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 de los activos de riesgo, como las acciones ordinarias de NVIDIA.
Tasas de retorno
NVIDIA Corp., tasas mensuales de retorno
| NVIDIA Corp. (NVDA) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioNVDA,t1 | DividendoNVDA,t1 | RNVDA,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 29 feb. 2016 | $7.84 | 1,932.23 | ||||
| 1. | 31 mar. 2016 | $8.91 | 13.65% | 2,059.74 | 6.60% | |
| 2. | 30 abr. 2016 | $8.88 | -0.34% | 2,065.30 | 0.27% | |
| 3. | 31 may. 2016 | $11.68 | $0.02875 | 31.86% | 2,096.95 | 1.53% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 31 dic. 2021 | $294.11 | $0.04 | -9.98% | 4,766.18 | 4.36% |
| 71. | 31 ene. 2022 | $244.86 | -16.75% | 4,515.55 | -5.26% | |
| Promedio (R): | 5.79% | 1.29% | ||||
| Desviación estándar: | 12.95% | 4.25% | ||||
| NVIDIA Corp. (NVDA) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioNVDA,t1 | DividendoNVDA,t1 | RNVDA,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 29 feb. 2016 | $7.84 | 1,932.23 | ||||
| 1. | 31 mar. 2016 | $8.91 | 13.65% | 2,059.74 | 6.60% | |
| 2. | 30 abr. 2016 | $8.88 | -0.34% | 2,065.30 | 0.27% | |
| 3. | 31 may. 2016 | $11.68 | $0.02875 | 31.86% | 2,096.95 | 1.53% |
| 4. | 30 jun. 2016 | $11.75 | 0.60% | 2,098.86 | 0.09% | |
| 5. | 31 jul. 2016 | $14.28 | 21.53% | 2,173.60 | 3.56% | |
| 6. | 31 ago. 2016 | $15.34 | $0.02875 | 7.62% | 2,170.95 | -0.12% |
| 7. | 30 sept. 2016 | $17.13 | 11.67% | 2,168.27 | -0.12% | |
| 8. | 31 oct. 2016 | $17.79 | 3.85% | 2,126.15 | -1.94% | |
| 9. | 30 nov. 2016 | $23.05 | $0.035 | 29.76% | 2,198.81 | 3.42% |
| 10. | 31 dic. 2016 | $26.69 | 15.79% | 2,238.83 | 1.82% | |
| 11. | 31 ene. 2017 | $27.30 | 2.29% | 2,278.87 | 1.79% | |
| 12. | 28 feb. 2017 | $25.37 | $0.035 | -6.94% | 2,363.64 | 3.72% |
| 13. | 31 mar. 2017 | $27.23 | 7.33% | 2,362.72 | -0.04% | |
| 14. | 30 abr. 2017 | $26.08 | -4.22% | 2,384.20 | 0.91% | |
| 15. | 31 may. 2017 | $36.09 | $0.035 | 38.52% | 2,411.80 | 1.16% |
| 16. | 30 jun. 2017 | $36.14 | 0.14% | 2,423.41 | 0.48% | |
| 17. | 31 jul. 2017 | $40.63 | 12.42% | 2,470.30 | 1.93% | |
| 18. | 31 ago. 2017 | $42.36 | $0.035 | 4.34% | 2,471.65 | 0.05% |
| 19. | 30 sept. 2017 | $44.69 | 5.50% | 2,519.36 | 1.93% | |
| 20. | 31 oct. 2017 | $51.70 | 15.69% | 2,575.26 | 2.22% | |
| 21. | 30 nov. 2017 | $50.18 | $0.0375 | -2.87% | 2,647.58 | 2.81% |
| 22. | 31 dic. 2017 | $48.38 | -3.59% | 2,673.61 | 0.98% | |
| 23. | 31 ene. 2018 | $61.45 | 27.02% | 2,823.81 | 5.62% | |
