Modelo de valoración de activos de capital (CAPM)
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 comunes de Autodesk.
Las tasas de rendimiento
Autodesk Inc., tasas de rendimiento mensuales
Autodesk Inc. (ADSK) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Fecha | PrecioADSK,t1 | DividendoADSK,t1 | RADSK,t2 | PrecioS&P 500,t | RS&P 500,t3 |
28 feb. 2014 | $52.48 | 1,859.45 | ||||
1. | 31 mar. 2014 | $49.18 | -6.29% | 1,872.34 | 0.69% | |
2. | 30 abr. 2014 | $48.02 | -2.36% | 1,883.95 | 0.62% | |
3. | 31 may. 2014 | $52.37 | 9.06% | 1,923.57 | 2.10% | |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | 31 dic. 2019 | $183.46 | 1.42% | 3,230.78 | 2.86% | |
71. | 31 ene. 2020 | $196.85 | 7.30% | 3,225.52 | -0.16% | |
Promedio (R): | 2.32% | 0.83% | ||||
Desviación típica: | 9.57% | 3.24% |
Fuente: Autodesk Inc. (NASDAQ:ADSK) | CAPM (www.stock-analysis-on.net)
Autodesk Inc. (ADSK) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Fecha | PrecioADSK,t1 | DividendoADSK,t1 | RADSK,t2 | PrecioS&P 500,t | RS&P 500,t3 |
28 feb. 2014 | $52.48 | 1,859.45 | ||||
1. | 31 mar. 2014 | $49.18 | -6.29% | 1,872.34 | 0.69% | |
2. | 30 abr. 2014 | $48.02 | -2.36% | 1,883.95 | 0.62% | |
3. | 31 may. 2014 | $52.37 | 9.06% | 1,923.57 | 2.10% | |
4. | 30 jun. 2014 | $56.38 | 7.66% | 1,960.23 | 1.91% | |
5. | 31 jul. 2014 | $53.35 | -5.37% | 1,930.67 | -1.51% | |
6. | 31 ago. 2014 | $53.64 | 0.54% | 2,003.37 | 3.77% | |
7. | 30 sept. 2014 | $55.10 | 2.72% | 1,972.29 | -1.55% | |
8. | 31 oct. 2014 | $57.54 | 4.43% | 2,018.05 | 2.32% | |
9. | 30 nov. 2014 | $62.00 | 7.75% | 2,067.56 | 2.45% | |
10. | 31 dic. 2014 | $60.06 | -3.13% | 2,058.90 | -0.42% | |
11. | 31 ene. 2015 | $54.01 | -10.07% | 1,994.99 | -3.10% | |
12. | 28 feb. 2015 | $64.24 | 18.94% | 2,104.50 | 5.49% | |
13. | 31 mar. 2015 | $58.64 | -8.72% | 2,067.89 | -1.74% | |
14. | 30 abr. 2015 | $56.83 | -3.09% | 2,085.51 | 0.85% | |
15. | 31 may. 2015 | $54.15 | -4.72% | 2,107.39 | 1.05% | |
16. | 30 jun. 2015 | $50.08 | -7.52% | 2,063.11 | -2.10% | |
17. | 31 jul. 2015 | $50.58 | 1.00% | 2,103.84 | 1.97% | |
18. | 31 ago. 2015 | $46.75 | -7.57% | 1,972.18 | -6.26% | |
19. | 30 sept. 2015 | $44.14 | -5.58% | 1,920.03 | -2.64% | |
20. | 31 oct. 2015 | $55.19 | 25.03% | 2,079.36 | 8.30% | |
21. | 30 nov. 2015 | $63.47 | 15.00% | 2,080.41 | 0.05% | |
22. | 31 dic. 2015 | $60.93 | -4.00% | 2,043.94 | -1.75% | |
23. | 31 ene. 2016 | $46.82 | -23.16% | 1,940.24 | -5.07% | |
24. | 29 feb. 2016 | $51.74 | 10.51% | 1,932.23 | -0.41% | |
25. | 31 mar. 2016 | $58.31 | 12.70% | 2,059.74 | 6.60% | |
26. | 30 abr. 2016 | $59.82 | 2.59% | 2,065.30 | 0.27% | |
27. | 31 may. 2016 | $58.27 | -2.59% | 2,096.95 | 1.53% | |
28. | 30 jun. 2016 | $54.14 | -7.09% | 2,098.86 | 0.09% | |
