Modelo de fijación de precios de activos de capital (CAPM)
El modelo de valoración 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 Hershey.
Tasas de retorno
Hershey Co., tasas mensuales de retorno
| Hershey Co. (HSY) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioHSY,t1 | DividendoHSY,t1 | RHSY,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2018 | $110.33 | 2,823.81 | ||||
| 1. | 28 feb. 2018 | $98.26 | $0.656 | -10.35% | 2,713.83 | -3.89% |
| 2. | 31 mar. 2018 | $98.96 | 0.71% | 2,640.87 | -2.69% | |
| 3. | 30 abr. 2018 | $91.94 | -7.09% | 2,648.05 | 0.27% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2022 | $235.17 | $1.036 | -1.07% | 4,080.11 | 5.38% |
| 59. | 31 dic. 2022 | $231.57 | -1.53% | 3,839.50 | -5.90% | |
| Promedio (R): | 1.57% | 0.67% | ||||
| Desviación estándar: | 4.95% | 5.40% | ||||
| Hershey Co. (HSY) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioHSY,t1 | DividendoHSY,t1 | RHSY,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2018 | $110.33 | 2,823.81 | ||||
| 1. | 28 feb. 2018 | $98.26 | $0.656 | -10.35% | 2,713.83 | -3.89% |
| 2. | 31 mar. 2018 | $98.96 | 0.71% | 2,640.87 | -2.69% | |
| 3. | 30 abr. 2018 | $91.94 | -7.09% | 2,648.05 | 0.27% | |
| 4. | 31 may. 2018 | $90.04 | $0.656 | -1.35% | 2,705.27 | 2.16% |
| 5. | 30 jun. 2018 | $93.06 | 3.35% | 2,718.37 | 0.48% | |
| 6. | 31 jul. 2018 | $98.21 | 5.53% | 2,816.29 | 3.60% | |
| 7. | 31 ago. 2018 | $100.52 | $0.722 | 3.09% | 2,901.52 | 3.03% |
| 8. | 30 sept. 2018 | $102.00 | 1.47% | 2,913.98 | 0.43% | |
| 9. | 31 oct. 2018 | $107.15 | 5.05% | 2,711.74 | -6.94% | |
| 10. | 30 nov. 2018 | $108.30 | $0.722 | 1.75% | 2,760.17 | 1.79% |
| 11. | 31 dic. 2018 | $107.18 | -1.03% | 2,506.85 | -9.18% | |
| 12. | 31 ene. 2019 | $106.10 | -1.01% | 2,704.10 | 7.87% | |
| 13. | 28 feb. 2019 | $110.68 | $0.722 | 5.00% | 2,784.49 | 2.97% |
| 14. | 31 mar. 2019 | $114.83 | 3.75% | 2,834.40 | 1.79% | |
| 15. | 30 abr. 2019 | $124.85 | 8.73% | 2,945.83 | 3.93% | |
| 16. | 31 may. 2019 | $131.96 | $0.722 | 6.27% | 2,752.06 | -6.58% |
| 17. | 30 jun. 2019 | $134.03 | 1.57% | 2,941.76 | 6.89% | |
| 18. | 31 jul. 2019 | $151.74 | 13.21% | 2,980.38 | 1.31% | |
| 19. | 31 ago. 2019 | $158.48 | $0.773 | 4.95% | 2,926.46 | -1.81% |
| 20. | 30 sept. 2019 | $154.99 | -2.20% | 2,976.74 | 1.72% | |
| 21. | 31 oct. 2019 | $146.87 | -5.24% | 3,037.56 | 2.04% | |
| 22. | 30 nov. 2019 | $148.16 | $0.773 | 1.40% | 3,140.98 | 3.40% |
| 23. | 31 dic. 2019 | $146.98 | -0.80% | 3,230.78 | 2.86% | |
| 24. | 31 ene. 2020 | $155.17 | 5.57% | 3,225.52 | -0.16% | |
| 25. | 29 feb. 2020 | $143.99 | $0.773 | -6.71% | 2,954.22 | -8.41% |