| 24. | 28 feb. 2018 | $60.50 | $0.0375 | -1.48% | 2,713.83 | -3.89% |
| 25. | 31 mar. 2018 | $57.90 | -4.30% | 2,640.87 | -2.69% | |
| 26. | 30 abr. 2018 | $56.23 | -2.88% | 2,648.05 | 0.27% | |
| 27. | 31 may. 2018 | $63.05 | $0.0375 | 12.20% | 2,705.27 | 2.16% |
| 28. | 30 jun. 2018 | $59.23 | -6.06% | 2,718.37 | 0.48% | |
| 29. | 31 jul. 2018 | $61.22 | 3.36% | 2,816.29 | 3.60% | |
| 30. | 31 ago. 2018 | $70.17 | $0.0375 | 14.68% | 2,901.52 | 3.03% |
| 31. | 30 sept. 2018 | $70.26 | 0.13% | 2,913.98 | 0.43% | |
| 32. | 31 oct. 2018 | $52.71 | -24.98% | 2,711.74 | -6.94% | |
| 33. | 30 nov. 2018 | $40.86 | $0.04 | -22.41% | 2,760.17 | 1.79% |
| 34. | 31 dic. 2018 | $33.38 | -18.31% | 2,506.85 | -9.18% | |
| 35. | 31 ene. 2019 | $35.94 | 7.67% | 2,704.10 | 7.87% | |
| 36. | 28 feb. 2019 | $38.57 | $0.04 | 7.43% | 2,784.49 | 2.97% |
| 37. | 31 mar. 2019 | $44.89 | 16.39% | 2,834.40 | 1.79% | |
| 38. | 30 abr. 2019 | $45.25 | 0.80% | 2,945.83 | 3.93% | |
| 39. | 31 may. 2019 | $33.87 | $0.04 | -25.06% | 2,752.06 | -6.58% |
| 40. | 30 jun. 2019 | $41.06 | 21.23% | 2,941.76 | 6.89% | |
| 41. | 31 jul. 2019 | $42.18 | 2.73% | 2,980.38 | 1.31% | |
| 42. | 31 ago. 2019 | $41.88 | $0.04 | -0.62% | 2,926.46 | -1.81% |
| 43. | 30 sept. 2019 | $43.52 | 3.92% | 2,976.74 | 1.72% | |
| 44. | 31 oct. 2019 | $50.26 | 15.49% | 3,037.56 | 2.04% | |
| 45. | 30 nov. 2019 | $54.19 | $0.04 | 7.90% | 3,140.98 | 3.40% |
| 46. | 31 dic. 2019 | $58.83 | 8.56% | 3,230.78 | 2.86% | |
| 47. | 31 ene. 2020 | $59.11 | 0.48% | 3,225.52 | -0.16% | |
| 48. | 29 feb. 2020 | $67.52 | $0.04 | 14.30% | 2,954.22 | -8.41% |
| 49. | 31 mar. 2020 | $65.90 | -2.40% | 2,584.59 | -12.51% | |
| 50. | 30 abr. 2020 | $73.07 | 10.88% | 2,912.43 | 12.68% | |
| 51. | 31 may. 2020 | $88.76 | 21.47% | 3,044.31 | 4.53% | |
| 52. | 30 jun. 2020 | $94.98 | $0.04 | 7.05% | 3,100.29 | 1.84% |
| 53. | 31 jul. 2020 | $106.15 | 11.76% | 3,271.12 | 5.51% | |
| 54. | 31 ago. 2020 | $133.75 | 26.00% | 3,500.31 | 7.01% | |
| 55. | 30 sept. 2020 | $135.31 | $0.04 | 1.20% | 3,363.00 | -3.92% |
| 56. | 31 oct. 2020 | $125.34 | -7.37% | 3,269.96 | -2.77% | |
| 57. | 30 nov. 2020 | $134.02 | 6.93% | 3,621.63 | 10.75% | |
| 58. | 31 dic. 2020 | $130.55 | $0.04 | -2.56% | 3,756.07 | 3.71% |
| 59. | 31 ene. 2021 | $129.90 | -0.50% | 3,714.24 | -1.11% | |
| 60. | 28 feb. 2021 | $137.15 | 5.58% | 3,811.15 | 2.61% | |
| 61. | 31 mar. 2021 | $133.48 | $0.04 | -2.65% | 3,972.89 | 4.24% |
| 62. | 30 abr. 2021 | $150.10 | 12.45% | 4,181.17 | 5.24% | |
| 63. | 31 may. 2021 | $162.45 | 8.23% | 4,204.11 | 0.55% | |
