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 Salesforce.
Tasas de retorno
Salesforce Inc., tasas mensuales de retorno
| Salesforce Inc. (CRM) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioCRM,t1 | DividendoCRM,t1 | RCRM,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 28 feb. 2018 | $116.25 | 2,713.83 | ||||
| 1. | 31 mar. 2018 | $116.30 | 0.04% | 2,640.87 | -2.69% | |
| 2. | 30 abr. 2018 | $120.99 | 4.03% | 2,648.05 | 0.27% | |
| 3. | 31 may. 2018 | $129.33 | 6.89% | 2,705.27 | 2.16% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 31 dic. 2023 | $263.14 | 4.46% | 4,769.83 | 4.42% | |
| 71. | 31 ene. 2024 | $281.09 | 6.82% | 4,845.65 | 1.59% | |
| Promedio (R): | 1.74% | 0.95% | ||||
| Desviación estándar: | 10.20% | 5.18% | ||||
| Salesforce Inc. (CRM) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioCRM,t1 | DividendoCRM,t1 | RCRM,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 28 feb. 2018 | $116.25 | 2,713.83 | ||||
| 1. | 31 mar. 2018 | $116.30 | 0.04% | 2,640.87 | -2.69% | |
| 2. | 30 abr. 2018 | $120.99 | 4.03% | 2,648.05 | 0.27% | |
| 3. | 31 may. 2018 | $129.33 | 6.89% | 2,705.27 | 2.16% | |
| 4. | 30 jun. 2018 | $136.40 | 5.47% | 2,718.37 | 0.48% | |
| 5. | 31 jul. 2018 | $137.15 | 0.55% | 2,816.29 | 3.60% | |
| 6. | 31 ago. 2018 | $152.68 | 11.32% | 2,901.52 | 3.03% | |
| 7. | 30 sept. 2018 | $159.03 | 4.16% | 2,913.98 | 0.43% | |
| 8. | 31 oct. 2018 | $137.24 | -13.70% | 2,711.74 | -6.94% | |
| 9. | 30 nov. 2018 | $142.76 | 4.02% | 2,760.17 | 1.79% | |
| 10. | 31 dic. 2018 | $136.97 | -4.06% | 2,506.85 | -9.18% | |
| 11. | 31 ene. 2019 | $151.97 | 10.95% | 2,704.10 | 7.87% | |
| 12. | 28 feb. 2019 | $163.65 | 7.69% | 2,784.49 | 2.97% | |
| 13. | 31 mar. 2019 | $158.37 | -3.23% | 2,834.40 | 1.79% | |
| 14. | 30 abr. 2019 | $165.35 | 4.41% | 2,945.83 | 3.93% | |
| 15. | 31 may. 2019 | $151.41 | -8.43% | 2,752.06 | -6.58% | |
| 16. | 30 jun. 2019 | $151.73 | 0.21% | 2,941.76 | 6.89% | |
| 17. | 31 jul. 2019 | $154.50 | 1.83% | 2,980.38 | 1.31% | |
| 18. | 31 ago. 2019 | $156.07 | 1.02% | 2,926.46 | -1.81% | |
| 19. | 30 sept. 2019 | $148.44 | -4.89% | 2,976.74 | 1.72% | |
| 20. | 31 oct. 2019 | $156.49 | 5.42% | 3,037.56 | 2.04% | |
| 21. | 30 nov. 2019 | $162.89 | 4.09% | 3,140.98 | 3.40% | |
| 22. | 31 dic. 2019 | $162.64 | -0.15% | 3,230.78 | 2.86% | |
| 23. | 31 ene. 2020 | $182.31 | 12.09% | 3,225.52 | -0.16% | |
