02 | -3.95% | 4,181.17 | 5.24% |
| 28. | 2021. 5. 31. | $189.82 | 5.16% | 4,204.11 | 0.55% | |
| 29. | 2021. 6. 30. | $192.30 | 1.31% | 4,297.50 | 2.22% | |
| 30. | 2021. 7. 31. | $190.62 | $1.02 | -0.34% | 4,395.26 | 2.27% |
| 31. | 2021. 8. 31. | $190.91 | 0.15% | 4,522.68 | 2.90% | |
| 32. | 2021. 9. 30. | $192.21 | 0.68% | 4,307.54 | -4.76% | |
| 33. | 2021. 10. 31. | $187.48 | $1.15 | -1.86% | 4,605.38 | 6.91% |
| 34. | 2021. 11. 30. | $192.37 | 2.61% | 4,567.00 | -0.83% | |
| 35. | 2021. 12. 31. | $188.47 | -2.03% | 4,766.18 | 4.36% | |
| 36. | 2022. 1. 31. | $179.49 | $1.15 | -4.15% | 4,515.55 | -5.26% |
| 37. | 2022. 2. 28. | $169.99 | -5.29% | 4,373.94 | -3.14% | |
| 38. | 2022. 3. 31. | $183.48 | 7.94% | 4,530.41 | 3.58% | |
| 39. | 2022. 4. 30. | $170.25 | -7.21% | 4,131.93 | -8.80% | |
| 40. | 2022. 5. 31. | $176.76 | $1.15 | 4.50% | 4,132.15 | 0.01% |
| 41. | 2022. 6. 30. | $153.65 | -13.07% | 3,785.38 | -8.39% | |
| 42. | 2022. 7. 31. | $178.89 | $1.15 | 17.18% | 4,130.29 | 9.11% |
| 43. | 2022. 8. 31. | $165.21 | -7.65% | 3,955.00 | -4.24% | |
| 44. | 2022. 9. 30. | $154.78 | -6.31% | 3,585.62 | -9.34% | |
| 45. | 2022. 10. 31. | $160.63 | $1.24 | 4.58% | 3,871.98 | 7.99% |
| 46. | 2022. 11. 30. | $180.46 | 12.35% | 4,080.11 | 5.38% | |
| 47. | 2022. 12. 31. | $165.22 | -8.45% | 3,839.50 | -5.90% | |
| 48. | 2023. 1. 31. | $177.21 | $1.24 | 8.01% | 4,076.60 | 6.18% |
| 49. | 2023. 2. 28. | $171.45 | -3.25% | 3,970.15 | -2.61% | |
| 50. | 2023. 3. 31. | $186.01 | 8.49% | 4,109.31 | 3.51% | |
| 51. | 2023. 4. 30. | $167.20 | -10.11% | 4,169.48 | 1.46% | |
| 52. | 2023. 5. 31. | $173.88 | $1.24 | 4.74% | 4,179.83 | 0.25% |
| 53. | 2023. 6. 30. | $180.02 | 3.53% | 4,376.86 | 4.71% | |
| 54. | 2023. 7. 31. | $180.00 | $1.24 | 0.68% | 4,588.96 | 4.85% |
| 55. | 2023. 8. 31. | $168.06 | -6.63% | 4,507.66 | -1.77% | |
| 56. | 2023. 9. 30. | $159.01 | -5.38% | 4,288.05 | -4.87% | |
| 57. | 2023. 10. 31. | $142.01 | $1.30 | -9.87% | 4,193.80 | -2.20% |
| 58. | 2023. 11. 30. | $152.71 | 7.53% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $170.46 | 11.62% | 4,769.83 | 4.42% | |
| 평균의 (R): | 1.38% | 1.11% | ||||
| 표준 편차: | 7.30% | 5.31% | ||||
모두 표시
1 보통주 주당 US$ 단위의 데이터로, 분할 및 주식 배당금에 맞게 조정됩니다.
