El modelo de fijación de precios de activos de capital (CAPM) indica cuál debería ser la tasa de rendimiento esperada o requerida sobre activos de riesgo como las acciones ordinarias de Adobe.
Tasas de retorno
Adobe Inc. (ADBE) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Fecha | PrecioADBE,t1 | DividendoADBE,t1 | RADBE,t2 | PrecioS&P 500,t | RS&P 500,t3 |
31 dic. 2016 | $102.95 | 2,238.83 | ||||
1. | 31 ene. 2017 | $113.38 | 10.13% | 2,278.87 | 1.79% | |
2. | 28 feb. 2017 | $118.34 | 4.37% | 2,363.64 | 3.72% | |
3. | 31 mar. 2017 | $130.13 | 9.96% | 2,362.72 | -0.04% | |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | 31 oct. 2022 | $318.50 | 15.73% | 3,871.98 | 7.99% | |
71. | 30 nov. 2022 | $344.93 | 8.30% | 4,080.11 | 5.38% | |
Promedio (R): | 2.10% | 0.97% | ||||
Desviación estándar: | 8.65% | 4.91% |
Adobe Inc. (ADBE) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Fecha | PrecioADBE,t1 | DividendoADBE,t1 | RADBE,t2 | PrecioS&P 500,t | RS&P 500,t3 |