| 24. | 29 feb. 2020 | $170.40 | -6.53% | 2,954.22 | -8.41% | |
| 25. | 31 mar. 2020 | $143.98 | -15.50% | 2,584.59 | -12.51% | |
| 26. | 30 abr. 2020 | $161.95 | 12.48% | 2,912.43 | 12.68% | |
| 27. | 31 may. 2020 | $174.79 | 7.93% | 3,044.31 | 4.53% | |
| 28. | 30 jun. 2020 | $187.33 | 7.17% | 3,100.29 | 1.84% | |
| 29. | 31 jul. 2020 | $194.85 | 4.01% | 3,271.12 | 5.51% | |
| 30. | 31 ago. 2020 | $272.65 | 39.93% | 3,500.31 | 7.01% | |
| 31. | 30 sept. 2020 | $251.32 | -7.82% | 3,363.00 | -3.92% | |
| 32. | 31 oct. 2020 | $232.27 | -7.58% | 3,269.96 | -2.77% | |
| 33. | 30 nov. 2020 | $245.80 | 5.83% | 3,621.63 | 10.75% | |
| 34. | 31 dic. 2020 | $222.53 | -9.47% | 3,756.07 | 3.71% | |
| 35. | 31 ene. 2021 | $225.56 | 1.36% | 3,714.24 | -1.11% | |
| 36. | 28 feb. 2021 | $216.50 | -4.02% | 3,811.15 | 2.61% | |
| 37. | 31 mar. 2021 | $211.87 | -2.14% | 3,972.89 | 4.24% | |
| 38. | 30 abr. 2021 | $230.32 | 8.71% | 4,181.17 | 5.24% | |
| 39. | 31 may. 2021 | $238.10 | 3.38% | 4,204.11 | 0.55% | |
| 40. | 30 jun. 2021 | $244.27 | 2.59% | 4,297.50 | 2.22% | |
| 41. | 31 jul. 2021 | $241.93 | -0.96% | 4,395.26 | 2.27% | |
| 42. | 31 ago. 2021 | $265.27 | 9.65% | 4,522.68 | 2.90% | |
| 43. | 30 sept. 2021 | $271.22 | 2.24% | 4,307.54 | -4.76% | |
| 44. | 31 oct. 2021 | $299.69 | 10.50% | 4,605.38 | 6.91% | |
| 45. | 30 nov. 2021 | $284.96 | -4.92% | 4,567.00 | -0.83% | |
| 46. | 31 dic. 2021 | $254.13 | -10.82% | 4,766.18 | 4.36% | |
| 47. | 31 ene. 2022 | $232.63 | -8.46% | 4,515.55 | -5.26% | |
| 48. | 28 feb. 2022 | $210.53 | -9.50% | 4,373.94 | -3.14% | |
| 49. | 31 mar. 2022 | $212.32 | 0.85% | 4,530.41 | 3.58% | |
| 50. | 30 abr. 2022 | $175.94 | -17.13% | 4,131.93 | -8.80% | |
| 51. | 31 may. 2022 | $160.24 | -8.92% | 4,132.15 | 0.01% | |
| 52. | 30 jun. 2022 | $165.04 | 3.00% | 3,785.38 | -8.39% | |
| 53. | 31 jul. 2022 | $184.02 | 11.50% | 4,130.29 | 9.11% | |
| 54. | 31 ago. 2022 | $156.12 | -15.16% | 3,955.00 | -4.24% | |
| 55. | 30 sept. 2022 | $143.84 | -7.87% | 3,585.62 | -9.34% | |
| 56. | 31 oct. 2022 | $162.59 | 13.04% | 3,871.98 | 7.99% | |
| 57. | 30 nov. 2022 | $160.25 | -1.44% | 4,080.11 | 5.38% | |
| 58. | 31 dic. 2022 | $132.59 | -17.26% | 3,839.50 | -5.90% | |
| 59. | 31 ene. 2023 | $167.97 | 26.68% | 4,076.60 | 6.18% | |
| 60. | 28 feb. 2023 | $163.61 | -2.60% | 3,970.15 | -2.61% | |
| 61. | 31 mar. 2023 | $199.78 | 22.11% | 4,109.31 | 3.51% | |
| 62. | 30 abr. 2023 | $198.37 | -0.71% | 4,169.48 | 1.46% | |
