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 Cisco.
Tasas de retorno
Cisco Systems Inc. (CSCO) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Fecha | PrecioCSCO,t1 | DividendoCSCO,t1 | RCSCO,t2 | PrecioS&P 500,t | RS&P 500,t3 |
31 ago. 2017 | $32.21 | 2,471.65 | ||||
1. | 30 sept. 2017 | $33.63 | 4.41% | 2,519.36 | 1.93% | |
2. | 31 oct. 2017 | $34.15 | $0.29 | 2.41% | 2,575.26 | 2.22% |
3. | 30 nov. 2017 | $37.30 | 9.22% | 2,647.58 | 2.81% | |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | 30 jun. 2023 | $51.74 | 4.17% | 4,376.86 | 4.71% | |
71. | 31 jul. 2023 | $52.04 | $0.39 | 1.33% | 4,588.96 | 4.85% |
Promedio (R): | 1.21% | 1.00% | ||||
Desviación estándar: | 7.46% | 5.07% |
Cisco Systems Inc. (CSCO) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Fecha | PrecioCSCO,t1 | DividendoCSCO,t1 | RCSCO,t2 | PrecioS&P 500,t | RS&P 500,t3 |
31 ago. 2017 | $32.21 | 2,471.65 | ||||
1. | 30 sept. 2017 | $33.63 | 4.41% | 2,519.36 | 1.93% | |
2. | 31 oct. 2017 | $34.15 | $0.29 | 2.41% | 2,575.26 | 2.22% |
3. | 30 nov. 2017 | $37.30 | 9.22% | 2,647.58 | 2.81% | |
4. | 31 dic. 2017 | $38.30 | 2.68% | 2,673.61 | 0.98% | |
5. | 31 ene. 2018 | $41.54 | $0.29 | 9.22% | 2,823.81 | 5.62% |
6. | 28 feb. 2018 | $44.78 | 7.80% | 2,713.83 | -3.89% | |
7. | 31 mar. 2018 | $42.89 | -4.22% | 2,640.87 | -2.69% | |
8. | 30 abr. 2018 | $44.29 | $0.33 | 4.03% | 2,648.05 | 0.27% |
9. | 31 may. 2018 | $42.71 | -3.57% | 2,705.27 | 2.16% | |
10. | 30 jun. 2018 | $43.03 | 0.75% | 2,718.37 | 0.48% | |
11. | 31 jul. 2018 | $42.29 | $0.33 | -0.95% | 2,816.29 | 3.60% |
12. | 31 ago. 2018 | $47.77 | 12.96% | 2,901.52 | 3.03% | |
13. | 30 sept. 2018 | $48.65 | 1.84% | 2,913.98 | 0.43% | |
14. | 31 oct. 2018 | $45.75 | $0.33 | -5.28% | 2,711.74 | -6.94% |
15. | 30 nov. 2018 | $47.87 | 4.63% | 2,760.17 | 1.79% | |
16. | 31 dic. 2018 | $43.33 | -9.48% | 2,506.85 | -9.18% | |
17. | 31 ene. 2019 | $47.29 | $0.33 | 9.90% | 2,704.10 | 7.87% |
18. | 28 feb. 2019 | $51.77 | 9.47% | 2,784.49 | 2.97% | |
19. | 31 mar. 2019 | $53.99 | 4.29% | 2,834.40 | 1.79% | |
20. | 30 abr. 2019 | $55.95 | $0.35 | 4.28% | 2,945.83 | 3.93% |
21. | 31 may. 2019 | $52.03 | -7.01% | 2,752.06 | -6.58% | |
22. | 30 jun. 2019 | $54.73 | 5.19% | 2,941.76 | 6.89% | |
23. | 31 jul. 2019 | $55.40 | $0.35 | 1.86% | 2,980.38 | 1.31% |
24. | 31 ago. 2019 | $46.81 | -15.51% | 2,926.46 | -1.81% | |
