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 Analog Devices.
Tasas de retorno
Analog Devices Inc. (ADI) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Fecha | PrecioADI,t1 | DividendoADI,t1 | RADI,t2 | PrecioS&P 500,t | RS&P 500,t3 |
30 nov. 2015 | $61.63 | 2,080.41 | ||||
1. | 31 dic. 2015 | $55.32 | $0.40 | -9.59% | 2,043.94 | -1.75% |
2. | 31 ene. 2016 | $53.86 | -2.64% | 1,940.24 | -5.07% | |
3. | 29 feb. 2016 | $52.99 | $0.42 | -0.84% | 1,932.23 | -0.41% |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | 30 sept. 2021 | $167.48 | 2.78% | 4,307.54 | -4.76% | |
71. | 31 oct. 2021 | $173.49 | 3.59% | 4,605.38 | 6.91% | |
Promedio (R): | 1.94% | 1.21% | ||||
Desviación estándar: | 7.62% | 4.24% |
Analog Devices Inc. (ADI) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Fecha | PrecioADI,t1 | DividendoADI,t1 | RADI,t2 | PrecioS&P 500,t | RS&P 500,t3 |
30 nov. 2015 | $61.63 | 2,080.41 | ||||
1. | 31 dic. 2015 | $55.32 | $0.40 | -9.59% | 2,043.94 | -1.75% |
2. | 31 ene. 2016 | $53.86 | -2.64% | 1,940.24 | -5.07% | |
3. | 29 feb. 2016 | $52.99 | $0.42 | -0.84% | 1,932.23 | -0.41% |
4. | 31 mar. 2016 | $59.19 | 11.70% | 2,059.74 | 6.60% | |
5. | 30 abr. 2016 | $56.32 | -4.85% | 2,065.30 | 0.27% | |
6. | 31 may. 2016 | $58.50 | $0.42 | 4.62% | 2,096.95 | 1.53% |
7. | 30 jun. 2016 | $56.64 | -3.18% | 2,098.86 | 0.09% | |
8. | 31 jul. 2016 | $63.83 | 12.69% | 2,173.60 | 3.56% | |
9. | 31 ago. 2016 | $62.56 | $0.42 | -1.33% | 2,170.95 | -0.12% |
10. | 30 sept. 2016 | $64.45 | 3.02% | 2,168.27 | -0.12% | |
11. | 31 oct. 2016 | $64.10 | -0.54% | 2,126.15 | -1.94% | |
12. | 30 nov. 2016 | $74.24 | $0.42 | 16.47% | 2,198.81 | 3.42% |
13. | 31 dic. 2016 | $72.62 | -2.18% | 2,238.83 | 1.82% | |
14. | 31 ene. 2017 | $74.94 | 3.19% | 2,278.87 | 1.79% | |
15. | 28 feb. 2017 | $81.93 | $0.45 | 9.93% | 2,363.64 | 3.72% |
16. | 31 mar. 2017 | $81.95 | 0.02% | 2,362.72 | -0.04% | |
17. | 30 abr. 2017 | $76.20 | -7.02% | 2,384.20 | 0.91% | |
18. | 31 may. 2017 | $85.76 | 12.55% | 2,411.80 | 1.16% | |
19. | 30 jun. 2017 | $77.80 | $0.45 | -8.76% | 2,423.41 | 0.48% |
20. | 31 jul. 2017 | $79.01 | 1.56% | 2,470.30 | 1.93% | |
21. | 31 ago. 2017 | $83.67 | 5.90% | 2,471.65 | 0.05% | |
22. | 30 sept. 2017 | $86.17 | $0.45 | 3.53% | 2,519.36 | 1.93% |
23. | 31 oct. 2017 | $91.30 | 5.95% | 2,575.26 | 2.22% | |
24. | 30 nov. 2017 | $86.11 | $0.45 | -5.19% | 2,647.58 | 2.81% |