31 dic. 2016 | $102.95 | 2,238.83 | ||||
1. | 31 ene. 2017 | $113.38 | 10.13% | 2,278.87 | 1.79% | |
2. | 28 feb. 2017 | $118.34 | 4.37% | 2,363.64 | 3.72% | |
3. | 31 mar. 2017 | $130.13 | 9.96% | 2,362.72 | -0.04% | |
4. | 30 abr. 2017 | $133.74 | 2.77% | 2,384.20 | 0.91% | |
5. | 31 may. 2017 | $141.86 | 6.07% | 2,411.80 | 1.16% | |
6. | 30 jun. 2017 | $141.44 | -0.30% | 2,423.41 | 0.48% | |
7. | 31 jul. 2017 | $146.49 | 3.57% | 2,470.30 | 1.93% | |
8. | 31 ago. 2017 | $155.16 | 5.92% | 2,471.65 | 0.05% | |
9. | 30 sept. 2017 | $149.18 | -3.85% | 2,519.36 | 1.93% | |
10. | 31 oct. 2017 | $175.16 | 17.42% | 2,575.26 | 2.22% | |
11. | 30 nov. 2017 | $181.47 | 3.60% | 2,647.58 | 2.81% | |
12. | 31 dic. 2017 | $175.24 | -3.43% | 2,673.61 | 0.98% | |
13. | 31 ene. 2018 | $199.76 | 13.99% | 2,823.81 | 5.62% | |
14. | 28 feb. 2018 | $209.13 | 4.69% | 2,713.83 | -3.89% | |
15. | 31 mar. 2018 | $216.08 | 3.32% | 2,640.87 | -2.69% | |
16. | 30 abr. 2018 | $221.60 | 2.55% | 2,648.05 | 0.27% | |
17. | 31 may. 2018 | $249.28 | 12.49% | 2,705.27 | 2.16% | |
18. | 30 jun. 2018 | $243.81 | -2.19% | 2,718.37 | 0.48% | |
19. | 31 jul. 2018 | $244.68 | 0.36% | 2,816.29 | 3.60% | |
20. | 31 ago. 2018 | $263.51 | 7.70% | 2,901.52 | 3.03% | |
21. | 30 sept. 2018 | $269.95 | 2.44% | 2,913.98 | 0.43% | |
22. | 31 oct. 2018 | $245.76 | -8.96% | 2,711.74 | -6.94% | |
23. | 30 nov. 2018 | $250.89 | 2.09% | 2,760.17 | 1.79% | |
24. | 31 dic. 2018 | $226.24 | -9.83% | 2,506.85 | -9.18% | |
25. | 31 ene. 2019 | $247.82 | 9.54% | 2,704.10 | 7.87% | |
26. | 28 feb. 2019 | $262.50 | 5.92% | 2,784.49 | 2.97% | |
27. | 31 mar. 2019 | $266.49 | 1.52% | 2,834.40 | 1.79% | |
28. | 30 abr. 2019 | $289.25 | 8.54% | 2,945.83 | 3.93% | |
29. | 31 may. 2019 | $270.90 | -6.34% | 2,752.06 | -6.58% | |
30. | 30 jun. 2019 | $294.65 | 8.77% | 2,941.76 | 6.89% | |
31. | 31 jul. 2019 | $298.86 | 1.43% | 2,980.38 | 1.31% | |
32. | 31 ago. 2019 | $284.51 | -4.80% | 2,926.46 | -1.81% | |
33. | 30 sept. 2019 | $276.25 | -2.90% | 2,976.74 | 1.72% | |
34. | 31 oct. 2019 | $277.93 | 0.61% | 3,037.56 | 2.04% | |
35. | 30 nov. 2019 | $309.53 | 11.37% | 3,140.98 | 3.40% | |
36. | 31 dic. 2019 | $329.81 | 6.55% | 3,230.78 | 2.86% | |
37. | 31 ene. 2020 | $351.14 | 6.47% | 3,225.52 | -0.16% | |
38. | 29 feb. 2020 | $345.12 | -1.71% | 2,954.22 | -8.41% | |
39. | 31 mar. 2020 | $318.24 | -7.79% | 2,584.59 | -12.51% | |
40. | 30 abr. 2020 | $353.64 | 11.12% | 2,912.43 | 12.68% | |
41. | 31 may. 2020 | $386.60 | 9.32% | 3,044.31 | 4.53% | |
42. | 30 jun. 2020 | $435.31 | 12.60% | 3,100.29 | 1.84% | |
43. | 31 jul. 2020 | $444.32 | 2.07% | 3,271.12 | 5.51% | |
44. | 31 ago. 2020 | $513.39 | 15.55% | 3,500.31 | 7.01% | |
45. | 30 sept. 2020 | $490.43 | -4.47% | 3,363.00 | -3.92% | |
