Modelo de fijación de precios de activos de capital (CAPM)
El modelo de fijación de precios de activos de capital (CAPM, por sus siglas en inglés) indica cuál debería ser la tasa de rendimiento esperada o requerida en activos de riesgo como las acciones ordinarias de TI.
Tasas de retorno
Texas Instruments Inc., tasas mensuales de retorno
| Texas Instruments Inc. (TXN) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioTXN,t1 | DividendoTXN,t1 | RTXN,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2019 | $100.68 | 2,704.10 | ||||
| 1. | 28 feb. 2019 | $105.78 | 5.07% | 2,784.49 | 2.97% | |
| 2. | 31 mar. 2019 | $106.07 | 0.27% | 2,834.40 | 1.79% | |
| 3. | 30 abr. 2019 | $117.83 | 11.09% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | $152.71 | 7.53% | 4,567.80 | 8.92% | |
| 59. | 31 dic. 2023 | $170.46 | 11.62% | 4,769.83 | 4.42% | |
| Promedio (R): | 1.38% | 1.11% | ||||
| Desviación estándar: | 7.30% | 5.31% | ||||
| Texas Instruments Inc. (TXN) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioTXN,t1 | DividendoTXN,t1 | RTXN,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2019 | $100.68 | 2,704.10 | ||||
