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 Mondelēz International.
Tasas de retorno
Mondelēz International Inc., tasas mensuales de retorno
| Mondelēz International Inc. (MDLZ) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioMDLZ,t1 | DividendoMDLZ,t1 | RMDLZ,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2019 | $46.26 | 2,704.10 | ||||
| 1. | 28 feb. 2019 | $47.16 | 1.95% | 2,784.49 | 2.97% | |
| 2. | 31 mar. 2019 | $49.92 | $0.26 | 6.40% | 2,834.40 | 1.79% |
| 3. | 30 abr. 2019 | $50.85 | 1.86% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | $71.06 | 7.33% | 4,567.80 | 8.92% | |
| 59. | 31 dic. 2023 | $72.43 | $0.425 | 2.53% | 4,769.83 | 4.42% |
| Promedio (R): | 1.08% | 1.11% | ||||
| Desviación estándar: | 5.19% | 5.31% | ||||
| Mondelēz International Inc. (MDLZ) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioMDLZ,t1 | DividendoMDLZ,t1 | RMDLZ,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2019 | $46.26 | 2,704.10 | ||||
| 1. | 28 feb. 2019 | $47.16 | 1.95% | 2,784.49 | 2.97% | |
| 2. | 31 mar. 2019 | $49.92 | $0.26 | 6.40% | 2,834.40 | 1.79% |
| 3. | 30 abr. 2019 | $50.85 | 1.86% | 2,945.83 | 3.93% | |
| 4. | 31 may. 2019 | $50.85 | 0.00% | 2,752.06 | -6.58% | |
| 5. | 30 jun. 2019 | $53.90 | $0.26 | 6.51% | 2,941.76 | 6.89% |
| 6. | 31 jul. 2019 | $53.49 | -0.76% | 2,980.38 | 1.31% | |
| 7. | 31 ago. 2019 | $55.22 | 3.23% | 2,926.46 | -1.81% | |
| 8. | 30 sept. 2019 | $55.32 | $0.285 | 0.70% | 2,976.74 | 1.72% |
| 9. | 31 oct. 2019 | $52.45 | -5.19% | 3,037.56 | 2.04% | |
| 10. | 30 nov. 2019 | $52.54 | 0.17% | 3,140.98 | 3.40% | |
| 11. | 31 dic. 2019 | $55.08 | $0.285 | 5.38% | 3,230.78 | 2.86% |
| 12. | 31 ene. 2020 | $57.38 | 4.18% | 3,225.52 | -0.16% | |
| 13. | 29 feb. 2020 | $52.80 | -7.98% | 2,954.22 | -8.41% | |
| 14. | 31 mar. 2020 | $50.08 | $0.285 | -4.61% | 2,584.59 | -12.51% |
| 15. | 30 abr. 2020 | $51.44 | 2.72% | 2,912.43 | 12.68% | |
| 16. | 31 may. 2020 | $52.12 | 1.32% | 3,044.31 | 4.53% | |
| 17. | 30 jun. 2020 | $51.13 | $0.285 | -1.35% | 3,100.29 | 1.84% |
| 18. | 31 jul. 2020 | $55.49 | 8.53% | 3,271.12 | 5.51% | |
| 19. | 31 ago. 2020 | $58.42 | 5.28% | 3,500.31 | 7.01% | |
| 20. | 30 sept. 2020 | $57.45 | $0.315 | -1.12% | 3,363.00 | -3.92% |
| 21. | 31 oct. 2020 | $53.12 | -7.54% | 3,269.96 | -2.77% | |
| 22. | 30 nov. 2020 | $57.45 | 8.15% | 3,621.63 | 10.75% | |
| 23. | 31 dic. 2020 | $58.47 | $0.315 | 2.32% | 3,756.07 | 3.71% |
| 24. | 31 ene. 2021 | $55.44 | -5.18% | 3,714.24 | -1.11% | |
| 25. | 28 feb. 2021 | $53.16 | -4.11% | 3,811.15 | 2.61% | |
| 26. | 31 mar. 2021 | $58.53 | $0.315 | 10.69% | 3,972.89 | 4.24% |