29. | 31 jul. 2016 | $59.45 | 9.81% | 2,173.60 | 3.56% | |
30. | 31 ago. 2016 | $67.40 | 13.37% | 2,170.95 | -0.12% | |
31. | 30 sept. 2016 | $72.33 | 7.31% | 2,168.27 | -0.12% | |
32. | 31 oct. 2016 | $72.28 | -0.07% | 2,126.15 | -1.94% | |
33. | 30 nov. 2016 | $72.61 | 0.46% | 2,198.81 | 3.42% | |
34. | 31 dic. 2016 | $74.01 | 1.93% | 2,238.83 | 1.82% | |
35. | 31 ene. 2017 | $81.34 | 9.90% | 2,278.87 | 1.79% | |
36. | 28 feb. 2017 | $86.30 | 6.10% | 2,363.64 | 3.72% | |
37. | 31 mar. 2017 | $86.47 | 0.20% | 2,362.72 | -0.04% | |
38. | 30 abr. 2017 | $90.07 | 4.16% | 2,384.20 | 0.91% | |
39. | 31 may. 2017 | $111.77 | 24.09% | 2,411.80 | 1.16% | |
40. | 30 jun. 2017 | $100.82 | -9.80% | 2,423.41 | 0.48% | |
41. | 31 jul. 2017 | $110.79 | 9.89% | 2,470.30 | 1.93% | |
42. | 31 ago. 2017 | $114.46 | 3.31% | 2,471.65 | 0.05% | |
43. | 30 sept. 2017 | $112.26 | -1.92% | 2,519.36 | 1.93% | |
44. | 31 oct. 2017 | $124.96 | 11.31% | 2,575.26 | 2.22% | |
45. | 30 nov. 2017 | $109.70 | -12.21% | 2,647.58 | 2.81% | |
46. | 31 dic. 2017 | $104.83 | -4.44% | 2,673.61 | 0.98% | |
47. | 31 ene. 2018 | $115.62 | 10.29% | 2,823.81 | 5.62% | |
48. | 28 feb. 2018 | $117.47 | 1.60% | 2,713.83 | -3.89% | |
49. | 31 mar. 2018 | $125.58 | 6.90% | 2,640.87 | -2.69% | |
50. | 30 abr. 2018 | $125.90 | 0.25% | 2,648.05 | 0.27% | |
51. | 31 may. 2018 | $129.10 | 2.54% | 2,705.27 | 2.16% | |
52. | 30 jun. 2018 | $131.09 | 1.54% | 2,718.37 | 0.48% | |
53. | 31 jul. 2018 | $128.44 | -2.02% | 2,816.29 | 3.60% | |
54. | 31 ago. 2018 | $154.35 | 20.17% | 2,901.52 | 3.03% | |
55. | 30 sept. 2018 | $156.11 | 1.14% | 2,913.98 | 0.43% | |
56. | 31 oct. 2018 | $129.25 | -17.21% | 2,711.74 | -6.94% | |
57. | 30 nov. 2018 | $144.50 | 11.80% | 2,760.17 | 1.79% | |
58. | 31 dic. 2018 | $128.61 | -11.00% | 2,506.85 | -9.18% | |
59. | 31 ene. 2019 | $147.20 | 14.45% | 2,704.10 | 7.87% | |
60. | 28 feb. 2019 | $163.01 | 10.74% | 2,784.49 | 2.97% | |
61. | 31 mar. 2019 | $155.82 | -4.41% | 2,834.40 | 1.79% | |
62. | 30 abr. 2019 | $178.21 | 14.37% | 2,945.83 | 3.93% | |
63. | 31 may. 2019 | $160.91 | -9.71% | 2,752.06 | -6.58% | |
64. | 30 jun. 2019 | $162.90 | 1.24% | 2,941.76 | 6.89% | |
65. | 31 jul. 2019 | $156.17 | -4.13% | 2,980.38 | 1.31% | |
66. | 31 ago. 2019 | $142.82 | -8.55% | 2,926.46 | -1.81% | |
67. | 30 sept. 2019 | $147.70 | 3.42% | 2,976.74 | 1.72% | |
68. | 31 oct. 2019 | $147.36 | -0.23% | 3,037.56 | 2.04% | |
69. | 30 nov. 2019 | $180.90 | 22.76% | 3,140.98 | 3.40% | |
70. | 31 dic. 2019 | $183.46 | 1.42% | 3,230.78 | 2.86% | |
71. | 31 ene. 2020 | $196.85 | 7.30% | 3,225.52 | -0.16% | |
Promedio (R): | 2.32% | 0.83% | ||||
Desviación típica: | 9.57% | 3.24% |
Fuente: Autodesk Inc. (NASDAQ:ADSK) | CAPM (www.stock-analysis-on.net)