25. | 30 sept. 2019 | $49.41 | 5.55% | 2,976.74 | 1.72% | |
26. | 31 oct. 2019 | $47.51 | $0.35 | -3.14% | 3,037.56 | 2.04% |
27. | 30 nov. 2019 | $45.31 | -4.63% | 3,140.98 | 3.40% | |
28. | 31 dic. 2019 | $47.96 | 5.85% | 3,230.78 | 2.86% | |
29. | 31 ene. 2020 | $45.97 | $0.35 | -3.42% | 3,225.52 | -0.16% |
30. | 29 feb. 2020 | $39.93 | -13.14% | 2,954.22 | -8.41% | |
31. | 31 mar. 2020 | $39.31 | -1.55% | 2,584.59 | -12.51% | |
32. | 30 abr. 2020 | $42.38 | $0.36 | 8.73% | 2,912.43 | 12.68% |
33. | 31 may. 2020 | $47.82 | 12.84% | 3,044.31 | 4.53% | |
34. | 30 jun. 2020 | $46.64 | -2.47% | 3,100.29 | 1.84% | |
35. | 31 jul. 2020 | $47.10 | $0.36 | 1.76% | 3,271.12 | 5.51% |
36. | 31 ago. 2020 | $42.22 | -10.36% | 3,500.31 | 7.01% | |
37. | 30 sept. 2020 | $39.39 | -6.70% | 3,363.00 | -3.92% | |
38. | 31 oct. 2020 | $35.90 | $0.36 | -7.95% | 3,269.96 | -2.77% |
39. | 30 nov. 2020 | $43.02 | 19.83% | 3,621.63 | 10.75% | |
40. | 31 dic. 2020 | $44.75 | 4.02% | 3,756.07 | 3.71% | |
41. | 31 ene. 2021 | $44.58 | $0.36 | 0.42% | 3,714.24 | -1.11% |
42. | 28 feb. 2021 | $44.87 | 0.65% | 3,811.15 | 2.61% | |
43. | 31 mar. 2021 | $51.71 | 15.24% | 3,972.89 | 4.24% | |
44. | 30 abr. 2021 | $50.91 | $0.37 | -0.83% | 4,181.17 | 5.24% |
45. | 31 may. 2021 | $52.90 | 3.91% | 4,204.11 | 0.55% | |
46. | 30 jun. 2021 | $53.00 | 0.19% | 4,297.50 | 2.22% | |
47. | 31 jul. 2021 | $55.37 | $0.37 | 5.17% | 4,395.26 | 2.27% |
48. | 31 ago. 2021 | $59.02 | 6.59% | 4,522.68 | 2.90% | |
49. | 30 sept. 2021 | $54.43 | -7.78% | 4,307.54 | -4.76% | |
50. | 31 oct. 2021 | $55.97 | $0.37 | 3.51% | 4,605.38 | 6.91% |
51. | 30 nov. 2021 | $54.84 | -2.02% | 4,567.00 | -0.83% | |
52. | 31 dic. 2021 | $63.37 | 15.55% | 4,766.18 | 4.36% | |
53. | 31 ene. 2022 | $55.67 | $0.37 | -11.57% | 4,515.55 | -5.26% |
54. | 28 feb. 2022 | $55.77 | 0.18% | 4,373.94 | -3.14% | |
55. | 31 mar. 2022 | $55.76 | -0.02% | 4,530.41 | 3.58% | |
56. | 30 abr. 2022 | $48.98 | $0.38 | -11.48% | 4,131.93 | -8.80% |
57. | 31 may. 2022 | $45.05 | -8.02% | 4,132.15 | 0.01% | |
58. | 30 jun. 2022 | $42.64 | -5.35% | 3,785.38 | -8.39% | |
59. | 31 jul. 2022 | $45.37 | $0.38 | 7.29% | 4,130.29 | 9.11% |
60. | 31 ago. 2022 | $44.72 | -1.43% | 3,955.00 | -4.24% | |
61. | 30 sept. 2022 | $40.00 | -10.55% | 3,585.62 | -9.34% | |
62. | 31 oct. 2022 | $45.43 | $0.38 | 14.53% | 3,871.98 | 7.99% |