46. | 31 oct. 2020 | $447.10 | -8.84% | 3,269.96 | -2.77% | |
47. | 30 nov. 2020 | $478.47 | 7.02% | 3,621.63 | 10.75% | |
48. | 31 dic. 2020 | $500.12 | 4.52% | 3,756.07 | 3.71% | |
49. | 31 ene. 2021 | $458.77 | -8.27% | 3,714.24 | -1.11% | |
50. | 28 feb. 2021 | $459.67 | 0.20% | 3,811.15 | 2.61% | |
51. | 31 mar. 2021 | $475.37 | 3.42% | 3,972.89 | 4.24% | |
52. | 30 abr. 2021 | $508.34 | 6.94% | 4,181.17 | 5.24% | |
53. | 31 may. 2021 | $504.58 | -0.74% | 4,204.11 | 0.55% | |
54. | 30 jun. 2021 | $585.64 | 16.06% | 4,297.50 | 2.22% | |
55. | 31 jul. 2021 | $621.63 | 6.15% | 4,395.26 | 2.27% | |
56. | 31 ago. 2021 | $663.70 | 6.77% | 4,522.68 | 2.90% | |
57. | 30 sept. 2021 | $575.72 | -13.26% | 4,307.54 | -4.76% | |
58. | 31 oct. 2021 | $650.36 | 12.96% | 4,605.38 | 6.91% | |
59. | 30 nov. 2021 | $669.85 | 3.00% | 4,567.00 | -0.83% | |
60. | 31 dic. 2021 | $567.06 | -15.35% | 4,766.18 | 4.36% | |
61. | 31 ene. 2022 | $534.30 | -5.78% | 4,515.55 | -5.26% | |
62. | 28 feb. 2022 | $467.68 | -12.47% | 4,373.94 | -3.14% | |
63. | 31 mar. 2022 | $455.62 | -2.58% | 4,530.41 | 3.58% | |
64. | 30 abr. 2022 | $395.95 | -13.10% | 4,131.93 | -8.80% | |
65. | 31 may. 2022 | $416.48 | 5.18% | 4,132.15 | 0.01% | |
66. | 30 jun. 2022 | $366.06 | -12.11% | 3,785.38 | -8.39% | |
67. | 31 jul. 2022 | $410.12 | 12.04% | 4,130.29 | 9.11% | |
68. | 31 ago. 2022 | $373.44 | -8.94% | 3,955.00 | -4.24% | |
69. | 30 sept. 2022 | $275.20 | -26.31% | 3,585.62 | -9.34% | |
70. | 31 oct. 2022 | $318.50 | 15.73% | 3,871.98 | 7.99% | |
71. | 30 nov. 2022 | $344.93 | 8.30% | 4,080.11 | 5.38% | |
Promedio (R): | 2.10% | 0.97% | ||||
Desviación estándar: | 8.65% | 4.91% |
Mostrar todo
1 Datos en US$ por acción ordinaria, ajustados por divisiones y dividendos de acciones.
2 Tasa de rendimiento de las acciones ordinarias de ADBE 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 | RADBE,t | RS&P 500,t | (RADBE,t–RADBE)2 | (RS&P 500,t–RS&P 500)2 | (RADBE,t–RADBE)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | 31 ene. 2017 | 10.13% | 1.79% | 64.57 | 0.67 | 6.58 |
2. | 28 feb. 2017 | 4.37% | 3.72% | 5.19 | 7.57 | 6.27 |
3. | 31 mar. 2017 | 9.96% | -0.04% | 61.89 | 1.02 | -7.93 |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | 31 oct. 2022 | 15.73% | 7.99% | 186.00 | 49.24 | 95.70 |
71. | 30 nov. 2022 | 8.30% | 5.38% | 38.47 | 19.42 | 27.33 |
Total (Σ): | 5,232.62 | 1,688.51 | 2,124.77 |
t | Fecha | RADBE,t | RS&P 500,t | (RADBE,t–RADBE)2 | (RS&P 500,t–RS&P 500)2 | (RADBE,t–RADBE)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | 31 ene. 2017 | 10.13% | 1.79% | 64.57 | 0.67 | 6.58 |
2. | 28 feb. 2017 | 4.37% | 3.72% | 5.19 | 7.57 | 6.27 |
3. | 31 mar. 2017 | 9.96% | -0.04% | 61.89 | 1.02 | -7.93 |
4. | 30 abr. 2017 | 2.77% | 0.91% | 0.46 | 0.00 | -0.04 |
5. | 31 may. 2017 | 6.07% | 1.16% | 15.81 | 0.04 | 0.75 |
