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 Microsoft.
Tasas de retorno
Microsoft Corp. (MSFT) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Fecha | PrecioMSFT,t1 | DividendoMSFT,t1 | RMSFT,t2 | PrecioS&P 500,t | RS&P 500,t3 |
31 jul. 2016 | $56.68 | 2,173.60 | ||||
1. | 31 ago. 2016 | $57.46 | $0.36 | 2.01% | 2,170.95 | -0.12% |
2. | 30 sept. 2016 | $57.60 | 0.24% | 2,168.27 | -0.12% | |
3. | 31 oct. 2016 | $59.92 | 4.03% | 2,126.15 | -1.94% | |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | 31 may. 2022 | $271.87 | $0.62 | -1.81% | 4,132.15 | 0.01% |
71. | 30 jun. 2022 | $256.83 | -5.53% | 3,785.38 | -8.39% | |
Promedio (R): | 2.42% | 0.89% | ||||
Desviación estándar: | 5.38% | 4.53% |
Microsoft Corp. (MSFT) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Fecha | PrecioMSFT,t1 | DividendoMSFT,t1 | RMSFT,t2 | PrecioS&P 500,t | RS&P 500,t3 |
31 jul. 2016 | $56.68 | 2,173.60 | ||||
1. | 31 ago. 2016 | $57.46 | $0.36 | 2.01% | 2,170.95 | -0.12% |
2. | 30 sept. 2016 | $57.60 | 0.24% | 2,168.27 | -0.12% | |
3. | 31 oct. 2016 | $59.92 | 4.03% | 2,126.15 | -1.94% | |
4. | 30 nov. 2016 | $60.26 | $0.39 | 1.22% | 2,198.81 | 3.42% |
5. | 31 dic. 2016 | $62.14 | 3.12% | 2,238.83 | 1.82% | |
6. | 31 ene. 2017 | $64.65 | 4.04% | 2,278.87 | 1.79% | |
7. | 28 feb. 2017 | $63.98 | $0.39 | -0.43% | 2,363.64 | 3.72% |
8. | 31 mar. 2017 | $65.86 | 2.94% | 2,362.72 | -0.04% | |
9. | 30 abr. 2017 | $68.46 | 3.95% | 2,384.20 | 0.91% | |
10. | 31 may. 2017 | $69.84 | $0.39 | 2.59% | 2,411.80 | 1.16% |
11. | 30 jun. 2017 | $68.93 | -1.30% | 2,423.41 | 0.48% | |
12. | 31 jul. 2017 | $72.70 | 5.47% | 2,470.30 | 1.93% | |
13. | 31 ago. 2017 | $74.77 | $0.39 | 3.38% | 2,471.65 | 0.05% |
14. | 30 sept. 2017 | $74.49 | -0.37% | 2,519.36 | 1.93% | |
15. | 31 oct. 2017 | $83.18 | 11.67% | 2,575.26 | 2.22% | |
16. | 30 nov. 2017 | $84.17 | $0.42 | 1.70% | 2,647.58 | 2.81% |
17. | 31 dic. 2017 | $85.54 | 1.63% | 2,673.61 | 0.98% | |
18. | 31 ene. 2018 | $95.01 | 11.07% | 2,823.81 | 5.62% | |
19. | 28 feb. 2018 | $93.77 | $0.42 | -0.86% | 2,713.83 | -3.89% |
20. | 31 mar. 2018 | $91.27 | -2.67% | 2,640.87 | -2.69% | |
21. | 30 abr. 2018 | $93.52 | 2.47% | 2,648.05 | 0.27% | |
22. | 31 may. 2018 | $98.84 | $0.42 | 6.14% | 2,705.27 | 2.16% |
23. | 30 jun. 2018 | $98.61 | -0.23% | 2,718.37 | 0.48% | |
24. | 31 jul. 2018 | $106.08 | 7.58% | 2,816.29 | 3.60% | |