| 27. | 30 abr. 2021 | $60.81 | 3.90% | 4,181.17 | 5.24% | |
| 28. | 31 may. 2021 | $63.53 | 4.47% | 4,204.11 | 0.55% | |
| 29. | 30 jun. 2021 | $62.44 | $0.315 | -1.22% | 4,297.50 | 2.22% |
| 30. | 31 jul. 2021 | $63.26 | 1.31% | 4,395.26 | 2.27% | |
| 31. | 31 ago. 2021 | $62.07 | -1.88% | 4,522.68 | 2.90% | |
| 32. | 30 sept. 2021 | $58.18 | $0.35 | -5.70% | 4,307.54 | -4.76% |
| 33. | 31 oct. 2021 | $60.74 | 4.40% | 4,605.38 | 6.91% | |
| 34. | 30 nov. 2021 | $58.94 | -2.96% | 4,567.00 | -0.83% | |
| 35. | 31 dic. 2021 | $66.31 | $0.35 | 13.10% | 4,766.18 | 4.36% |
| 36. | 31 ene. 2022 | $67.03 | 1.09% | 4,515.55 | -5.26% | |
| 37. | 28 feb. 2022 | $65.48 | -2.31% | 4,373.94 | -3.14% | |
| 38. | 31 mar. 2022 | $62.78 | $0.35 | -3.59% | 4,530.41 | 3.58% |
| 39. | 30 abr. 2022 | $64.48 | 2.71% | 4,131.93 | -8.80% | |
| 40. | 31 may. 2022 | $63.56 | -1.43% | 4,132.15 | 0.01% | |
| 41. | 30 jun. 2022 | $62.09 | $0.35 | -1.76% | 3,785.38 | -8.39% |
| 42. | 31 jul. 2022 | $64.04 | 3.14% | 4,130.29 | 9.11% | |
| 43. | 31 ago. 2022 | $61.86 | -3.40% | 3,955.00 | -4.24% | |
| 44. | 30 sept. 2022 | $54.83 | $0.385 | -10.74% | 3,585.62 | -9.34% |
| 45. | 31 oct. 2022 | $61.48 | 12.13% | 3,871.98 | 7.99% | |
| 46. | 30 nov. 2022 | $67.61 | 9.97% | 4,080.11 | 5.38% | |
| 47. | 31 dic. 2022 | $66.65 | $0.385 | -0.85% | 3,839.50 | -5.90% |
| 48. | 31 ene. 2023 | $65.44 | -1.82% | 4,076.60 | 6.18% | |
| 49. | 28 feb. 2023 | $65.18 | -0.40% | 3,970.15 | -2.61% | |
| 50. | 31 mar. 2023 | $69.72 | $0.385 | 7.56% | 4,109.31 | 3.51% |
| 51. | 30 abr. 2023 | $76.72 | 10.04% | 4,169.48 | 1.46% | |
| 52. | 31 may. 2023 | $73.41 | -4.31% | 4,179.83 | 0.25% | |
| 53. | 30 jun. 2023 | $72.94 | $0.385 | -0.12% | 4,376.86 | 4.71% |
| 54. | 31 jul. 2023 | $74.13 | 1.63% | 4,588.96 | 4.85% | |
| 55. | 31 ago. 2023 | $71.26 | -3.87% | 4,507.66 | -1.77% | |
| 56. | 30 sept. 2023 | $69.40 | $0.425 | -2.01% | 4,288.05 | -4.87% |
| 57. | 31 oct. 2023 | $66.21 | -4.60% | 4,193.80 | -2.20% | |
| 58. | 30 nov. 2023 | $71.06 | 7.33% | 4,567.80 | 8.92% | |
| 59. | 31 dic. 2023 | $72.43 | $0.425 | 2.53% | 4,769.83 | 4.42% |
| Promedio (R): | 1.08% | 1.11% | ||||
| Desviación estándar: | 5.19% | 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 MDLZ 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
Mondelēz International Inc., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RMDLZ,t | RS&P 500,t | (RMDLZ,t–RMDLZ)2 | (RS&P 500,t–RS&P 500)2 | (RMDLZ,t–RMDLZ)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2019 | 1.95% | 2.97% | 0.75 | 3.49 | 1.61 |
| 2. | 31 mar. 2019 | 6.40% | 1.79% | 28.32 | 0.47 | 3.65 |
