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 activos de riesgo como las acciones ordinarias de First Solar.
Tasas de retorno
First Solar Inc., tasas mensuales de retorno
| First Solar Inc. (FSLR) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioFSLR,t1 | DividendoFSLR,t1 | RFSLR,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2018 | $67.17 | 2,823.81 | ||||
| 1. | 28 feb. 2018 | $62.85 | -6.43% | 2,713.83 | -3.89% | |
| 2. | 31 mar. 2018 | $70.98 | 12.94% | 2,640.87 | -2.69% | |
| 3. | 30 abr. 2018 | $70.91 | -0.10% | 2,648.05 | 0.27% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2022 | $172.53 | 18.52% | 4,080.11 | 5.38% | |
| 59. | 31 dic. 2022 | $149.79 | -13.18% | 3,839.50 | -5.90% | |
| Promedio (R): | 2.28% | 0.67% | ||||
| Desviación estándar: | 14.10% | 5.40% | ||||
| First Solar Inc. (FSLR) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioFSLR,t1 | DividendoFSLR,t1 | RFSLR,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2018 | $67.17 | 2,823.81 | ||||
| 1. | 28 feb. 2018 | $62.85 | -6.43% | 2,713.83 | -3.89% | |
| 2. | 31 mar. 2018 | $70.98 | 12.94% | 2,640.87 | -2.69% | |
| 3. | 30 abr. 2018 | $70.91 | -0.10% | 2,648.05 | 0.27% | |
| 4. | 31 may. 2018 | $67.61 | -4.65% | 2,705.27 | 2.16% | |
| 5. | 30 jun. 2018 | $52.66 | -22.11% | 2,718.37 | 0.48% | |
| 6. | 31 jul. 2018 | $52.35 | -0.59% | 2,816.29 | 3.60% | |
| 7. | 31 ago. 2018 | $52.08 | -0.52% | 2,901.52 | 3.03% | |
| 8. | 30 sept. 2018 | $48.42 | -7.03% | 2,913.98 | 0.43% | |
| 9. | 31 oct. 2018 | $41.80 | -13.67% | 2,711.74 | -6.94% | |
| 10. | 30 nov. 2018 | $44.45 | 6.34% | 2,760.17 | 1.79% | |
| 11. | 31 dic. 2018 | $42.46 | -4.48% | 2,506.85 | -9.18% | |
| 12. | 31 ene. 2019 | $50.59 | 19.15% | 2,704.10 | 7.87% | |
| 13. | 28 feb. 2019 | $52.55 | 3.87% | 2,784.49 | 2.97% | |
| 14. | 31 mar. 2019 | $52.84 | 0.55% | 2,834.40 | 1.79% | |
| 15. | 30 abr. 2019 | $61.53 | 16.45% | 2,945.83 | 3.93% | |
| 16. | 31 may. 2019 | $58.04 | -5.67% | 2,752.06 | -6.58% | |
| 17. | 30 jun. 2019 | $65.68 | 13.16% | 2,941.76 | 6.89% | |
| 18. | 31 jul. 2019 | $64.49 | -1.81% | 2,980.38 | 1.31% | |
| 19. | 31 ago. 2019 | $62.07 | -3.75% | 2,926.46 | -1.81% | |
| 20. | 30 sept. 2019 | $58.01 | -6.54% | 2,976.74 | 1.72% | |
| 21. | 31 oct. 2019 | $51.79 | -10.72% | 3,037.56 | 2.04% | |
| 22. | 30 nov. 2019 | $55.24 | 6.66% | 3,140.98 | 3.40% | |
| 23. | 31 dic. 2019 | $55.96 | 1.30% | 3,230.78 | 2.86% | |
| 24. | 31 ene. 2020 | $49.58 | -11.40% | 3,225.52 | -0.16% | |
| 25. | 29 feb. 2020 | $45.77 | -7.68% | 2,954.22 | -8.41% | |
| 26. | 31 mar. 2020 | $36.06 | -21.21% | 2,584.59 | -12.51% | |
| 27. | 30 abr. 2020 | $44.01 | 22.05% | 2,912.43 | 12.68% | |
| 28. | 31 may. 2020 | $46.62 | 5.93% | 3,044.31 | 4.53% | |