25. | 31 ago. 2018 | $112.33 | $0.42 | 6.29% | 2,901.52 | 3.03% |
26. | 30 sept. 2018 | $114.37 | 1.82% | 2,913.98 | 0.43% | |
27. | 31 oct. 2018 | $106.81 | -6.61% | 2,711.74 | -6.94% | |
28. | 30 nov. 2018 | $110.89 | $0.46 | 4.25% | 2,760.17 | 1.79% |
29. | 31 dic. 2018 | $101.57 | -8.40% | 2,506.85 | -9.18% | |
30. | 31 ene. 2019 | $104.43 | 2.82% | 2,704.10 | 7.87% | |
31. | 28 feb. 2019 | $112.03 | $0.46 | 7.72% | 2,784.49 | 2.97% |
32. | 31 mar. 2019 | $117.94 | 5.28% | 2,834.40 | 1.79% | |
33. | 30 abr. 2019 | $130.60 | 10.73% | 2,945.83 | 3.93% | |
34. | 31 may. 2019 | $123.68 | $0.46 | -4.95% | 2,752.06 | -6.58% |
35. | 30 jun. 2019 | $133.96 | 8.31% | 2,941.76 | 6.89% | |
36. | 31 jul. 2019 | $136.27 | 1.72% | 2,980.38 | 1.31% | |
37. | 31 ago. 2019 | $137.86 | $0.46 | 1.50% | 2,926.46 | -1.81% |
38. | 30 sept. 2019 | $139.03 | 0.85% | 2,976.74 | 1.72% | |
39. | 31 oct. 2019 | $143.37 | 3.12% | 3,037.56 | 2.04% | |
40. | 30 nov. 2019 | $151.38 | $0.51 | 5.94% | 3,140.98 | 3.40% |
41. | 31 dic. 2019 | $157.70 | 4.17% | 3,230.78 | 2.86% | |
42. | 31 ene. 2020 | $170.23 | 7.95% | 3,225.52 | -0.16% | |
43. | 29 feb. 2020 | $162.01 | $0.51 | -4.53% | 2,954.22 | -8.41% |
44. | 31 mar. 2020 | $157.71 | -2.65% | 2,584.59 | -12.51% | |
45. | 30 abr. 2020 | $179.21 | 13.63% | 2,912.43 | 12.68% | |
46. | 31 may. 2020 | $183.25 | $0.51 | 2.54% | 3,044.31 | 4.53% |
47. | 30 jun. 2020 | $203.51 | 11.06% | 3,100.29 | 1.84% | |
48. | 31 jul. 2020 | $205.01 | 0.74% | 3,271.12 | 5.51% | |
49. | 31 ago. 2020 | $225.53 | $0.51 | 10.26% | 3,500.31 | 7.01% |
50. | 30 sept. 2020 | $210.33 | -6.74% | 3,363.00 | -3.92% | |
51. | 31 oct. 2020 | $202.47 | -3.74% | 3,269.96 | -2.77% | |
52. | 30 nov. 2020 | $214.07 | $0.56 | 6.01% | 3,621.63 | 10.75% |
53. | 31 dic. 2020 | $222.42 | 3.90% | 3,756.07 | 3.71% | |
54. | 31 ene. 2021 | $231.96 | 4.29% | 3,714.24 | -1.11% | |
55. | 28 feb. 2021 | $232.38 | $0.56 | 0.42% | 3,811.15 | 2.61% |
56. | 31 mar. 2021 | $235.77 | 1.46% | 3,972.89 | 4.24% | |
57. | 30 abr. 2021 | $252.18 | 6.96% | 4,181.17 | 5.24% | |
58. | 31 may. 2021 | $249.68 | $0.56 | -0.77% | 4,204.11 | 0.55% |
59. | 30 jun. 2021 | $270.90 | 8.50% | 4,297.50 | 2.22% | |
60. | 31 jul. 2021 | $284.91 | 5.17% | 4,395.26 | 2.27% | |
61. | 31 ago. 2021 | $301.88 | $0.56 | 6.15% | 4,522.68 | 2.90% |
62. | 30 sept. 2021 | $281.92 | -6.61% | 4,307.54 | -4.76% | |