| 26. | 31 mar. 2020 | $132.50 | -7.98% | 2,584.59 | -12.51% | |
| 27. | 30 abr. 2020 | $132.43 | -0.05% | 2,912.43 | 12.68% | |
| 28. | 31 may. 2020 | $135.68 | $0.773 | 3.04% | 3,044.31 | 4.53% |
| 29. | 30 jun. 2020 | $129.62 | -4.47% | 3,100.29 | 1.84% | |
| 30. | 31 jul. 2020 | $145.41 | 12.18% | 3,271.12 | 5.51% | |
| 31. | 31 ago. 2020 | $148.64 | $0.804 | 2.77% | 3,500.31 | 7.01% |
| 32. | 30 sept. 2020 | $143.34 | -3.57% | 3,363.00 | -3.92% | |
| 33. | 31 oct. 2020 | $137.46 | -4.10% | 3,269.96 | -2.77% | |
| 34. | 30 nov. 2020 | $147.89 | $0.804 | 8.17% | 3,621.63 | 10.75% |
| 35. | 31 dic. 2020 | $152.33 | 3.00% | 3,756.07 | 3.71% | |
| 36. | 31 ene. 2021 | $145.44 | -4.52% | 3,714.24 | -1.11% | |
| 37. | 28 feb. 2021 | $145.65 | $0.804 | 0.70% | 3,811.15 | 2.61% |
| 38. | 31 mar. 2021 | $158.16 | 8.59% | 3,972.89 | 4.24% | |
| 39. | 30 abr. 2021 | $164.30 | 3.88% | 4,181.17 | 5.24% | |
| 40. | 31 may. 2021 | $173.05 | $0.804 | 5.81% | 4,204.11 | 0.55% |
| 41. | 30 jun. 2021 | $174.18 | 0.65% | 4,297.50 | 2.22% | |
| 42. | 31 jul. 2021 | $178.88 | 2.70% | 4,395.26 | 2.27% | |
| 43. | 31 ago. 2021 | $177.70 | $0.901 | -0.16% | 4,522.68 | 2.90% |
| 44. | 30 sept. 2021 | $169.25 | -4.76% | 4,307.54 | -4.76% | |
| 45. | 31 oct. 2021 | $175.35 | 3.60% | 4,605.38 | 6.91% | |
| 46. | 30 nov. 2021 | $177.49 | $0.901 | 1.73% | 4,567.00 | -0.83% |
| 47. | 31 dic. 2021 | $193.47 | 9.00% | 4,766.18 | 4.36% | |
| 48. | 31 ene. 2022 | $197.07 | 1.86% | 4,515.55 | -5.26% | |
| 49. | 28 feb. 2022 | $202.26 | $0.901 | 3.09% | 4,373.94 | -3.14% |
| 50. | 31 mar. 2022 | $216.63 | 7.10% | 4,530.41 | 3.58% | |
| 51. | 30 abr. 2022 | $225.77 | 4.22% | 4,131.93 | -8.80% | |
| 52. | 31 may. 2022 | $211.71 | $0.901 | -5.83% | 4,132.15 | 0.01% |
| 53. | 30 jun. 2022 | $215.16 | 1.63% | 3,785.38 | -8.39% | |
| 54. | 31 jul. 2022 | $227.96 | 5.95% | 4,130.29 | 9.11% | |
| 55. | 31 ago. 2022 | $224.67 | $1.036 | -0.99% | 3,955.00 | -4.24% |
| 56. | 30 sept. 2022 | $220.47 | -1.87% | 3,585.62 | -9.34% | |
| 57. | 31 oct. 2022 | $238.77 | 8.30% | 3,871.98 | 7.99% | |
| 58. | 30 nov. 2022 | $235.17 | $1.036 | -1.07% | 4,080.11 | 5.38% |
| 59. | 31 dic. 2022 | $231.57 | -1.53% | 3,839.50 | -5.90% | |
| Promedio (R): | 1.57% | 0.67% | ||||
| Desviación estándar: | 4.95% | 5.40% | ||||
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 HSY 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
Hershey Co., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RHSY,t | RS&P 500,t | (RHSY,t–RHSY)2 | (RS&P 500,t–RS&P 500)2 | (RHSY,t–RHSY)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2018 | -10.35% | -3.89% | 142.02 | 20.81 | 54.36 |