| 63. | 31 may. 2023 | $223.38 | 12.61% | 4,179.83 | 0.25% | |
| 64. | 30 jun. 2023 | $211.26 | -5.43% | 4,376.86 | 4.71% | |
| 65. | 31 jul. 2023 | $225.01 | 6.51% | 4,588.96 | 4.85% | |
| 66. | 31 ago. 2023 | $221.46 | -1.58% | 4,507.66 | -1.77% | |
| 67. | 30 sept. 2023 | $202.78 | -8.43% | 4,288.05 | -4.87% | |
| 68. | 31 oct. 2023 | $200.83 | -0.96% | 4,193.80 | -2.20% | |
| 69. | 30 nov. 2023 | $251.90 | 25.43% | 4,567.80 | 8.92% | |
| 70. | 31 dic. 2023 | $263.14 | 4.46% | 4,769.83 | 4.42% | |
| 71. | 31 ene. 2024 | $281.09 | 6.82% | 4,845.65 | 1.59% | |
| Promedio (R): | 1.74% | 0.95% | ||||
| Desviación estándar: | 10.20% | 5.18% | ||||
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 CRM 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
Salesforce Inc., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RCRM,t | RS&P 500,t | (RCRM,t–RCRM)2 | (RS&P 500,t–RS&P 500)2 | (RCRM,t–RCRM)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 mar. 2018 | 0.04% | -2.69% | 2.87 | 13.26 | 6.17 |
| 2. | 30 abr. 2018 | 4.03% | 0.27% | 5.27 | 0.46 | -1.56 |
| 3. | 31 may. 2018 | 6.89% | 2.16% | 26.59 | 1.46 | 6.23 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 31 dic. 2023 | 4.46% | 4.42% | 7.43 | 12.04 | 9.46 |
| 71. | 31 ene. 2024 | 6.82% | 1.59% | 25.85 | 0.41 | 3.24 |
| Total (Σ): | 7,284.09 | 1,876.53 | 2,389.03 | |||
| t | Fecha | RCRM,t | RS&P 500,t | (RCRM,t–RCRM)2 | (RS&P 500,t–RS&P 500)2 | (RCRM,t–RCRM)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 mar. 2018 | 0.04% | -2.69% | 2.87 | 13.26 | 6.17 |
| 2. | 30 abr. 2018 | 4.03% | 0.27% | 5.27 | 0.46 | -1.56 |
| 3. | 31 may. 2018 | 6.89% | 2.16% | 26.59 | 1.46 | 6.23 |
| 4. | 30 jun. 2018 | 5.47% | 0.48% | 13.91 | 0.22 | -1.75 |
| 5. | 31 jul. 2018 | 0.55% | 3.60% | 1.41 | 7.02 | -3.14 |
| 6. | 31 ago. 2018 | 11.32% | 3.03% | 91.90 | 4.30 | 19.88 |
| 7. | 30 sept. 2018 | 4.16% | 0.43% | 5.87 | 0.27 | -1.27 |
| 8. | 31 oct. 2018 | -13.70% | -6.94% | 238.35 | 62.30 | 121.86 |
| 9. | 30 nov. 2018 | 4.02% | 1.79% | 5.22 | 0.69 | 1.90 |
| 10. | 31 dic. 2018 | -4.06% | -9.18% | 33.55 | 102.63 | 58.68 |
| 11. | 31 ene. 2019 | 10.95% | 7.87% | 84.91 | 47.82 | 63.72 |
| 12. | 28 feb. 2019 | 7.69% | 2.97% | 35.39 | 4.08 | 12.02 |
| 13. | 31 mar. 2019 | -3.23% | 1.79% | 24.63 | 0.70 | -4.17 |
| 14. | 30 abr. 2019 | 4.41% | 3.93% | 7.13 | 8.87 | 7.95 |
| 15. | 31 may. 2019 | -8.43% | -6.58% | 103.38 | 56.71 | 76.57 |
