Modelo de fijación de precios 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 en activos de riesgo como las acciones ordinarias de Corning.
Tasas de retorno
Corning Inc., tasas mensuales de retorno
| Corning Inc. (GLW) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioGLW,t1 | DividendoGLW,t1 | RGLW,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2019 | $33.26 | 2,704.10 | ||||
| 1. | 28 feb. 2019 | $34.81 | $0.20 | 5.26% | 2,784.49 | 2.97% |
| 2. | 31 mar. 2019 | $33.10 | -4.91% | 2,834.40 | 1.79% | |
| 3. | 30 abr. 2019 | $31.85 | -3.78% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | $28.49 | $0.28 | 7.51% | 4,567.80 | 8.92% |
| 59. | 31 dic. 2023 | $30.45 | 6.88% | 4,769.83 | 4.42% | |
| Promedio (R): | 0.45% | 1.11% | ||||
| Desviación estándar: | 8.46% | 5.31% | ||||
| Corning Inc. (GLW) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioGLW,t1 | DividendoGLW,t1 | RGLW,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2019 | $33.26 | 2,704.10 | ||||
| 1. | 28 feb. 2019 | $34.81 | $0.20 | 5.26% | 2,784.49 | 2.97% |
| 2. | 31 mar. 2019 | $33.10 | -4.91% | 2,834.40 | 1.79% | |
| 3. | 30 abr. 2019 | $31.85 | -3.78% | 2,945.83 | 3.93% | |
| 4. | 31 may. 2019 | $28.84 | $0.20 | -8.82% | 2,752.06 | -6.58% |
| 5. | 30 jun. 2019 | $33.23 | 15.22% | 2,941.76 | 6.89% | |
| 6. | 31 jul. 2019 | $30.75 | -7.46% | 2,980.38 | 1.31% | |
| 7. | 31 ago. 2019 | $27.85 | $0.20 | -8.78% | 2,926.46 | -1.81% |
| 8. | 30 sept. 2019 | $28.52 | 2.41% | 2,976.74 | 1.72% | |
| 9. | 31 oct. 2019 | $29.63 | 3.89% | 3,037.56 | 2.04% | |
| 10. | 30 nov. 2019 | $29.04 | $0.20 | -1.32% | 3,140.98 | 3.40% |
| 11. | 31 dic. 2019 | $29.11 | 0.24% | 3,230.78 | 2.86% | |
| 12. | 31 ene. 2020 | $26.69 | -8.31% | 3,225.52 | -0.16% | |
| 13. | 29 feb. 2020 | $23.86 | $0.22 | -9.78% | 2,954.22 | -8.41% |
| 14. | 31 mar. 2020 | $20.54 | -13.91% | 2,584.59 | -12.51% | |
| 15. | 30 abr. 2020 | $22.01 | 7.16% | 2,912.43 | 12.68% | |
| 16. | 31 may. 2020 | $22.79 | $0.22 | 4.54% | 3,044.31 | 4.53% |
| 17. | 30 jun. 2020 | $25.90 | 13.65% | 3,100.29 | 1.84% | |
| 18. | 31 jul. 2020 | $31.00 | 19.69% | 3,271.12 | 5.51% | |
| 19. | 31 ago. 2020 | $32.46 | $0.22 | 5.42% | 3,500.31 | 7.01% |
| 20. | 30 sept. 2020 | $32.41 | -0.15% | 3,363.00 | -3.92% | |
| 21. | 31 oct. 2020 | $31.97 | -1.36% | 3,269.96 | -2.77% | |
| 22. | 30 nov. 2020 | $37.42 | $0.22 | 17.74% | 3,621.63 | 10.75% |
| 23. | 31 dic. 2020 | $36.00 | -3.79% | 3,756.07 | 3.71% | |
| 24. | 31 ene. 2021 | $35.87 | -0.36% | 3,714.24 | -1.11% | |
| 25. | 28 feb. 2021 | $38.24 | $0.24 | 7.28% | 3,811.15 | 2.61% |
| 26. | 31 mar. 2021 | $43.51 | 13.78% | 3,972.89 | 4.24% | |
