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 Lockheed Martin.
Tasas de retorno
Lockheed Martin Corp., tasas mensuales de retorno
| Lockheed Martin Corp. (LMT) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioLMT,t1 | DividendoLMT,t1 | RLMT,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2019 | $289.69 | 2,704.10 | ||||
| 1. | 28 feb. 2019 | $309.41 | $2.20 | 7.57% | 2,784.49 | 2.97% |
| 2. | 31 mar. 2019 | $300.16 | -2.99% | 2,834.40 | 1.79% | |
| 3. | 30 abr. 2019 | $333.33 | 11.05% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | $447.77 | $3.15 | -0.82% | 4,567.80 | 8.92% |
| 59. | 31 dic. 2023 | $453.24 | 1.22% | 4,769.83 | 4.42% | |
| Promedio (R): | 1.20% | 1.11% | ||||
| Desviación estándar: | 6.70% | 5.31% | ||||
| Lockheed Martin Corp. (LMT) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioLMT,t1 | DividendoLMT,t1 | RLMT,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2019 | $289.69 | 2,704.10 | ||||
| 1. | 28 feb. 2019 | $309.41 | $2.20 | 7.57% | 2,784.49 | 2.97% |
| 2. | 31 mar. 2019 | $300.16 | -2.99% | 2,834.40 | 1.79% | |
| 3. | 30 abr. 2019 | $333.33 | 11.05% | 2,945.83 | 3.93% | |
| 4. | 31 may. 2019 | $338.54 | $2.20 | 2.22% | 2,752.06 | -6.58% |
| 5. | 30 jun. 2019 | $363.54 | 7.38% | 2,941.76 | 6.89% | |
| 6. | 31 jul. 2019 | $362.17 | -0.38% | 2,980.38 | 1.31% | |
| 7. | 31 ago. 2019 | $384.11 | $2.20 | 6.67% | 2,926.46 | -1.81% |
| 8. | 30 sept. 2019 | $390.06 | 1.55% | 2,976.74 | 1.72% | |
| 9. | 31 oct. 2019 | $376.68 | -3.43% | 3,037.56 | 2.04% | |
| 10. | 30 nov. 2019 | $391.03 | $2.40 | 4.45% | 3,140.98 | 3.40% |
| 11. | 31 dic. 2019 | $389.38 | -0.42% | 3,230.78 | 2.86% | |
| 12. | 31 ene. 2020 | $428.12 | 9.95% | 3,225.52 | -0.16% | |
| 13. | 29 feb. 2020 | $369.87 | $2.40 | -13.05% | 2,954.22 | -8.41% |
| 14. | 31 mar. 2020 | $338.95 | -8.36% | 2,584.59 | -12.51% | |
| 15. | 30 abr. 2020 | $389.06 | 14.78% | 2,912.43 | 12.68% | |
| 16. | 31 may. 2020 | $388.44 | $2.40 | 0.46% | 3,044.31 | 4.53% |
| 17. | 30 jun. 2020 | $364.92 | -6.05% | 3,100.29 | 1.84% | |
| 18. | 31 jul. 2020 | $378.97 | 3.85% | 3,271.12 | 5.51% | |
| 19. | 31 ago. 2020 | $390.26 | $2.40 | 3.61% | 3,500.31 | 7.01% |
| 20. | 30 sept. 2020 | $383.28 | -1.79% | 3,363.00 | -3.92% | |
| 21. | 31 oct. 2020 | $350.13 | -8.65% | 3,269.96 | -2.77% | |
| 22. | 30 nov. 2020 | $365.00 | $2.60 | 4.99% | 3,621.63 | 10.75% |
| 23. | 31 dic. 2020 | $354.98 | -2.75% | 3,756.07 | 3.71% | |
| 24. | 31 ene. 2021 | $321.82 | -9.34% | 3,714.24 | -1.11% | |
| 25. | 28 feb. 2021 | $330.25 | $2.60 | 3.43% | 3,811.15 | 2.61% |
| 26. | 31 mar. 2021 | $369.50 | 11.88% | 3,972.89 | 4.24% | |