Mostrar todo
1 Datos en dólares estadounidenses por acción ordinaria, ajustados por divisiones y dividendos en acciones.
2 Tasa de rendimiento de las acciones ordinarias de ADSK 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
Autodesk Inc., cálculo de varianza y covarianza de retornos
t | Fecha | RADSK,t | RS&P 500,t | (RADSK,t–RADSK)2 | (RS&P 500,t–RS&P 500)2 | (RADSK,t–RADSK)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | 31 mar. 2014 | -6.29% | 0.69% | 74.11 | 0.02 | 1.18 |
2. | 30 abr. 2014 | -2.36% | 0.62% | 21.90 | 0.04 | 0.99 |
3. | 31 may. 2014 | 9.06% | 2.10% | 45.40 | 1.62 | 8.57 |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | 31 dic. 2019 | 1.42% | 2.86% | 0.82 | 4.11 | -1.84 |
71. | 31 ene. 2020 | 7.30% | -0.16% | 24.78 | 0.99 | -4.95 |
Total (Σ): | 6,408.39 | 734.39 | 1,363.17 |
t | Fecha | RADSK,t | RS&P 500,t | (RADSK,t–RADSK)2 | (RS&P 500,t–RS&P 500)2 | (RADSK,t–RADSK)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | 31 mar. 2014 | -6.29% | 0.69% | 74.11 | 0.02 | 1.18 |
2. | 30 abr. 2014 | -2.36% | 0.62% | 21.90 | 0.04 | 0.99 |
3. | 31 may. 2014 | 9.06% | 2.10% | 45.40 | 1.62 | 8.57 |
4. | 30 jun. 2014 | 7.66% | 1.91% | 28.48 | 1.16 | 5.74 |
5. | 31 jul. 2014 | -5.37% | -1.51% | 59.21 | 5.47 | 18.00 |
6. | 31 ago. 2014 | 0.54% | 3.77% | 3.16 | 8.61 | -5.22 |
7. | 30 sept. 2014 | 2.72% | -1.55% | 0.16 | 5.67 | -0.96 |
8. | 31 oct. 2014 | 4.43% | 2.32% | 4.44 | 2.22 | 3.14 |
9. | 30 nov. 2014 | 7.75% | 2.45% | 29.49 | 2.63 | 8.81 |
10. | 31 dic. 2014 | -3.13% | -0.42% | 29.70 | 1.56 | 6.81 |
11. | 31 ene. 2015 | -10.07% | -3.10% | 153.61 | 15.48 | 48.77 |
12. | 28 feb. 2015 | 18.94% | 5.49% | 276.23 | 21.70 | 77.42 |
13. | 31 mar. 2015 | -8.72% | -1.74% | 121.84 | 6.61 | 28.37 |
14. | 30 abr. 2015 | -3.09% | 0.85% | 29.24 | 0.00 | -0.12 |
15. | 31 may. 2015 | -4.72% | 1.05% | 49.51 | 0.05 | -1.54 |
16. | 30 jun. 2015 | -7.52% | -2.10% | 96.77 | 8.60 | 28.84 |
17. | 31 jul. 2015 | 1.00% | 1.97% | 1.75 | 1.31 | -1.51 |
18. | 31 ago. 2015 | -7.57% | -6.26% | 97.87 | 50.25 | 70.13 |
19. | 30 sept. 2015 | -5.58% | -2.64% | 62.47 | 12.08 | 27.47 |
20. | 31 oct. 2015 | 25.03% | 8.30% | 515.89 | 55.76 | 169.61 |
21. | 30 nov. 2015 | 15.00% | 0.05% | 160.83 | 0.61 | -9.90 |
22. | 31 dic. 2015 | -4.00% | -1.75% | 39.98 | 6.68 | 16.34 |