63. | 30 nov. 2022 | $49.72 | 9.44% | 4,080.11 | 5.38% | |
64. | 31 dic. 2022 | $47.64 | -4.18% | 3,839.50 | -5.90% | |
65. | 31 ene. 2023 | $48.67 | $0.38 | 2.96% | 4,076.60 | 6.18% |
66. | 28 feb. 2023 | $48.42 | -0.51% | 3,970.15 | -2.61% | |
67. | 31 mar. 2023 | $52.28 | 7.97% | 4,109.31 | 3.51% | |
68. | 30 abr. 2023 | $47.25 | $0.39 | -8.88% | 4,169.48 | 1.46% |
69. | 31 may. 2023 | $49.67 | 5.12% | 4,179.83 | 0.25% | |
70. | 30 jun. 2023 | $51.74 | 4.17% | 4,376.86 | 4.71% | |
71. | 31 jul. 2023 | $52.04 | $0.39 | 1.33% | 4,588.96 | 4.85% |
Promedio (R): | 1.21% | 1.00% | ||||
Desviación estándar: | 7.46% | 5.07% |
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 CSCO 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 | RCSCO,t | RS&P 500,t | (RCSCO,t–RCSCO)2 | (RS&P 500,t–RS&P 500)2 | (RCSCO,t–RCSCO)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | 30 sept. 2017 | 4.41% | 1.93% | 10.24 | 0.86 | 2.97 |
2. | 31 oct. 2017 | 2.41% | 2.22% | 1.44 | 1.48 | 1.46 |
3. | 30 nov. 2017 | 9.22% | 2.81% | 64.26 | 3.26 | 14.47 |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | 30 jun. 2023 | 4.17% | 4.71% | 8.76 | 13.77 | 10.98 |
71. | 31 jul. 2023 | 1.33% | 4.85% | 0.02 | 14.77 | 0.48 |
Total (Σ): | 3,898.64 | 1,800.45 | 1,763.04 |
t | Fecha | RCSCO,t | RS&P 500,t | (RCSCO,t–RCSCO)2 | (RS&P 500,t–RS&P 500)2 | (RCSCO,t–RCSCO)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | 30 sept. 2017 | 4.41% | 1.93% | 10.24 | 0.86 | 2.97 |
2. | 31 oct. 2017 | 2.41% | 2.22% | 1.44 | 1.48 | 1.46 |
3. | 30 nov. 2017 | 9.22% | 2.81% | 64.26 | 3.26 | 14.47 |
4. | 31 dic. 2017 | 2.68% | 0.98% | 2.17 | 0.00 | -0.03 |
5. | 31 ene. 2018 | 9.22% | 5.62% | 64.14 | 21.29 | 36.96 |
6. | 28 feb. 2018 | 7.80% | -3.89% | 43.45 | 23.99 | -32.29 |
7. | 31 mar. 2018 | -4.22% | -2.69% | 29.47 | 13.63 | 20.04 |
8. | 30 abr. 2018 | 4.03% | 0.27% | 7.98 | 0.53 | -2.07 |
9. | 31 may. 2018 | -3.57% | 2.16% | 22.80 | 1.34 | -5.53 |
10. | 30 jun. 2018 | 0.75% | 0.48% | 0.21 | 0.27 | 0.24 |
11. | 31 jul. 2018 | -0.95% | 3.60% | 4.67 | 6.75 | -5.62 |
12. | 31 ago. 2018 | 12.96% | 3.03% | 138.07 | 4.09 | 23.77 |
13. | 30 sept. 2018 | 1.84% | 0.43% | 0.40 | 0.33 | -0.36 |
14. | 31 oct. 2018 | -5.28% | -6.94% | 42.13 | 63.10 | 51.56 |
15. | 30 nov. 2018 | 4.63% | 1.79% | 11.74 | 0.61 | 2.68 |
