Modelo de fijación de precios de activos de capital (CAPM)
El modelo de fijación de precios de activos de capital (CAPM) indica cuál debería ser la tasa de rendimiento esperada o requerida de los 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. 2017 | $75.54 | 2,278.87 | ||||
| 1. | 28 feb. 2017 | $76.62 | 1.43% | 2,363.64 | 3.72% | |
| 2. | 31 mar. 2017 | $80.56 | 5.14% | 2,362.72 | -0.04% | |
| 3. | 30 abr. 2017 | $79.18 | $0.50 | -1.09% | 2,384.20 | 0.91% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2021 | $192.37 | 2.61% | 4,567.00 | -0.83% | |
| 59. | 31 dic. 2021 | $188.47 | -2.03% | 4,766.18 | 4.36% | |
| Promedio (R): | 1.96% | 1.36% | ||||
| Desviación estándar: | 6.12% | 4.48% | ||||
| 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. 2017 | $75.54 | 2,278.87 | ||||
| 1. | 28 feb. 2017 | $76.62 | 1.43% | 2,363.64 | 3.72% | |
| 2. | 31 mar. 2017 | $80.56 | 5.14% | 2,362.72 | -0.04% | |
| 3. | 30 abr. 2017 | $79.18 | $0.50 | -1.09% | 2,384.20 | 0.91% |
| 4. | 31 may. 2017 | $82.49 | 4.18% | 2,411.80 | 1.16% | |
| 5. | 30 jun. 2017 | $76.93 | -6.74% | 2,423.41 | 0.48% | |
| 6. | 31 jul. 2017 | $81.38 | $0.50 | 6.43% | 2,470.30 | 1.93% |
| 7. | 31 ago. 2017 | $82.82 | 1.77% | 2,471.65 | 0.05% | |
| 8. | 30 sept. 2017 | $89.64 | 8.23% | 2,519.36 | 1.93% | |
| 9. | 31 oct. 2017 | $96.69 | $0.62 | 8.56% | 2,575.26 | 2.22% |
| 10. | 30 nov. 2017 | $97.29 | 0.62% | 2,647.58 | 2.81% | |
| 11. | 31 dic. 2017 | $104.44 | 7.35% | 2,673.61 | 0.98% | |
| 12. | 31 ene. 2018 | $109.67 | $0.62 | 5.60% | 2,823.81 | 5.62% |
| 13. | 28 feb. 2018 | $108.35 | -1.20% | 2,713.83 | -3.89% | |
| 14. | 31 mar. 2018 | $103.89 | -4.12% | 2,640.87 | -2.69% | |
| 15. | 30 abr. 2018 | $101.43 | -2.37% | 2,648.05 | 0.27% | |
| 16. | 31 may. 2018 | $111.91 | $0.62 | 10.94% | 2,705.27 | 2.16% |
| 17. | 30 jun. 2018 | $110.25 | -1.48% | 2,718.37 | 0.48% | |
| 18. | 31 jul. 2018 | $111.32 | $0.62 | 1.53% | 2,816.29 | 3.60% |
| 19. | 31 ago. 2018 | $112.40 | 0.97% | 2,901.52 | 3.03% | |
| 20. | 30 sept. 2018 | $107.29 | -4.55% | 2,913.98 | 0.43% | |
| 21. | 31 oct. 2018 | $92.83 | $0.77 | -12.76% | 2,711.74 | -6.94% |
| 22. | 30 nov. 2018 | $99.85 | 7.56% | 2,760.17 | 1.79% | |
| 23. | 31 dic. 2018 | $94.50 | -5.36% | 2,506.85 | -9.18% | |
| 24. | 31 ene. 2019 | $100.68 | $0.77 | 7.35% | 2,704.10 | 7.87% |
| 25. | 28 feb. 2019 | $105.78 | 5.07% | 2,784.49 | 2.97% | |
| 26. | 31 mar. 2019 | $106.07 | 0.27% | 2,834.40 | 1.79% | |
| 27. | 30 abr. 2019 | $117.83 | 11.09% | 2,945.83 | 3.93% | |
| 28. | 31 may. 2019 | $104.31 | $0.77 | -10.82% | 2,752.06 | -6.58% |