| 27. | 30 abr. 2021 | $380.56 | 2.99% | 4,181.17 | 5.24% | |
| 28. | 31 may. 2021 | $382.20 | $2.60 | 1.11% | 4,204.11 | 0.55% |
| 29. | 30 jun. 2021 | $378.35 | -1.01% | 4,297.50 | 2.22% | |
| 30. | 31 jul. 2021 | $371.67 | -1.77% | 4,395.26 | 2.27% | |
| 31. | 31 ago. 2021 | $359.80 | $2.60 | -2.49% | 4,522.68 | 2.90% |
| 32. | 30 sept. 2021 | $345.10 | -4.09% | 4,307.54 | -4.76% | |
| 33. | 31 oct. 2021 | $332.32 | -3.70% | 4,605.38 | 6.91% | |
| 34. | 30 nov. 2021 | $333.32 | $2.80 | 1.14% | 4,567.00 | -0.83% |
| 35. | 31 dic. 2021 | $355.41 | 6.63% | 4,766.18 | 4.36% | |
| 36. | 31 ene. 2022 | $389.13 | 9.49% | 4,515.55 | -5.26% | |
| 37. | 28 feb. 2022 | $433.80 | $2.80 | 12.20% | 4,373.94 | -3.14% |
| 38. | 31 mar. 2022 | $441.40 | 1.75% | 4,530.41 | 3.58% | |
| 39. | 30 abr. 2022 | $432.12 | -2.10% | 4,131.93 | -8.80% | |
| 40. | 31 may. 2022 | $440.11 | $2.80 | 2.50% | 4,132.15 | 0.01% |
| 41. | 30 jun. 2022 | $429.96 | -2.31% | 3,785.38 | -8.39% | |
| 42. | 31 jul. 2022 | $413.81 | -3.76% | 4,130.29 | 9.11% | |
| 43. | 31 ago. 2022 | $420.11 | $2.80 | 2.20% | 3,955.00 | -4.24% |
| 44. | 30 sept. 2022 | $386.29 | -8.05% | 3,585.62 | -9.34% | |
| 45. | 31 oct. 2022 | $486.68 | 25.99% | 3,871.98 | 7.99% | |
| 46. | 30 nov. 2022 | $485.19 | $3.00 | 0.31% | 4,080.11 | 5.38% |
| 47. | 31 dic. 2022 | $486.49 | 0.27% | 3,839.50 | -5.90% | |
| 48. | 31 ene. 2023 | $463.26 | -4.78% | 4,076.60 | 6.18% | |
| 49. | 28 feb. 2023 | $474.26 | $3.00 | 3.02% | 3,970.15 | -2.61% |
| 50. | 31 mar. 2023 | $472.73 | -0.32% | 4,109.31 | 3.51% | |
| 51. | 30 abr. 2023 | $464.45 | -1.75% | 4,169.48 | 1.46% | |
| 52. | 31 may. 2023 | $444.01 | $3.00 | -3.75% | 4,179.83 | 0.25% |
| 53. | 30 jun. 2023 | $460.38 | 3.69% | 4,376.86 | 4.71% | |
| 54. | 31 jul. 2023 | $446.37 | -3.04% | 4,588.96 | 4.85% | |
| 55. | 31 ago. 2023 | $448.35 | $3.00 | 1.12% | 4,507.66 | -1.77% |
| 56. | 30 sept. 2023 | $408.96 | -8.79% | 4,288.05 | -4.87% | |
| 57. | 31 oct. 2023 | $454.64 | 11.17% | 4,193.80 | -2.20% | |
| 58. | 30 nov. 2023 | $447.77 | $3.15 | -0.82% | 4,567.80 | 8.92% |
| 59. | 31 dic. 2023 | $453.24 | 1.22% | 4,769.83 | 4.42% | |
| Promedio (R): | 1.20% | 1.11% | ||||
| Desviación estándar: | 6.70% | 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 LMT 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
Lockheed Martin Corp., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RLMT,t | RS&P 500,t | (RLMT,t–RLMT)2 | (RS&P 500,t–RS&P 500)2 | (RLMT,t–RLMT)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2019 | 7.57% | 2.97% | 40.51 | 3.49 | 11.88 |
| 2. | 31 mar. 2019 | -2.99% | 1.79% | 17.57 | 0.47 | -2.88 |