16. | 31 dic. 2018 | -9.48% | -9.18% | 114.32 | 103.65 | 108.85 |
17. | 31 ene. 2019 | 9.90% | 7.87% | 75.56 | 47.13 | 59.68 |
18. | 28 feb. 2019 | 9.47% | 2.97% | 68.32 | 3.88 | 16.28 |
19. | 31 mar. 2019 | 4.29% | 1.79% | 9.49 | 0.62 | 2.43 |
20. | 30 abr. 2019 | 4.28% | 3.93% | 9.43 | 8.57 | 8.99 |
21. | 31 may. 2019 | -7.01% | -6.58% | 67.47 | 57.47 | 62.27 |
22. | 30 jun. 2019 | 5.19% | 6.89% | 15.85 | 34.69 | 23.45 |
23. | 31 jul. 2019 | 1.86% | 1.31% | 0.43 | 0.10 | 0.20 |
24. | 31 ago. 2019 | -15.51% | -1.81% | 279.34 | 7.91 | 47.01 |
25. | 30 sept. 2019 | 5.55% | 1.72% | 18.89 | 0.51 | 3.11 |
26. | 31 oct. 2019 | -3.14% | 2.04% | 18.88 | 1.08 | -4.52 |
27. | 30 nov. 2019 | -4.63% | 3.40% | 34.09 | 5.77 | -14.02 |
28. | 31 dic. 2019 | 5.85% | 2.86% | 21.54 | 3.44 | 8.61 |
29. | 31 ene. 2020 | -3.42% | -0.16% | 21.41 | 1.36 | 5.40 |
30. | 29 feb. 2020 | -13.14% | -8.41% | 205.84 | 88.63 | 135.07 |
31. | 31 mar. 2020 | -1.55% | -12.51% | 7.62 | 182.66 | 37.31 |
32. | 30 abr. 2020 | 8.73% | 12.68% | 56.51 | 136.45 | 87.81 |
33. | 31 may. 2020 | 12.84% | 4.53% | 135.22 | 12.42 | 40.99 |
34. | 30 jun. 2020 | -2.47% | 1.84% | 13.51 | 0.70 | -3.07 |
35. | 31 jul. 2020 | 1.76% | 5.51% | 0.30 | 20.31 | 2.48 |
36. | 31 ago. 2020 | -10.36% | 7.01% | 133.84 | 36.04 | -69.45 |
37. | 30 sept. 2020 | -6.70% | -3.92% | 62.58 | 24.27 | 38.97 |
38. | 31 oct. 2020 | -7.95% | -2.77% | 83.80 | 14.21 | 34.51 |
39. | 30 nov. 2020 | 19.83% | 10.75% | 346.89 | 95.09 | 181.62 |
40. | 31 dic. 2020 | 4.02% | 3.71% | 7.92 | 7.34 | 7.62 |
41. | 31 ene. 2021 | 0.42% | -1.11% | 0.61 | 4.48 | 1.66 |
42. | 28 feb. 2021 | 0.65% | 2.61% | 0.31 | 2.58 | -0.90 |
43. | 31 mar. 2021 | 15.24% | 4.24% | 197.01 | 10.50 | 45.49 |
44. | 30 abr. 2021 | -0.83% | 5.24% | 4.16 | 17.97 | -8.65 |
45. | 31 may. 2021 | 3.91% | 0.55% | 7.29 | 0.21 | -1.23 |
46. | 30 jun. 2021 | 0.19% | 2.22% | 1.04 | 1.48 | -1.24 |
47. | 31 jul. 2021 | 5.17% | 2.27% | 15.70 | 1.62 | 5.04 |
48. | 31 ago. 2021 | 6.59% | 2.90% | 28.99 | 3.59 | 10.21 |
49. | 30 sept. 2021 | -7.78% | -4.76% | 80.73 | 33.18 | 51.76 |
50. | 31 oct. 2021 | 3.51% | 6.91% | 5.30 | 34.94 | 13.60 |
51. | 30 nov. 2021 | -2.02% | -0.83% | 10.41 | 3.37 | 5.93 |
52. | 31 dic. 2021 | 15.55% | 4.36% | 205.82 | 11.28 | 48.18 |
53. | 31 ene. 2022 | -11.57% | -5.26% | 163.20 | 39.21 | 79.99 |
54. | 28 feb. 2022 | 0.18% | -3.14% | 1.06 | 17.13 | 4.26 |