23. | 31 ene. 2016 | -23.16% | -5.07% | 649.15 | 34.86 | 150.43 |
24. | 29 feb. 2016 | 10.51% | -0.41% | 67.04 | 1.55 | -10.18 |
25. | 31 mar. 2016 | 12.70% | 6.60% | 107.69 | 33.27 | 59.86 |
26. | 30 abr. 2016 | 2.59% | 0.27% | 0.07 | 0.31 | -0.15 |
27. | 31 may. 2016 | -2.59% | 1.53% | 24.13 | 0.49 | -3.45 |
28. | 30 jun. 2016 | -7.09% | 0.09% | 88.52 | 0.55 | 6.96 |
29. | 31 jul. 2016 | 9.81% | 3.56% | 56.06 | 7.45 | 20.44 |
30. | 31 ago. 2016 | 13.37% | -0.12% | 122.14 | 0.91 | -10.53 |
31. | 30 sept. 2016 | 7.31% | -0.12% | 24.94 | 0.91 | -4.77 |
32. | 31 oct. 2016 | -0.07% | -1.94% | 5.71 | 7.69 | 6.63 |
33. | 30 nov. 2016 | 0.46% | 3.42% | 3.48 | 6.69 | -4.82 |
34. | 31 dic. 2016 | 1.93% | 1.82% | 0.15 | 0.98 | -0.39 |
35. | 31 ene. 2017 | 9.90% | 1.79% | 57.51 | 0.92 | 7.26 |
36. | 28 feb. 2017 | 6.10% | 3.72% | 14.27 | 8.35 | 10.91 |
37. | 31 mar. 2017 | 0.20% | -0.04% | 4.51 | 0.76 | 1.85 |
38. | 30 abr. 2017 | 4.16% | 0.91% | 3.39 | 0.01 | 0.14 |
39. | 31 may. 2017 | 24.09% | 1.16% | 474.00 | 0.11 | 7.12 |
40. | 30 jun. 2017 | -9.80% | 0.48% | 146.84 | 0.12 | 4.23 |
41. | 31 jul. 2017 | 9.89% | 1.93% | 57.28 | 1.22 | 8.36 |
42. | 31 ago. 2017 | 3.31% | 0.05% | 0.98 | 0.60 | -0.77 |
43. | 30 sept. 2017 | -1.92% | 1.93% | 18.00 | 1.21 | -4.67 |
44. | 31 oct. 2017 | 11.31% | 2.22% | 80.86 | 1.93 | 12.48 |
45. | 30 nov. 2017 | -12.21% | 2.81% | 211.20 | 3.91 | -28.74 |
46. | 31 dic. 2017 | -4.44% | 0.98% | 45.70 | 0.02 | -1.03 |
47. | 31 ene. 2018 | 10.29% | 5.62% | 63.55 | 22.92 | 38.16 |
48. | 28 feb. 2018 | 1.60% | -3.89% | 0.52 | 22.33 | 3.41 |
49. | 31 mar. 2018 | 6.90% | -2.69% | 21.00 | 12.38 | -16.13 |
50. | 30 abr. 2018 | 0.25% | 0.27% | 4.27 | 0.31 | 1.15 |
51. | 31 may. 2018 | 2.54% | 2.16% | 0.05 | 1.77 | 0.29 |
52. | 30 jun. 2018 | 1.54% | 0.48% | 0.61 | 0.12 | 0.27 |
53. | 31 jul. 2018 | -2.02% | 3.60% | 18.86 | 7.68 | -12.03 |
54. | 31 ago. 2018 | 20.17% | 3.03% | 318.70 | 4.82 | 39.20 |
55. | 30 sept. 2018 | 1.14% | 0.43% | 1.39 | 0.16 | 0.47 |
56. | 31 oct. 2018 | -17.21% | -6.94% | 381.29 | 60.39 | 151.74 |
57. | 30 nov. 2018 | 11.80% | 1.79% | 89.83 | 0.91 | 9.05 |
58. | 31 dic. 2018 | -11.00% | -9.18% | 177.35 | 100.17 | 133.29 |
59. | 31 ene. 2019 | 14.45% | 7.87% | 147.23 | 49.53 | 85.39 |
60. | 28 feb. 2019 | 10.74% | 2.97% | 70.89 | 4.59 | 18.04 |