| 64. | 30 jun. 2021 | $200.02 | $0.04 | 23.15% | 4,297.50 | 2.22% |
| 65. | 31 jul. 2021 | $194.99 | -2.51% | 4,395.26 | 2.27% | |
| 66. | 31 ago. 2021 | $223.85 | $0.04 | 14.82% | 4,522.68 | 2.90% |
| 67. | 30 sept. 2021 | $207.16 | -7.46% | 4,307.54 | -4.76% | |
| 68. | 31 oct. 2021 | $255.67 | 23.42% | 4,605.38 | 6.91% | |
| 69. | 30 nov. 2021 | $326.76 | 27.81% | 4,567.00 | -0.83% | |
| 70. | 31 dic. 2021 | $294.11 | $0.04 | -9.98% | 4,766.18 | 4.36% |
| 71. | 31 ene. 2022 | $244.86 | -16.75% | 4,515.55 | -5.26% | |
| Promedio (R): | 5.79% | 1.29% | ||||
| Desviación estándar: | 12.95% | 4.25% | ||||
Mostrar todo
1 Datos en US$ por acción de acciones ordinarias, ajustados por escisiones y dividendos de acciones.
2 Tasa de rendimiento de las acciones ordinarias de NVDA 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
NVIDIA Corp., cálculo de varianza y covarianza de rendimientos
| t | Fecha | RNVDA,t | RS&P 500,t | (RNVDA,t–RNVDA)2 | (RS&P 500,t–RS&P 500)2 | (RNVDA,t–RNVDA)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 mar. 2016 | 13.65% | 6.60% | 61.69 | 28.16 | 41.68 |
| 2. | 30 abr. 2016 | -0.34% | 0.27% | 37.58 | 1.05 | 6.27 |
| 3. | 31 may. 2016 | 31.86% | 1.53% | 679.21 | 0.06 | 6.26 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 31 dic. 2021 | -9.98% | 4.36% | 248.80 | 9.42 | -48.41 |
| 71. | 31 ene. 2022 | -16.75% | -5.26% | 508.01 | 42.91 | 147.65 |
| Total (Σ): | 11,742.48 | 1,262.70 | 1,818.37 | |||
| t | Fecha | RNVDA,t | RS&P 500,t | (RNVDA,t–RNVDA)2 | (RS&P 500,t–RS&P 500)2 | (RNVDA,t–RNVDA)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 mar. 2016 | 13.65% | 6.60% | 61.69 | 28.16 | 41.68 |
| 2. | 30 abr. 2016 | -0.34% | 0.27% | 37.58 | 1.05 | 6.27 |
| 3. | 31 may. 2016 | 31.86% | 1.53% | 679.21 | 0.06 | 6.26 |
| 4. | 30 jun. 2016 | 0.60% | 0.09% | 26.98 | 1.44 | 6.24 |
| 5. | 31 jul. 2016 | 21.53% | 3.56% | 247.69 | 5.15 | 35.71 |
| 6. | 31 ago. 2016 | 7.62% | -0.12% | 3.35 | 2.00 | -2.59 |
| 7. | 30 sept. 2016 | 11.67% | -0.12% | 34.52 | 2.00 | -8.32 |
| 8. | 31 oct. 2016 | 3.85% | -1.94% | 3.77 | 10.46 | 6.28 |
| 9. | 30 nov. 2016 | 29.76% | 3.42% | 574.58 | 4.52 | 50.94 |
| 10. | 31 dic. 2016 | 15.79% | 1.82% | 99.96 | 0.28 | 5.28 |
| 11. | 31 ene. 2017 | 2.29% | 1.79% | 12.31 | 0.25 | -1.74 |
| 12. | 28 feb. 2017 | -6.94% | 3.72% | 162.18 | 5.89 | -30.92 |
| 13. | 31 mar. 2017 | 7.33% | -0.04% | 2.37 | 1.77 | -2.05 |
| 14. | 30 abr. 2017 | -4.22% | 0.91% | 100.34 | 0.15 | 3.84 |
| 15. | 31 may. 2017 | 38.52% | 1.16% | 1,070.76 | 0.02 | -4.41 |