| 29. | 30 jun. 2019 | $114.76 | 10.02% | 2,941.76 | 6.89% | |
| 30. | 31 jul. 2019 | $125.01 | $0.77 | 9.60% | 2,980.38 | 1.31% |
| 31. | 31 ago. 2019 | $123.75 | -1.01% | 2,926.46 | -1.81% | |
| 32. | 30 sept. 2019 | $129.24 | 4.44% | 2,976.74 | 1.72% | |
| 33. | 31 oct. 2019 | $117.99 | $0.90 | -8.01% | 3,037.56 | 2.04% |
| 34. | 30 nov. 2019 | $120.21 | 1.88% | 3,140.98 | 3.40% | |
| 35. | 31 dic. 2019 | $128.29 | 6.72% | 3,230.78 | 2.86% | |
| 36. | 31 ene. 2020 | $120.65 | $0.90 | -5.25% | 3,225.52 | -0.16% |
| 37. | 29 feb. 2020 | $114.14 | -5.40% | 2,954.22 | -8.41% | |
| 38. | 31 mar. 2020 | $99.93 | -12.45% | 2,584.59 | -12.51% | |
| 39. | 30 abr. 2020 | $116.07 | 16.15% | 2,912.43 | 12.68% | |
| 40. | 31 may. 2020 | $118.74 | $0.90 | 3.08% | 3,044.31 | 4.53% |
| 41. | 30 jun. 2020 | $126.97 | 6.93% | 3,100.29 | 1.84% | |
| 42. | 31 jul. 2020 | $127.55 | $0.90 | 1.17% | 3,271.12 | 5.51% |
| 43. | 31 ago. 2020 | $142.15 | 11.45% | 3,500.31 | 7.01% | |
| 44. | 30 sept. 2020 | $142.79 | 0.45% | 3,363.00 | -3.92% | |
| 45. | 31 oct. 2020 | $144.59 | $1.02 | 1.97% | 3,269.96 | -2.77% |
| 46. | 30 nov. 2020 | $161.25 | 11.52% | 3,621.63 | 10.75% | |
| 47. | 31 dic. 2020 | $164.13 | 1.79% | 3,756.07 | 3.71% | |
| 48. | 31 ene. 2021 | $165.69 | $1.02 | 1.57% | 3,714.24 | -1.11% |
| 49. | 28 feb. 2021 | $172.27 | 3.97% | 3,811.15 | 2.61% | |
| 50. | 31 mar. 2021 | $188.99 | 9.71% | 3,972.89 | 4.24% | |
| 51. | 30 abr. 2021 | $180.51 | $1.02 | -3.95% | 4,181.17 | 5.24% |
| 52. | 31 may. 2021 | $189.82 | 5.16% | 4,204.11 | 0.55% | |
| 53. | 30 jun. 2021 | $192.30 | 1.31% | 4,297.50 | 2.22% | |
| 54. | 31 jul. 2021 | $190.62 | $1.02 | -0.34% | 4,395.26 | 2.27% |
| 55. | 31 ago. 2021 | $190.91 | 0.15% | 4,522.68 | 2.90% | |
| 56. | 30 sept. 2021 | $192.21 | 0.68% | 4,307.54 | -4.76% | |
| 57. | 31 oct. 2021 | $187.48 | $1.15 | -1.86% | 4,605.38 | 6.91% |
| 58. | 30 nov. 2021 | $192.37 | 2.61% | 4,567.00 | -0.83% | |
| 59. | 31 dic. 2021 | $188.47 | -2.03% | 4,766.18 | 4.36% | |
| Promedio (R): | 1.96% | 1.36% | ||||
| Desviación estándar: | 6.12% | 4.48% | ||||
Mostrar todo
1 Datos en US$ por acción de acciones ordinarias, ajustados por escisiones 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 varianza y covarianza de 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. 2017 | 1.43% | 3.72% | 0.28 | 5.58 | -1.25 |
| 2. | 31 mar. 2017 | 5.14% | -0.04% | 10.13 | 1.95 | -4.45 |
| 3. | 30 abr. 2017 | -1.09% | 0.91% | 9.32 | 0.20 | 1.37 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2021 | 2.61% | -0.83% | 0.42 | 4.80 | -1.42 |
| 59. | 31 dic. 2021 | -2.03% | 4.36% | 15.90 | 9.02 | -11.98 |