25. | 31 dic. 2017 | $89.03 | 3.39% | 2,673.61 | 0.98% | |
26. | 31 ene. 2018 | $91.88 | 3.20% | 2,823.81 | 5.62% | |
27. | 28 feb. 2018 | $90.15 | -1.88% | 2,713.83 | -3.89% | |
28. | 31 mar. 2018 | $91.13 | $0.48 | 1.62% | 2,640.87 | -2.69% |
29. | 30 abr. 2018 | $87.35 | -4.15% | 2,648.05 | 0.27% | |
30. | 31 may. 2018 | $97.18 | 11.25% | 2,705.27 | 2.16% | |
31. | 30 jun. 2018 | $95.92 | $0.48 | -0.80% | 2,718.37 | 0.48% |
32. | 31 jul. 2018 | $96.14 | 0.23% | 2,816.29 | 3.60% | |
33. | 31 ago. 2018 | $98.85 | $0.48 | 3.32% | 2,901.52 | 3.03% |
34. | 30 sept. 2018 | $92.46 | -6.46% | 2,913.98 | 0.43% | |
35. | 31 oct. 2018 | $83.71 | -9.46% | 2,711.74 | -6.94% | |
36. | 30 nov. 2018 | $91.92 | $0.48 | 10.38% | 2,760.17 | 1.79% |
37. | 31 dic. 2018 | $85.83 | -6.63% | 2,506.85 | -9.18% | |
38. | 31 ene. 2019 | $98.86 | 15.18% | 2,704.10 | 7.87% | |
39. | 28 feb. 2019 | $106.96 | $0.54 | 8.74% | 2,784.49 | 2.97% |
40. | 31 mar. 2019 | $105.27 | -1.58% | 2,834.40 | 1.79% | |
41. | 30 abr. 2019 | $116.24 | 10.42% | 2,945.83 | 3.93% | |
42. | 31 may. 2019 | $96.62 | $0.54 | -16.41% | 2,752.06 | -6.58% |
43. | 30 jun. 2019 | $112.87 | 16.82% | 2,941.76 | 6.89% | |
44. | 31 jul. 2019 | $117.46 | 4.07% | 2,980.38 | 1.31% | |
45. | 31 ago. 2019 | $109.83 | $0.54 | -6.04% | 2,926.46 | -1.81% |
46. | 30 sept. 2019 | $111.73 | 1.73% | 2,976.74 | 1.72% | |
47. | 31 oct. 2019 | $106.63 | -4.56% | 3,037.56 | 2.04% | |
48. | 30 nov. 2019 | $112.95 | 5.93% | 3,140.98 | 3.40% | |
49. | 31 dic. 2019 | $118.84 | $0.54 | 5.69% | 3,230.78 | 2.86% |
50. | 31 ene. 2020 | $109.75 | -7.65% | 3,225.52 | -0.16% | |
51. | 29 feb. 2020 | $109.05 | $0.62 | -0.07% | 2,954.22 | -8.41% |
52. | 31 mar. 2020 | $89.65 | -17.79% | 2,584.59 | -12.51% | |
53. | 30 abr. 2020 | $109.60 | 22.25% | 2,912.43 | 12.68% | |
54. | 31 may. 2020 | $112.95 | $0.62 | 3.62% | 3,044.31 | 4.53% |
55. | 30 jun. 2020 | $122.64 | 8.58% | 3,100.29 | 1.84% | |
56. | 31 jul. 2020 | $114.85 | -6.35% | 3,271.12 | 5.51% | |
57. | 31 ago. 2020 | $116.88 | $0.62 | 2.31% | 3,500.31 | 7.01% |
58. | 30 sept. 2020 | $116.74 | -0.12% | 3,363.00 | -3.92% | |
59. | 31 oct. 2020 | $118.53 | 1.53% | 3,269.96 | -2.77% | |
60. | 30 nov. 2020 | $139.08 | 17.34% | 3,621.63 | 10.75% | |
61. | 31 dic. 2020 | $147.73 | $0.62 | 6.67% | 3,756.07 | 3.71% |
62. | 31 ene. 2021 | $147.33 | -0.27% | 3,714.24 | -1.11% | |