| 16. | 30 jun. 2017 | 0.14% | 0.48% | 31.98 | 0.66 | 4.59 |
| 17. | 31 jul. 2017 | 12.42% | 1.93% | 43.96 | 0.41 | 4.26 |
| 18. | 31 ago. 2017 | 4.34% | 0.05% | 2.10 | 1.53 | 1.79 |
| 19. | 30 sept. 2017 | 5.50% | 1.93% | 0.09 | 0.41 | -0.19 |
| 20. | 31 oct. 2017 | 15.69% | 2.22% | 97.86 | 0.86 | 9.17 |
| 21. | 30 nov. 2017 | -2.87% | 2.81% | 75.01 | 2.30 | -13.13 |
| 22. | 31 dic. 2017 | -3.59% | 0.98% | 88.00 | 0.10 | 2.90 |
| 23. | 31 ene. 2018 | 27.02% | 5.62% | 450.36 | 18.71 | 91.80 |
| 24. | 28 feb. 2018 | -1.48% | -3.89% | 52.98 | 26.90 | 37.75 |
| 25. | 31 mar. 2018 | -4.30% | -2.69% | 101.83 | 15.85 | 40.17 |
| 26. | 30 abr. 2018 | -2.88% | 0.27% | 75.31 | 1.04 | 8.85 |
| 27. | 31 may. 2018 | 12.20% | 2.16% | 40.98 | 0.75 | 5.56 |
| 28. | 30 jun. 2018 | -6.06% | 0.48% | 140.48 | 0.65 | 9.58 |
| 29. | 31 jul. 2018 | 3.36% | 3.60% | 5.92 | 5.34 | -5.62 |
| 30. | 31 ago. 2018 | 14.68% | 3.03% | 78.98 | 3.01 | 15.41 |
| 31. | 30 sept. 2018 | 0.13% | 0.43% | 32.10 | 0.74 | 4.89 |
| 32. | 31 oct. 2018 | -24.98% | -6.94% | 946.93 | 67.78 | 253.34 |
| 33. | 30 nov. 2018 | -22.41% | 1.79% | 795.20 | 0.24 | -13.92 |
| 34. | 31 dic. 2018 | -18.31% | -9.18% | 580.81 | 109.62 | 252.33 |
| 35. | 31 ene. 2019 | 7.67% | 7.87% | 3.52 | 43.25 | 12.33 |
| 36. | 28 feb. 2019 | 7.43% | 2.97% | 2.67 | 2.82 | 2.75 |
| 37. | 31 mar. 2019 | 16.39% | 1.79% | 112.19 | 0.25 | 5.30 |
| 38. | 30 abr. 2019 | 0.80% | 3.93% | 24.92 | 6.96 | -13.17 |
| 39. | 31 may. 2019 | -25.06% | -6.58% | 951.99 | 61.94 | 242.82 |
| 40. | 30 jun. 2019 | 21.23% | 6.89% | 238.23 | 31.37 | 86.45 |
| 41. | 31 jul. 2019 | 2.73% | 1.31% | 9.40 | 0.00 | -0.06 |
| 42. | 31 ago. 2019 | -0.62% | -1.81% | 41.09 | 9.62 | 19.88 |
| 43. | 30 sept. 2019 | 3.92% | 1.72% | 3.53 | 0.18 | -0.80 |
| 44. | 31 oct. 2019 | 15.49% | 2.04% | 93.96 | 0.56 | 7.28 |
| 45. | 30 nov. 2019 | 7.90% | 3.40% | 4.43 | 4.46 | 4.45 |
| 46. | 31 dic. 2019 | 8.56% | 2.86% | 7.67 | 2.45 | 4.34 |
| 47. | 31 ene. 2020 | 0.48% | -0.16% | 28.28 | 2.12 | 7.74 |
| 48. | 29 feb. 2020 | 14.30% | -8.41% | 72.28 | 94.15 | -82.50 |
| 49. | 31 mar. 2020 | -2.40% | -12.51% | 67.12 | 190.56 | 113.10 |
| 50. | 30 abr. 2020 | 10.88% | 12.68% | 25.87 | 129.78 | 57.95 |
| 51. | 31 may. 2020 | 21.47% | 4.53% | 245.83 | 10.47 | 50.74 |
| 52. | 30 jun. 2020 | 7.05% | 1.84% | 1.59 | 0.30 | 0.69 |
| 53. | 31 jul. 2020 | 11.76% | 5.51% | 35.60 | 17.79 | 25.17 |
| 54. | 31 ago. 2020 | 26.00% | 7.01% | 408.34 | 32.65 | 115.47 |
| 55. | 30 sept. 2020 | 1.20% | -3.92% | 21.14 | 27.20 | 23.98 |
