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 Fortinet.
Tasas de retorno
Fortinet Inc. (FTNT) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Fecha | PrecioFTNT,t1 | DividendoFTNT,t1 | RFTNT,t2 | PrecioS&P 500,t | RS&P 500,t3 |
31 ene. 2018 | $9.21 | 2,823.81 | ||||
1. | 28 feb. 2018 | $10.09 | 9.55% | 2,713.83 | -3.89% | |
2. | 31 mar. 2018 | $10.72 | 6.24% | 2,640.87 | -2.69% | |
3. | 30 abr. 2018 | $11.07 | 3.26% | 2,648.05 | 0.27% | |
. | . | . | . | . | . | . |
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58. | 30 nov. 2022 | $53.16 | -7.00% | 4,080.11 | 5.38% | |
59. | 31 dic. 2022 | $48.89 | -8.03% | 3,839.50 | -5.90% | |
Promedio (R): | 3.50% | 0.67% | ||||
Desviación estándar: | 11.47% | 5.40% |
Fortinet Inc. (FTNT) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Fecha | PrecioFTNT,t1 | DividendoFTNT,t1 | RFTNT,t2 | PrecioS&P 500,t | RS&P 500,t3 |
31 ene. 2018 | $9.21 | 2,823.81 | ||||
1. | 28 feb. 2018 | $10.09 | 9.55% | 2,713.83 | -3.89% | |
2. | 31 mar. 2018 | $10.72 | 6.24% | 2,640.87 | -2.69% | |
3. | 30 abr. 2018 | $11.07 | 3.26% | 2,648.05 | 0.27% | |
4. | 31 may. 2018 | $12.24 | 10.57% | 2,705.27 | 2.16% | |
5. | 30 jun. 2018 | $12.49 | 2.04% | 2,718.37 | 0.48% | |
6. | 31 jul. 2018 | $12.58 | 0.72% | 2,816.29 | 3.60% | |
7. | 31 ago. 2018 | $16.75 | 33.15% | 2,901.52 | 3.03% | |
8. | 30 sept. 2018 | $18.45 | 10.15% | 2,913.98 | 0.43% | |
9. | 31 oct. 2018 | $16.44 | -10.89% | 2,711.74 | -6.94% | |
10. | 30 nov. 2018 | $14.77 | -10.16% | 2,760.17 | 1.79% | |
11. | 31 dic. 2018 | $14.09 | -4.60% | 2,506.85 | -9.18% | |
12. | 31 ene. 2019 | $15.31 | 8.66% | 2,704.10 | 7.87% | |
13. | 28 feb. 2019 | $17.36 | 13.39% | 2,784.49 | 2.97% | |
14. | 31 mar. 2019 | $16.79 | -3.28% | 2,834.40 | 1.79% | |
15. | 30 abr. 2019 | $18.68 | 11.26% | 2,945.83 | 3.93% | |
16. | 31 may. 2019 | $14.50 | -22.38% | 2,752.06 | -6.58% | |
17. | 30 jun. 2019 | $15.37 | 6.00% | 2,941.76 | 6.89% | |
18. | 31 jul. 2019 | $16.06 | 4.49% | 2,980.38 | 1.31% | |
19. | 31 ago. 2019 | $15.84 | -1.37% | 2,926.46 | -1.81% | |
20. | 30 sept. 2019 | $15.35 | -3.09% | 2,976.74 | 1.72% | |
21. | 31 oct. 2019 | $16.31 | 6.25% | 3,037.56 | 2.04% | |
22. | 30 nov. 2019 | $21.02 | 28.88% | 3,140.98 | 3.40% | |
23. | 31 dic. 2019 | $21.35 | 1.57% | 3,230.78 | 2.86% | |
24. | 31 ene. 2020 | $23.07 | 8.06% | 3,225.52 | -0.16% | |
25. | 29 feb. 2020 | $20.41 | -11.53% | 2,954.22 | -8.41% | |
26. | 31 mar. 2020 | $20.23 | -0.88% | 2,584.59 | -12.51% | |
27. | 30 abr. 2020 | $21.55 | 6.52% | 2,912.43 | 12.68% | |
28. | 31 may. 2020 | $27.84 | 29.19% | 3,044.31 | 4.53% | |