| 1. | 28 feb. 2019 | $105.78 | 5.07% | 2,784.49 | 2.97% | |
| 2. | 31 mar. 2019 | $106.07 | 0.27% | 2,834.40 | 1.79% | |
| 3. | 30 abr. 2019 | $117.83 | 11.09% | 2,945.83 | 3.93% | |
| 4. | 31 may. 2019 | $104.31 | $0.77 | -10.82% | 2,752.06 | -6.58% |
| 5. | 30 jun. 2019 | $114.76 | 10.02% | 2,941.76 | 6.89% | |
| 6. | 31 jul. 2019 | $125.01 | $0.77 | 9.60% | 2,980.38 | 1.31% |
| 7. | 31 ago. 2019 | $123.75 | -1.01% | 2,926.46 | -1.81% | |
| 8. | 30 sept. 2019 | $129.24 | 4.44% | 2,976.74 | 1.72% | |
| 9. | 31 oct. 2019 | $117.99 | $0.90 | -8.01% | 3,037.56 | 2.04% |
| 10. | 30 nov. 2019 | $120.21 | 1.88% | 3,140.98 | 3.40% | |
| 11. | 31 dic. 2019 | $128.29 | 6.72% | 3,230.78 | 2.86% | |
| 12. | 31 ene. 2020 | $120.65 | $0.90 | -5.25% | 3,225.52 | -0.16% |
| 13. | 29 feb. 2020 | $114.14 | -5.40% | 2,954.22 | -8.41% | |
| 14. | 31 mar. 2020 | $99.93 | -12.45% | 2,584.59 | -12.51% | |
| 15. | 30 abr. 2020 | $116.07 | 16.15% | 2,912.43 | 12.68% | |
| 16. | 31 may. 2020 | $118.74 | $0.90 | 3.08% | 3,044.31 | 4.53% |
| 17. | 30 jun. 2020 | $126.97 | 6.93% | 3,100.29 | 1.84% | |
| 18. | 31 jul. 2020 | $127.55 | $0.90 | 1.17% | 3,271.12 | 5.51% |
| 19. | 31 ago. 2020 | $142.15 | 11.45% | 3,500.31 | 7.01% | |
| 20. | 30 sept. 2020 | $142.79 | 0.45% | 3,363.00 | -3.92% | |
| 21. | 31 oct. 2020 | $144.59 | $1.02 | 1.97% | 3,269.96 | -2.77% |
| 22. | 30 nov. 2020 | $161.25 | 11.52% | 3,621.63 | 10.75% | |
| 23. | 31 dic. 2020 | $164.13 | 1.79% | 3,756.07 | 3.71% | |
| 24. | 31 ene. 2021 | $165.69 | $1.02 | 1.57% | 3,714.24 | -1.11% |
| 25. | 28 feb. 2021 | $172.27 | 3.97% | 3,811.15 | 2.61% | |
| 26. | 31 mar. 2021 | $188.99 | 9.71% | 3,972.89 | 4.24% | |
| 27. | 30 abr. 2021 | $180.51 | $1.02 | -3.95% | 4,181.17 | 5.24% |
| 28. | 31 may. 2021 | $189.82 | 5.16% | 4,204.11 | 0.55% | |
| 29. | 30 jun. 2021 | $192.30 | 1.31% | 4,297.50 | 2.22% | |
| 30. | 31 jul. 2021 | $190.62 | $1.02 | -0.34% | 4,395.26 | 2.27% |
| 31. | 31 ago. 2021 | $190.91 | 0.15% | 4,522.68 | 2.90% | |
| 32. | 30 sept. 2021 | $192.21 | 0.68% | 4,307.54 | -4.76% | |
| 33. | 31 oct. 2021 | $187.48 | $1.15 | -1.86% | 4,605.38 | 6.91% |
| 34. | 30 nov. 2021 | $192.37 | 2.61% | 4,567.00 | -0.83% | |
| 35. | 31 dic. 2021 | $188.47 | -2.03% | 4,766.18 | 4.36% | |
| 36. | 31 ene. 2022 | $179.49 | $1.15 | -4.15% | 4,515.55 | -5.26% |
| 37. | 28 feb. 2022 | $169.99 | -5.29% | 4,373.94 | -3.14% | |
| 38. | 31 mar. 2022 | $183.48 | 7.94% | 4,530.41 | 3.58% | |
| 39. | 30 abr. 2022 | $170.25 | -7.21% | 4,131.93 | -8.80% | |
| 40. | 31 may. 2022 | $176.76 | $1.15 | 4.50% | 4,132.15 | 0.01% |
| 41. | 30 jun. 2022 | $153.65 | -13.07% | 3,785.38 | -8.39% | |
| 42. | 31 jul. 2022 | $178.89 | $1.15 | 17.18% | 4,130.29 | 9.11% |
| 43. | 31 ago. 2022 | $165.21 | -7.65% | 3,955.00 | -4.24% | |
| 44. | 30 sept. 2022 | $154.78 | -6.31% | 3,585.62 | -9.34% | |
| 45. | 31 oct. 2022 | $160.63 | $1.24 | 4.58% | 3,871.98 | 7.99% |
| 46. | 30 nov. 2022 | $180.46 | 12.35% | 4,080.11 | 5.38% | |
| 47. | 31 dic. 2022 | $165.22 | -8.45% | 3,839.50 | -5.90% | |
| 48. | 31 ene. 2023 | $177.21 | $1.24 | 8.01% | 4,076.60 | 6.18% |
| 49. | 28 feb. 2023 | $171.45 | -3.25% | 3,970.15 | -2.61% | |
| 50. | 31 mar. 2023 | $186.01 | 8.49% | 4,109.31 | 3.51% | |
| 51. | 30 abr. 2023 | $167.20 | -10.11% | 4,169.48 | 1.46% | |