| 2. | 31 mar. 2018 | 0.71% | -2.69% | 0.74 | 11.26 | 2.88 |
| 3. | 30 abr. 2018 | -7.09% | 0.27% | 75.09 | 0.16 | 3.42 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2022 | -1.07% | 5.38% | 7.00 | 22.17 | -12.46 |
| 59. | 31 dic. 2022 | -1.53% | -5.90% | 9.63 | 43.08 | 20.37 |
| Total (Σ): | 1,420.62 | 1,691.48 | 625.74 | |||
| t | Fecha | RHSY,t | RS&P 500,t | (RHSY,t–RHSY)2 | (RS&P 500,t–RS&P 500)2 | (RHSY,t–RHSY)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2018 | -10.35% | -3.89% | 142.02 | 20.81 | 54.36 |
| 2. | 31 mar. 2018 | 0.71% | -2.69% | 0.74 | 11.26 | 2.88 |
| 3. | 30 abr. 2018 | -7.09% | 0.27% | 75.09 | 0.16 | 3.42 |
| 4. | 31 may. 2018 | -1.35% | 2.16% | 8.56 | 2.23 | -4.37 |
| 5. | 30 jun. 2018 | 3.35% | 0.48% | 3.18 | 0.03 | -0.33 |
| 6. | 31 jul. 2018 | 5.53% | 3.60% | 15.70 | 8.62 | 11.63 |
| 7. | 31 ago. 2018 | 3.09% | 3.03% | 2.30 | 5.57 | 3.58 |
| 8. | 30 sept. 2018 | 1.47% | 0.43% | 0.01 | 0.06 | 0.02 |
| 9. | 31 oct. 2018 | 5.05% | -6.94% | 12.09 | 57.87 | -26.45 |
| 10. | 30 nov. 2018 | 1.75% | 1.79% | 0.03 | 1.25 | 0.20 |
| 11. | 31 dic. 2018 | -1.03% | -9.18% | 6.79 | 96.91 | 25.65 |
| 12. | 31 ene. 2019 | -1.01% | 7.87% | 6.65 | 51.87 | -18.58 |
| 13. | 28 feb. 2019 | 5.00% | 2.97% | 11.73 | 5.32 | 7.90 |
| 14. | 31 mar. 2019 | 3.75% | 1.79% | 4.74 | 1.27 | 2.45 |
| 15. | 30 abr. 2019 | 8.73% | 3.93% | 51.18 | 10.66 | 23.36 |
| 16. | 31 may. 2019 | 6.27% | -6.58% | 22.10 | 52.48 | -34.06 |
| 17. | 30 jun. 2019 | 1.57% | 6.89% | 0.00 | 38.77 | -0.02 |
| 18. | 31 jul. 2019 | 13.21% | 1.31% | 135.53 | 0.42 | 7.52 |
| 19. | 31 ago. 2019 | 4.95% | -1.81% | 11.42 | 6.13 | -8.37 |
| 20. | 30 sept. 2019 | -2.20% | 1.72% | 14.24 | 1.11 | -3.97 |
| 21. | 31 oct. 2019 | -5.24% | 2.04% | 46.39 | 1.89 | -9.38 |
| 22. | 30 nov. 2019 | 1.40% | 3.40% | 0.03 | 7.50 | -0.46 |
| 23. | 31 dic. 2019 | -0.80% | 2.86% | 5.61 | 4.81 | -5.19 |
| 24. | 31 ene. 2020 | 5.57% | -0.16% | 16.00 | 0.69 | -3.32 |
| 25. | 29 feb. 2020 | -6.71% | -8.41% | 68.54 | 82.40 | 75.15 |
| 26. | 31 mar. 2020 | -7.98% | -12.51% | 91.23 | 173.67 | 125.88 |
| 27. | 30 abr. 2020 | -0.05% | 12.68% | 2.64 | 144.43 | -19.53 |
| 28. | 31 may. 2020 | 3.04% | 4.53% | 2.15 | 14.91 | 5.66 |
| 29. | 30 jun. 2020 | -4.47% | 1.84% | 36.46 | 1.37 | -7.08 |
| 30. | 31 jul. 2020 | 12.18% | 5.51% | 112.57 | 23.46 | 51.39 |
| 31. | 31 ago. 2020 | 2.77% | 7.01% | 1.45 | 40.19 | 7.62 |
| 32. | 30 sept. 2020 | -3.57% | -3.92% | 26.39 | 21.06 | 23.58 |
| 33. | 31 oct. 2020 | -4.10% | -2.77% | 32.19 | 11.79 | 19.48 |
| 34. | 30 nov. 2020 | 8.17% | 10.75% | 43.57 | 101.77 | 66.59 |
| 35. | 31 dic. 2020 | 3.00% | 3.71% | 2.05 | 9.28 | 4.36 |