29. | 30 jun. 2020 | $27.45 | -1.40% | 3,100.29 | 1.84% | |
30. | 31 jul. 2020 | $27.66 | 0.77% | 3,271.12 | 5.51% | |
31. | 31 ago. 2020 | $26.40 | -4.56% | 3,500.31 | 7.01% | |
32. | 30 sept. 2020 | $23.56 | -10.76% | 3,363.00 | -3.92% | |
33. | 31 oct. 2020 | $22.07 | -6.32% | 3,269.96 | -2.77% | |
34. | 30 nov. 2020 | $24.65 | 11.69% | 3,621.63 | 10.75% | |
35. | 31 dic. 2020 | $29.71 | 20.53% | 3,756.07 | 3.71% | |
36. | 31 ene. 2021 | $28.95 | -2.56% | 3,714.24 | -1.11% | |
37. | 28 feb. 2021 | $33.77 | 16.65% | 3,811.15 | 2.61% | |
38. | 31 mar. 2021 | $36.88 | 9.21% | 3,972.89 | 4.24% | |
39. | 30 abr. 2021 | $40.85 | 10.76% | 4,181.17 | 5.24% | |
40. | 31 may. 2021 | $43.71 | 7.00% | 4,204.11 | 0.55% | |
41. | 30 jun. 2021 | $47.64 | 8.99% | 4,297.50 | 2.22% | |
42. | 31 jul. 2021 | $54.45 | 14.29% | 4,395.26 | 2.27% | |
43. | 31 ago. 2021 | $63.03 | 15.76% | 4,522.68 | 2.90% | |
44. | 30 sept. 2021 | $58.41 | -7.33% | 4,307.54 | -4.76% | |
45. | 31 oct. 2021 | $67.27 | 15.17% | 4,605.38 | 6.91% | |
46. | 30 nov. 2021 | $66.42 | -1.26% | 4,567.00 | -0.83% | |
47. | 31 dic. 2021 | $71.88 | 8.22% | 4,766.18 | 4.36% | |
48. | 31 ene. 2022 | $59.45 | -17.29% | 4,515.55 | -5.26% | |
49. | 28 feb. 2022 | $68.90 | 15.90% | 4,373.94 | -3.14% | |
50. | 31 mar. 2022 | $68.35 | -0.80% | 4,530.41 | 3.58% | |
51. | 30 abr. 2022 | $57.80 | -15.44% | 4,131.93 | -8.80% | |
52. | 31 may. 2022 | $58.83 | 1.78% | 4,132.15 | 0.01% | |
53. | 30 jun. 2022 | $56.58 | -3.82% | 3,785.38 | -8.39% | |
54. | 31 jul. 2022 | $59.65 | 5.43% | 4,130.29 | 9.11% | |
55. | 31 ago. 2022 | $48.69 | -18.37% | 3,955.00 | -4.24% | |
56. | 30 sept. 2022 | $49.13 | 0.90% | 3,585.62 | -9.34% | |
57. | 31 oct. 2022 | $57.16 | 16.34% | 3,871.98 | 7.99% | |
58. | 30 nov. 2022 | $53.16 | -7.00% | 4,080.11 | 5.38% | |
59. | 31 dic. 2022 | $48.89 | -8.03% | 3,839.50 | -5.90% | |
Promedio (R): | 3.50% | 0.67% | ||||
Desviación estándar: | 11.47% | 5.40% |
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 FTNT 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 | RFTNT,t | RS&P 500,t | (RFTNT,t–RFTNT)2 | (RS&P 500,t–RS&P 500)2 | (RFTNT,t–RFTNT)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | 28 feb. 2018 | 9.55% | -3.89% | 36.72 | 20.81 | -27.64 |
2. | 31 mar. 2018 | 6.24% | -2.69% | 7.56 | 11.26 | -9.22 |
3. | 30 abr. 2018 | 3.26% | 0.27% | 0.05 | 0.16 | 0.09 |
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58. | 30 nov. 2022 | -7.00% | 5.38% | 110.10 | 22.17 | -49.41 |
59. | 31 dic. 2022 | -8.03% | -5.90% | 132.88 | 43.08 | 75.66 |