| 27. | 30 abr. 2021 | $44.21 | 1.61% | 4,181.17 | 5.24% | |
| 28. | 31 may. 2021 | $43.63 | $0.24 | -0.77% | 4,204.11 | 0.55% |
| 29. | 30 jun. 2021 | $40.90 | -6.26% | 4,297.50 | 2.22% | |
| 30. | 31 jul. 2021 | $41.86 | 2.35% | 4,395.26 | 2.27% | |
| 31. | 31 ago. 2021 | $39.99 | $0.24 | -3.89% | 4,522.68 | 2.90% |
| 32. | 30 sept. 2021 | $36.49 | -8.75% | 4,307.54 | -4.76% | |
| 33. | 31 oct. 2021 | $35.57 | -2.52% | 4,605.38 | 6.91% | |
| 34. | 30 nov. 2021 | $37.09 | $0.24 | 4.95% | 4,567.00 | -0.83% |
| 35. | 31 dic. 2021 | $37.23 | 0.38% | 4,766.18 | 4.36% | |
| 36. | 31 ene. 2022 | $42.04 | 12.92% | 4,515.55 | -5.26% | |
| 37. | 28 feb. 2022 | $40.40 | $0.27 | -3.26% | 4,373.94 | -3.14% |
| 38. | 31 mar. 2022 | $36.91 | -8.64% | 4,530.41 | 3.58% | |
| 39. | 30 abr. 2022 | $35.19 | -4.66% | 4,131.93 | -8.80% | |
| 40. | 31 may. 2022 | $35.82 | $0.27 | 2.56% | 4,132.15 | 0.01% |
| 41. | 30 jun. 2022 | $31.51 | -12.03% | 3,785.38 | -8.39% | |
| 42. | 31 jul. 2022 | $36.76 | 16.66% | 4,130.29 | 9.11% | |
| 43. | 31 ago. 2022 | $34.32 | $0.27 | -5.90% | 3,955.00 | -4.24% |
| 44. | 30 sept. 2022 | $29.02 | -15.44% | 3,585.62 | -9.34% | |
| 45. | 31 oct. 2022 | $32.17 | 10.85% | 3,871.98 | 7.99% | |
| 46. | 30 nov. 2022 | $34.13 | $0.27 | 6.93% | 4,080.11 | 5.38% |
| 47. | 31 dic. 2022 | $31.94 | -6.42% | 3,839.50 | -5.90% | |
| 48. | 31 ene. 2023 | $34.61 | 8.36% | 4,076.60 | 6.18% | |
| 49. | 28 feb. 2023 | $33.95 | $0.28 | -1.10% | 3,970.15 | -2.61% |
| 50. | 31 mar. 2023 | $35.28 | 3.92% | 4,109.31 | 3.51% | |
| 51. | 30 abr. 2023 | $33.22 | -5.84% | 4,169.48 | 1.46% | |
| 52. | 31 may. 2023 | $30.81 | $0.28 | -6.41% | 4,179.83 | 0.25% |
| 53. | 30 jun. 2023 | $35.04 | 13.73% | 4,376.86 | 4.71% | |
| 54. | 31 jul. 2023 | $33.94 | -3.14% | 4,588.96 | 4.85% | |
| 55. | 31 ago. 2023 | $32.82 | $0.28 | -2.47% | 4,507.66 | -1.77% |
| 56. | 30 sept. 2023 | $30.47 | -7.16% | 4,288.05 | -4.87% | |
| 57. | 31 oct. 2023 | $26.76 | -12.18% | 4,193.80 | -2.20% | |
| 58. | 30 nov. 2023 | $28.49 | $0.28 | 7.51% | 4,567.80 | 8.92% |
| 59. | 31 dic. 2023 | $30.45 | 6.88% | 4,769.83 | 4.42% | |
| Promedio (R): | 0.45% | 1.11% | ||||
| Desviación estándar: | 8.46% | 5.31% | ||||
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 GLW 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
Corning Inc., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RGLW,t | RS&P 500,t | (RGLW,t–RGLW)2 | (RS&P 500,t–RS&P 500)2 | (RGLW,t–RGLW)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2019 | 5.26% | 2.97% | 23.19 | 3.49 | 8.99 |
| 2. | 31 mar. 2019 | -4.91% | 1.79% | 28.71 | 0.47 | -3.68 |