| 3. | 30 abr. 2019 | 11.05% | 3.93% | 97.00 | 7.98 | 27.83 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | -0.82% | 8.92% | 4.08 | 61.03 | -15.78 |
| 59. | 31 dic. 2023 | 1.22% | 4.42% | 0.00 | 11.00 | 0.07 |
| Total (Σ): | 2,605.09 | 1,634.30 | 792.22 | |||
| t | Fecha | RLMT,t | RS&P 500,t | (RLMT,t–RLMT)2 | (RS&P 500,t–RS&P 500)2 | (RLMT,t–RLMT)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2019 | 7.57% | 2.97% | 40.51 | 3.49 | 11.88 |
| 2. | 31 mar. 2019 | -2.99% | 1.79% | 17.57 | 0.47 | -2.88 |
| 3. | 30 abr. 2019 | 11.05% | 3.93% | 97.00 | 7.98 | 27.83 |
| 4. | 31 may. 2019 | 2.22% | -6.58% | 1.04 | 59.04 | -7.85 |
| 5. | 30 jun. 2019 | 7.38% | 6.89% | 38.23 | 33.49 | 35.78 |
| 6. | 31 jul. 2019 | -0.38% | 1.31% | 2.49 | 0.04 | -0.33 |
| 7. | 31 ago. 2019 | 6.67% | -1.81% | 29.85 | 8.50 | -15.93 |
| 8. | 30 sept. 2019 | 1.55% | 1.72% | 0.12 | 0.37 | 0.21 |
| 9. | 31 oct. 2019 | -3.43% | 2.04% | 21.46 | 0.88 | -4.34 |
| 10. | 30 nov. 2019 | 4.45% | 3.40% | 10.53 | 5.28 | 7.46 |
| 11. | 31 dic. 2019 | -0.42% | 2.86% | 2.64 | 3.07 | -2.85 |
| 12. | 31 ene. 2020 | 9.95% | -0.16% | 76.51 | 1.61 | -11.10 |
| 13. | 29 feb. 2020 | -13.05% | -8.41% | 202.99 | 90.57 | 135.59 |
| 14. | 31 mar. 2020 | -8.36% | -12.51% | 91.42 | 185.44 | 130.21 |
| 15. | 30 abr. 2020 | 14.78% | 12.68% | 184.47 | 134.06 | 157.26 |
| 16. | 31 may. 2020 | 0.46% | 4.53% | 0.55 | 11.71 | -2.55 |
| 17. | 30 jun. 2020 | -6.05% | 1.84% | 52.66 | 0.54 | -5.32 |
| 18. | 31 jul. 2020 | 3.85% | 5.51% | 7.01 | 19.40 | 11.66 |
| 19. | 31 ago. 2020 | 3.61% | 7.01% | 5.81 | 34.82 | 14.22 |
| 20. | 30 sept. 2020 | -1.79% | -3.92% | 8.94 | 25.29 | 15.04 |
| 21. | 31 oct. 2020 | -8.65% | -2.77% | 97.04 | 15.00 | 38.15 |
| 22. | 30 nov. 2020 | 4.99% | 10.75% | 14.35 | 93.10 | 36.55 |
| 23. | 31 dic. 2020 | -2.75% | 3.71% | 15.58 | 6.79 | -10.29 |
| 24. | 31 ene. 2021 | -9.34% | -1.11% | 111.16 | 4.93 | 23.40 |
| 25. | 28 feb. 2021 | 3.43% | 2.61% | 4.95 | 2.26 | 3.35 |
| 26. | 31 mar. 2021 | 11.88% | 4.24% | 114.13 | 9.85 | 33.52 |
| 27. | 30 abr. 2021 | 2.99% | 5.24% | 3.21 | 17.11 | 7.41 |
| 28. | 31 may. 2021 | 1.11% | 0.55% | 0.01 | 0.31 | 0.05 |
| 29. | 30 jun. 2021 | -1.01% | 2.22% | 4.88 | 1.24 | -2.46 |
| 30. | 31 jul. 2021 | -1.77% | 2.27% | 8.81 | 1.37 | -3.47 |
| 31. | 31 ago. 2021 | -2.49% | 2.90% | 13.66 | 3.22 | -6.63 |
| 32. | 30 sept. 2021 | -4.09% | -4.76% | 27.96 | 34.37 | 31.00 |
| 33. | 31 oct. 2021 | -3.70% | 6.91% | 24.06 | 33.74 | -28.49 |
| 34. | 30 nov. 2021 | 1.14% | -0.83% | 0.00 | 3.76 | 0.11 |
| 35. | 31 dic. 2021 | 6.63% | 4.36% | 29.43 | 10.60 | 17.66 |
| 36. | 31 ene. 2022 | 9.49% | -5.26% | 68.65 | 40.51 | -52.73 |
| 37. | 28 feb. 2022 | 12.20% | -3.14% | 120.94 | 17.99 | -46.65 |