| 52. | 31 may. 2023 | $173.88 | $1.24 | 4.74% | 4,179.83 | 0.25% |
| 53. | 30 jun. 2023 | $180.02 | 3.53% | 4,376.86 | 4.71% | |
| 54. | 31 jul. 2023 | $180.00 | $1.24 | 0.68% | 4,588.96 | 4.85% |
| 55. | 31 ago. 2023 | $168.06 | -6.63% | 4,507.66 | -1.77% | |
| 56. | 30 sept. 2023 | $159.01 | -5.38% | 4,288.05 | -4.87% | |
| 57. | 31 oct. 2023 | $142.01 | $1.30 | -9.87% | 4,193.80 | -2.20% |
| 58. | 30 nov. 2023 | $152.71 | 7.53% | 4,567.80 | 8.92% | |
| 59. | 31 dic. 2023 | $170.46 | 11.62% | 4,769.83 | 4.42% | |
| Promedio (R): | 1.38% | 1.11% | ||||
| Desviación estándar: | 7.30% | 5.31% | ||||
Mostrar todo
1 Datos en dólares estadounidenses por acción ordinaria, ajustados por divisiones y dividendos de acciones.
2 Tasa de rendimiento de las acciones ordinarias de TXN durante el período t.
3 Tasa de rendimiento del S&P 500 (el proxy de la cartera de mercado) durante el período t.
Varianza y covarianza
Texas Instruments Inc., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | 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. | 28 feb. 2019 | 5.07% | 2.97% | 13.59 | 3.49 | 6.88 |
| 2. | 31 mar. 2019 | 0.27% | 1.79% | 1.22 | 0.47 | -0.76 |
| 3. | 30 abr. 2019 | 11.09% | 3.93% | 94.24 | 7.98 | 27.43 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | 7.53% | 8.92% | 37.89 | 61.03 | 48.09 |
| 59. | 31 dic. 2023 | 11.62% | 4.42% | 104.94 | 11.00 | 33.98 |
| Total (Σ): | 3,089.71 | 1,634.30 | 1,704.50 | |||
| t | Fecha | 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. | 28 feb. 2019 | 5.07% | 2.97% | 13.59 | 3.49 | 6.88 |
| 2. | 31 mar. 2019 | 0.27% | 1.79% | 1.22 | 0.47 | -0.76 |
| 3. | 30 abr. 2019 | 11.09% | 3.93% | 94.24 | 7.98 | 27.43 |
| 4. | 31 may. 2019 | -10.82% | -6.58% | 148.84 | 59.04 | 93.74 |
| 5. | 30 jun. 2019 | 10.02% | 6.89% | 74.63 | 33.49 | 50.00 |
| 6. | 31 jul. 2019 | 9.60% | 1.31% | 67.62 | 0.04 | 1.70 |
| 7. | 31 ago. 2019 | -1.01% | -1.81% | 5.70 | 8.50 | 6.96 |
| 8. | 30 sept. 2019 | 4.44% | 1.72% | 9.35 | 0.37 | 1.87 |
| 9. | 31 oct. 2019 | -8.01% | 2.04% | 88.13 | 0.88 | -8.80 |
| 10. | 30 nov. 2019 | 1.88% | 3.40% | 0.25 | 5.28 | 1.15 |
| 11. | 31 dic. 2019 | 6.72% | 2.86% | 28.54 | 3.07 | 9.37 |
| 12. | 31 ene. 2020 | -5.25% | -0.16% | 44.00 | 1.61 | 8.41 |
| 13. | 29 feb. 2020 | -5.40% | -8.41% | 45.90 | 90.57 | 64.48 |
| 14. | 31 mar. 2020 | -12.45% | -12.51% | 191.24 | 185.44 | 188.32 |
| 15. | 30 abr. 2020 | 16.15% | 12.68% | 218.21 | 134.06 | 171.04 |
| 16. | 31 may. 2020 | 3.08% | 4.53% | 2.88 | 11.71 | 5.81 |
| 17. | 30 jun. 2020 | 6.93% | 1.84% | 30.82 | 0.54 | 4.07 |
| 18. | 31 jul. 2020 | 1.17% | 5.51% | 0.05 | 19.40 | -0.94 |
| 19. | 31 ago. 2020 | 11.45% | 7.01% | 101.35 | 34.82 | 59.40 |
| 20. | 30 sept. 2020 | 0.45% | -3.92% | 0.86 | 25.29 | 4.67 |
| 21. | 31 oct. 2020 | 1.97% | -2.77% | 0.35 | 15.00 | -2.31 |
| 22. | 30 nov. 2020 | 11.52% | 10.75% | 102.88 | 93.10 | 97.87 |
| 23. | 31 dic. 2020 | 1.79% | 3.71% | 0.17 | 6.79 | 1.06 |
| 24. | 31 ene. 2021 | 1.57% | -1.11% | 0.04 | 4.93 | -0.43 |
| 25. | 28 feb. 2021 | 3.97% | 2.61% | 6.72 | 2.26 | 3.90 |
| 26. | 31 mar. 2021 | 9.71% | 4.24% | 69.33 | 9.85 | 26.13 |
| 27. | 30 abr. 2021 | -3.95% | 5.24% | 28.37 | 17.11 | -22.03 |
| 28. | 31 may. 2021 | 5.16% | 0.55% | 14.28 | 0.31 | -2.11 |
| 29. | 30 jun. 2021 | 1.31% | 2.22% | 0.01 | 1.24 | -0.08 |