| 3. | 30 abr. 2019 | -3.78% | 3.93% | 17.82 | 7.98 | -11.93 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | 7.51% | 8.92% | 49.92 | 61.03 | 55.20 |
| 59. | 31 dic. 2023 | 6.88% | 4.42% | 41.40 | 11.00 | 21.34 |
| Total (Σ): | 4,149.94 | 1,634.30 | 1,756.92 | |||
| t | Fecha | RGLW,t | RS&P 500,t | (RGLW,t–RGLW)2 | (RS&P 500,t–RS&P 500)2 | (RGLW,t–RGLW)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2019 | 5.26% | 2.97% | 23.19 | 3.49 | 8.99 |
| 2. | 31 mar. 2019 | -4.91% | 1.79% | 28.71 | 0.47 | -3.68 |
| 3. | 30 abr. 2019 | -3.78% | 3.93% | 17.82 | 7.98 | -11.93 |
| 4. | 31 may. 2019 | -8.82% | -6.58% | 85.90 | 59.04 | 71.21 |
| 5. | 30 jun. 2019 | 15.22% | 6.89% | 218.34 | 33.49 | 85.51 |
| 6. | 31 jul. 2019 | -7.46% | 1.31% | 62.55 | 0.04 | -1.64 |
| 7. | 31 ago. 2019 | -8.78% | -1.81% | 85.12 | 8.50 | 26.89 |
| 8. | 30 sept. 2019 | 2.41% | 1.72% | 3.84 | 0.37 | 1.20 |
| 9. | 31 oct. 2019 | 3.89% | 2.04% | 11.88 | 0.88 | 3.23 |
| 10. | 30 nov. 2019 | -1.32% | 3.40% | 3.10 | 5.28 | -4.05 |
| 11. | 31 dic. 2019 | 0.24% | 2.86% | 0.04 | 3.07 | -0.36 |
| 12. | 31 ene. 2020 | -8.31% | -0.16% | 76.72 | 1.61 | 11.11 |
| 13. | 29 feb. 2020 | -9.78% | -8.41% | 104.54 | 90.57 | 97.31 |
| 14. | 31 mar. 2020 | -13.91% | -12.51% | 206.21 | 185.44 | 195.55 |
| 15. | 30 abr. 2020 | 7.16% | 12.68% | 45.04 | 134.06 | 77.71 |
| 16. | 31 may. 2020 | 4.54% | 4.53% | 16.79 | 11.71 | 14.02 |
| 17. | 30 jun. 2020 | 13.65% | 1.84% | 174.26 | 0.54 | 9.68 |
| 18. | 31 jul. 2020 | 19.69% | 5.51% | 370.39 | 19.40 | 84.76 |
| 19. | 31 ago. 2020 | 5.42% | 7.01% | 24.74 | 34.82 | 29.35 |
| 20. | 30 sept. 2020 | -0.15% | -3.92% | 0.36 | 25.29 | 3.01 |
| 21. | 31 oct. 2020 | -1.36% | -2.77% | 3.25 | 15.00 | 6.98 |
| 22. | 30 nov. 2020 | 17.74% | 10.75% | 298.94 | 93.10 | 166.83 |
| 23. | 31 dic. 2020 | -3.79% | 3.71% | 17.98 | 6.79 | -11.05 |
| 24. | 31 ene. 2021 | -0.36% | -1.11% | 0.65 | 4.93 | 1.79 |
| 25. | 28 feb. 2021 | 7.28% | 2.61% | 46.66 | 2.26 | 10.27 |
| 26. | 31 mar. 2021 | 13.78% | 4.24% | 177.85 | 9.85 | 41.85 |
| 27. | 30 abr. 2021 | 1.61% | 5.24% | 1.35 | 17.11 | 4.81 |
| 28. | 31 may. 2021 | -0.77% | 0.55% | 1.48 | 0.31 | 0.68 |
| 29. | 30 jun. 2021 | -6.26% | 2.22% | 44.93 | 1.24 | -7.48 |
| 30. | 31 jul. 2021 | 2.35% | 2.27% | 3.62 | 1.37 | 2.22 |
| 31. | 31 ago. 2021 | -3.89% | 2.90% | 18.83 | 3.22 | -7.78 |
| 32. | 30 sept. 2021 | -8.75% | -4.76% | 84.60 | 34.37 | 53.92 |
| 33. | 31 oct. 2021 | -2.52% | 6.91% | 8.80 | 33.74 | -17.23 |
| 34. | 30 nov. 2021 | 4.95% | -0.83% | 20.27 | 3.76 | -8.73 |
| 35. | 31 dic. 2021 | 0.38% | 4.36% | 0.00 | 10.60 | -0.22 |
| 36. | 31 ene. 2022 | 12.92% | -5.26% | 155.61 | 40.51 | -79.39 |
| 37. | 28 feb. 2022 | -3.26% | -3.14% | 13.72 | 17.99 | 15.71 |