63. | 28 feb. 2021 | $155.82 | $0.69 | 6.23% | 3,811.15 | 2.61% |
64. | 31 mar. 2021 | $155.08 | -0.47% | 3,972.89 | 4.24% | |
65. | 30 abr. 2021 | $153.16 | -1.24% | 4,181.17 | 5.24% | |
66. | 31 may. 2021 | $164.60 | $0.69 | 7.92% | 4,204.11 | 0.55% |
67. | 30 jun. 2021 | $172.16 | 4.59% | 4,297.50 | 2.22% | |
68. | 31 jul. 2021 | $167.42 | -2.75% | 4,395.26 | 2.27% | |
69. | 31 ago. 2021 | $162.95 | $0.69 | -2.26% | 4,522.68 | 2.90% |
70. | 30 sept. 2021 | $167.48 | 2.78% | 4,307.54 | -4.76% | |
71. | 31 oct. 2021 | $173.49 | 3.59% | 4,605.38 | 6.91% | |
Promedio (R): | 1.94% | 1.21% | ||||
Desviación estándar: | 7.62% | 4.24% |
Mostrar todo
1 Datos en US$ por acción de acciones ordinarias, ajustados por escisiones y dividendos de acciones.
2 Tasa de rendimiento de las acciones ordinarias de ADI 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 | RADI,t | RS&P 500,t | (RADI,t–RADI)2 | (RS&P 500,t–RS&P 500)2 | (RADI,t–RADI)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | 31 dic. 2015 | -9.59% | -1.75% | 132.83 | 8.81 | 34.20 |
2. | 31 ene. 2016 | -2.64% | -5.07% | 20.93 | 39.54 | 28.77 |
3. | 29 feb. 2016 | -0.84% | -0.41% | 7.68 | 2.65 | 4.51 |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
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70. | 30 sept. 2021 | 2.78% | -4.76% | 0.71 | 35.66 | -5.04 |
71. | 31 oct. 2021 | 3.59% | 6.91% | 2.73 | 32.49 | 9.42 |
Total (Σ): | 4,066.80 | 1,258.13 | 1,502.92 |
t | Fecha | RADI,t | RS&P 500,t | (RADI,t–RADI)2 | (RS&P 500,t–RS&P 500)2 | (RADI,t–RADI)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | 31 dic. 2015 | -9.59% | -1.75% | 132.83 | 8.81 | 34.20 |
2. | 31 ene. 2016 | -2.64% | -5.07% | 20.93 | 39.54 | 28.77 |
3. | 29 feb. 2016 | -0.84% | -0.41% | 7.68 | 2.65 | 4.51 |
4. | 31 mar. 2016 | 11.70% | 6.60% | 95.35 | 28.99 | 52.58 |
5. | 30 abr. 2016 | -4.85% | 0.27% | 46.03 | 0.89 | 6.41 |
6. | 31 may. 2016 | 4.62% | 1.53% | 7.19 | 0.10 | 0.85 |
7. | 30 jun. 2016 | -3.18% | 0.09% | 26.17 | 1.26 | 5.75 |
8. | 31 jul. 2016 | 12.69% | 3.56% | 115.74 | 5.51 | 25.24 |
9. | 31 ago. 2016 | -1.33% | -0.12% | 10.68 | 1.79 | 4.37 |
10. | 30 sept. 2016 | 3.02% | -0.12% | 1.18 | 1.79 | -1.45 |
11. | 31 oct. 2016 | -0.54% | -1.94% | 6.14 | 9.97 | 7.83 |
12. | 30 nov. 2016 | 16.47% | 3.42% | 211.37 | 4.85 | 32.03 |
13. | 31 dic. 2016 | -2.18% | 1.82% | 16.96 | 0.37 | -2.49 |
14. | 31 ene. 2017 | 3.19% | 1.79% | 1.59 | 0.33 | 0.72 |
