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 en activos de riesgo como las acciones ordinarias de RTX.
Tasas de retorno
RTX Corp., tasas mensuales de retorno
| RTX Corp. (RTX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioRTX,t1 | DividendoRTX,t1 | RRTX,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2019 | $118.07 | 2,704.10 | ||||
| 1. | 28 feb. 2019 | $125.67 | $0.735 | 7.06% | 2,784.49 | 2.97% |
| 2. | 31 mar. 2019 | $128.89 | 2.56% | 2,834.40 | 1.79% | |
| 3. | 30 abr. 2019 | $142.61 | 10.64% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | $81.48 | $0.59 | 0.84% | 4,567.80 | 8.92% |
| 59. | 31 dic. 2023 | $84.14 | 3.26% | 4,769.83 | 4.42% | |
| Promedio (R): | 0.57% | 1.11% | ||||
| Desviación estándar: | 8.83% | 5.31% | ||||
| RTX Corp. (RTX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioRTX,t1 | DividendoRTX,t1 | RRTX,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2019 | $118.07 | 2,704.10 | ||||
| 1. | 28 feb. 2019 | $125.67 | $0.735 | 7.06% | 2,784.49 | 2.97% |
| 2. | 31 mar. 2019 | $128.89 | 2.56% | 2,834.40 | 1.79% | |
| 3. | 30 abr. 2019 | $142.61 | 10.64% | 2,945.83 | 3.93% | |
| 4. | 31 may. 2019 | $126.30 | $0.735 | -10.92% | 2,752.06 | -6.58% |
| 5. | 30 jun. 2019 | $130.20 | 3.09% | 2,941.76 | 6.89% | |
| 6. | 31 jul. 2019 | $133.60 | 2.61% | 2,980.38 | 1.31% | |
| 7. | 31 ago. 2019 | $130.24 | $0.735 | -1.96% | 2,926.46 | -1.81% |
| 8. | 30 sept. 2019 | $136.52 | 4.82% | 2,976.74 | 1.72% | |
| 9. | 31 oct. 2019 | $143.58 | 5.17% | 3,037.56 | 2.04% | |
| 10. | 30 nov. 2019 | $148.34 | $0.735 | 3.83% | 3,140.98 | 3.40% |
| 11. | 31 dic. 2019 | $149.76 | 0.96% | 3,230.78 | 2.86% | |
| 12. | 31 ene. 2020 | $150.20 | 0.29% | 3,225.52 | -0.16% | |
| 13. | 29 feb. 2020 | $130.59 | $0.735 | -12.57% | 2,954.22 | -8.41% |
| 14. | 31 mar. 2020 | $94.33 | $35.50 | -0.58% | 2,584.59 | -12.51% |
| 15. | 30 abr. 2020 | $64.81 | -31.29% | 2,912.43 | 12.68% | |
| 16. | 31 may. 2020 | $64.52 | $0.475 | 0.29% | 3,044.31 | 4.53% |
| 17. | 30 jun. 2020 | $61.62 | -4.49% | 3,100.29 | 1.84% | |
| 18. | 31 jul. 2020 | $56.68 | -8.02% | 3,271.12 | 5.51% | |
| 19. | 31 ago. 2020 | $61.00 | $0.475 | 8.46% | 3,500.31 | 7.01% |
| 20. | 30 sept. 2020 | $57.54 | -5.67% | 3,363.00 | -3.92% | |
| 21. | 31 oct. 2020 | $54.32 | -5.60% | 3,269.96 | -2.77% | |
| 22. | 30 nov. 2020 | $71.72 | $0.475 | 32.91% | 3,621.63 | 10.75% |
| 23. | 31 dic. 2020 | $71.51 | -0.29% | 3,756.07 | 3.71% | |
| 24. | 31 ene. 2021 | $66.73 | -6.68% | 3,714.24 | -1.11% | |
| 25. | 28 feb. 2021 | $71.99 | $0.475 | 8.59% | 3,811.15 | 2.61% |
| 26. | 31 mar. 2021 | $77.27 | 7.33% | 3,972.89 | 4.24% | |