63. | 31 oct. 2021 | $331.62 | 17.63% | 4,605.38 | 6.91% | |
64. | 30 nov. 2021 | $330.59 | $0.62 | -0.12% | 4,567.00 | -0.83% |
65. | 31 dic. 2021 | $336.32 | 1.73% | 4,766.18 | 4.36% | |
66. | 31 ene. 2022 | $310.98 | -7.53% | 4,515.55 | -5.26% | |
67. | 28 feb. 2022 | $298.79 | $0.62 | -3.72% | 4,373.94 | -3.14% |
68. | 31 mar. 2022 | $308.31 | 3.19% | 4,530.41 | 3.58% | |
69. | 30 abr. 2022 | $277.52 | -9.99% | 4,131.93 | -8.80% | |
70. | 31 may. 2022 | $271.87 | $0.62 | -1.81% | 4,132.15 | 0.01% |
71. | 30 jun. 2022 | $256.83 | -5.53% | 3,785.38 | -8.39% | |
Promedio (R): | 2.42% | 0.89% | ||||
Desviación estándar: | 5.38% | 4.53% |
Mostrar todo
1 Datos en US$ por acción de acciones ordinarias, ajustados por escisiones y dividendos de acciones.
2 Tasa de rendimiento de las acciones ordinarias de MSFT 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 | RMSFT,t | RS&P 500,t | (RMSFT,t–RMSFT)2 | (RS&P 500,t–RS&P 500)2 | (RMSFT,t–RMSFT)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | 31 ago. 2016 | 2.01% | -0.12% | 0.17 | 1.02 | 0.41 |
2. | 30 sept. 2016 | 0.24% | -0.12% | 4.73 | 1.02 | 2.20 |
3. | 31 oct. 2016 | 4.03% | -1.94% | 2.59 | 8.00 | -4.55 |
. | . | . | . | . | . | . |
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70. | 31 may. 2022 | -1.81% | 0.01% | 17.90 | 0.78 | 3.73 |
71. | 30 jun. 2022 | -5.53% | -8.39% | 63.22 | 86.09 | 73.77 |
Total (Σ): | 2,027.88 | 1,437.21 | 1,305.14 |
t | Fecha | RMSFT,t | RS&P 500,t | (RMSFT,t–RMSFT)2 | (RS&P 500,t–RS&P 500)2 | (RMSFT,t–RMSFT)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | 31 ago. 2016 | 2.01% | -0.12% | 0.17 | 1.02 | 0.41 |
2. | 30 sept. 2016 | 0.24% | -0.12% | 4.73 | 1.02 | 2.20 |
3. | 31 oct. 2016 | 4.03% | -1.94% | 2.59 | 8.00 | -4.55 |
4. | 30 nov. 2016 | 1.22% | 3.42% | 1.44 | 6.40 | -3.04 |
5. | 31 dic. 2016 | 3.12% | 1.82% | 0.49 | 0.87 | 0.65 |
6. | 31 ene. 2017 | 4.04% | 1.79% | 2.63 | 0.81 | 1.46 |
7. | 28 feb. 2017 | -0.43% | 3.72% | 8.13 | 8.03 | -8.08 |
8. | 31 mar. 2017 | 2.94% | -0.04% | 0.27 | 0.86 | -0.48 |
9. | 30 abr. 2017 | 3.95% | 0.91% | 2.34 | 0.00 | 0.03 |
10. | 31 may. 2017 | 2.59% | 1.16% | 0.03 | 0.07 | 0.05 |
11. | 30 jun. 2017 | -1.30% | 0.48% | 13.85 | 0.16 | 1.51 |
12. | 31 jul. 2017 | 5.47% | 1.93% | 9.31 | 1.10 | 3.20 |
13. | 31 ago. 2017 | 3.38% | 0.05% | 0.93 | 0.69 | -0.80 |
14. | 30 sept. 2017 | -0.37% | 1.93% | 7.80 | 1.09 | -2.92 |