15. | 28 feb. 2017 | 9.93% | 3.72% | 63.88 | 6.28 | 20.02 |
16. | 31 mar. 2017 | 0.02% | -0.04% | 3.65 | 1.57 | 2.40 |
17. | 30 abr. 2017 | -7.02% | 0.91% | 80.14 | 0.09 | 2.74 |
18. | 31 may. 2017 | 12.55% | 1.16% | 112.58 | 0.00 | -0.61 |
19. | 30 jun. 2017 | -8.76% | 0.48% | 114.33 | 0.54 | 7.84 |
20. | 31 jul. 2017 | 1.56% | 1.93% | 0.14 | 0.52 | -0.27 |
21. | 31 ago. 2017 | 5.90% | 0.05% | 15.70 | 1.35 | -4.60 |
22. | 30 sept. 2017 | 3.53% | 1.93% | 2.53 | 0.51 | 1.14 |
23. | 31 oct. 2017 | 5.95% | 2.22% | 16.14 | 1.01 | 4.03 |
24. | 30 nov. 2017 | -5.19% | 2.81% | 50.80 | 2.54 | -11.36 |
25. | 31 dic. 2017 | 3.39% | 0.98% | 2.12 | 0.05 | -0.34 |
26. | 31 ene. 2018 | 3.20% | 5.62% | 1.60 | 19.39 | 5.57 |
27. | 28 feb. 2018 | -1.88% | -3.89% | 14.58 | 26.11 | 19.51 |
28. | 31 mar. 2018 | 1.62% | -2.69% | 0.10 | 15.23 | 1.23 |
29. | 30 abr. 2018 | -4.15% | 0.27% | 37.01 | 0.89 | 5.74 |
30. | 31 may. 2018 | 11.25% | 2.16% | 86.82 | 0.90 | 8.82 |
31. | 30 jun. 2018 | -0.80% | 0.48% | 7.50 | 0.53 | 2.00 |
32. | 31 jul. 2018 | 0.23% | 3.60% | 2.91 | 5.70 | -4.07 |
33. | 31 ago. 2018 | 3.32% | 3.03% | 1.91 | 3.28 | 2.50 |
34. | 30 sept. 2018 | -6.46% | 0.43% | 70.56 | 0.62 | 6.60 |
35. | 31 oct. 2018 | -9.46% | -6.94% | 129.94 | 66.50 | 92.96 |
36. | 30 nov. 2018 | 10.38% | 1.79% | 71.32 | 0.33 | 4.82 |
37. | 31 dic. 2018 | -6.63% | -9.18% | 73.29 | 108.00 | 88.97 |
38. | 31 ene. 2019 | 15.18% | 7.87% | 175.44 | 44.27 | 88.13 |
39. | 28 feb. 2019 | 8.74% | 2.97% | 46.29 | 3.09 | 11.96 |
40. | 31 mar. 2019 | -1.58% | 1.79% | 12.36 | 0.33 | -2.03 |
41. | 30 abr. 2019 | 10.42% | 3.93% | 72.00 | 7.38 | 23.05 |
42. | 31 may. 2019 | -16.41% | -6.58% | 336.72 | 60.72 | 142.99 |
43. | 30 jun. 2019 | 16.82% | 6.89% | 221.50 | 32.24 | 84.51 |
44. | 31 jul. 2019 | 4.07% | 1.31% | 4.54 | 0.01 | 0.21 |
45. | 31 ago. 2019 | -6.04% | -1.81% | 63.55 | 9.14 | 24.11 |
46. | 30 sept. 2019 | 1.73% | 1.72% | 0.04 | 0.25 | -0.10 |
47. | 31 oct. 2019 | -4.56% | 2.04% | 42.25 | 0.69 | -5.39 |
48. | 30 nov. 2019 | 5.93% | 3.40% | 15.93 | 4.80 | 8.74 |
49. | 31 dic. 2019 | 5.69% | 2.86% | 14.12 | 2.70 | 6.18 |
50. | 31 ene. 2020 | -7.65% | -0.16% | 91.87 | 1.90 | 13.20 |
51. | 29 feb. 2020 | -0.07% | -8.41% | 4.03 | 92.65 | 19.33 |
52. | 31 mar. 2020 | -17.79% | -12.51% | 389.10 | 188.42 | 270.77 |
53. | 30 abr. 2020 | 22.25% | 12.68% | 412.80 | 131.56 | 233.04 |