| 27. | 30 abr. 2021 | $83.24 | 7.73% | 4,181.17 | 5.24% | |
| 28. | 31 may. 2021 | $88.71 | $0.51 | 7.18% | 4,204.11 | 0.55% |
| 29. | 30 jun. 2021 | $85.31 | -3.83% | 4,297.50 | 2.22% | |
| 30. | 31 jul. 2021 | $86.95 | 1.92% | 4,395.26 | 2.27% | |
| 31. | 31 ago. 2021 | $84.76 | $0.51 | -1.93% | 4,522.68 | 2.90% |
| 32. | 30 sept. 2021 | $85.96 | 1.42% | 4,307.54 | -4.76% | |
| 33. | 31 oct. 2021 | $88.86 | 3.37% | 4,605.38 | 6.91% | |
| 34. | 30 nov. 2021 | $80.92 | $0.51 | -8.36% | 4,567.00 | -0.83% |
| 35. | 31 dic. 2021 | $86.06 | 6.35% | 4,766.18 | 4.36% | |
| 36. | 31 ene. 2022 | $90.19 | 4.80% | 4,515.55 | -5.26% | |
| 37. | 28 feb. 2022 | $102.70 | $0.51 | 14.44% | 4,373.94 | -3.14% |
| 38. | 31 mar. 2022 | $99.07 | -3.53% | 4,530.41 | 3.58% | |
| 39. | 30 abr. 2022 | $94.91 | -4.20% | 4,131.93 | -8.80% | |
| 40. | 31 may. 2022 | $95.12 | $0.55 | 0.80% | 4,132.15 | 0.01% |
| 41. | 30 jun. 2022 | $96.11 | 1.04% | 3,785.38 | -8.39% | |
| 42. | 31 jul. 2022 | $93.21 | -3.02% | 4,130.29 | 9.11% | |
| 43. | 31 ago. 2022 | $89.75 | $0.55 | -3.12% | 3,955.00 | -4.24% |
| 44. | 30 sept. 2022 | $81.86 | -8.79% | 3,585.62 | -9.34% | |
| 45. | 31 oct. 2022 | $94.82 | 15.83% | 3,871.98 | 7.99% | |
| 46. | 30 nov. 2022 | $98.72 | $0.55 | 4.69% | 4,080.11 | 5.38% |
| 47. | 31 dic. 2022 | $100.92 | 2.23% | 3,839.50 | -5.90% | |
| 48. | 31 ene. 2023 | $99.85 | -1.06% | 4,076.60 | 6.18% | |
| 49. | 28 feb. 2023 | $98.09 | $0.55 | -1.21% | 3,970.15 | -2.61% |
| 50. | 31 mar. 2023 | $97.93 | -0.16% | 4,109.31 | 3.51% | |
| 51. | 30 abr. 2023 | $99.90 | 2.01% | 4,169.48 | 1.46% | |
| 52. | 31 may. 2023 | $92.14 | $0.59 | -7.18% | 4,179.83 | 0.25% |
| 53. | 30 jun. 2023 | $97.96 | 6.32% | 4,376.86 | 4.71% | |
| 54. | 31 jul. 2023 | $87.93 | -10.24% | 4,588.96 | 4.85% | |
| 55. | 31 ago. 2023 | $86.04 | $0.59 | -1.48% | 4,507.66 | -1.77% |
| 56. | 30 sept. 2023 | $71.97 | -16.35% | 4,288.05 | -4.87% | |
| 57. | 31 oct. 2023 | $81.39 | 13.09% | 4,193.80 | -2.20% | |
| 58. | 30 nov. 2023 | $81.48 | $0.59 | 0.84% | 4,567.80 | 8.92% |
| 59. | 31 dic. 2023 | $84.14 | 3.26% | 4,769.83 | 4.42% | |
| Promedio (R): | 0.57% | 1.11% | ||||
| Desviación estándar: | 8.83% | 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 RTX 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
RTX Corp., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RRTX,t | RS&P 500,t | (RRTX,t–RRTX)2 | (RS&P 500,t–RS&P 500)2 | (RRTX,t–RRTX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2019 | 7.06% | 2.97% | 42.17 | 3.49 | 12.12 |
| 2. | 31 mar. 2019 | 2.56% | 1.79% | 3.99 | 0.47 | 1.37 |