| 29. | 30 jun. 2020 | $49.50 | 6.18% | 3,100.29 | 1.84% | |
| 30. | 31 jul. 2020 | $59.55 | 20.30% | 3,271.12 | 5.51% | |
| 31. | 31 ago. 2020 | $76.59 | 28.61% | 3,500.31 | 7.01% | |
| 32. | 30 sept. 2020 | $66.20 | -13.57% | 3,363.00 | -3.92% | |
| 33. | 31 oct. 2020 | $87.05 | 31.50% | 3,269.96 | -2.77% | |
| 34. | 30 nov. 2020 | $93.43 | 7.33% | 3,621.63 | 10.75% | |
| 35. | 31 dic. 2020 | $98.92 | 5.88% | 3,756.07 | 3.71% | |
| 36. | 31 ene. 2021 | $99.15 | 0.23% | 3,714.24 | -1.11% | |
| 37. | 28 feb. 2021 | $81.02 | -18.29% | 3,811.15 | 2.61% | |
| 38. | 31 mar. 2021 | $87.30 | 7.75% | 3,972.89 | 4.24% | |
| 39. | 30 abr. 2021 | $76.53 | -12.34% | 4,181.17 | 5.24% | |
| 40. | 31 may. 2021 | $76.11 | -0.55% | 4,204.11 | 0.55% | |
| 41. | 30 jun. 2021 | $90.51 | 18.92% | 4,297.50 | 2.22% | |
| 42. | 31 jul. 2021 | $86.04 | -4.94% | 4,395.26 | 2.27% | |
| 43. | 31 ago. 2021 | $94.00 | 9.25% | 4,522.68 | 2.90% | |
| 44. | 30 sept. 2021 | $95.46 | 1.55% | 4,307.54 | -4.76% | |
| 45. | 31 oct. 2021 | $119.59 | 25.28% | 4,605.38 | 6.91% | |
| 46. | 30 nov. 2021 | $103.60 | -13.37% | 4,567.00 | -0.83% | |
| 47. | 31 dic. 2021 | $87.16 | -15.87% | 4,766.18 | 4.36% | |
| 48. | 31 ene. 2022 | $78.38 | -10.07% | 4,515.55 | -5.26% | |
| 49. | 28 feb. 2022 | $75.29 | -3.94% | 4,373.94 | -3.14% | |
| 50. | 31 mar. 2022 | $83.74 | 11.22% | 4,530.41 | 3.58% | |
| 51. | 30 abr. 2022 | $73.03 | -12.79% | 4,131.93 | -8.80% | |
| 52. | 31 may. 2022 | $70.61 | -3.31% | 4,132.15 | 0.01% | |
| 53. | 30 jun. 2022 | $68.13 | -3.51% | 3,785.38 | -8.39% | |
| 54. | 31 jul. 2022 | $99.17 | 45.56% | 4,130.29 | 9.11% | |
| 55. | 31 ago. 2022 | $127.55 | 28.62% | 3,955.00 | -4.24% | |
| 56. | 30 sept. 2022 | $132.27 | 3.70% | 3,585.62 | -9.34% | |
| 57. | 31 oct. 2022 | $145.57 | 10.06% | 3,871.98 | 7.99% | |
| 58. | 30 nov. 2022 | $172.53 | 18.52% | 4,080.11 | 5.38% | |
| 59. | 31 dic. 2022 | $149.79 | -13.18% | 3,839.50 | -5.90% | |
| Promedio (R): | 2.28% | 0.67% | ||||
| Desviación estándar: | 14.10% | 5.40% | ||||
Mostrar todo
1 Datos en US$ por acción ordinaria, ajustados por divisiones y dividendos de acciones.
2 Tasa de rendimiento de las acciones ordinarias de FSLR 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
First Solar Inc., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RFSLR,t | RS&P 500,t | (RFSLR,t–RFSLR)2 | (RS&P 500,t–RS&P 500)2 | (RFSLR,t–RFSLR)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2018 | -6.43% | -3.89% | 75.96 | 20.81 | 39.75 |
| 2. | 31 mar. 2018 | 12.94% | -2.69% | 113.46 | 11.26 | -35.74 |
| 3. | 30 abr. 2018 | -0.10% | 0.27% | 5.68 | 0.16 | 0.94 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2022 | 18.52% | 5.38% | 263.62 | 22.17 | 76.45 |
| 59. | 31 dic. 2022 | -13.18% | -5.90% | 239.14 | 43.08 | 101.50 |