| 3. | 30 abr. 2019 | 1.86% | 3.93% | 0.61 | 7.98 | 2.21 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | 7.33% | 8.92% | 38.97 | 61.03 | 48.77 |
| 59. | 31 dic. 2023 | 2.53% | 4.42% | 2.08 | 11.00 | 4.79 |
| Total (Σ): | 1,563.88 | 1,634.30 | 960.54 | |||
| t | Fecha | RMDLZ,t | RS&P 500,t | (RMDLZ,t–RMDLZ)2 | (RS&P 500,t–RS&P 500)2 | (RMDLZ,t–RMDLZ)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2019 | 1.95% | 2.97% | 0.75 | 3.49 | 1.61 |
| 2. | 31 mar. 2019 | 6.40% | 1.79% | 28.32 | 0.47 | 3.65 |
| 3. | 30 abr. 2019 | 1.86% | 3.93% | 0.61 | 7.98 | 2.21 |
| 4. | 31 may. 2019 | 0.00% | -6.58% | 1.17 | 59.04 | 8.32 |
| 5. | 30 jun. 2019 | 6.51% | 6.89% | 29.45 | 33.49 | 31.41 |
| 6. | 31 jul. 2019 | -0.76% | 1.31% | 3.40 | 0.04 | -0.38 |
| 7. | 31 ago. 2019 | 3.23% | -1.81% | 4.63 | 8.50 | -6.27 |
| 8. | 30 sept. 2019 | 0.70% | 1.72% | 0.15 | 0.37 | -0.24 |
| 9. | 31 oct. 2019 | -5.19% | 2.04% | 39.32 | 0.88 | -5.88 |
| 10. | 30 nov. 2019 | 0.17% | 3.40% | 0.83 | 5.28 | -2.09 |
| 11. | 31 dic. 2019 | 5.38% | 2.86% | 18.44 | 3.07 | 7.53 |
| 12. | 31 ene. 2020 | 4.18% | -0.16% | 9.57 | 1.61 | -3.92 |
| 13. | 29 feb. 2020 | -7.98% | -8.41% | 82.16 | 90.57 | 86.26 |
| 14. | 31 mar. 2020 | -4.61% | -12.51% | 32.42 | 185.44 | 77.54 |
| 15. | 30 abr. 2020 | 2.72% | 12.68% | 2.67 | 134.06 | 18.91 |
| 16. | 31 may. 2020 | 1.32% | 4.53% | 0.06 | 11.71 | 0.82 |
| 17. | 30 jun. 2020 | -1.35% | 1.84% | 5.93 | 0.54 | -1.78 |
| 18. | 31 jul. 2020 | 8.53% | 5.51% | 55.43 | 19.40 | 32.79 |
| 19. | 31 ago. 2020 | 5.28% | 7.01% | 17.62 | 34.82 | 24.77 |
| 20. | 30 sept. 2020 | -1.12% | -3.92% | 4.86 | 25.29 | 11.08 |
| 21. | 31 oct. 2020 | -7.54% | -2.77% | 74.29 | 15.00 | 33.38 |
| 22. | 30 nov. 2020 | 8.15% | 10.75% | 49.97 | 93.10 | 68.21 |
| 23. | 31 dic. 2020 | 2.32% | 3.71% | 1.54 | 6.79 | 3.24 |
| 24. | 31 ene. 2021 | -5.18% | -1.11% | 39.24 | 4.93 | 13.90 |
| 25. | 28 feb. 2021 | -4.11% | 2.61% | 26.99 | 2.26 | -7.81 |
| 26. | 31 mar. 2021 | 10.69% | 4.24% | 92.39 | 9.85 | 30.16 |
| 27. | 30 abr. 2021 | 3.90% | 5.24% | 7.91 | 17.11 | 11.64 |
| 28. | 31 may. 2021 | 4.47% | 0.55% | 11.50 | 0.31 | -1.89 |
| 29. | 30 jun. 2021 | -1.22% | 2.22% | 5.30 | 1.24 | -2.57 |
| 30. | 31 jul. 2021 | 1.31% | 2.27% | 0.05 | 1.37 | 0.27 |
| 31. | 31 ago. 2021 | -1.88% | 2.90% | 8.78 | 3.22 | -5.31 |
| 32. | 30 sept. 2021 | -5.70% | -4.76% | 46.04 | 34.37 | 39.78 |
| 33. | 31 oct. 2021 | 4.40% | 6.91% | 11.01 | 33.74 | 19.27 |
| 34. | 30 nov. 2021 | -2.96% | -0.83% | 16.37 | 3.76 | 7.85 |
| 35. | 31 dic. 2021 | 13.10% | 4.36% | 144.38 | 10.60 | 39.12 |
| 36. | 31 ene. 2022 | 1.09% | -5.26% | 0.00 | 40.51 | -0.02 |
| 37. | 28 feb. 2022 | -2.31% | -3.14% | 11.52 | 17.99 | 14.40 |