| 3. | 30 abr. 2019 | 10.64% | 3.93% | 101.59 | 7.98 | 28.48 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | 0.84% | 8.92% | 0.07 | 61.03 | 2.11 |
| 59. | 31 dic. 2023 | 3.26% | 4.42% | 7.28 | 11.00 | 8.95 |
| Total (Σ): | 4,517.76 | 1,634.30 | 631.07 | |||
| t | Fecha | RRTX,t | RS&P 500,t | (RRTX,t–RRTX)2 | (RS&P 500,t–RS&P 500)2 | (RRTX,t–RRTX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2019 | 7.06% | 2.97% | 42.17 | 3.49 | 12.12 |
| 2. | 31 mar. 2019 | 2.56% | 1.79% | 3.99 | 0.47 | 1.37 |
| 3. | 30 abr. 2019 | 10.64% | 3.93% | 101.59 | 7.98 | 28.48 |
| 4. | 31 may. 2019 | -10.92% | -6.58% | 131.95 | 59.04 | 88.26 |
| 5. | 30 jun. 2019 | 3.09% | 6.89% | 6.36 | 33.49 | 14.60 |
| 6. | 31 jul. 2019 | 2.61% | 1.31% | 4.18 | 0.04 | 0.42 |
| 7. | 31 ago. 2019 | -1.96% | -1.81% | 6.40 | 8.50 | 7.38 |
| 8. | 30 sept. 2019 | 4.82% | 1.72% | 18.11 | 0.37 | 2.61 |
| 9. | 31 oct. 2019 | 5.17% | 2.04% | 21.21 | 0.88 | 4.32 |
| 10. | 30 nov. 2019 | 3.83% | 3.40% | 10.64 | 5.28 | 7.50 |
| 11. | 31 dic. 2019 | 0.96% | 2.86% | 0.15 | 3.07 | 0.69 |
| 12. | 31 ene. 2020 | 0.29% | -0.16% | 0.07 | 1.61 | 0.35 |
| 13. | 29 feb. 2020 | -12.57% | -8.41% | 172.46 | 90.57 | 124.98 |
| 14. | 31 mar. 2020 | -0.58% | -12.51% | 1.32 | 185.44 | 15.63 |
| 15. | 30 abr. 2020 | -31.29% | 12.68% | 1,015.07 | 134.06 | -368.89 |
| 16. | 31 may. 2020 | 0.29% | 4.53% | 0.08 | 11.71 | -0.96 |
| 17. | 30 jun. 2020 | -4.49% | 1.84% | 25.61 | 0.54 | -3.71 |
| 18. | 31 jul. 2020 | -8.02% | 5.51% | 73.66 | 19.40 | -37.80 |
| 19. | 31 ago. 2020 | 8.46% | 7.01% | 62.32 | 34.82 | 46.58 |
| 20. | 30 sept. 2020 | -5.67% | -3.92% | 38.91 | 25.29 | 31.37 |
| 21. | 31 oct. 2020 | -5.60% | -2.77% | 37.97 | 15.00 | 23.86 |
| 22. | 30 nov. 2020 | 32.91% | 10.75% | 1,045.95 | 93.10 | 312.05 |
| 23. | 31 dic. 2020 | -0.29% | 3.71% | 0.74 | 6.79 | -2.24 |
| 24. | 31 ene. 2021 | -6.68% | -1.11% | 52.56 | 4.93 | 16.09 |
| 25. | 28 feb. 2021 | 8.59% | 2.61% | 64.46 | 2.26 | 12.07 |
| 26. | 31 mar. 2021 | 7.33% | 4.24% | 45.81 | 9.85 | 21.24 |
| 27. | 30 abr. 2021 | 7.73% | 5.24% | 51.27 | 17.11 | 29.62 |
| 28. | 31 may. 2021 | 7.18% | 0.55% | 43.80 | 0.31 | -3.69 |
| 29. | 30 jun. 2021 | -3.83% | 2.22% | 19.35 | 1.24 | -4.91 |
| 30. | 31 jul. 2021 | 1.92% | 2.27% | 1.84 | 1.37 | 1.59 |
| 31. | 31 ago. 2021 | -1.93% | 2.90% | 6.24 | 3.22 | -4.48 |
| 32. | 30 sept. 2021 | 1.42% | -4.76% | 0.72 | 34.37 | -4.98 |
| 33. | 31 oct. 2021 | 3.37% | 6.91% | 7.88 | 33.74 | 16.31 |
| 34. | 30 nov. 2021 | -8.36% | -0.83% | 79.70 | 3.76 | 17.31 |
| 35. | 31 dic. 2021 | 6.35% | 4.36% | 33.48 | 10.60 | 18.84 |
| 36. | 31 ene. 2022 | 4.80% | -5.26% | 17.92 | 40.51 | -26.94 |
| 37. | 28 feb. 2022 | 14.44% | -3.14% | 192.39 | 17.99 | -58.84 |