15. | 31 oct. 2017 | 11.67% | 2.22% | 85.51 | 1.77 | 12.32 |
16. | 30 nov. 2017 | 1.70% | 2.81% | 0.52 | 3.69 | -1.39 |
17. | 31 dic. 2017 | 1.63% | 0.98% | 0.63 | 0.01 | -0.08 |
18. | 31 ene. 2018 | 11.07% | 5.62% | 74.86 | 22.38 | 40.93 |
19. | 28 feb. 2018 | -0.86% | -3.89% | 10.77 | 22.86 | 15.69 |
20. | 31 mar. 2018 | -2.67% | -2.69% | 25.86 | 12.78 | 18.18 |
21. | 30 abr. 2018 | 2.47% | 0.27% | 0.00 | 0.38 | -0.03 |
22. | 31 may. 2018 | 6.14% | 2.16% | 13.83 | 1.62 | 4.74 |
23. | 30 jun. 2018 | -0.23% | 0.48% | 7.03 | 0.16 | 1.07 |
24. | 31 jul. 2018 | 7.58% | 3.60% | 26.59 | 7.37 | 14.00 |
25. | 31 ago. 2018 | 6.29% | 3.03% | 14.97 | 4.58 | 8.28 |
26. | 30 sept. 2018 | 1.82% | 0.43% | 0.36 | 0.21 | 0.28 |
27. | 31 oct. 2018 | -6.61% | -6.94% | 81.52 | 61.26 | 70.67 |
28. | 30 nov. 2018 | 4.25% | 1.79% | 3.35 | 0.81 | 1.65 |
29. | 31 dic. 2018 | -8.40% | -9.18% | 117.15 | 101.29 | 108.93 |
30. | 31 ene. 2019 | 2.82% | 7.87% | 0.16 | 48.74 | 2.77 |
31. | 28 feb. 2019 | 7.72% | 2.97% | 28.08 | 4.35 | 11.06 |
32. | 31 mar. 2019 | 5.28% | 1.79% | 8.16 | 0.82 | 2.59 |
33. | 30 abr. 2019 | 10.73% | 3.93% | 69.15 | 9.27 | 25.32 |
34. | 31 may. 2019 | -4.95% | -6.58% | 54.25 | 55.72 | 54.98 |
35. | 30 jun. 2019 | 8.31% | 6.89% | 34.73 | 36.08 | 35.39 |
36. | 31 jul. 2019 | 1.72% | 1.31% | 0.48 | 0.18 | -0.30 |
37. | 31 ago. 2019 | 1.50% | -1.81% | 0.84 | 7.27 | 2.47 |
38. | 30 sept. 2019 | 0.85% | 1.72% | 2.47 | 0.69 | -1.31 |
39. | 31 oct. 2019 | 3.12% | 2.04% | 0.49 | 1.34 | 0.81 |
40. | 30 nov. 2019 | 5.94% | 3.40% | 12.42 | 6.34 | 8.87 |
41. | 31 dic. 2019 | 4.17% | 2.86% | 3.08 | 3.89 | 3.46 |
42. | 31 ene. 2020 | 7.95% | -0.16% | 30.54 | 1.10 | -5.80 |
43. | 29 feb. 2020 | -4.53% | -8.41% | 48.28 | 86.45 | 64.60 |
44. | 31 mar. 2020 | -2.65% | -12.51% | 25.74 | 179.52 | 67.97 |
45. | 30 abr. 2020 | 13.63% | 12.68% | 125.75 | 139.19 | 132.30 |
46. | 31 may. 2020 | 2.54% | 4.53% | 0.01 | 13.26 | 0.44 |
47. | 30 jun. 2020 | 11.06% | 1.84% | 74.60 | 0.91 | 8.22 |
48. | 31 jul. 2020 | 0.74% | 5.51% | 2.83 | 21.38 | -7.78 |
49. | 31 ago. 2020 | 10.26% | 7.01% | 61.45 | 37.45 | 47.97 |
50. | 30 sept. 2020 | -6.74% | -3.92% | 83.88 | 23.13 | 44.05 |
51. | 31 oct. 2020 | -3.74% | -2.77% | 37.89 | 13.35 | 22.49 |
52. | 30 nov. 2020 | 6.01% | 10.75% | 12.87 | 97.38 | 35.40 |
53. | 31 dic. 2020 | 3.90% | 3.71% | 2.20 | 7.98 | 4.19 |