Total (Σ): | 7,624.03 | 1,691.48 | 1,932.55 |
t | Fecha | RFTNT,t | RS&P 500,t | (RFTNT,t–RFTNT)2 | (RS&P 500,t–RS&P 500)2 | (RFTNT,t–RFTNT)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | 28 feb. 2018 | 9.55% | -3.89% | 36.72 | 20.81 | -27.64 |
2. | 31 mar. 2018 | 6.24% | -2.69% | 7.56 | 11.26 | -9.22 |
3. | 30 abr. 2018 | 3.26% | 0.27% | 0.05 | 0.16 | 0.09 |
4. | 31 may. 2018 | 10.57% | 2.16% | 50.04 | 2.23 | 10.57 |
5. | 30 jun. 2018 | 2.04% | 0.48% | 2.11 | 0.03 | 0.26 |
6. | 31 jul. 2018 | 0.72% | 3.60% | 7.70 | 8.62 | -8.14 |
7. | 31 ago. 2018 | 33.15% | 3.03% | 879.28 | 5.57 | 69.97 |
8. | 30 sept. 2018 | 10.15% | 0.43% | 44.28 | 0.06 | -1.58 |
9. | 31 oct. 2018 | -10.89% | -6.94% | 207.06 | 57.87 | 109.46 |
10. | 30 nov. 2018 | -10.16% | 1.79% | 186.41 | 1.25 | -15.28 |
11. | 31 dic. 2018 | -4.60% | -9.18% | 65.59 | 96.91 | 79.73 |
12. | 31 ene. 2019 | 8.66% | 7.87% | 26.66 | 51.87 | 37.19 |
13. | 28 feb. 2019 | 13.39% | 2.97% | 97.91 | 5.32 | 22.82 |
14. | 31 mar. 2019 | -3.28% | 1.79% | 45.95 | 1.27 | -7.63 |
15. | 30 abr. 2019 | 11.26% | 3.93% | 60.24 | 10.66 | 25.34 |
16. | 31 may. 2019 | -22.38% | -6.58% | 669.36 | 52.48 | 187.43 |
17. | 30 jun. 2019 | 6.00% | 6.89% | 6.27 | 38.77 | 15.60 |
18. | 31 jul. 2019 | 4.49% | 1.31% | 0.99 | 0.42 | 0.64 |
19. | 31 ago. 2019 | -1.37% | -1.81% | 23.67 | 6.13 | 12.04 |
20. | 30 sept. 2019 | -3.09% | 1.72% | 43.41 | 1.11 | -6.93 |
21. | 31 oct. 2019 | 6.25% | 2.04% | 7.61 | 1.89 | 3.80 |
22. | 30 nov. 2019 | 28.88% | 3.40% | 644.29 | 7.50 | 69.50 |
23. | 31 dic. 2019 | 1.57% | 2.86% | 3.71 | 4.81 | -4.22 |
24. | 31 ene. 2020 | 8.06% | -0.16% | 20.80 | 0.69 | -3.78 |
25. | 29 feb. 2020 | -11.53% | -8.41% | 225.76 | 82.40 | 136.39 |
26. | 31 mar. 2020 | -0.88% | -12.51% | 19.16 | 173.67 | 57.68 |
27. | 30 abr. 2020 | 6.52% | 12.68% | 9.18 | 144.43 | 36.41 |
28. | 31 may. 2020 | 29.19% | 4.53% | 660.12 | 14.91 | 99.21 |
29. | 30 jun. 2020 | -1.40% | 1.84% | 23.97 | 1.37 | -5.74 |
30. | 31 jul. 2020 | 0.77% | 5.51% | 7.45 | 23.46 | -13.22 |
31. | 31 ago. 2020 | -4.56% | 7.01% | 64.81 | 40.19 | -51.04 |
32. | 30 sept. 2020 | -10.76% | -3.92% | 203.14 | 21.06 | 65.41 |
33. | 31 oct. 2020 | -6.32% | -2.77% | 96.42 | 11.79 | 33.71 |
34. | 30 nov. 2020 | 11.69% | 10.75% | 67.16 | 101.77 | 82.67 |
35. | 31 dic. 2020 | 20.53% | 3.71% | 290.10 | 9.28 | 51.87 |
36. | 31 ene. 2021 | -2.56% | -1.11% | 36.64 | 3.17 | 10.78 |
37. | 28 feb. 2021 | 16.65% | 2.61% | 173.03 | 3.77 | 25.55 |
38. | 31 mar. 2021 | 9.21% | 4.24% | 32.65 | 12.80 | 20.44 |
39. | 30 abr. 2021 | 10.76% | 5.24% | 52.85 | 20.94 | 33.26 |