| 38. | 31 mar. 2022 | -8.64% | 3.58% | 82.52 | 6.11 | -22.45 |
| 39. | 30 abr. 2022 | -4.66% | -8.80% | 26.07 | 98.04 | 50.55 |
| 40. | 31 may. 2022 | 2.56% | 0.01% | 4.46 | 1.21 | -2.32 |
| 41. | 30 jun. 2022 | -12.03% | -8.39% | 155.70 | 90.21 | 118.51 |
| 42. | 31 jul. 2022 | 16.66% | 9.11% | 262.95 | 64.09 | 129.82 |
| 43. | 31 ago. 2022 | -5.90% | -4.24% | 40.31 | 28.62 | 33.96 |
| 44. | 30 sept. 2022 | -15.44% | -9.34% | 252.44 | 109.11 | 165.96 |
| 45. | 31 oct. 2022 | 10.85% | 7.99% | 108.35 | 47.34 | 71.62 |
| 46. | 30 nov. 2022 | 6.93% | 5.38% | 42.07 | 18.23 | 27.69 |
| 47. | 31 dic. 2022 | -6.42% | -5.90% | 47.09 | 49.04 | 48.06 |
| 48. | 31 ene. 2023 | 8.36% | 6.18% | 62.63 | 25.70 | 40.12 |
| 49. | 28 feb. 2023 | -1.10% | -2.61% | 2.38 | 13.82 | 5.74 |
| 50. | 31 mar. 2023 | 3.92% | 3.51% | 12.05 | 5.76 | 8.33 |
| 51. | 30 abr. 2023 | -5.84% | 1.46% | 39.50 | 0.13 | -2.25 |
| 52. | 31 may. 2023 | -6.41% | 0.25% | 47.02 | 0.74 | 5.88 |
| 53. | 30 jun. 2023 | 13.73% | 4.71% | 176.46 | 13.02 | 47.93 |
| 54. | 31 jul. 2023 | -3.14% | 4.85% | 12.85 | 13.99 | -13.41 |
| 55. | 31 ago. 2023 | -2.47% | -1.77% | 8.53 | 8.28 | 8.40 |
| 56. | 30 sept. 2023 | -7.16% | -4.87% | 57.85 | 35.73 | 45.47 |
| 57. | 31 oct. 2023 | -12.18% | -2.20% | 159.30 | 10.92 | 41.70 |
| 58. | 30 nov. 2023 | 7.51% | 8.92% | 49.92 | 61.03 | 55.20 |
| 59. | 31 dic. 2023 | 6.88% | 4.42% | 41.40 | 11.00 | 21.34 |
| Total (Σ): | 4,149.94 | 1,634.30 | 1,756.92 | |||
Mostrar todo
VarianzaGLW = Σ(RGLW,t–RGLW)2 ÷ (59 – 1)
= 4,149.94 ÷ (59 – 1)
= 71.55
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
CovarianzaGLW, S&P 500 = Σ(RGLW,t–RGLW)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,756.92 ÷ (59 – 1)
= 30.29
Estimación sistemática del riesgo (β)
| VarianzaGLW | 71.55 |
| VarianzaS&P 500 | 28.18 |
| CovarianzaGLW, S&P 500 | 30.29 |
| Coeficiente de correlaciónGLW, S&P 5001 | 0.67 |
| βGLW2 | 1.08 |
| αGLW3 | -0.74% |
Cálculos
1 Coeficiente de correlaciónGLW, S&P 500
= CovarianzaGLW, S&P 500 ÷ (Desviación estándarGLW × Desviación estándarS&P 500)
= 30.29 ÷ (8.46% × 5.31%)
= 0.67
2 βGLW
= CovarianzaGLW, S&P 500 ÷ VarianzaS&P 500
= 30.29 ÷ 28.18
= 1.08
3 αGLW
= PromedioGLW – βGLW × PromedioS&P 500
= 0.45% – 1.08 × 1.11%
= -0.74%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.67% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.79% |
| Riesgo sistemático de Corning acciones ordinarias | βGLW | 1.08 |
| Tasa de rendimiento esperada de las acciones ordinarias de Corning3 | E(RGLW) | 14.47% |
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(RGLW) = RF + βGLW [E(RM) – RF]
= 4.67% + 1.08 [13.79% – 4.67%]
= 14.47%