| 38. | 31 mar. 2022 | -3.59% | 3.58% | 21.82 | 6.11 | -11.54 |
| 39. | 30 abr. 2022 | 2.71% | -8.80% | 2.64 | 98.04 | -16.10 |
| 40. | 31 may. 2022 | -1.43% | 0.01% | 6.30 | 1.21 | 2.76 |
| 41. | 30 jun. 2022 | -1.76% | -8.39% | 8.09 | 90.21 | 27.02 |
| 42. | 31 jul. 2022 | 3.14% | 9.11% | 4.24 | 64.09 | 16.48 |
| 43. | 31 ago. 2022 | -3.40% | -4.24% | 20.13 | 28.62 | 24.00 |
| 44. | 30 sept. 2022 | -10.74% | -9.34% | 139.81 | 109.11 | 123.51 |
| 45. | 31 oct. 2022 | 12.13% | 7.99% | 122.02 | 47.34 | 76.00 |
| 46. | 30 nov. 2022 | 9.97% | 5.38% | 79.00 | 18.23 | 37.95 |
| 47. | 31 dic. 2022 | -0.85% | -5.90% | 3.74 | 49.04 | 13.54 |
| 48. | 31 ene. 2023 | -1.82% | 6.18% | 8.40 | 25.70 | -14.69 |
| 49. | 28 feb. 2023 | -0.40% | -2.61% | 2.19 | 13.82 | 5.50 |
| 50. | 31 mar. 2023 | 7.56% | 3.51% | 41.91 | 5.76 | 15.53 |
| 51. | 30 abr. 2023 | 10.04% | 1.46% | 80.24 | 0.13 | 3.21 |
| 52. | 31 may. 2023 | -4.31% | 0.25% | 29.12 | 0.74 | 4.63 |
| 53. | 30 jun. 2023 | -0.12% | 4.71% | 1.44 | 13.02 | -4.32 |
| 54. | 31 jul. 2023 | 1.63% | 4.85% | 0.30 | 13.99 | 2.05 |
| 55. | 31 ago. 2023 | -3.87% | -1.77% | 24.54 | 8.28 | 14.25 |
| 56. | 30 sept. 2023 | -2.01% | -4.87% | 9.59 | 35.73 | 18.51 |
| 57. | 31 oct. 2023 | -4.60% | -2.20% | 32.25 | 10.92 | 18.76 |
| 58. | 30 nov. 2023 | 7.33% | 8.92% | 38.97 | 61.03 | 48.77 |
| 59. | 31 dic. 2023 | 2.53% | 4.42% | 2.08 | 11.00 | 4.79 |
| Total (Σ): | 1,563.88 | 1,634.30 | 960.54 | |||
Mostrar todo
VarianzaMDLZ = Σ(RMDLZ,t–RMDLZ)2 ÷ (59 – 1)
= 1,563.88 ÷ (59 – 1)
= 26.96
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
CovarianzaMDLZ, S&P 500 = Σ(RMDLZ,t–RMDLZ)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 960.54 ÷ (59 – 1)
= 16.56
Estimación sistemática del riesgo (β)
| VarianzaMDLZ | 26.96 |
| VarianzaS&P 500 | 28.18 |
| CovarianzaMDLZ, S&P 500 | 16.56 |
| Coeficiente de correlaciónMDLZ, S&P 5001 | 0.60 |
| βMDLZ2 | 0.59 |
| αMDLZ3 | 0.43% |
Cálculos
1 Coeficiente de correlaciónMDLZ, S&P 500
= CovarianzaMDLZ, S&P 500 ÷ (Desviación estándarMDLZ × Desviación estándarS&P 500)
= 16.56 ÷ (5.19% × 5.31%)
= 0.60
2 βMDLZ
= CovarianzaMDLZ, S&P 500 ÷ VarianzaS&P 500
= 16.56 ÷ 28.18
= 0.59
3 αMDLZ
= PromedioMDLZ – βMDLZ × PromedioS&P 500
= 1.08% – 0.59 × 1.11%
= 0.43%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.44% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.77% |
| Riesgo sistemático de Mondelēz International acciones ordinarias | βMDLZ | 0.59 |
| Tasa de rendimiento esperada de las acciones ordinarias de Mondelēz International3 | E(RMDLZ) | 9.92% |
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(RMDLZ) = RF + βMDLZ [E(RM) – RF]
= 4.44% + 0.59 [13.77% – 4.44%]
= 9.92%