54. | 31 may. 2020 | 3.62% | 4.53% | 2.84 | 10.98 | 5.59 |
55. | 30 jun. 2020 | 8.58% | 1.84% | 44.13 | 0.39 | 4.15 |
56. | 31 jul. 2020 | -6.35% | 5.51% | 68.69 | 18.45 | -35.60 |
57. | 31 ago. 2020 | 2.31% | 7.01% | 0.14 | 33.55 | 2.15 |
58. | 30 sept. 2020 | -0.12% | -3.92% | 4.23 | 26.39 | 10.56 |
59. | 31 oct. 2020 | 1.53% | -2.77% | 0.16 | 15.85 | 1.60 |
60. | 30 nov. 2020 | 17.34% | 10.75% | 237.21 | 91.01 | 146.93 |
61. | 31 dic. 2020 | 6.67% | 3.71% | 22.37 | 6.24 | 11.81 |
62. | 31 ene. 2021 | -0.27% | -1.11% | 4.87 | 5.42 | 5.14 |
63. | 28 feb. 2021 | 6.23% | 2.61% | 18.45 | 1.94 | 5.99 |
64. | 31 mar. 2021 | -0.47% | 4.24% | 5.81 | 9.18 | -7.30 |
65. | 30 abr. 2021 | -1.24% | 5.24% | 10.07 | 16.22 | -12.78 |
66. | 31 may. 2021 | 7.92% | 0.55% | 35.81 | 0.44 | -3.99 |
67. | 30 jun. 2021 | 4.59% | 2.22% | 7.06 | 1.01 | 2.68 |
68. | 31 jul. 2021 | -2.75% | 2.27% | 21.99 | 1.12 | -4.97 |
69. | 31 ago. 2021 | -2.26% | 2.90% | 17.59 | 2.84 | -7.06 |
70. | 30 sept. 2021 | 2.78% | -4.76% | 0.71 | 35.66 | -5.04 |
71. | 31 oct. 2021 | 3.59% | 6.91% | 2.73 | 32.49 | 9.42 |
Total (Σ): | 4,066.80 | 1,258.13 | 1,502.92 |
Mostrar todo
VarianzaADI = Σ(RADI,t–RADI)2 ÷ (71 – 1)
= 4,066.80 ÷ (71 – 1)
= 58.10
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,258.13 ÷ (71 – 1)
= 17.97
CovarianzaADI, S&P 500 = Σ(RADI,t–RADI)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 1,502.92 ÷ (71 – 1)
= 21.47
Estimación sistemática del riesgo (β)
VarianzaADI | 58.10 |
VarianzaS&P 500 | 17.97 |
CovarianzaADI, S&P 500 | 21.47 |
Coeficiente de correlaciónADI, S&P 5001 | 0.66 |
βADI2 | 1.19 |
αADI3 | 0.48% |
Cálculos
1 Coeficiente de correlaciónADI, S&P 500
= CovarianzaADI, S&P 500 ÷ (Desviación estándarADI × Desviación estándarS&P 500)
= 21.47 ÷ (7.62% × 4.24%)
= 0.66
2 βADI
= CovarianzaADI, S&P 500 ÷ VarianzaS&P 500
= 21.47 ÷ 17.97
= 1.19
3 αADI
= PromedioADI – βADI × PromedioS&P 500
= 1.94% – 1.19 × 1.21%
= 0.48%
Tasa de rendimiento esperada
Suposiciones | ||
Tasa de rendimiento de LT Treasury Composite1 | RF | 3.12% |
Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.11% |
Riesgo sistemático de acciones ordinarias Analog Devices | βADI | 1.19 |
Tasa de rendimiento esperada de las acciones ordinarias de Analog Devices3 | E(RADI) | 15.06% |
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(RADI) = RF + βADI [E(RM) – RF]
= 3.12% + 1.19 [13.11% – 3.12%]
= 15.06%