| 56. | 31 oct. 2020 | -7.37% | -2.77% | 173.23 | 16.47 | 53.42 |
| 57. | 30 nov. 2020 | 6.93% | 10.75% | 1.28 | 89.54 | 10.71 |
| 58. | 31 dic. 2020 | -2.56% | 3.71% | 69.77 | 5.86 | -20.21 |
| 59. | 31 ene. 2021 | -0.50% | -1.11% | 39.58 | 5.79 | 15.14 |
| 60. | 28 feb. 2021 | 5.58% | 2.61% | 0.05 | 1.73 | -0.28 |
| 61. | 31 mar. 2021 | -2.65% | 4.24% | 71.24 | 8.71 | -24.91 |
| 62. | 30 abr. 2021 | 12.45% | 5.24% | 44.32 | 15.60 | 26.30 |
| 63. | 31 may. 2021 | 8.23% | 0.55% | 5.93 | 0.55 | -1.81 |
| 64. | 30 jun. 2021 | 23.15% | 2.22% | 301.30 | 0.86 | 16.13 |
| 65. | 31 jul. 2021 | -2.51% | 2.27% | 69.03 | 0.97 | -8.16 |
| 66. | 31 ago. 2021 | 14.82% | 2.90% | 81.50 | 2.58 | 14.51 |
| 67. | 30 sept. 2021 | -7.46% | -4.76% | 175.55 | 36.59 | 80.15 |
| 68. | 31 oct. 2021 | 23.42% | 6.91% | 310.57 | 31.61 | 99.08 |
| 69. | 30 nov. 2021 | 27.81% | -0.83% | 484.52 | 4.52 | -46.79 |
| 70. | 31 dic. 2021 | -9.98% | 4.36% | 248.80 | 9.42 | -48.41 |
| 71. | 31 ene. 2022 | -16.75% | -5.26% | 508.01 | 42.91 | 147.65 |
| Total (Σ): | 11,742.48 | 1,262.70 | 1,818.37 | |||
Mostrar todo
VarianzaNVDA = Σ(RNVDA,t–RNVDA)2 ÷ (71 – 1)
= 11,742.48 ÷ (71 – 1)
= 167.75
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,262.70 ÷ (71 – 1)
= 18.04
CovarianzaNVDA, S&P 500 = Σ(RNVDA,t–RNVDA)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 1,818.37 ÷ (71 – 1)
= 25.98
Estimación sistemática del riesgo (β)
| VarianzaNVDA | 167.75 |
| VarianzaS&P 500 | 18.04 |
| CovarianzaNVDA, S&P 500 | 25.98 |
| Coeficiente de correlaciónNVDA, S&P 5001 | 0.47 |
| βNVDA2 | 1.44 |
| αNVDA3 | 3.93% |
Cálculos
1 Coeficiente de correlaciónNVDA, S&P 500
= CovarianzaNVDA, S&P 500 ÷ (Desviación estándarNVDA × Desviación estándarS&P 500)
= 25.98 ÷ (12.95% × 4.25%)
= 0.47
2 βNVDA
= CovarianzaNVDA, S&P 500 ÷ VarianzaS&P 500
= 25.98 ÷ 18.04
= 1.44
3 αNVDA
= PromedioNVDA – βNVDA × PromedioS&P 500
= 5.79% – 1.44 × 1.29%
= 3.93%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento de LT Treasury Composite1 | RF | 3.19% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 12.22% |
| Riesgo sistemático de acciones ordinarias NVIDIA | βNVDA | 1.44 |
| Tasa de rendimiento esperada de las acciones ordinarias de NVIDIA3 | E(RNVDA) | 16.19% |
1 Promedio no ponderado de los rendimientos de las ofertas en todos los bonos del Tesoro de los Estados Unidos con cupón fijo pendientes, ni vencidos ni exigibles en menos de 10 años (proxy de tasa de rendimiento libre de riesgo).
3 E(RNVDA) = RF + βNVDA [E(RM) – RF]
= 3.19% + 1.44 [12.22% – 3.19%]
= 16.19%