2 기간 t 동안 TXN의 보통주에 대한 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)에 대한 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. | 2019. 2. 28. | 5.07% | 2.97% | 13.59 | 3.49 | 6.88 |
| 2. | 2019. 3. 31. | 0.27% | 1.79% | 1.22 | 0.47 | -0.76 |
| 3. | 2019. 4. 30. | 11.09% | 3.93% | 94.24 | 7.98 | 27.43 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | 7.53% | 8.92% | 37.89 | 61.03 | 48.09 |
| 59. | 2023. 12. 31. | 11.62% | 4.42% | 104.94 | 11.00 | 33.98 |
| 합계 (Σ): | 3,089.71 | 1,634.30 | 1,704.50 | |||
| 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. | 2019. 2. 28. | 5.07% | 2.97% | 13.59 | 3.49 | 6.88 |
| 2. | 2019. 3. 31. | 0.27% | 1.79% | 1.22 | 0.47 | -0.76 |
| 3. | 2019. 4. 30. | 11.09% | 3.93% | 94.24 | 7.98 | 27.43 |
| 4. | 2019. 5. 31. | -10.82% | -6.58% | 148.84 | 59.04 | 93.74 |
| 5. | 2019. 6. 30. | 10.02% | 6.89% | 74.63 | 33.49 | 50.00 |
| 6. | 2019. 7. 31. | 9.60% | 1.31% | 67.62 | 0.04 | 1.70 |
| 7. | 2019. 8. 31. | -1.01% | -1.81% | 5.70 | 8.50 | 6.96 |
| 8. | 2019. 9. 30. | 4.44% | 1.72% | 9.35 | 0.37 | 1.87 |
| 9. | 2019. 10. 31. | -8.01% | 2.04% | 88.13 | 0.88 | -8.80 |
| 10. | 2019. 11. 30. | 1.88% | 3.40% | 0.25 | 5.28 | 1.15 |
| 11. | 2019. 12. 31. | 6.72% | 2.86% | 28.54 | 3.07 | 9.37 |
| 12. | 2020. 1. 31. | -5.25% | -0.16% | 44.00 | 1.61 | 8.41 |
| 13. | 2020. 2. 29. | -5.40% | -8.41% | 45.90 | 90.57 | 64.48 |
| 14. | 2020. 3. 31. | -12.45% | -12.51% | 191.24 | 185.44 | 188.32 |
| 15. | 2020. 4. 30. | 16.15% | 12.68% | 218.21 | 134.06 | 171.04 |
| 16. | 2020. 5. 31. | 3.08% | 4.53% | 2.88 | 11.71 | 5.81 |
| 17. | 2020. 6. 30. | 6.93% | 1.84% | 30.82 | 0.54 | 4.07 |
| 18. | 2020. 7. 31. | 1.17% | 5.51% | 0.05 | 19.40 | -0.94 |
| 19. | 2020. 8. 31. | 11.45% | 7.01% | 101.35 | 34.82 | 59.40 |
| 20. | 2020. 9. 30. | 0.45% | -3.92% | 0.86 | 25.29 | 4.67 |
| 21. | 2020. 10. 31. | 1.97% | -2.77% | 0.35 | 15.00 | -2.31 |
| 22. | 2020. 11. 30. | 11.52% | 10.75% | 102.88 | 93.10 | 97.87 |
| 23. | 2020. 12. 31. | 1.79% | 3.71% | 0.17 | 6.79 | 1.06 |
| 24. | 2021. 1. 31. | 1.57% | -1.11% | 0.04 | 4.93 | -0.43 |
| 25. | 2021. 2. 28. | 3.97% | 2.61% | 6.72 | 2.26 | 3.90 |
| 26. | 2021. 3. 31. | 9.71% | 4.24% | 69.33 | 9.85 | 26.13 |
| 27. | 2021. 4. 30. | -3.95% | 5.24% | 28.37 | 17.11 | -22.03 |
| 28. | 2021. 5. 31. | 5.16% | 0.55% | 14.28 | 0.31 | -2.11 |
| 29. | 2021. 6. 30. | 1.31% | 2.22% | 0.01 | 1.24 | -0.08 |
| 30. | 2021. 7. 31. | -0.34% | 2.27% | 2.97 | 1.37 | -2.01 |
| 31. | 2021. 8. 31. | 0.15% | 2.90% | 1.51 | 3.22 | -2.20 |
| 32. | 2021. 9. 30. | 0.68% | -4.76% | 0.49 | 34.37 | 4.09 |
| 33. | 2021. 10. 31. | -1.86% | 6.91% | 10.51 | 33.74 | -18.83 |