| Total (Σ): | 2,175.66 | 1,164.17 | 1,071.74 | |||
| 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. 2017 | 1.43% | 3.72% | 0.28 | 5.58 | -1.25 |
| 2. | 31 mar. 2017 | 5.14% | -0.04% | 10.13 | 1.95 | -4.45 |
| 3. | 30 abr. 2017 | -1.09% | 0.91% | 9.32 | 0.20 | 1.37 |
| 4. | 31 may. 2017 | 4.18% | 1.16% | 4.93 | 0.04 | -0.44 |
| 5. | 30 jun. 2017 | -6.74% | 0.48% | 75.69 | 0.77 | 7.63 |
| 6. | 31 jul. 2017 | 6.43% | 1.93% | 20.02 | 0.33 | 2.58 |
| 7. | 31 ago. 2017 | 1.77% | 0.05% | 0.04 | 1.70 | 0.25 |
| 8. | 30 sept. 2017 | 8.23% | 1.93% | 39.37 | 0.33 | 3.59 |
| 9. | 31 oct. 2017 | 8.56% | 2.22% | 43.51 | 0.74 | 5.68 |
| 10. | 30 nov. 2017 | 0.62% | 2.81% | 1.79 | 2.10 | -1.94 |
| 11. | 31 dic. 2017 | 7.35% | 0.98% | 29.04 | 0.14 | -2.02 |
| 12. | 31 ene. 2018 | 5.60% | 5.62% | 13.26 | 18.15 | 15.51 |
| 13. | 28 feb. 2018 | -1.20% | -3.89% | 10.01 | 27.59 | 16.62 |
| 14. | 31 mar. 2018 | -4.12% | -2.69% | 36.92 | 16.37 | 24.59 |
| 15. | 30 abr. 2018 | -2.37% | 0.27% | 18.73 | 1.18 | 4.70 |
| 16. | 31 may. 2018 | 10.94% | 2.16% | 80.70 | 0.64 | 7.21 |
| 17. | 30 jun. 2018 | -1.48% | 0.48% | 11.86 | 0.76 | 3.01 |
| 18. | 31 jul. 2018 | 1.53% | 3.60% | 0.18 | 5.04 | -0.96 |
| 19. | 31 ago. 2018 | 0.97% | 3.03% | 0.98 | 2.78 | -1.65 |
| 20. | 30 sept. 2018 | -4.55% | 0.43% | 42.33 | 0.86 | 6.04 |
| 21. | 31 oct. 2018 | -12.76% | -6.94% | 216.67 | 68.86 | 122.15 |
| 22. | 30 nov. 2018 | 7.56% | 1.79% | 31.38 | 0.18 | 2.40 |
| 23. | 31 dic. 2018 | -5.36% | -9.18% | 53.55 | 111.00 | 77.10 |
| 24. | 31 ene. 2019 | 7.35% | 7.87% | 29.10 | 42.39 | 35.12 |
| 25. | 28 feb. 2019 | 5.07% | 2.97% | 9.64 | 2.61 | 5.02 |
| 26. | 31 mar. 2019 | 0.27% | 1.79% | 2.84 | 0.19 | -0.73 |
| 27. | 30 abr. 2019 | 11.09% | 3.93% | 83.30 | 6.62 | 23.49 |
| 28. | 31 may. 2019 | -10.82% | -6.58% | 163.35 | 62.97 | 101.42 |
| 29. | 30 jun. 2019 | 10.02% | 6.89% | 64.93 | 30.64 | 44.60 |
| 30. | 31 jul. 2019 | 9.60% | 1.31% | 58.41 | 0.00 | -0.34 |
| 31. | 31 ago. 2019 | -1.01% | -1.81% | 8.81 | 10.03 | 9.40 |
| 32. | 30 sept. 2019 | 4.44% | 1.72% | 6.13 | 0.13 | 0.89 |
| 33. | 31 oct. 2019 | -8.01% | 2.04% | 99.37 | 0.47 | -6.83 |
| 34. | 30 nov. 2019 | 1.88% | 3.40% | 0.01 | 4.19 | -0.16 |
| 35. | 31 dic. 2019 | 6.72% | 2.86% | 22.67 | 2.25 | 7.15 |
| 36. | 31 ene. 2020 | -5.25% | -0.16% | 52.04 | 2.31 | 10.97 |
| 37. | 29 feb. 2020 | -5.40% | -8.41% | 54.11 | 95.43 | 71.86 |
| 38. | 31 mar. 2020 | -12.45% | -12.51% | 207.64 | 192.37 | 199.86 |
| 39. | 30 abr. 2020 | 16.15% | 12.68% | 201.39 | 128.29 | 160.74 |
| 40. | 31 may. 2020 | 3.08% | 4.53% | 1.24 | 10.05 | 3.54 |
| 41. | 30 jun. 2020 | 6.93% | 1.84% | 24.71 | 0.23 | 2.39 |