| 38. | 31 mar. 2022 | 1.75% | 3.58% | 0.30 | 6.11 | 1.36 |
| 39. | 30 abr. 2022 | -2.10% | -8.80% | 10.92 | 98.04 | 32.72 |
| 40. | 31 may. 2022 | 2.50% | 0.01% | 1.68 | 1.21 | -1.43 |
| 41. | 30 jun. 2022 | -2.31% | -8.39% | 12.31 | 90.21 | 33.32 |
| 42. | 31 jul. 2022 | -3.76% | 9.11% | 24.58 | 64.09 | -39.69 |
| 43. | 31 ago. 2022 | 2.20% | -4.24% | 0.99 | 28.62 | -5.33 |
| 44. | 30 sept. 2022 | -8.05% | -9.34% | 85.60 | 109.11 | 96.64 |
| 45. | 31 oct. 2022 | 25.99% | 7.99% | 614.36 | 47.34 | 170.54 |
| 46. | 30 nov. 2022 | 0.31% | 5.38% | 0.79 | 18.23 | -3.81 |
| 47. | 31 dic. 2022 | 0.27% | -5.90% | 0.87 | 49.04 | 6.54 |
| 48. | 31 ene. 2023 | -4.78% | 6.18% | 35.72 | 25.70 | -30.30 |
| 49. | 28 feb. 2023 | 3.02% | -2.61% | 3.31 | 13.82 | -6.77 |
| 50. | 31 mar. 2023 | -0.32% | 3.51% | 2.32 | 5.76 | -3.66 |
| 51. | 30 abr. 2023 | -1.75% | 1.46% | 8.72 | 0.13 | -1.06 |
| 52. | 31 may. 2023 | -3.75% | 0.25% | 24.57 | 0.74 | 4.25 |
| 53. | 30 jun. 2023 | 3.69% | 4.71% | 6.18 | 13.02 | 8.97 |
| 54. | 31 jul. 2023 | -3.04% | 4.85% | 18.02 | 13.99 | -15.88 |
| 55. | 31 ago. 2023 | 1.12% | -1.77% | 0.01 | 8.28 | 0.25 |
| 56. | 30 sept. 2023 | -8.79% | -4.87% | 99.75 | 35.73 | 59.70 |
| 57. | 31 oct. 2023 | 11.17% | -2.20% | 99.36 | 10.92 | -32.93 |
| 58. | 30 nov. 2023 | -0.82% | 8.92% | 4.08 | 61.03 | -15.78 |
| 59. | 31 dic. 2023 | 1.22% | 4.42% | 0.00 | 11.00 | 0.07 |
| Total (Σ): | 2,605.09 | 1,634.30 | 792.22 | |||
Mostrar todo
VarianzaLMT = Σ(RLMT,t–RLMT)2 ÷ (59 – 1)
= 2,605.09 ÷ (59 – 1)
= 44.92
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
CovarianzaLMT, S&P 500 = Σ(RLMT,t–RLMT)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 792.22 ÷ (59 – 1)
= 13.66
Estimación sistemática del riesgo (β)
| VarianzaLMT | 44.92 |
| VarianzaS&P 500 | 28.18 |
| CovarianzaLMT, S&P 500 | 13.66 |
| Coeficiente de correlaciónLMT, S&P 5001 | 0.38 |
| βLMT2 | 0.48 |
| αLMT3 | 0.67% |
Cálculos
1 Coeficiente de correlaciónLMT, S&P 500
= CovarianzaLMT, S&P 500 ÷ (Desviación estándarLMT × Desviación estándarS&P 500)
= 13.66 ÷ (6.70% × 5.31%)
= 0.38
2 βLMT
= CovarianzaLMT, S&P 500 ÷ VarianzaS&P 500
= 13.66 ÷ 28.18
= 0.48
3 αLMT
= PromedioLMT – βLMT × PromedioS&P 500
= 1.20% – 0.48 × 1.11%
= 0.67%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.67% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.79% |
| Riesgo sistemático de Lockheed Martin acciones ordinarias | βLMT | 0.48 |
| Tasa de rendimiento esperada de las acciones ordinarias de Lockheed Martin3 | E(RLMT) | 9.09% |
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(RLMT) = RF + βLMT [E(RM) – RF]
= 4.67% + 0.48 [13.79% – 4.67%]
= 9.09%