61. | 31 mar. 2019 | -4.41% | 1.79% | 45.31 | 0.92 | -6.47 |
62. | 30 abr. 2019 | 14.37% | 3.93% | 145.16 | 9.61 | 37.36 |
63. | 31 may. 2019 | -9.71% | -6.58% | 144.68 | 54.89 | 89.11 |
64. | 30 jun. 2019 | 1.24% | 6.89% | 1.18 | 36.75 | -6.57 |
65. | 31 jul. 2019 | -4.13% | 1.31% | 41.63 | 0.23 | -3.11 |
66. | 31 ago. 2019 | -8.55% | -1.81% | 118.14 | 6.97 | 28.69 |
67. | 30 sept. 2019 | 3.42% | 1.72% | 1.20 | 0.79 | 0.97 |
68. | 31 oct. 2019 | -0.23% | 2.04% | 6.51 | 1.47 | -3.09 |
69. | 30 nov. 2019 | 22.76% | 3.40% | 417.79 | 6.63 | 52.61 |
70. | 31 dic. 2019 | 1.42% | 2.86% | 0.82 | 4.11 | -1.84 |
71. | 31 ene. 2020 | 7.30% | -0.16% | 24.78 | 0.99 | -4.95 |
Total (Σ): | 6,408.39 | 734.39 | 1,363.17 |
Show all
VarianzaADSK = Σ(RADSK,t–RADSK)2 ÷ (71 – 1)
= 6,408.39 ÷ (71 – 1)
= 91.55
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 734.39 ÷ (71 – 1)
= 10.49
CovarianzaADSK, S&P 500 = Σ(RADSK,t–RADSK)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 1,363.17 ÷ (71 – 1)
= 19.47
Estimación sistemática de riesgos (β)
VarianzaADSK | 91.55 |
VarianzaS&P 500 | 10.49 |
CovarianzaADSK, S&P 500 | 19.47 |
Coeficiente de correlaciónADSK, S&P 5001 | 0.63 |
βADSK2 | 1.86 |
αADSK3 | 0.78% |
Fuente: Autodesk Inc. (NASDAQ:ADSK) | CAPM (www.stock-analysis-on.net)
Cálculos
1 Coeficiente de correlaciónADSK, S&P 500
= CovarianzaADSK, S&P 500 ÷ (Desviación típicaADSK × Desviación típicaS&P 500)
= 19.47 ÷ (9.57% × 3.24%)
= 0.63
2 βADSK
= CovarianzaADSK, S&P 500 ÷ VarianzaS&P 500
= 19.47 ÷ 10.49
= 1.86
3 αADSK
= PromedioADSK – βADSK × PromedioS&P 500
= 2.32% – 1.86 × 0.83%
= 0.78%
Tasa de rendimiento esperada
Supuestos | ||
Tasa de rendimiento de LT Treasury Composite1 | RF | 2.05% |
Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 12.38% |
Riesgo sistemático de las acciones ordinarias de Autodesk | βADSK | 1.86 |
Tasa de rendimiento esperada de las acciones ordinarias de Autodesk3 | E(RADSK) | 21.22% |
Fuente: Autodesk Inc. (NASDAQ:ADSK) | CAPM (www.stock-analysis-on.net)
1 Promedio no ponderado de los rendimientos de las ofertas de todos los bonos del Tesoro de EE. UU. De cupón fijo en circulación que no vencen ni son exigibles en menos de 10 años (proxy de tasa de rendimiento sin riesgo).
3 E(RADSK) = RF + βADSK [E(RM) – RF]
= 2.05% + 1.86 [12.38% – 2.05%]
= 21.22%