| Total (Σ): | 11,524.42 | 1,691.48 | 2,253.67 | |||
| t | Fecha | RFSLR,t | RS&P 500,t | (RFSLR,t–RFSLR)2 | (RS&P 500,t–RS&P 500)2 | (RFSLR,t–RFSLR)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2018 | -6.43% | -3.89% | 75.96 | 20.81 | 39.75 |
| 2. | 31 mar. 2018 | 12.94% | -2.69% | 113.46 | 11.26 | -35.74 |
| 3. | 30 abr. 2018 | -0.10% | 0.27% | 5.68 | 0.16 | 0.94 |
| 4. | 31 may. 2018 | -4.65% | 2.16% | 48.13 | 2.23 | -10.37 |
| 5. | 30 jun. 2018 | -22.11% | 0.48% | 595.17 | 0.03 | 4.45 |
| 6. | 31 jul. 2018 | -0.59% | 3.60% | 8.25 | 8.62 | -8.43 |
| 7. | 31 ago. 2018 | -0.52% | 3.03% | 7.84 | 5.57 | -6.61 |
| 8. | 30 sept. 2018 | -7.03% | 0.43% | 86.71 | 0.06 | 2.21 |
| 9. | 31 oct. 2018 | -13.67% | -6.94% | 254.59 | 57.87 | 121.38 |
| 10. | 30 nov. 2018 | 6.34% | 1.79% | 16.45 | 1.25 | 4.54 |
| 11. | 31 dic. 2018 | -4.48% | -9.18% | 45.71 | 96.91 | 66.56 |
| 12. | 31 ene. 2019 | 19.15% | 7.87% | 284.38 | 51.87 | 121.45 |
| 13. | 28 feb. 2019 | 3.87% | 2.97% | 2.53 | 5.32 | 3.67 |
| 14. | 31 mar. 2019 | 0.55% | 1.79% | 3.00 | 1.27 | -1.95 |
| 15. | 30 abr. 2019 | 16.45% | 3.93% | 200.56 | 10.66 | 46.23 |
| 16. | 31 may. 2019 | -5.67% | -6.58% | 63.30 | 52.48 | 57.64 |
| 17. | 30 jun. 2019 | 13.16% | 6.89% | 118.36 | 38.77 | 67.74 |
| 18. | 31 jul. 2019 | -1.81% | 1.31% | 16.78 | 0.42 | -2.65 |
| 19. | 31 ago. 2019 | -3.75% | -1.81% | 36.44 | 6.13 | 14.95 |
| 20. | 30 sept. 2019 | -6.54% | 1.72% | 77.88 | 1.11 | -9.28 |
| 21. | 31 oct. 2019 | -10.72% | 2.04% | 169.16 | 1.89 | -17.90 |
| 22. | 30 nov. 2019 | 6.66% | 3.40% | 19.16 | 7.50 | 11.99 |
| 23. | 31 dic. 2019 | 1.30% | 2.86% | 0.96 | 4.81 | -2.15 |
| 24. | 31 ene. 2020 | -11.40% | -0.16% | 187.28 | 0.69 | 11.35 |
| 25. | 29 feb. 2020 | -7.68% | -8.41% | 99.37 | 82.40 | 90.49 |
| 26. | 31 mar. 2020 | -21.21% | -12.51% | 552.19 | 173.67 | 309.68 |
| 27. | 30 abr. 2020 | 22.05% | 12.68% | 390.56 | 144.43 | 237.50 |
| 28. | 31 may. 2020 | 5.93% | 4.53% | 13.30 | 14.91 | 14.08 |
| 29. | 30 jun. 2020 | 6.18% | 1.84% | 15.16 | 1.37 | 4.56 |
| 30. | 31 jul. 2020 | 20.30% | 5.51% | 324.69 | 23.46 | 87.27 |
| 31. | 31 ago. 2020 | 28.61% | 7.01% | 693.30 | 40.19 | 166.93 |
| 32. | 30 sept. 2020 | -13.57% | -3.92% | 251.21 | 21.06 | 72.74 |
| 33. | 31 oct. 2020 | 31.50% | -2.77% | 853.31 | 11.79 | -100.29 |
| 34. | 30 nov. 2020 | 7.33% | 10.75% | 25.45 | 101.77 | 50.89 |
| 35. | 31 dic. 2020 | 5.88% | 3.71% | 12.90 | 9.28 | 10.94 |
| 36. | 31 ene. 2021 | 0.23% | -1.11% | 4.21 | 3.17 | 3.65 |
| 37. | 28 feb. 2021 | -18.29% | 2.61% | 423.10 | 3.77 | -39.96 |
| 38. | 31 mar. 2021 | 7.75% | 4.24% | 29.89 | 12.80 | 19.56 |
| 39. | 30 abr. 2021 | -12.34% | 5.24% | 213.77 | 20.94 | -66.90 |
| 40. | 31 may. 2021 | -0.55% | 0.55% | 8.02 | 0.01 | 0.33 |