6. | 30 jun. 2017 | -0.30% | 0.48% | 5.72 | 0.24 | 1.17 |
7. | 31 jul. 2017 | 3.57% | 1.93% | 2.17 | 0.93 | 1.42 |
8. | 31 ago. 2017 | 5.92% | 0.05% | 14.61 | 0.84 | -3.50 |
9. | 30 sept. 2017 | -3.85% | 1.93% | 35.40 | 0.92 | -5.72 |
10. | 31 oct. 2017 | 17.42% | 2.22% | 234.68 | 1.56 | 19.15 |
11. | 30 nov. 2017 | 3.60% | 2.81% | 2.27 | 3.38 | 2.77 |
12. | 31 dic. 2017 | -3.43% | 0.98% | 30.57 | 0.00 | -0.08 |
13. | 31 ene. 2018 | 13.99% | 5.62% | 141.52 | 21.61 | 55.31 |
14. | 28 feb. 2018 | 4.69% | -3.89% | 6.73 | 23.66 | -12.62 |
15. | 31 mar. 2018 | 3.32% | -2.69% | 1.51 | 13.38 | -4.49 |
16. | 30 abr. 2018 | 2.55% | 0.27% | 0.21 | 0.49 | -0.32 |
17. | 31 may. 2018 | 12.49% | 2.16% | 108.06 | 1.42 | 12.39 |
18. | 30 jun. 2018 | -2.19% | 0.48% | 18.41 | 0.23 | 2.08 |
19. | 31 jul. 2018 | 0.36% | 3.60% | 3.02 | 6.93 | -4.58 |
20. | 31 ago. 2018 | 7.70% | 3.03% | 31.36 | 4.23 | 11.52 |
21. | 30 sept. 2018 | 2.44% | 0.43% | 0.12 | 0.29 | -0.19 |
22. | 31 oct. 2018 | -8.96% | -6.94% | 122.25 | 62.56 | 87.45 |
23. | 30 nov. 2018 | 2.09% | 1.79% | 0.00 | 0.67 | -0.01 |
24. | 31 dic. 2018 | -9.83% | -9.18% | 142.11 | 102.95 | 120.96 |
25. | 31 ene. 2019 | 9.54% | 7.87% | 55.39 | 47.60 | 51.35 |
26. | 28 feb. 2019 | 5.92% | 2.97% | 14.65 | 4.02 | 7.67 |
27. | 31 mar. 2019 | 1.52% | 1.79% | 0.33 | 0.68 | -0.47 |
28. | 30 abr. 2019 | 8.54% | 3.93% | 41.54 | 8.78 | 19.09 |
29. | 31 may. 2019 | -6.34% | -6.58% | 71.23 | 56.95 | 63.69 |
30. | 30 jun. 2019 | 8.77% | 6.89% | 44.51 | 35.09 | 39.52 |
31. | 31 jul. 2019 | 1.43% | 1.31% | 0.44 | 0.12 | -0.23 |
32. | 31 ago. 2019 | -4.80% | -1.81% | 47.57 | 7.72 | 19.16 |
33. | 30 sept. 2019 | -2.90% | 1.72% | 24.99 | 0.56 | -3.75 |
34. | 31 oct. 2019 | 0.61% | 2.04% | 2.21 | 1.15 | -1.60 |
35. | 30 nov. 2019 | 11.37% | 3.40% | 86.01 | 5.93 | 22.59 |
36. | 31 dic. 2019 | 6.55% | 2.86% | 19.86 | 3.57 | 8.42 |
37. | 31 ene. 2020 | 6.47% | -0.16% | 19.11 | 1.28 | -4.95 |
38. | 29 feb. 2020 | -1.71% | -8.41% | 14.52 | 87.98 | 35.74 |
39. | 31 mar. 2020 | -7.79% | -12.51% | 97.70 | 181.73 | 133.25 |
40. | 30 abr. 2020 | 11.12% | 12.68% | 81.50 | 137.25 | 105.77 |
41. | 31 may. 2020 | 9.32% | 4.53% | 52.19 | 12.67 | 25.71 |
42. | 30 jun. 2020 | 12.60% | 1.84% | 110.33 | 0.76 | 9.14 |
43. | 31 jul. 2020 | 2.07% | 5.51% | 0.00 | 20.62 | -0.12 |
44. | 31 ago. 2020 | 15.55% | 7.01% | 180.88 | 36.45 | 81.20 |
45. | 30 sept. 2020 | -4.47% | -3.92% | 43.14 | 23.93 | 32.13 |
46. | 31 oct. 2020 | -8.84% | -2.77% | 119.49 | 13.95 | 40.83 |
47. | 30 nov. 2020 | 7.02% | 10.75% | 24.21 | 95.76 | 48.15 |
48. | 31 dic. 2020 | 4.52% | 3.71% | 5.90 | 7.53 | 6.66 |
49. | 31 ene. 2021 | -8.27% | -1.11% | 107.41 | 4.34 | 21.58 |
50. | 28 feb. 2021 | 0.20% | 2.61% | 3.61 | 2.69 | -3.12 |
51. | 31 mar. 2021 | 3.42% | 4.24% | 1.74 | 10.73 | 4.32 |