| 38. | 31 mar. 2022 | -3.53% | 3.58% | 16.81 | 6.11 | -10.13 |
| 39. | 30 abr. 2022 | -4.20% | -8.80% | 22.70 | 98.04 | 47.18 |
| 40. | 31 may. 2022 | 0.80% | 0.01% | 0.06 | 1.21 | -0.26 |
| 41. | 30 jun. 2022 | 1.04% | -8.39% | 0.23 | 90.21 | -4.51 |
| 42. | 31 jul. 2022 | -3.02% | 9.11% | 12.84 | 64.09 | -28.69 |
| 43. | 31 ago. 2022 | -3.12% | -4.24% | 13.60 | 28.62 | 19.73 |
| 44. | 30 sept. 2022 | -8.79% | -9.34% | 87.55 | 109.11 | 97.74 |
| 45. | 31 oct. 2022 | 15.83% | 7.99% | 233.06 | 47.34 | 105.04 |
| 46. | 30 nov. 2022 | 4.69% | 5.38% | 17.03 | 18.23 | 17.62 |
| 47. | 31 dic. 2022 | 2.23% | -5.90% | 2.76 | 49.04 | -11.64 |
| 48. | 31 ene. 2023 | -1.06% | 6.18% | 2.64 | 25.70 | -8.24 |
| 49. | 28 feb. 2023 | -1.21% | -2.61% | 3.16 | 13.82 | 6.61 |
| 50. | 31 mar. 2023 | -0.16% | 3.51% | 0.53 | 5.76 | -1.75 |
| 51. | 30 abr. 2023 | 2.01% | 1.46% | 2.09 | 0.13 | 0.52 |
| 52. | 31 may. 2023 | -7.18% | 0.25% | 59.95 | 0.74 | 6.64 |
| 53. | 30 jun. 2023 | 6.32% | 4.71% | 33.07 | 13.02 | 20.75 |
| 54. | 31 jul. 2023 | -10.24% | 4.85% | 116.74 | 13.99 | -40.41 |
| 55. | 31 ago. 2023 | -1.48% | -1.77% | 4.18 | 8.28 | 5.88 |
| 56. | 30 sept. 2023 | -16.35% | -4.87% | 286.24 | 35.73 | 101.14 |
| 57. | 31 oct. 2023 | 13.09% | -2.20% | 156.83 | 10.92 | -41.37 |
| 58. | 30 nov. 2023 | 0.84% | 8.92% | 0.07 | 61.03 | 2.11 |
| 59. | 31 dic. 2023 | 3.26% | 4.42% | 7.28 | 11.00 | 8.95 |
| Total (Σ): | 4,517.76 | 1,634.30 | 631.07 | |||
Mostrar todo
VarianzaRTX = Σ(RRTX,t–RRTX)2 ÷ (59 – 1)
= 4,517.76 ÷ (59 – 1)
= 77.89
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
CovarianzaRTX, S&P 500 = Σ(RRTX,t–RRTX)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 631.07 ÷ (59 – 1)
= 10.88
Estimación sistemática del riesgo (β)
| VarianzaRTX | 77.89 |
| VarianzaS&P 500 | 28.18 |
| CovarianzaRTX, S&P 500 | 10.88 |
| Coeficiente de correlaciónRTX, S&P 5001 | 0.23 |
| βRTX2 | 0.39 |
| αRTX3 | 0.14% |
Cálculos
1 Coeficiente de correlaciónRTX, S&P 500
= CovarianzaRTX, S&P 500 ÷ (Desviación estándarRTX × Desviación estándarS&P 500)
= 10.88 ÷ (8.83% × 5.31%)
= 0.23
2 βRTX
= CovarianzaRTX, S&P 500 ÷ VarianzaS&P 500
= 10.88 ÷ 28.18
= 0.39
3 αRTX
= PromedioRTX – βRTX × PromedioS&P 500
= 0.57% – 0.39 × 1.11%
= 0.14%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.65% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.79% |
| Riesgo sistemático de RTX acciones ordinarias | βRTX | 0.39 |
| Tasa de rendimiento esperada de las acciones ordinarias de RTX3 | E(RRTX) | 8.18% |
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(RRTX) = RF + βRTX [E(RM) – RF]
= 4.65% + 0.39 [13.79% – 4.65%]
= 8.18%