| 41. | 30 jun. 2021 | 18.92% | 2.22% | 276.76 | 2.42 | 25.86 |
| 42. | 31 jul. 2021 | -4.94% | 2.27% | 52.17 | 2.59 | -11.62 |
| 43. | 31 ago. 2021 | 9.25% | 2.90% | 48.55 | 4.98 | 15.55 |
| 44. | 30 sept. 2021 | 1.55% | -4.76% | 0.53 | 29.42 | 3.96 |
| 45. | 31 oct. 2021 | 25.28% | 6.91% | 528.71 | 39.03 | 143.66 |
| 46. | 30 nov. 2021 | -13.37% | -0.83% | 245.07 | 2.25 | 23.48 |
| 47. | 31 dic. 2021 | -15.87% | 4.36% | 329.52 | 13.65 | -67.07 |
| 48. | 31 ene. 2022 | -10.07% | -5.26% | 152.71 | 35.11 | 73.22 |
| 49. | 28 feb. 2022 | -3.94% | -3.14% | 38.77 | 14.46 | 23.68 |
| 50. | 31 mar. 2022 | 11.22% | 3.58% | 79.91 | 8.47 | 26.02 |
| 51. | 30 abr. 2022 | -12.79% | -8.80% | 227.21 | 89.54 | 142.63 |
| 52. | 31 may. 2022 | -3.31% | 0.01% | 31.33 | 0.44 | 3.70 |
| 53. | 30 jun. 2022 | -3.51% | -8.39% | 33.60 | 82.06 | 52.51 |
| 54. | 31 jul. 2022 | 45.56% | 9.11% | 1,872.81 | 71.32 | 365.47 |
| 55. | 31 ago. 2022 | 28.62% | -4.24% | 693.46 | 24.11 | -129.32 |
| 56. | 30 sept. 2022 | 3.70% | -9.34% | 2.01 | 100.12 | -14.17 |
| 57. | 31 oct. 2022 | 10.06% | 7.99% | 60.39 | 53.58 | 56.88 |
| 58. | 30 nov. 2022 | 18.52% | 5.38% | 263.62 | 22.17 | 76.45 |
| 59. | 31 dic. 2022 | -13.18% | -5.90% | 239.14 | 43.08 | 101.50 |
| Total (Σ): | 11,524.42 | 1,691.48 | 2,253.67 | |||
Mostrar todo
VarianzaFSLR = Σ(RFSLR,t–RFSLR)2 ÷ (59 – 1)
= 11,524.42 ÷ (59 – 1)
= 198.70
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,691.48 ÷ (59 – 1)
= 29.16
CovarianzaFSLR, S&P 500 = Σ(RFSLR,t–RFSLR)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,253.67 ÷ (59 – 1)
= 38.86
Estimación sistemática del riesgo (β)
| VarianzaFSLR | 198.70 |
| VarianzaS&P 500 | 29.16 |
| CovarianzaFSLR, S&P 500 | 38.86 |
| Coeficiente de correlaciónFSLR, S&P 5001 | 0.51 |
| βFSLR2 | 1.33 |
| αFSLR3 | 1.40% |
Cálculos
1 Coeficiente de correlaciónFSLR, S&P 500
= CovarianzaFSLR, S&P 500 ÷ (Desviación estándarFSLR × Desviación estándarS&P 500)
= 38.86 ÷ (14.10% × 5.40%)
= 0.51
2 βFSLR
= CovarianzaFSLR, S&P 500 ÷ VarianzaS&P 500
= 38.86 ÷ 29.16
= 1.33
3 αFSLR
= PromedioFSLR – βFSLR × PromedioS&P 500
= 2.28% – 1.33 × 0.67%
= 1.40%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento de LT Treasury Composite1 | RF | 3.84% |
| Tasa de rendimiento esperada en la cartera de mercado2 | E(RM) | 13.71% |
| Riesgo sistemático de acciones ordinarias First Solar | βFSLR | 1.33 |
| Tasa de rendimiento esperada de las acciones ordinarias de First Solar3 | E(RFSLR) | 16.98% |
1 Promedio no ponderado de los rendimientos de las ofertas de todos los bonos del Tesoro de los Estados Unidos de cupón fijo en circulación que no vencen ni se pueden exigir en menos de 10 años (proxy de tasa de rendimiento libre de riesgo).
3 E(RFSLR) = RF + βFSLR [E(RM) – RF]
= 3.84% + 1.33 [13.71% – 3.84%]
= 16.98%