| 16. | 30 jun. 2019 | 0.21% | 6.89% | 2.33 | 35.28 | -9.06 |
| 17. | 31 jul. 2019 | 1.83% | 1.31% | 0.01 | 0.13 | 0.03 |
| 18. | 31 ago. 2019 | 1.02% | -1.81% | 0.52 | 7.63 | 1.99 |
| 19. | 30 sept. 2019 | -4.89% | 1.72% | 43.90 | 0.59 | -5.07 |
| 20. | 31 oct. 2019 | 5.42% | 2.04% | 13.59 | 1.19 | 4.02 |
| 21. | 30 nov. 2019 | 4.09% | 3.40% | 5.54 | 6.01 | 5.77 |
| 22. | 31 dic. 2019 | -0.15% | 2.86% | 3.57 | 3.63 | -3.60 |
| 23. | 31 ene. 2020 | 12.09% | -0.16% | 107.27 | 1.24 | -11.56 |
| 24. | 29 feb. 2020 | -6.53% | -8.41% | 68.39 | 87.68 | 77.44 |
| 25. | 31 mar. 2020 | -15.50% | -12.51% | 297.27 | 181.30 | 232.15 |
| 26. | 30 abr. 2020 | 12.48% | 12.68% | 115.43 | 137.63 | 126.04 |
| 27. | 31 may. 2020 | 7.93% | 4.53% | 38.34 | 12.78 | 22.14 |
| 28. | 30 jun. 2020 | 7.17% | 1.84% | 29.57 | 0.78 | 4.82 |
| 29. | 31 jul. 2020 | 4.01% | 5.51% | 5.19 | 20.77 | 10.38 |
| 30. | 31 ago. 2020 | 39.93% | 7.01% | 1,458.58 | 36.65 | 231.19 |
| 31. | 30 sept. 2020 | -7.82% | -3.92% | 91.39 | 23.77 | 46.61 |
| 32. | 31 oct. 2020 | -7.58% | -2.77% | 86.80 | 13.83 | 34.65 |
| 33. | 30 nov. 2020 | 5.83% | 10.75% | 16.71 | 96.07 | 40.07 |
| 34. | 31 dic. 2020 | -9.47% | 3.71% | 125.53 | 7.61 | -30.91 |
| 35. | 31 ene. 2021 | 1.36% | -1.11% | 0.14 | 4.27 | 0.78 |
| 36. | 28 feb. 2021 | -4.02% | 2.61% | 33.10 | 2.74 | -9.53 |
| 37. | 31 mar. 2021 | -2.14% | 4.24% | 15.02 | 10.83 | -12.75 |
| 38. | 30 abr. 2021 | 8.71% | 5.24% | 48.60 | 18.40 | 29.90 |
| 39. | 31 may. 2021 | 3.38% | 0.55% | 2.69 | 0.16 | -0.66 |
| 40. | 30 jun. 2021 | 2.59% | 2.22% | 0.73 | 1.61 | 1.08 |
| 41. | 31 jul. 2021 | -0.96% | 2.27% | 7.26 | 1.75 | -3.56 |
| 42. | 31 ago. 2021 | 9.65% | 2.90% | 62.58 | 3.79 | 15.39 |
| 43. | 30 sept. 2021 | 2.24% | -4.76% | 0.26 | 32.60 | -2.89 |
| 44. | 31 oct. 2021 | 10.50% | 6.91% | 76.74 | 35.54 | 52.22 |
| 45. | 30 nov. 2021 | -4.92% | -0.83% | 44.25 | 3.19 | 11.88 |
| 46. | 31 dic. 2021 | -10.82% | 4.36% | 157.65 | 11.62 | -42.80 |
| 47. | 31 ene. 2022 | -8.46% | -5.26% | 103.98 | 38.58 | 63.34 |
| 48. | 28 feb. 2022 | -9.50% | -3.14% | 126.27 | 16.72 | 45.95 |
| 49. | 31 mar. 2022 | 0.85% | 3.58% | 0.79 | 6.89 | -2.33 |
| 50. | 30 abr. 2022 | -17.13% | -8.80% | 356.13 | 95.04 | 183.97 |
| 51. | 31 may. 2022 | -8.92% | 0.01% | 113.64 | 0.90 | 10.10 |
| 52. | 30 jun. 2022 | 3.00% | -8.39% | 1.58 | 87.33 | -11.76 |
| 53. | 31 jul. 2022 | 11.50% | 9.11% | 95.32 | 66.56 | 79.66 |