40. | 31 may. 2021 | 7.00% | 0.55% | 12.29 | 0.01 | -0.41 |
41. | 30 jun. 2021 | 8.99% | 2.22% | 30.21 | 2.42 | 8.54 |
42. | 31 jul. 2021 | 14.29% | 2.27% | 116.63 | 2.59 | 17.37 |
43. | 31 ago. 2021 | 15.76% | 2.90% | 150.37 | 4.98 | 27.37 |
44. | 30 sept. 2021 | -7.33% | -4.76% | 117.18 | 29.42 | 58.71 |
45. | 31 oct. 2021 | 15.17% | 6.91% | 136.27 | 39.03 | 72.93 |
46. | 30 nov. 2021 | -1.26% | -0.83% | 22.65 | 2.25 | 7.14 |
47. | 31 dic. 2021 | 8.22% | 4.36% | 22.33 | 13.65 | 17.46 |
48. | 31 ene. 2022 | -17.29% | -5.26% | 432.13 | 35.11 | 123.17 |
49. | 28 feb. 2022 | 15.90% | -3.14% | 153.77 | 14.46 | -47.16 |
50. | 31 mar. 2022 | -0.80% | 3.58% | 18.43 | 8.47 | -12.50 |
51. | 30 abr. 2022 | -15.44% | -8.80% | 358.36 | 89.54 | 179.13 |
52. | 31 may. 2022 | 1.78% | 0.01% | 2.93 | 0.44 | 1.13 |
53. | 30 jun. 2022 | -3.82% | -8.39% | 53.58 | 82.06 | 66.31 |
54. | 31 jul. 2022 | 5.43% | 9.11% | 3.73 | 71.32 | 16.31 |
55. | 31 ago. 2022 | -18.37% | -4.24% | 478.25 | 24.11 | 107.39 |
56. | 30 sept. 2022 | 0.90% | -9.34% | 6.72 | 100.12 | 25.93 |
57. | 31 oct. 2022 | 16.34% | 7.99% | 165.10 | 53.58 | 94.05 |
58. | 30 nov. 2022 | -7.00% | 5.38% | 110.10 | 22.17 | -49.41 |
59. | 31 dic. 2022 | -8.03% | -5.90% | 132.88 | 43.08 | 75.66 |
Total (Σ): | 7,624.03 | 1,691.48 | 1,932.55 |
Mostrar todo
VarianzaFTNT = Σ(RFTNT,t–RFTNT)2 ÷ (59 – 1)
= 7,624.03 ÷ (59 – 1)
= 131.45
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,691.48 ÷ (59 – 1)
= 29.16
CovarianzaFTNT, S&P 500 = Σ(RFTNT,t–RFTNT)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,932.55 ÷ (59 – 1)
= 33.32
Estimación sistemática del riesgo (β)
VarianzaFTNT | 131.45 |
VarianzaS&P 500 | 29.16 |
CovarianzaFTNT, S&P 500 | 33.32 |
Coeficiente de correlaciónFTNT, S&P 5001 | 0.54 |
βFTNT2 | 1.14 |
αFTNT3 | 2.73% |
Cálculos
1 Coeficiente de correlaciónFTNT, S&P 500
= CovarianzaFTNT, S&P 500 ÷ (Desviación estándarFTNT × Desviación estándarS&P 500)
= 33.32 ÷ (11.47% × 5.40%)
= 0.54
2 βFTNT
= CovarianzaFTNT, S&P 500 ÷ VarianzaS&P 500
= 33.32 ÷ 29.16
= 1.14
3 αFTNT
= PromedioFTNT – βFTNT × PromedioS&P 500
= 3.50% – 1.14 × 0.67%
= 2.73%
Tasa de rendimiento esperada
Suposiciones | ||
Tasa de rendimiento del LT Treasury Composite1 | RF | 4.62% |
Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.69% |
Riesgo sistemático de Fortinet acciones ordinarias | βFTNT | 1.14 |
Tasa de rendimiento esperada de las acciones ordinarias de Fortinet3 | E(RFTNT) | 14.98% |
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(RFTNT) = RF + βFTNT [E(RM) – RF]
= 4.62% + 1.14 [13.69% – 4.62%]
= 14.98%