| 36. | 31 ene. 2021 | -4.52% | -1.11% | 37.15 | 3.17 | 10.85 |
| 37. | 28 feb. 2021 | 0.70% | 2.61% | 0.77 | 3.77 | -1.70 |
| 38. | 31 mar. 2021 | 8.59% | 4.24% | 49.24 | 12.80 | 25.10 |
| 39. | 30 abr. 2021 | 3.88% | 5.24% | 5.34 | 20.94 | 10.57 |
| 40. | 31 may. 2021 | 5.81% | 0.55% | 18.00 | 0.01 | -0.50 |
| 41. | 30 jun. 2021 | 0.65% | 2.22% | 0.84 | 2.42 | -1.43 |
| 42. | 31 jul. 2021 | 2.70% | 2.27% | 1.27 | 2.59 | 1.81 |
| 43. | 31 ago. 2021 | -0.16% | 2.90% | 2.99 | 4.98 | -3.86 |
| 44. | 30 sept. 2021 | -4.76% | -4.76% | 40.03 | 29.42 | 34.32 |
| 45. | 31 oct. 2021 | 3.60% | 6.91% | 4.13 | 39.03 | 12.70 |
| 46. | 30 nov. 2021 | 1.73% | -0.83% | 0.03 | 2.25 | -0.24 |
| 47. | 31 dic. 2021 | 9.00% | 4.36% | 55.23 | 13.65 | 27.46 |
| 48. | 31 ene. 2022 | 1.86% | -5.26% | 0.08 | 35.11 | -1.71 |
| 49. | 28 feb. 2022 | 3.09% | -3.14% | 2.31 | 14.46 | -5.78 |
| 50. | 31 mar. 2022 | 7.10% | 3.58% | 30.61 | 8.47 | 16.10 |
| 51. | 30 abr. 2022 | 4.22% | -8.80% | 7.01 | 89.54 | -25.05 |
| 52. | 31 may. 2022 | -5.83% | 0.01% | 54.77 | 0.44 | 4.89 |
| 53. | 30 jun. 2022 | 1.63% | -8.39% | 0.00 | 82.06 | -0.52 |
| 54. | 31 jul. 2022 | 5.95% | 9.11% | 19.16 | 71.32 | 36.97 |
| 55. | 31 ago. 2022 | -0.99% | -4.24% | 6.56 | 24.11 | 12.57 |
| 56. | 30 sept. 2022 | -1.87% | -9.34% | 11.84 | 100.12 | 34.43 |
| 57. | 31 oct. 2022 | 8.30% | 7.99% | 45.27 | 53.58 | 49.25 |
| 58. | 30 nov. 2022 | -1.07% | 5.38% | 7.00 | 22.17 | -12.46 |
| 59. | 31 dic. 2022 | -1.53% | -5.90% | 9.63 | 43.08 | 20.37 |
| Total (Σ): | 1,420.62 | 1,691.48 | 625.74 | |||
Mostrar todo
VarianzaHSY = Σ(RHSY,t–RHSY)2 ÷ (59 – 1)
= 1,420.62 ÷ (59 – 1)
= 24.49
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,691.48 ÷ (59 – 1)
= 29.16
CovarianzaHSY, S&P 500 = Σ(RHSY,t–RHSY)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 625.74 ÷ (59 – 1)
= 10.79
Estimación sistemática del riesgo (β)
| VarianzaHSY | 24.49 |
| VarianzaS&P 500 | 29.16 |
| CovarianzaHSY, S&P 500 | 10.79 |
| Coeficiente de correlaciónHSY, S&P 5001 | 0.40 |
| βHSY2 | 0.37 |
| αHSY3 | 1.33% |
Cálculos
1 Coeficiente de correlaciónHSY, S&P 500
= CovarianzaHSY, S&P 500 ÷ (Desviación estándarHSY × Desviación estándarS&P 500)
= 10.79 ÷ (4.95% × 5.40%)
= 0.40
2 βHSY
= CovarianzaHSY, S&P 500 ÷ VarianzaS&P 500
= 10.79 ÷ 29.16
= 0.37
3 αHSY
= PromedioHSY – βHSY × PromedioS&P 500
= 1.57% – 0.37 × 0.67%
= 1.33%
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 Hershey acciones ordinarias | βHSY | 0.37 |
| Tasa de rendimiento esperada de las acciones ordinarias de Hershey3 | E(RHSY) | 8.04% |
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(RHSY) = RF + βHSY [E(RM) – RF]
= 4.67% + 0.37 [13.79% – 4.67%]
= 8.04%