| 54. | 31 ago. 2022 | -15.16% | -4.24% | 285.55 | 27.01 | 87.82 |
| 55. | 30 sept. 2022 | -7.87% | -9.34% | 92.21 | 105.94 | 98.83 |
| 56. | 31 oct. 2022 | 13.04% | 7.99% | 127.66 | 49.47 | 79.47 |
| 57. | 30 nov. 2022 | -1.44% | 5.38% | 10.09 | 19.56 | -14.05 |
| 58. | 31 dic. 2022 | -17.26% | -5.90% | 360.90 | 46.92 | 130.13 |
| 59. | 31 ene. 2023 | 26.68% | 6.18% | 622.35 | 27.27 | 130.28 |
| 60. | 28 feb. 2023 | -2.60% | -2.61% | 18.77 | 12.70 | 15.44 |
| 61. | 31 mar. 2023 | 22.11% | 3.51% | 414.96 | 6.51 | 51.99 |
| 62. | 30 abr. 2023 | -0.71% | 1.46% | 5.97 | 0.26 | -1.25 |
| 63. | 31 may. 2023 | 12.61% | 0.25% | 118.18 | 0.50 | -7.66 |
| 64. | 30 jun. 2023 | -5.43% | 4.71% | 51.30 | 14.14 | -26.94 |
| 65. | 31 jul. 2023 | 6.51% | 4.85% | 22.77 | 15.16 | 18.58 |
| 66. | 31 ago. 2023 | -1.58% | -1.77% | 10.99 | 7.42 | 9.03 |
| 67. | 30 sept. 2023 | -8.43% | -4.87% | 103.46 | 33.93 | 59.25 |
| 68. | 31 oct. 2023 | -0.96% | -2.20% | 7.28 | 9.93 | 8.50 |
| 69. | 30 nov. 2023 | 25.43% | 8.92% | 561.34 | 63.44 | 188.71 |
| 70. | 31 dic. 2023 | 4.46% | 4.42% | 7.43 | 12.04 | 9.46 |
| 71. | 31 ene. 2024 | 6.82% | 1.59% | 25.85 | 0.41 | 3.24 |
| Total (Σ): | 7,284.09 | 1,876.53 | 2,389.03 | |||
Mostrar todo
VarianzaCRM = Σ(RCRM,t–RCRM)2 ÷ (71 – 1)
= 7,284.09 ÷ (71 – 1)
= 104.06
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,876.53 ÷ (71 – 1)
= 26.81
CovarianzaCRM, S&P 500 = Σ(RCRM,t–RCRM)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 2,389.03 ÷ (71 – 1)
= 34.13
Estimación sistemática del riesgo (β)
| VarianzaCRM | 104.06 |
| VarianzaS&P 500 | 26.81 |
| CovarianzaCRM, S&P 500 | 34.13 |
| Coeficiente de correlaciónCRM, S&P 5001 | 0.65 |
| βCRM2 | 1.27 |
| αCRM3 | 0.52% |
Cálculos
1 Coeficiente de correlaciónCRM, S&P 500
= CovarianzaCRM, S&P 500 ÷ (Desviación estándarCRM × Desviación estándarS&P 500)
= 34.13 ÷ (10.20% × 5.18%)
= 0.65
2 βCRM
= CovarianzaCRM, S&P 500 ÷ VarianzaS&P 500
= 34.13 ÷ 26.81
= 1.27
3 αCRM
= PromedioCRM – βCRM × PromedioS&P 500
= 1.74% – 1.27 × 0.95%
= 0.52%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.50% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.77% |
| Riesgo sistemático de Salesforce acciones ordinarias | βCRM | 1.27 |
| Tasa de rendimiento esperada de las acciones ordinarias de Salesforce3 | E(RCRM) | 16.30% |
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(RCRM) = RF + βCRM [E(RM) – RF]
= 4.50% + 1.27 [13.77% – 4.50%]
= 16.30%