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. (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
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 |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
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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%