| 30. | 31 jul. 2021 | -0.34% | 2.27% | 2.97 | 1.37 | -2.01 |
| 31. | 31 ago. 2021 | 0.15% | 2.90% | 1.51 | 3.22 | -2.20 |
| 32. | 30 sept. 2021 | 0.68% | -4.76% | 0.49 | 34.37 | 4.09 |
| 33. | 31 oct. 2021 | -1.86% | 6.91% | 10.51 | 33.74 | -18.83 |
| 34. | 30 nov. 2021 | 2.61% | -0.83% | 1.51 | 3.76 | -2.38 |
| 35. | 31 dic. 2021 | -2.03% | 4.36% | 11.60 | 10.60 | -11.09 |
| 36. | 31 ene. 2022 | -4.15% | -5.26% | 30.62 | 40.51 | 35.22 |
| 37. | 28 feb. 2022 | -5.29% | -3.14% | 44.52 | 17.99 | 28.30 |
| 38. | 31 mar. 2022 | 7.94% | 3.58% | 42.99 | 6.11 | 16.20 |
| 39. | 30 abr. 2022 | -7.21% | -8.80% | 73.79 | 98.04 | 85.05 |
| 40. | 31 may. 2022 | 4.50% | 0.01% | 9.73 | 1.21 | -3.43 |
| 41. | 30 jun. 2022 | -13.07% | -8.39% | 208.90 | 90.21 | 137.28 |
| 42. | 31 jul. 2022 | 17.18% | 9.11% | 249.52 | 64.09 | 126.46 |
| 43. | 31 ago. 2022 | -7.65% | -4.24% | 81.48 | 28.62 | 48.29 |
| 44. | 30 sept. 2022 | -6.31% | -9.34% | 59.17 | 109.11 | 80.35 |
| 45. | 31 oct. 2022 | 4.58% | 7.99% | 10.25 | 47.34 | 22.03 |
| 46. | 30 nov. 2022 | 12.35% | 5.38% | 120.25 | 18.23 | 46.82 |
| 47. | 31 dic. 2022 | -8.45% | -5.90% | 96.52 | 49.04 | 68.80 |
| 48. | 31 ene. 2023 | 8.01% | 6.18% | 43.93 | 25.70 | 33.60 |
| 49. | 28 feb. 2023 | -3.25% | -2.61% | 21.43 | 13.82 | 17.21 |
| 50. | 31 mar. 2023 | 8.49% | 3.51% | 50.59 | 5.76 | 17.07 |
| 51. | 30 abr. 2023 | -10.11% | 1.46% | 132.06 | 0.13 | -4.12 |
| 52. | 31 may. 2023 | 4.74% | 0.25% | 11.27 | 0.74 | -2.88 |
| 53. | 30 jun. 2023 | 3.53% | 4.71% | 4.63 | 13.02 | 7.76 |
| 54. | 31 jul. 2023 | 0.68% | 4.85% | 0.49 | 13.99 | -2.62 |
| 55. | 31 ago. 2023 | -6.63% | -1.77% | 64.20 | 8.28 | 23.06 |
| 56. | 30 sept. 2023 | -5.38% | -4.87% | 45.75 | 35.73 | 40.44 |
| 57. | 31 oct. 2023 | -9.87% | -2.20% | 126.63 | 10.92 | 37.18 |
| 58. | 30 nov. 2023 | 7.53% | 8.92% | 37.89 | 61.03 | 48.09 |
| 59. | 31 dic. 2023 | 11.62% | 4.42% | 104.94 | 11.00 | 33.98 |
| Total (Σ): | 3,089.71 | 1,634.30 | 1,704.50 | |||
Mostrar todo
VarianzaTXN = Σ(RTXN,t–RTXN)2 ÷ (59 – 1)
= 3,089.71 ÷ (59 – 1)
= 53.27
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
CovarianzaTXN, S&P 500 = Σ(RTXN,t–RTXN)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,704.50 ÷ (59 – 1)
= 29.39
Estimación sistemática del riesgo (β)
| VarianzaTXN | 53.27 |
| VarianzaS&P 500 | 28.18 |
| CovarianzaTXN, S&P 500 | 29.39 |
| Coeficiente de correlaciónTXN, S&P 5001 | 0.76 |
| βTXN2 | 1.04 |
| αTXN3 | 0.23% |
Cálculos
1 Coeficiente de correlaciónTXN, S&P 500
= CovarianzaTXN, S&P 500 ÷ (Desviación estándarTXN × Desviación estándarS&P 500)
= 29.39 ÷ (7.30% × 5.31%)
= 0.76
2 βTXN
= CovarianzaTXN, S&P 500 ÷ VarianzaS&P 500
= 29.39 ÷ 28.18
= 1.04
3 αTXN
= PromedioTXN – βTXN × PromedioS&P 500
= 1.38% – 1.04 × 1.11%
= 0.23%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.56% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.77% |
| Riesgo sistemático de TI acciones ordinarias | βTXN | 1.04 |
| Tasa de rendimiento esperada de las acciones ordinarias de TI3 | E(RTXN) | 14.16% |
1 Promedio no ponderado de los rendimientos de las ofertas de todos los bonos del Tesoro de EE. UU. con cupón fijo en circulación que no vencen ni son rescatables en menos de 10 años (proxy de tasa de rendimiento libre de riesgo).
3 E(RTXN) = RF + βTXN [E(RM) – RF]
= 4.56% + 1.04 [13.77% – 4.56%]
= 14.16%