52. | 30 abr. 2021 | 6.94% | 5.24% | 23.42 | 18.26 | 20.68 |
53. | 31 may. 2021 | -0.74% | 0.55% | 8.04 | 0.18 | 1.19 |
54. | 30 jun. 2021 | 16.06% | 2.22% | 195.13 | 1.57 | 17.50 |
55. | 31 jul. 2021 | 6.15% | 2.27% | 16.40 | 1.71 | 5.29 |
56. | 31 ago. 2021 | 6.77% | 2.90% | 21.83 | 3.73 | 9.02 |
57. | 30 sept. 2021 | -13.26% | -4.76% | 235.68 | 32.79 | 87.90 |
58. | 31 oct. 2021 | 12.96% | 6.91% | 118.13 | 35.35 | 64.62 |
59. | 30 nov. 2021 | 3.00% | -0.83% | 0.81 | 3.25 | -1.62 |
60. | 31 dic. 2021 | -15.35% | 4.36% | 304.19 | 11.51 | -59.17 |
61. | 31 ene. 2022 | -5.78% | -5.26% | 61.98 | 38.78 | 49.03 |
62. | 28 feb. 2022 | -12.47% | -3.14% | 212.12 | 16.85 | 59.79 |
63. | 31 mar. 2022 | -2.58% | 3.58% | 21.85 | 6.80 | -12.19 |
64. | 30 abr. 2022 | -13.10% | -8.80% | 230.80 | 95.35 | 148.35 |
65. | 31 may. 2022 | 5.18% | 0.01% | 9.54 | 0.93 | -2.98 |
66. | 30 jun. 2022 | -12.11% | -8.39% | 201.70 | 87.63 | 132.94 |
67. | 31 jul. 2022 | 12.04% | 9.11% | 98.81 | 66.30 | 80.94 |
68. | 31 ago. 2022 | -8.94% | -4.24% | 121.87 | 27.17 | 57.55 |
69. | 30 sept. 2022 | -26.31% | -9.34% | 806.71 | 106.27 | 292.79 |
70. | 31 oct. 2022 | 15.73% | 7.99% | 186.00 | 49.24 | 95.70 |
71. | 30 nov. 2022 | 8.30% | 5.38% | 38.47 | 19.42 | 27.33 |
Total (Σ): | 5,232.62 | 1,688.51 | 2,124.77 |
Mostrar todo
VarianzaADBE = Σ(RADBE,t–RADBE)2 ÷ (71 – 1)
= 5,232.62 ÷ (71 – 1)
= 74.75
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,688.51 ÷ (71 – 1)
= 24.12
CovarianzaADBE, S&P 500 = Σ(RADBE,t–RADBE)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 2,124.77 ÷ (71 – 1)
= 30.35
Estimación sistemática del riesgo (β)
VarianzaADBE | 74.75 |
VarianzaS&P 500 | 24.12 |
CovarianzaADBE, S&P 500 | 30.35 |
Coeficiente de correlaciónADBE, S&P 5001 | 0.71 |
βADBE2 | 1.26 |
αADBE3 | 0.88% |
Cálculos
1 Coeficiente de correlaciónADBE, S&P 500
= CovarianzaADBE, S&P 500 ÷ (Desviación estándarADBE × Desviación estándarS&P 500)
= 30.35 ÷ (8.65% × 4.91%)
= 0.71
2 βADBE
= CovarianzaADBE, S&P 500 ÷ VarianzaS&P 500
= 30.35 ÷ 24.12
= 1.26
3 αADBE
= PromedioADBE – βADBE × PromedioS&P 500
= 2.10% – 1.26 × 0.97%
= 0.88%
Tasa de rendimiento esperada
Suposiciones | ||
Tasa de rendimiento de LT Treasury Composite1 | RF | 4.37% |
Tasa de rendimiento esperada en la cartera de mercado2 | E(RM) | 13.31% |
Riesgo sistemático de Adobe acciones ordinarias | βADBE | 1.26 |
Tasa de rendimiento esperada de las acciones ordinarias de Adobe3 | E(RADBE) | 15.61% |
1 Promedio no ponderado de los rendimientos de las ofertas de todos los bonos del Tesoro de los Estados Unidos de cupón fijo en circulación que no vencen ni se pueden exigir en menos de 10 años (proxy de tasa de rendimiento libre de riesgo).
3 E(RADBE) = RF + βADBE [E(RM) – RF]
= 4.37% + 1.26 [13.31% – 4.37%]
= 15.61%