| 34. | 2021. 11. 30. | 2.61% | -0.83% | 1.51 | 3.76 | -2.38 |
| 35. | 2021. 12. 31. | -2.03% | 4.36% | 11.60 | 10.60 | -11.09 |
| 36. | 2022. 1. 31. | -4.15% | -5.26% | 30.62 | 40.51 | 35.22 |
| 37. | 2022. 2. 28. | -5.29% | -3.14% | 44.52 | 17.99 | 28.30 |
| 38. | 2022. 3. 31. | 7.94% | 3.58% | 42.99 | 6.11 | 16.20 |
| 39. | 2022. 4. 30. | -7.21% | -8.80% | 73.79 | 98.04 | 85.05 |
| 40. | 2022. 5. 31. | 4.50% | 0.01% | 9.73 | 1.21 | -3.43 |
| 41. | 2022. 6. 30. | -13.07% | -8.39% | 208.90 | 90.21 | 137.28 |
| 42. | 2022. 7. 31. | 17.18% | 9.11% | 249.52 | 64.09 | 126.46 |
| 43. | 2022. 8. 31. | -7.65% | -4.24% | 81.48 | 28.62 | 48.29 |
| 44. | 2022. 9. 30. | -6.31% | -9.34% | 59.17 | 109.11 | 80.35 |
| 45. | 2022. 10. 31. | 4.58% | 7.99% | 10.25 | 47.34 | 22.03 |
| 46. | 2022. 11. 30. | 12.35% | 5.38% | 120.25 | 18.23 | 46.82 |
| 47. | 2022. 12. 31. | -8.45% | -5.90% | 96.52 | 49.04 | 68.80 |
| 48. | 2023. 1. 31. | 8.01% | 6.18% | 43.93 | 25.70 | 33.60 |
| 49. | 2023. 2. 28. | -3.25% | -2.61% | 21.43 | 13.82 | 17.21 |
| 50. | 2023. 3. 31. | 8.49% | 3.51% | 50.59 | 5.76 | 17.07 |
| 51. | 2023. 4. 30. | -10.11% | 1.46% | 132.06 | 0.13 | -4.12 |
| 52. | 2023. 5. 31. | 4.74% | 0.25% | 11.27 | 0.74 | -2.88 |
| 53. | 2023. 6. 30. | 3.53% | 4.71% | 4.63 | 13.02 | 7.76 |
| 54. | 2023. 7. 31. | 0.68% | 4.85% | 0.49 | 13.99 | -2.62 |
| 55. | 2023. 8. 31. | -6.63% | -1.77% | 64.20 | 8.28 | 23.06 |
| 56. | 2023. 9. 30. | -5.38% | -4.87% | 45.75 | 35.73 | 40.44 |
| 57. | 2023. 10. 31. | -9.87% | -2.20% | 126.63 | 10.92 | 37.18 |
| 58. | 2023. 11. 30. | 7.53% | 8.92% | 37.89 | 61.03 | 48.09 |
| 59. | 2023. 12. 31. | 11.62% | 4.42% | 104.94 | 11.00 | 33.98 |
| 합계 (Σ): | 3,089.71 | 1,634.30 | 1,704.50 | |||
모두 표시
분산TXN = Σ(RTXN,t–RTXN)2 ÷ (59 – 1)
= 3,089.71 ÷ (59 – 1)
= 53.27
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산TXN, S&P 500 = Σ(RTXN,t–RTXN)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,704.50 ÷ (59 – 1)
= 29.39
체계적인 위험 추정 (β)
| 분산TXN | 53.27 |
| 분산S&P 500 | 28.18 |
| 공분산TXN, S&P 500 | 29.39 |
| 상관 계수TXN, S&P 5001 | 0.76 |
| βTXN2 | 1.04 |
| αTXN3 | 0.23% |
계산
1 상관 계수TXN, S&P 500
= 공분산TXN, S&P 500 ÷ (표준 편차TXN × 표준 편차S&P 500)
= 29.39 ÷ (7.30% × 5.31%)
= 0.76
2 βTXN
= 공분산TXN, S&P 500 ÷ 분산S&P 500
= 29.39 ÷ 28.18
= 1.04
3 αTXN
= 평균의TXN – βTXN × 평균의S&P 500
= 1.38% – 1.04 × 1.11%
= 0.23%
예상 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.86% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.54% |
| 보통주의 체계적 위험TI | βTXN | 1.04 |
| TI 보통주에 대한 예상 수익률3 | E(RTXN) | 13.91% |
1 10년 이내에 만기가 되지 않거나 콜 가능하지 않은 모든 미결제 고정 쿠폰 미국 재무부 채권에 대한 입찰 수익률의 가중 평균(무위험 수익률 프록시).
2 자세히 보기 »
3 E(RTXN) = RF + βTXN [E(RM) – RF]
= 4.86% + 1.04 [13.54% – 4.86%]
= 13.91%