| 42. | 31 jul. 2020 | 1.17% | 5.51% | 0.63 | 17.24 | -3.30 |
| 43. | 31 ago. 2020 | 11.45% | 7.01% | 89.99 | 31.91 | 53.58 |
| 44. | 30 sept. 2020 | 0.45% | -3.92% | 2.28 | 27.89 | 7.97 |
| 45. | 31 oct. 2020 | 1.97% | -2.77% | 0.00 | 17.01 | -0.06 |
| 46. | 30 nov. 2020 | 11.52% | 10.75% | 91.44 | 88.30 | 89.85 |
| 47. | 31 dic. 2020 | 1.79% | 3.71% | 0.03 | 5.54 | -0.41 |
| 48. | 31 ene. 2021 | 1.57% | -1.11% | 0.15 | 6.11 | 0.96 |
| 49. | 28 feb. 2021 | 3.97% | 2.61% | 4.05 | 1.57 | 2.52 |
| 50. | 31 mar. 2021 | 9.71% | 4.24% | 60.00 | 8.33 | 22.35 |
| 51. | 30 abr. 2021 | -3.95% | 5.24% | 34.90 | 15.09 | -22.95 |
| 52. | 31 may. 2021 | 5.16% | 0.55% | 10.22 | 0.65 | -2.59 |
| 53. | 30 jun. 2021 | 1.31% | 2.22% | 0.43 | 0.75 | -0.56 |
| 54. | 31 jul. 2021 | -0.34% | 2.27% | 5.30 | 0.84 | -2.11 |
| 55. | 31 ago. 2021 | 0.15% | 2.90% | 3.27 | 2.38 | -2.79 |
| 56. | 30 sept. 2021 | 0.68% | -4.76% | 1.64 | 37.39 | 7.82 |
| 57. | 31 oct. 2021 | -1.86% | 6.91% | 14.61 | 30.87 | -21.24 |
| 58. | 30 nov. 2021 | 2.61% | -0.83% | 0.42 | 4.80 | -1.42 |
| 59. | 31 dic. 2021 | -2.03% | 4.36% | 15.90 | 9.02 | -11.98 |
| Total (Σ): | 2,175.66 | 1,164.17 | 1,071.74 | |||
Mostrar todo
VarianzaTXN = Σ(RTXN,t–RTXN)2 ÷ (59 – 1)
= 2,175.66 ÷ (59 – 1)
= 37.51
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,164.17 ÷ (59 – 1)
= 20.07
CovarianzaTXN, S&P 500 = Σ(RTXN,t–RTXN)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,071.74 ÷ (59 – 1)
= 18.48
Estimación sistemática del riesgo (β)
| VarianzaTXN | 37.51 |
| VarianzaS&P 500 | 20.07 |
| CovarianzaTXN, S&P 500 | 18.48 |
| Coeficiente de correlaciónTXN, S&P 5001 | 0.67 |
| βTXN2 | 0.92 |
| αTXN3 | 0.71% |
Cálculos
1 Coeficiente de correlaciónTXN, S&P 500
= CovarianzaTXN, S&P 500 ÷ (Desviación estándarTXN × Desviación estándarS&P 500)
= 18.48 ÷ (6.12% × 4.48%)
= 0.67
2 βTXN
= CovarianzaTXN, S&P 500 ÷ VarianzaS&P 500
= 18.48 ÷ 20.07
= 0.92
3 αTXN
= PromedioTXN – βTXN × PromedioS&P 500
= 1.96% – 0.92 × 1.36%
= 0.71%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento de LT Treasury Composite1 | RF | 3.27% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 12.20% |
| Riesgo sistemático de acciones ordinarias TI | βTXN | 0.92 |
| Tasa de rendimiento esperada de las acciones ordinarias de TI3 | E(RTXN) | 11.49% |
1 Promedio no ponderado de los rendimientos de las ofertas en todos los bonos del Tesoro de los Estados Unidos con cupón fijo pendientes, ni vencidos ni exigibles en menos de 10 años (proxy de tasa de rendimiento libre de riesgo).
3 E(RTXN) = RF + βTXN [E(RM) – RF]
= 3.27% + 0.92 [12.20% – 3.27%]
= 11.49%