55. | 31 mar. 2022 | -0.02% | 3.58% | 1.50 | 6.63 | -3.16 |
56. | 30 abr. 2022 | -11.48% | -8.80% | 160.93 | 96.02 | 124.31 |
57. | 31 may. 2022 | -8.02% | 0.01% | 85.22 | 1.00 | 9.21 |
58. | 30 jun. 2022 | -5.35% | -8.39% | 43.00 | 88.27 | 61.61 |
59. | 31 jul. 2022 | 7.29% | 9.11% | 37.04 | 65.75 | 49.34 |
60. | 31 ago. 2022 | -1.43% | -4.24% | 6.97 | 27.53 | 13.86 |
61. | 30 sept. 2022 | -10.55% | -9.34% | 138.36 | 106.97 | 121.66 |
62. | 31 oct. 2022 | 14.53% | 7.99% | 177.34 | 48.76 | 92.99 |
63. | 30 nov. 2022 | 9.44% | 5.38% | 67.82 | 19.11 | 36.00 |
64. | 31 dic. 2022 | -4.18% | -5.90% | 29.07 | 47.62 | 37.20 |
65. | 31 ene. 2023 | 2.96% | 6.18% | 3.07 | 26.75 | 9.06 |
66. | 28 feb. 2023 | -0.51% | -2.61% | 2.96 | 13.06 | 6.22 |
67. | 31 mar. 2023 | 7.97% | 3.51% | 45.75 | 6.26 | 16.92 |
68. | 30 abr. 2023 | -8.88% | 1.46% | 101.67 | 0.21 | -4.65 |
69. | 31 may. 2023 | 5.12% | 0.25% | 15.32 | 0.57 | -2.96 |
70. | 30 jun. 2023 | 4.17% | 4.71% | 8.76 | 13.77 | 10.98 |
71. | 31 jul. 2023 | 1.33% | 4.85% | 0.02 | 14.77 | 0.48 |
Total (Σ): | 3,898.64 | 1,800.45 | 1,763.04 |
Mostrar todo
VarianzaCSCO = Σ(RCSCO,t–RCSCO)2 ÷ (71 – 1)
= 3,898.64 ÷ (71 – 1)
= 55.69
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,800.45 ÷ (71 – 1)
= 25.72
CovarianzaCSCO, S&P 500 = Σ(RCSCO,t–RCSCO)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 1,763.04 ÷ (71 – 1)
= 25.19
Estimación sistemática del riesgo (β)
VarianzaCSCO | 55.69 |
VarianzaS&P 500 | 25.72 |
CovarianzaCSCO, S&P 500 | 25.19 |
Coeficiente de correlaciónCSCO, S&P 5001 | 0.67 |
βCSCO2 | 0.98 |
αCSCO3 | 0.23% |
Cálculos
1 Coeficiente de correlaciónCSCO, S&P 500
= CovarianzaCSCO, S&P 500 ÷ (Desviación estándarCSCO × Desviación estándarS&P 500)
= 25.19 ÷ (7.46% × 5.07%)
= 0.67
2 βCSCO
= CovarianzaCSCO, S&P 500 ÷ VarianzaS&P 500
= 25.19 ÷ 25.72
= 0.98
3 αCSCO
= PromedioCSCO – βCSCO × PromedioS&P 500
= 1.21% – 0.98 × 1.00%
= 0.23%
Tasa de rendimiento esperada
Suposiciones | ||
Tasa de rendimiento del LT Treasury Composite1 | RF | 4.53% |
Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.63% |
Riesgo sistemático de Cisco acciones ordinarias | βCSCO | 0.98 |
Tasa de rendimiento esperada de las acciones ordinarias de Cisco3 | E(RCSCO) | 13.44% |
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(RCSCO) = RF + βCSCO [E(RM) – RF]
= 4.53% + 0.98 [13.63% – 4.53%]
= 13.44%