54. | 31 ene. 2021 | 4.29% | -1.11% | 3.50 | 4.00 | -3.74 |
55. | 28 feb. 2021 | 0.42% | 2.61% | 3.99 | 2.97 | -3.44 |
56. | 31 mar. 2021 | 1.46% | 4.24% | 0.92 | 11.27 | -3.22 |
57. | 30 abr. 2021 | 6.96% | 5.24% | 20.62 | 18.97 | 19.78 |
58. | 31 may. 2021 | -0.77% | 0.55% | 10.16 | 0.11 | 1.08 |
59. | 30 jun. 2021 | 8.50% | 2.22% | 36.97 | 1.78 | 8.12 |
60. | 31 jul. 2021 | 5.17% | 2.27% | 7.58 | 1.93 | 3.82 |
61. | 31 ago. 2021 | 6.15% | 2.90% | 13.94 | 4.05 | 7.51 |
62. | 30 sept. 2021 | -6.61% | -4.76% | 81.56 | 31.85 | 50.97 |
63. | 31 oct. 2021 | 17.63% | 6.91% | 231.35 | 36.33 | 91.68 |
64. | 30 nov. 2021 | -0.12% | -0.83% | 6.46 | 2.96 | 4.37 |
65. | 31 dic. 2021 | 1.73% | 4.36% | 0.47 | 12.07 | -2.38 |
66. | 31 ene. 2022 | -7.53% | -5.26% | 99.07 | 37.76 | 61.17 |
67. | 28 feb. 2022 | -3.72% | -3.14% | 37.69 | 16.18 | 24.70 |
68. | 31 mar. 2022 | 3.19% | 3.58% | 0.59 | 7.24 | 2.06 |
69. | 30 abr. 2022 | -9.99% | -8.80% | 153.90 | 93.75 | 120.12 |
70. | 31 may. 2022 | -1.81% | 0.01% | 17.90 | 0.78 | 3.73 |
71. | 30 jun. 2022 | -5.53% | -8.39% | 63.22 | 86.09 | 73.77 |
Total (Σ): | 2,027.88 | 1,437.21 | 1,305.14 |
Mostrar todo
VarianzaMSFT = Σ(RMSFT,t–RMSFT)2 ÷ (71 – 1)
= 2,027.88 ÷ (71 – 1)
= 28.97
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,437.21 ÷ (71 – 1)
= 20.53
CovarianzaMSFT, S&P 500 = Σ(RMSFT,t–RMSFT)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 1,305.14 ÷ (71 – 1)
= 18.64
Estimación sistemática del riesgo (β)
VarianzaMSFT | 28.97 |
VarianzaS&P 500 | 20.53 |
CovarianzaMSFT, S&P 500 | 18.64 |
Coeficiente de correlaciónMSFT, S&P 5001 | 0.76 |
βMSFT2 | 0.91 |
αMSFT3 | 1.61% |
Cálculos
1 Coeficiente de correlaciónMSFT, S&P 500
= CovarianzaMSFT, S&P 500 ÷ (Desviación estándarMSFT × Desviación estándarS&P 500)
= 18.64 ÷ (5.38% × 4.53%)
= 0.76
2 βMSFT
= CovarianzaMSFT, S&P 500 ÷ VarianzaS&P 500
= 18.64 ÷ 20.53
= 0.91
3 αMSFT
= PromedioMSFT – βMSFT × PromedioS&P 500
= 2.42% – 0.91 × 0.89%
= 1.61%
Tasa de rendimiento esperada
Suposiciones | ||
Tasa de rendimiento de LT Treasury Composite1 | RF | 3.24% |
Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 12.24% |
Riesgo sistemático de acciones ordinarias Microsoft | βMSFT | 0.91 |
Tasa de rendimiento esperada de las acciones ordinarias de Microsoft3 | E(RMSFT) | 11.42% |
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(RMSFT) = RF + βMSFT [E(RM) – RF]
= 3.24% + 0.91 [12.24% – 3.24%]
= 11.42%